{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_48149/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_48149","id":"gutenberg_48149","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/48149","summary":null,"tags":["Category: Philosophy & Ethics","Philosophy, Spanish"],"text":"Note: Images of the original pages are available through\n      Internet Archive/American Libraries. See\n      https://archive.org/details/fundamentalphilo01balm\n\n\nTranscriber's note:\n\n      Text enclosed by underscores is in italics (_italics_).\n\n      A carat character is used to denote superscription. A\n      single character following the carat is superscripted\n      (example: 2^a). Multiple superscripted characters are\n      enclosed by curly brackets (example: 1^{i\u00e8re}).\n\n\n\n\n\nFUNDAMENTAL PHILOSOPHY.\n\nby\n\nREV. JAMES BALMES.\n\nTranslated from the Spanish by\n\nHenry F. Brownson, M.A.\n\nIn Two Volumes.\n\nVOL. I.\n\n\n\n\n\n\n\nNew York:\nD. & J. Sadlier & Co., 164 William Street,\nBoston:--128 Federal Street.\nMontreal:--Cor. of Notre Dame and St. Francis Xavier Sts.\n1856.\n\nEntered according to Act of Congress, in the year 1856,\nBy D. & J. Sadlier & Co.,\n\nIn the Clerk's Office of the District Court of the United States for\nthe Southern District of New York.\n\nNew York:\nBillin & Brother, Printers, XX North William St.\n\n\n\n\nCONTENTS OF VOL. I.\n\n\n  BOOK FIRST.\n\n  ON CERTAINTY.\n\n  CHAPTER                                                            PAGE\n\n          I. Importance and Utility of the Question of Certainty        3\n\n         II. True State of the Question                                 7\n\n        III. Certainty of the Human Race and Philosophical Certainty   14\n\n         IV. Existence of Transcendental Science in the Absolute\n             Intellectual Order                                        24\n\n          V. Transcendental Science in the Human Intellectual Order\n             cannot emanate from the Senses                            32\n\n         VI. Transcendental Science.--Insufficiency of Real Truths     37\n\n        VII. The Philosophy of the Me cannot produce Transcendental\n             Science                                                   41\n\n       VIII. Universal Identity                                        56\n\n         IX. Universal Identity,--Continued                            64\n\n          X. Problem of Representation: Monads of Leibnitz             67\n\n         XI. Problem of Representation examined                        71\n\n        XII. Immediate Intelligibility                                 76\n\n       XIII. Representation of Causality and Ideality                  83\n\n        XIV. Impossibility of Finding the first Principle in the\n             Ideal Order                                               89\n\n         XV. The Indispensable Condition of all Human\n             Knowledge.--Means of perceiving Truth                     92\n\n        XVI. Confusion of Ideas in Disputes on the Fundamental\n             Principle                                                102\n\n       XVII. Thought and Existence.--Descartes' Principle             105\n\n      XVIII. The Principle of Descartes, continued.--His Method       111\n\n        XIX. Value of the Principle, I Think:--Its Analysis           118\n\n         XX. True Sense of the Principle of Contradiction.--Kant's\n             Opinion                                                  126\n\n        XXI. Does the Principle of Contradiction merit the Title of\n             Fundamental; and if so, in what Sense?                   140\n\n       XXII. The Principle of Evidence                                146\n\n      XXIII. The Criterion of Consciousness                           151\n\n       XXIV. The Criterion of Evidence                                157\n\n        XXV. The Objective Value of Ideas                             163\n\n       XXVI. Can all Cognitions be reduced to the Perception of\n             Identity?                                                171\n\n      XXVII. Continuation of the same subject                         176\n\n     XXVIII. Continuation of the same subject                         183\n\n       XXIX. Are there true Synthetic Judgments _a priori_ in the\n             Sense of Kant?                                           188\n\n        XXX. Vico's Criterion                                         200\n\n       XXXI. Continuation of the same subject                         212\n\n      XXXII. The Criterion on Common Sense                            219\n\n     XXXIII. Error of Lamennais on Common Consent                     230\n\n      XXXIV. Summary and Conclusion                                   253\n\n\n  BOOK SECOND.\n\n  ON SENSATION.\n\n          I. Sensation in Itself                                      249\n\n         II. Matter is incapable of Sensation                         255\n\n        III. Sleep and Waking                                         263\n\n         IV. Relation of Sensations to an External World              267\n\n          V. An Idealist Hypothesis                                   273\n\n         VI. Is the External and Immediate Cause of Sensations a Free\n             Cause?                                                   276\n\n        VII. Analysis of the Objectiveness of Sensations              279\n\n       VIII. Sensation of Extension                                   283\n\n         IX. Objectiveness of the Sensation of Extension              287\n\n          X. Force of Touch to make Sensations Objective              293\n\n         XI. Inferiority of Touch compared with other Senses          296\n\n        XII. Can Sight alone give us the Idea of a Surface?           302\n\n       XIII. Cheselden's Blind Man                                    310\n\n        XIV. Can Sight give us the Idea of a Solid?                   315\n\n         XV. Sight and Motion                                         319\n\n        XVI. Possibility of other Senses                              324\n\n       XVII. Existence of New Senses                                  328\n\n      XVIII. Solution of Lamennais' Objection                         333\n\n\n  BOOK THIRD.\n\n  EXTENSION AND SPACE.\n\n          I. Extension Inseparable from the Idea of Body              339\n\n         II. Extension not Perceptible as the Direct and Immediate\n             Object of Sensations                                     345\n\n        III. Scientific Fruitfulness of the Idea of Extension         348\n\n         IV. Reality of Extension                                     357\n\n          V. Geometrical Exactness Realized in Nature                 360\n\n         VI. Remarks on Extension                                     365\n\n        VII. Space.--Nothing                                          369\n\n       VIII. Descartes and Leibnitz on Space                          375\n\n         IX. Opinion of those who attribute to Space a Nature\n             distinct from Bodies                                     380\n\n          X. Opinion of those who hold Space to be the Immensity of\n             God                                                      382\n\n         XI. Fenelon's Opinion                                        386\n\n        XII. What Space consists in                                   391\n\n       XIII. New Difficulties                                         396\n\n        XIV. Another Important Consequence                            400\n\n         XV. Illusion of Fixed Points in Space                        403\n\n        XVI. Observations on Kant's Opinion                           407\n\n       XVII. Inability of Kant's Doctrine to solve the Problem of\n             the Possibility of Experience                            415\n\n      XVIII. The Problem of Sensible Experience                       418\n\n        XIX. Extension abstracted from Phenomena                      421\n\n         XX. Are there Absolute Magnitudes?                           427\n\n        XXI. Pure Intelligibility of the Extended World               432\n\n       XXII. Infinite Divisibility                                    436\n\n      XXIII. Unextended Points                                        439\n\n       XXIV. A Conjecture on the Transcendental Notion of Extension   442\n\n        XXV. Harmony of the Real, Phenomenal, and Ideal Orders        446\n\n       XXVI. Character of the Relations of the Real Order to the\n             Phenomenal                                               450\n\n      XXVII. Whether every Thing must be in some Place                452\n\n     XXVIII. Contingency of Corporeal Relations                       459\n\n       XXIX. Solution of two Difficulties                             462\n\n        XXX. Passive Sensibility                                      466\n\n       XXXI. Possibility of a greater Sphere in active Sensibility    469\n\n      XXXII. Possibility of the Penetration of Bodies                 480\n\n     XXXIII. A Triumph of Religion in the Field of Philosophy         483\n\n      XXXIV. Conclusion and Summing up                                489\n\n\n  NOTES TO BOOK FIRST                                                 495\n\n  NOTE TO BOOK SECOND                                                 514\n\n  NOTES TO BOOK THIRD                                                 517\n\n\n\n\nINTRODUCTION.\n\n\nThe following translation of the great work of the lamented\nJames Balmes on Philosophy, was undertaken at my suggestion and\nrecommendation, and thus far I hold myself responsible for it. I have\ncompared a considerable portion of it with the original, and as far as\nI have compared it, I have found it faithfully executed. The translator\nappears to me to have rendered the author's thought with exactness and\nprecision, in a style not inferior to his own.\n\nI have not added, as was originally contemplated, any Notes to those\nof the author. To have done so, would have swelled the volumes to an\nunreasonable size, and upon further consideration, they did not seem\nto me to be necessary. They would, in fact, have been an impertinence\non my part, and the reader will rather thank me for not having done\nit. The work goes forth, therefore, as it came from the hands of its\nillustrious author, with no addition or abbreviation, or change, except\nwhat was demanded by the difference between the Spanish and English\nidioms.\n\nJames Balmes, in whose premature death in 1849, the friends of\nreligion and science have still to deplore a serious loss, was one of\nthe greatest writers and profoundest thinkers of Spain, and indeed\nof our times. He is well and favorably known to the American public\nby his excellent work on European civilization,--a work which has\nbeen translated into the principal languages of Europe. In that work\nhe proved himself a man of free and liberal thought, of brilliant\ngenius, and varied and profound learning. But his work on the bases of\nphilosophy is his master-piece, and, taken as a whole, the greatest\nwork that has been published on that important subject in the\nnineteenth century.\n\nYet it is rather as a criticism on the various erroneous systems of\nphilosophy in modern times, than as containing a system of philosophy\nitself, that I have wished it translated and circulated in English.\nAs a refutation of Bacon, Locke, Hume, and Condillac, Kant, Fichte,\nSchelling, and Spinoza, it is a master-piece, and leaves little to\ndesire. In determining the fundamental principles of philosophy, and\nconstructing a system in accordance with the real world, the author is\nnot always, in my judgment, successful, and must yield to his Italian\ncontemporary, the unhappy Abbate Gioberti.\n\nWhen criticizing the errors of others, the distinguished author\nreasons as an ontologist, but when developing his own system, he is\nalmost a psychologist. His ontology is usually sound, indeed, and\nhis conclusions are for the most part just, but not always logically\nobtained. He recognizes no philosophical formula which embraces the\nwhole subject-matter of philosophy, and does not appear to be aware\nthat the _primum philosophicum_ is and must be a synthesis; and hence\nhe falls into what we may call, not eclecticism, but syncretism.\nThis is owing to the fact that his genius is critical rather than\nconstructive, and more apt to demolish than to build up.\n\nWhat I regard as the chief error of the illustrious Spaniard, is his\nnot recognizing that conceptions without intuitions are, as Kant justly\nmaintains, empty, purely subjective, the mind itself; and hence, while\ndenying that we have intuition of the infinite, contending that we\nhave a real and objectively valid conception of it. Throughout his\nbook the reader will find him maintaining that the human mind may, by\ndiscursion, attain to valid conceptions of a reality which transcends\nintuition. This I regard as an error. Discursion is an act of\nreflection, and though there is always less there can never be more in\nreflection than in intuition. If we have no intuition of the infinite,\nwe have and can have no proper conception of it, and what is taken\nto be a conception of it is simply the human mind itself, and of no\nobjective application or validity.\n\nThe excellent author is misled on this point, by supposing that in\nintuition of the intelligible the mind is the actor and not simply the\nspectator, and that an intuition of the infinite implies an infinite\nintuition. In both cases he is mistaken. In intuition we are simply\nspectators, and the object affirms itself to us. In intuition of the\ninfinite, it is not we who perceive and affirm the infinite, by our\nown intellectual act, but the infinite that reveals and affirms itself\nto our intellect. In apprehending the infinite as thus revealed and\naffirmed, we of course apprehend it in a finite, not in an infinite\nmanner. That which is intuitively apprehended is infinite, but the\nsubjective apprehension is finite. The limitation is on the part of the\nsubject, not on the part of the object.\n\nThe error arises from failing to distinguish sharply between intuition\nand reflection. In intuition the principal and primary actor is the\nintelligible object. In reflection it is the intellective subject; in\nthe intuitive order the object presents itself as it is, with its own\ncharacteristics; in the reflective order it is represented with the\nlimitations and characteristics of the thinking subject. As the subject\nis limited, its conceptions are limited, and represent the infinite\nnot as infinite, but as the not-finite; and it is in the reflective\norder, if we operate on our conceptions, instead of our intuitions,\nonly by a discursive process that we can come to the conclusion that\nthe not-finite is the infinite. The author not distinguishing the two\norders, and taking conceptions which belong to the reflective order\nas if they belonged to the intuitive order, supposes that we may\nhave valid conceptions beyond the sphere of intuition. But a little\nreflection should have taught him that, if he had no intuition, he\ncould have no conception of the infinite.\n\nFollowing St. Thomas and all philosophers of the first order,\nthe author very properly maintains that it is by the divine\nintelligibility, or the divine light, that the human mind sees whatever\nit does see; but he shrinks from saying that we have intuition of God\nhimself. So far as we are to understand intuition of God as intuition,\nor open vision of him as he is in himself, he is undoubtedly right.\nBut objects are intelligible only in the light of God, and it is only\nby this light that we apprehend them. Do we ever apprehend objects by\nthe light of God without apprehending the light which renders them\napprehensible? In apprehending the object, we apprehend first of all\nthe light which is the medium of its apprehension. The light of God is\nGod, and if we have intuition of the light, we must have intuition of\nhim who is the true light that \"enlighteneth every man coming into this\nworld.\" We cannot see God as he is in himself, not because he is not\nintelligible in himself, but because of the excess of his light, which\ndazzles and blinds our eyes through their weakness. So, very few of us\ncan look steadily in the face of the sun without being dazzled, yet not\ntherefore is it to be said we cannot and do not see the sun.\n\nThe author does not seem to be aware that _substance_ as distinguished\nfrom being or existence is an abstraction, and therefore purely\nsubjective, and no object of intuition. Abstract from a thing all its\nproperties or attributes, and you have remaining simply zero. The\nsubstance is properly the concrete thing itself, and in the real order\nis distinguishable simply from its phenomena, or _accidents_,--an\nabstract term,--not from its so-called attributes or properties.\nHence, the question, so much disputed, whether we perceive substances\nthemselves, is only the question, whether we see things themselves or\nonly their phenomena. This question the Scottish school of Reid and\nSir William Hamilton, have settled forever, and if it had not, Balmes\nhas done it, making the correction I have suggested, in a manner that\nleaves nothing further to be said.\n\nThe author's proofs of the fact of creation are strong and well\nput, but fail to be absolutely conclusive in consequence of his not\nrecognizing intuition of the creative act. They all presuppose this\nintuition, and are conclusive, because we in reality have it; but by\ndenying that we have it, the author renders them formally inconclusive.\nWe have intuition of God, real and necessary being, we have also\nintuition of things or existences, and therefore must have intuition\nof the creative act, for things or existences are only the external\nterminus of the creative act itself. Hence it is that Gioberti very\nproperly makes the ideal formula, or _primum philosophicum_, the\nsynthetic judgment, _Ens creat existentias_. Real and necessary Being\ncreates existences. This formula or judgment in all its terms is given\nintuitively, and simultaneously, and it is because it is so given we\nare able at one blow to confound the skeptic, the atheist, and the\npantheist. The illustrious Spaniard, uses in all his argument this\nformula, but he does so unconsciously, in contradiction, in fact, to\nhis express statements, because he could not reason a moment, form a\nsingle conclusion without it. His argument in itself is good, but his\nexplication of it is sometimes in fault.\n\nIf the learned and excellent author had recognized the fact that we\nhave intuition of the creative act of the first cause, and the further\nfact that all second causes, in their several spheres and degree,\nimitate or copy the first, he would have succeeded better in explaining\ntheir operation. He does not seem to perceive clearly that the _nexus_\nwhich binds together cause and effect is the act of the cause, which is\nin its own nature causative of the effect, and by denying all intuition\nof this _nexus_, he seems to leave us in the position where Hume left\nus, because it is impossible to attain by discursion to any objective\nreality of which we have no intuition.\n\nThese are all or nearly all the criticisms I am disposed to make upon\nthe admirable work of Balmes. They are important, no doubt, but really\ndetract much less from its value than it would seem. It has, in spite\nof these defects, rare and positive merits. The author has not indeed\na synthetic genius, but his powers of analysis are unsurpassed, and\nas far as my philosophical reading goes, unequalled. He has not given\nus the last word of philosophy, but he has given us precisely the\nwork most needed in the present anarchical state of philosophical\nscience. Not one of the errors to be detected in his work is peculiar\nto himself, and the most that the most ill-natured critic can say\nagainst him is, that, while he retains and defends all the truth in\nthe prevailing philosophy of the schools, he has not escaped all its\nerrors. Wherever he departs from scholastic tradition he follows truth,\nand is defective only where that tradition is itself defective. He has\nadvanced far, corrected innumerable errors, poured a flood of light on\na great variety of profound, intricate, and important problems, without\nintroducing a new or adding any thing to confirm an old error. This is\nhigh praise, but the philosophic reader will concede that it is well\nmerited.\n\nThe work is well adapted to create a taste for solid studies. It is\nwritten in a calm, clear, and dignified style, sometimes rising to true\neloquence. The author threw his whole mind and soul into his work, and\nshows himself everywhere animated by a pure and noble spirit, free from\nall pride of opinion, all love of theorizing, and all dogmatism. He\nevidently writes solely for the purpose of advancing the cause of truth\nand virtue, religion and civilization, and the effect of his writings\non the heart is no less salutary than their effect on the mind.\n\nI have wished the work to be translated and given to the English\nand American public, not as a work free from all objections, but as\nadmirably adapted to the present state of the English and American\nmind, as admirably fitted to correct the more dangerous errors now\nprevalent among us, and to prepare the way for the elaboration of a\npositive philosophy worthy of the name. We had nothing in English\nto compare with it, and it is far better adapted to the English and\nAmerican genius than the misty speculations we are importing, and\nattempting to naturalize, from Germany. It will lead no man into any\nerror which he does not already entertain, and few, perhaps none, can\nread it without positive benefit, at least without getting rid of many\nerrors.\n\nWith these remarks I commit these volumes to the public, bespeaking\nfor them a candid consideration. The near relation in which I stand\nto the translator makes me anxious that his labors should be received\nwith a kindly regard. He who translates well a good book from a foreign\nlanguage into his own, does a service to his country next to that of\nwriting a good book himself.\n\n  O. A. BROWNSON.\n\n  AUGUST 7, 1856.\n\n\n\n\nBOOK FIRST.\n\nON CERTAINTY.\n\n\n\n\nFUNDAMENTAL PHILOSOPHY.\n\n\n\n\nCHAPTER I.\n\nIMPORTANCE AND UTILITY OF THE QUESTION OF CERTAINTY.\n\n\n1. We should begin the study of philosophy by examining the question of\ncertainty; before raising the edifice, we must lay the foundation.\n\nEver since there has been philosophy, that is, ever since men first\nreflected on themselves and the beings around them, they have been\nengaged with those questions which have for their object the basis\nof human knowledge, and this shows that on this subject serious\ndifficulties are encountered. Inquirers, however, have not been\ndiscouraged by the sterility of philosophical labors; and this shows\nthat in the last term of the investigation an object of high importance\nis discovered.\n\nPhilosophers have cavilled in the most extravagant manner upon the\nquestions of certainty; on few subjects has the history of the human\nmind presented such lamentable aberrations. This consideration may\nexcite suspicion that such investigations offer nothing solid to the\nmind, and serve only to feed the vanity of the sophist. But here, as\nelsewhere, we attribute no exaggerated importance to the opinions of\nphilosophers, and we are very far from believing that they ought to be\nregarded as the legitimate representatives of human reason. It cannot,\nhowever, be denied that they are in the intellectual order the most\nactive portion of the human race. When the whole body of philosophers\ndispute, humanity itself may be said to dispute. Every fact affecting\nthe human race merits a thorough examination; to undervalue it, on\naccount of the sophisms which envelop it, is to fall into the worst\nof all sophisms. There should be no contradiction between reason and\ncommon sense; yet such a contradiction there would be, if we should,\nin the name of common sense, contemn what occupies the reason of the\nmost enlightened minds. Oftentimes it happens that what is grave and\nsignificant, that which makes a thinking man meditate, is the result\nneither of a disputation, nor of the arguments therein adduced, but\nthe simple existence of the dispute itself. In itself it is sometimes\nof little importance, but by reason of what it indicates, of great\nconsequence.\n\n2. All philosophical questions are in some manner involved in that of\ncertainty. When we have completely unfolded this, we have examined\nunder one aspect or another all that human reason can conceive of God,\nman, and the universe. At first sight it may perhaps seem to be the\nsimple foundation of the scientific structure; but in this foundation,\nif we carefully examine it, we shall see the whole edifice represented:\nit is a plane whereon is projected, visibly and in fair perspective,\nthe whole body it is to support.\n\n3. However limited may be the direct and immediate result of these\ninvestigations, they are of incalculable advantage. It is highly\nimportant to acquire science, but not less important to know its\nlimits. Near these limits there are shoals which the navigator ought to\nknow. It is by examining the question of certainty that we ascertain\nthe limits of human science.\n\nIn descending to the depths to which these questions lead us, the\nunderstanding grows dim, and the heart is awed with a religious fear.\nA moment ago we were contemplating the edifice of human knowledge,\nand grew proud to see it with its colossal dimensions, its beautiful\nforms, its fine and bold construction; we enter it, and are led through\ndeep caverns, and, as if by enchantment, the foundation seems to be\nsubtilized, to evaporate, and the superb edifice remains floating in\nthe air.\n\n4. It must be remarked that in entering on the examination of\nthe question of certainty, we do not conceal from ourselves its\ndifficulties. To conceal would not be to solve them; on the contrary,\nthe first condition necessary to their complete solution, is to see\nthem with perfect clearness, and to feel their full force. It is no\nhumiliation to the human understanding to seek those limits beyond\nwhich it cannot pass, but it is to elevate and confirm it. Thus the\nintrepid naturalist, when in search of some object he has penetrated\nto the bowels of the earth, feels a mixture of terror and pride to be\nthus buried in subterranean caverns, with just light enough to see\nimmense masses barely suspended above his head and unfathomable abysses\nbeneath his feet. There is something sublime, something attractive\nand captivating in the obscurity of the mysteries of science, in\nuncertainty itself, in the very assaults of doubt, threatening to\ndestroy in one instant the work accomplished by the human mind only in\nthe space of long ages. The greatest men have at all times enjoyed the\ncontemplation of these mysteries. The genius which spread its wings\nover the east, over Greece and Rome, over the schools of the Middle\nAges, is the same we now behold in modern Europe. Plato, Aristotle,\nSt. Augustine, Abelard, St. Anselm, St. Thomas of Aquin, Luis Vives,\nBacon, Descartes, Malebranche, and Leibnitz, all, each in his own way,\nfelt the sublime inspiration of philosophy.\n\nWhatever tends to raise man to lofty contemplation in the sanctuary of\nhis soul, contributes to his aggrandizement; for it separates him from\nnatural objects, reminds him of his noble origin, and proclaims to him\nhis high destiny. In a mechanical and sensual age, when every thing\nseems opposed to the activity of the powers of the soul, except when\nthey administer to the wants of the body, it is well to renew those\ngreat questions in which the mind roams free and untrammelled over\nunbounden realms of space.\n\nOnly intellect can examine itself. The stone falls, but knows not that\nit falls; the ray calcines and pulverizes, ignorant of its power; the\nflower knows not that its beauty is enchanting; and the brute beast\nfollows his instincts, but asks not the reason of them. Man alone, a\nfragile organization, appearing for a moment on earth again to return\nto the dust, harbors a spirit, which first inspects the external world,\nand then, anxious to ascertain its own nature, enters into itself as\ninto a sanctuary, and becomes its own oracle. What am I? What do I do?\nWhat do I think? What phenomena do I experience within myself? Why am I\nsubject to them? What is their cause, their order of production, their\nrelations? The mind asks itself these questions,--serious and difficult\nindeed, but noble and sublime questions; an unfailing proof that there\nis within us something superior to inert matter susceptible only of\nmotion and a variety of forms, that there is something, which, by an\ninternal activity, spontaneous and rooted in our very nature, presents\nus an image of that infinite Activity, a single act of whose will\ncreated the world from nothing.(1)\n\n\n\n\nCHAPTER II.\n\nTRUE STATE OF THE QUESTION.\n\n\n5. That we have certainty, common sense assures us, but what is its\nbasis, and how it is acquired, are two difficult questions, which it is\nfor philosophy to answer.\n\nThree very different questions are involved in that of certainty;\nand if confounded, they contribute not a little to the creation of\ndifficulties, and the confusion of matters which, even when they have\ntheir various aspects most accurately marked, are sufficiently hard and\ncomplicated.\n\nIt will greatly conduce to the due determination of our ideas,\ncarefully to distinguish between the existence of certainty, its basis,\nand the mode in which it is acquired. Its existence is an indisputable\nfact; its basis the object of philosophical researches, and the mode of\nacquiring it frequently a concealed phenomenon not open to observation.\n\n6. That bodies exist is a fact that no man of sane mind can doubt. No\nquestions raised upon this point can ever shake our firm conviction\nin the existence, without us, of what we call the corporeal world.\nThis conviction is a phenomenon of our existence. Explain it, perhaps\nwe cannot; but we certainly cannot deny it; we submit to it as to an\ninevitable necessity.\n\nWhat is the basis of certainty? Here we have not a simple fact, but\na question solved by every philosopher in his own way. Descartes and\nMalebranche recur to the veracity of God; Locke and Condillac to the\npeculiar character and evolution of certain sensations.\n\nHow does man acquire this certainty? He knows not: he had it before\nreflecting on it; he is astounded to hear it made a matter of dispute,\nand he might never have suspected it could be asked, why we are certain\nthat what affects our senses exists. It is of no use to ask him how\nhe made so precious an acquisition; he regards it as a fact scarcely\ndistinct from his own existence. He has no recollection of the order\nof sensations in his infancy; he finds his mind now developed, but is\nas ignorant of the laws of its development as he is of those which\npresided over the generation and growth of his body.\n\n7. Philosophy should begin by explaining, not by disputing the fact of\ncertainty. If we are certain of nothing, it is absolutely impossible\nfor us to advance a single step in any science, or to take any part\nwhatever in the affairs of life. A thorough-going skeptic would be\ninsane, and that too with insanity of the highest grade. To such a one,\nall communication with other men, all succession of external actions,\nall thoughts, and even acts of the will would be impossible. Let us,\nthen, admit the fact, and not be so extravagant as to say that madness\nsits on the threshold of philosophy.\n\nIt is the part of philosophy to analyze, not to destroy its object;\nfor by destroying its object it destroys itself. Every argument must\nhave a resting-point, which must be a fact. Whether it be internal\nor external, idea or object, the fact must exist: we must begin by\nsupposing something, and this something we call a fact. Whoever begins\nby denying or doubting all facts, is like the anatomist, who, before\ndissecting a corpse, burns it, and casts its ashes to the wind.\n\n8. Philosophy then, it may be said, commences not with an examination,\nbut with an affirmation. Granted, and this is a truth whose admission\ncloses the door on much sophistry, and sheds a brilliant light over\nthe whole theory of certainty.\n\nPhilosophers are deceived when they imagine that they begin by\ndoubting. Nothing is more false; when they think, they affirm, if\nnothing else, at least their own doubt: whenever they reason, they\nassert the connection of ideas, that is, the whole logical world.\n\nFichte, who certainly was not easily satisfied with anything, begins\nto treat of the basis of human knowledge by making an affirmation, and\nthis he confesses with an ingenuousness that does him honor. Speaking\nof reflection, the foundation of his philosophy, he says: \"The rules\nto which this reflection is subject, are not proved to be valid, but\nare tacitly presupposed to be known and admitted. They are, in their\nremotest origin, derived from a principle, the legitimacy of which\ncan only be established on condition that _they are valid_. This is a\ncircle, but an _inevitable circle_. But supposing it to be inevitable,\nand that we frankly confess it so to be, it is, in order to establish\nthe highest principle, allowable _to trust all the laws of general\nlogic_. We must start on the road of reflection with a proposition\nconceded by all the world without any contradiction.\"[1]\n\n[1] Fichte, _Grundlage der gesammten Wissenschaftslehre_. Theil. i., \u00a7\n1. Ed. Berlin, 1845, p. 92.\n\n9. Certainty is to us a happy necessity; nature imposes it, and\nphilosophers do not cast off nature. Pyrrho once came very near being\nhit by a stone, but he very naturally took good care to get out of\nits way, without stopping to examine whether it was a real stone, or\nonly the appearance of one. The bystanders laughed at him for this,\nand, at the same time, showed how inconsistent this act was with his\ndoctrine; but he gave this answer, which, under the circumstances, was\nexceedingly profound: \"It is hard entirely to throw off human nature.\"\n\n10. In sound philosophy, then, the question turns not upon the\nexistence of certainty, but upon its motives, and the means of\nacquiring it. It is an inheritance of which we cannot divest ourselves,\nalthough we repudiate those very titles which guaranty its possession\nto us. Who is not certain that he thinks, feels, wills; that he has a\nbody, and that there are around him others similar to his, of which\nthe corporeal universe consists? Prior to all systems, humanity was in\npossession of this certainty, so, also, is every individual, although\nhe may never during his whole life have once asked himself what the\nworld is, what bodies are, or in what sensation, thought, and will\nconsist. Not even if we examine the foundations of certainty and\nacknowledge the serious difficulties concerning them, which arise from\nratiocination, is it possible to doubt everything. There never was, in\nall the rigor of the word, a true skeptic.\n\n11. It is the same with certainty as with other objects of human\nknowledge. The fact is presented to us in all its magnitude, and with\nall clearness; but we do not penetrate to its innermost nature. Our\nunderstanding is as well provided with means to acquire knowledge\nof phenomena in the spiritual as in the material order, and it is\nsufficiently perspicacious to detect, delineate, and classify the laws\nto which they are subject; but when it would ascend to the cognition\nof the very essence of things, or would investigate the principles of\nthe science which makes its boast, it feels its strength fail, and the\nground whereon it stands, tremble and sink beneath its feet.\n\nHappily, man possesses certainty independently of philosophical\nsystems, not limited to phenomena of the soul, but extending as far as\nis needed in order to direct his conduct, both with regard to himself\nand to external objects. Before inquiring if there is certainty, all\nmen were certain that they thought, willed, felt, that they had a body\nwhose motions were governed by the will, and that there existed an\nassemblage of various bodies, called the universe. Since inquiries with\nregard to certainty were first instituted, it has remained the same\nwith all men, even with those who disputed it; not one of whom could\never go farther than Pyrrho, and succeed in casting off human nature.\n\n12. We cannot determine to what extent the force of mind of some\nphilosophers, engaged in combatting nature, may have succeeded in\ncreating doubt on many points, but certain it is: first, that no one\never went so far as to doubt the internal phenomena whose presence he\nfelt inwardly; second, that if indeed any one ever did persuade himself\nthat no external object corresponded to these phenomena, this must have\nbeen so strange an exception as to merit, in the history of science,\nand in the eyes of sound philosophy, no more weight than the illusions\nof a maniac. If Berkely went so far as to deny the existence of\nbodies, thus making the sophisms of reason triumph over the instincts\nof nature, he is alone, and in opposition to all mankind, and richly\nmerits to have this saying applied to him: \"Insanity is insanity still,\nno matter how sublime it may be.\"\n\nThose very philosophers, who carried their skepticism the farthest,\nagreed upon the necessity of accommodating themselves in practice to\nthe appearances of the senses, and of reserving doubt for the world of\nspeculation. Philosophers may dispute on every thing as much as they\nplease, but, the dispute over, they cease to be philosophers, and are\nagain men, similar to other men, and, like them all, enjoy the fruits\nof certainty. This, Hume, who denied with Berkely the existence of\nbodies, confesses: \"I dine,\" he says; \"I play a game at backgammon;\nI converse, and am happy with my friends; and when, after three or\nfour hours of amusement, I would return to these speculations, they\nappear so cold, so strained, and so ridiculous, that I cannot find it\nin my heart to enter into them any farther. Here, then, I find myself\nabsolutely and necessarily determined to live, and talk, and act, like\nother people, in the common affairs of life.\"[2]\n\n[2] _Treatise of Human Nature_, vol. i., p. 467.\n\n13. We must, in discussing certainty, guard against the feverish desire\nof shaking the foundations of human reason. We should, in this class\nof questions, seek a thorough knowledge of the principles of science,\nand the laws which govern the development of our mind. To labor to\ndestroy them is to mistake the object of true philosophy: we have\nonly to make them a matter of observation, just as we do those of the\nmaterial world, without any intention of disturbing the admirable order\nprevailing in the universe. Skeptics, who, in order to render their\nphilosophy more solid, begin by doubting every thing, resemble the man,\nwho, desirous of ascertaining, and exactly determining the phenomena of\nlife, should bare his bosom, and thrust the knife into his heart.\n\nSobriety is as necessary to the health of the mind, as to that of\nthe body: there is no wisdom without prudence, no philosophy without\njudgment. In the soul of man there is a divine light which directs him\nwith admirable certainty. If we do not persist in extinguishing it, its\nsplendor guides us, and when we reach the term of science it shows it\nto us, and makes us read in distinct characters the words,--_enough,\nyou can go no farther_. These words are written by the Author of all\nbeings; he it is that has given laws to the body as well as to the\nmind, and he contains in his infinite essence the ultimate reason of\nall things.\n\n14. The certainty which is prior to all examination is not blind; on\nthe contrary, it springs either from the clearness of the intellectual\nvision, or from an instinct conformable to reason: it is not opposed\nto reason, but is its basis. Our mind, in discursive reasoning, knows\ntruth by the connection of propositions, or by the light which is\nreflected from one truth upon another. In primitive certainty the\nvision is by direct light, and does not need reflection.\n\nWhen, then, we note the existence of certainty, we do not speak of a\nblind fact, nor do we seek to extinguish the light in its very source;\nwe would rather say, that it is more brilliant there than in its\nradiations. We see a body whose splendor illumines the world in which\nwe live; ought we, if requested to explain its nature and its relations\nwith other objects, to begin by destroying these? When naturalists\nwould examine the nature of light, and determine its laws, they do not\nbegin by removing the light itself, and placing themselves in darkness.\n\n15. True, this method of philosophizing is somewhat dogmatic, but\ndogmatic as it is, it has on its side, as we have seen, Pyrrho,\nHume, and Fichte. It is not simply a method of philosophy, it is the\nvoluntary submission of our very nature to an inevitable necessity,\nthe combination of reason with instinct, a simultaneous attention to\ndifferent voices calling from the depths of our soul. According to\nPascal, \"nature confounds the Pyrrhonians, and reason the dogmatists.\"\nThis passes for a profound saying, and is so under a certain aspect;\nbut it is notwithstanding somewhat inexact. The confusion is not the\nsame in both cases: reason does not confound the dogmatist, unless he\nseparates it from nature; but nature confounds the Pyrrhonian, either\nalone or joined with reason. The true dogmatist founds his reason upon\nnature; it knows itself, confesses the impossibility of proving every\nthing, and does not arbitrarily assume any principle that it needs\nunless nature itself furnishes it. And thus it does not confound the\ndogmatist, when guided by it he seeks a sure foundation for it. Nature,\nwhen it confounds the Pyrrhonian, attests the triumph of the reason of\ndogmatists, whose principal argument against Pyrrhonians, is the voice\nof nature itself. Pascal's thought would have been more exact if thus\nworded: nature confounds the Pyrrhonian and is necessary to the reason\nof dogmatists. This is less antithetical, but more true. Dogmatists\ndo not deny nature; reason without it is impotent; to exercise its\nstrength it needs a resting point. With such, Archimedes offered to\nmove the earth, without this his immense lever could not stir a single\natom.(2)\n\n\n\n\nCHAPTER III.\n\nCERTAINTY OF THE HUMAN RACE, AND PHILOSOPHICAL CERTAINTY.\n\n\n16. Certainty does not originate in reflection; it is the spontaneous\nproduct of man's nature, and is annexed to the direct act of the\nintellectual and sensitive faculties. It is a condition necessary to\nthe exercise of both, and without it life were a chaos; we therefore\npossess it instinctively, and without any reflection, and we enjoy the\nfruit of this as of all those other benefits of the Creator, which are\ninseparably joined to our existence.\n\n17. It is, then, necessary to distinguish between the certainty of the\nhuman race and philosophical certainty, although, to speak frankly, it\nis not easy to conceive what can be the value of any human certainty\ndistinct from that of the human race. If we set aside the efforts\nwhich the philosopher sometimes makes to discover the basis of human\nknowledge, we shall readily find him confounded with the rest of\nmankind. This cavil leaves no trace in his mind with respect to the\ncertainty of all that the human race is certain of. He then discovers\nthat the doubt which he felt was not a real doubt, although he may\nhave deluded himself into a contrary belief. His doubts were simple\nsuppositions, nothing more. When his meditation is over, and perhaps\neven while it lasts, he finds that he is as certain as the most\nignorant individual of his internal acts, the existence of his own\nbody, of other bodies around him, and of a thousand other things, which\nconstitute the amount of knowledge requisite to the wants of life.\n\nQuestion all, from the infant of a few summers, to the sage of many\nyears and mature judgment, on the certainty of their own existence,\ntheir acts internal or external, their friends and relatives, the\npeople among whom they dwell, objects seen or heard of, and you will\nnot detect any hesitation in their answers, or any kind of difference\nin the grades of their certainty. If they have no knowledge of the\nphilosophical questions touching these matters, you may read in their\ncountenances wonder and astonishment that any one should seriously\ninvestigate things so _evident_.\n\n18. Impossible as it is for us to know in what manner the sensitive,\nintellectual, and moral powers of children are developed, it is equally\nimpossible to prove a _a priori_, by analyzing the operations of his\nmind, that reflex acts do not concur to the formation of certainty;\nbut it will not be difficult to find proofs of this in the exercise\nof these faculties when well developed. If we observe attentively,\nwe shall see that the child's faculties habitually operate in a\ndirect, not a reflex manner; which shows that the development is made\ndirectly, not by reflection. Were the primitive development the work\nof reflexion, the reflective power would be great in the child. But\nthis is not the case. Very few men are ever endowed with it, and in the\ngreater part of them it is very nearly null. They who attain to it,\nacquire it only by assiduous labor, and not without great violence to\nhimself, can any one pass from direct to reflex cognition.\n\n19. No matter what you teach a child, he perceives it indeed, but call\nhis attention to the perception itself, and his understanding is at\nonce obscured and confused. Let us make the experiment. Suppose we\nwould teach a child the elements of geometry.\n\n\"Do you see this figure bounded by three lines? It is called a\ntriangle; the lines are called sides, and the points where they unite\nthe vertices of the angles.\"--\"I understand that.\"--\"Do you see this\nother figure bounded by four lines? It is called quadrilateral, and,\nlike the triangle, has its sides and vertices of angles.\"--\"Very\nwell.\"--\"Can a quadrilateral figure be a triangle, or _vice\nversa_?\"--\"It cannot.\"--\"Never?\"--\"Never.\"--\"Why not?\"--\"One has three,\nand the other four sides: how then can they be the same thing?\"--\"Who\nknows? It may seem so to you, but--\"--\"See here! This has three, and\nthis four sides; and three and four are not the same thing.\"\n\nTorture his understanding as much as you please, but you cannot drive\nhim from his position: and thus we see that his perception and his\nreason operate directly, that is, by direct application to the object.\nOf himself he does not direct his attention to his own internal acts,\ndoes not think upon his own thoughts, does not combine reflex ideas,\nnor seek in them the certainty of his judgment.\n\n20. And here we detect a vital error in the art of thinking as it has\nhitherto been taught. The young intellect is exercised in reflection,\nthe most difficult part of science, which is as inconsiderate as it\nwould be to commence his physical development by the most painful\ngymnastic exercises. Man's scientific development should be governed by\nhis natural development, which is direct not reflex.\n\n21. Let us apply this remark to the exercise of the senses. \"Do you\nhear that music?\" asks the child.--\"What music?\"--\"Did you not hear\nit? Are you deaf?\"--\"It _seems_ to you that you hear it.\"--\"But, sir,\nI hear it so distinctly! How can it be possible?\"--\"But how do you\nknow?\"--\"I hear it.\"\n\nFrom his _I hear it_ you cannot drive him: he will not hesitate a\nmoment, nor will he appeal to any reflex act in order to avoid your\nimportunities. \"_I hear it_: do not you hear it?\" He asks nothing\nmore, and all your philosophy cannot equal the _irresistible force_\nof sensation which assures him that there is music, and that whoever\ndoubts it is either deaf or in jest.\n\n22. Had the faculties of the child been developed by alternate direct\nand reflex acts; had he, when acquiring knowledge of things, thought\nof something besides the things themselves; evidently a continuation\nof such acts would have left some impression on his mind, and urged\nto assign the motives of his certainty, he would indicate those very\nmeans that he made use of in the gradual development of his faculties;\nhe would abstract the object, retire into himself, think upon his own\nthought in one way or another, and thus encounter the difficulty.\nNothing of this character takes place, which proves that no such\nreflex acts have been performed, that there have been only perceptions\naccompanied by internal consciousness and certainty of their existence;\nbut all in a confused, instinctive manner, without any thing like\nphilosophical reflection.\n\n23. What has been said of the child, may be proved true also of adults,\nhowever clear and perfect their intellect. If not initiated into\nquestions of philosophy, they will give very nearly the same answers to\ndifficulties proposed on the same matters, and even upon many others\nmore exposed to doubt. Experience proves better than all ratiocination\nthat no one acquires certainty by reflex acts.\n\n24. Philosophers teach that the sources of certainty are the internal\nsense or consciousness of acts, the external senses, common sense,\nreason, and authority. A few examples will show us that there is\nreflection in all these, and how most men, and even philosophers, when\nthey act like men and not like philosophers, think.\n\n25. Suppose a clear-headed person, one however who is ignorant of the\nquestions of certainty, has just seen some monument, the _Escurial_\nfor instance, which leaves a lively and lasting impression on his\nmind, and while he recollects his gratification on seeing it, try to\nmake him doubt the existence of this recollection in his mind, and\nits correspondence as well with the act of seeing as with the edifice\nitself, and he will very certainly think you are in jest, or will\nbe astounded, and will suspect you of being out of your senses. He\ndiscovers no difference between things different as are the actual\nexistence of his recollection, its correspondence with the past act of\nseeing, and the agreement of both with the edifice seen. He knows in\nthis case no more than a child of six years: \"I recollect it, I saw it,\nit is as I recollect it.\" This is all his science: he neither reflects,\nnor separates; all is direct and simultaneous.\n\nNo matter what suppositions you make, you can never get from the\nmajority of men any better account of the phenomena of the internal\nsense, than you got from the supposed individual's recollection of\nthe _Escurial_: \"all that I know is that it is so.\" There are here no\nreflex acts; certainty attends the direct act, and no philosophical\nconsiderations can add one iota to the security given by the very\nforce of things, and the instinct of nature.\n\n26. Example of the testimony of the senses.\n\nIf we see any object, no matter what, at a proper distance and in\nsufficient light, we judge of its size, figure, and color, and we\nare very confident of the truth of our judgment, although we may\nnever, in all our life, have thought of a theory of sensation, or\nof the relations of our organs, either to each other or to external\nobjects. No reflex act accompanies the formation of our judgment; all\nis done instinctively, and without the intervention of philosophical\nconsiderations. We see it, and nothing else: this is enough for\ncertainty. It is only after having handled books in which the question\nof certainty is agitated, that we turn our attention to our own acts;\nbut this attention, it is to be remarked, lasts only so long as we are\nengaged in the scientific analysis; when this is forgotten, which it\nvery soon is, we return to our general routine, and seldom recur to\nphilosophy.\n\nNote well that we speak here of the certainty of the judgment formed\nin consequence of sensation only in so far as it is connected with\nthe uses of life, and not at all of its greater or less exactness\nwith respect to the nature of things. Thus it matters little that we\nconsider colors as inherent qualities of bodies, although in reality\nthey are not; it is sufficient that the judgment formed does not\nin any sense change our relations to objects, whatever may be the\nphilosophical theory.\n\n27. Example of common sense.\n\nIn the presence of a numerous assembly, throw a quantity of printer's\ntypes at random upon the ground, and tell the bystanders that their\nnames will all be found printed. They will all with one accord laugh at\nyour folly. But what is the reason of this? Have they all reflected\nupon the basis of their certainty? Assuredly they have not.\n\n28. Example of reason.\n\nWe all reason, and in many cases rightly. Without art or reflection\nof any kind, we often distinguish the solid from the futile, the\nsophistical from the conclusive. This does not require us to regard the\ncourse of our understanding; without scarcely noticing it we follow\nthe right road; and a man may, in his life, have formed a thousand\nrigorous and exact ratiocinations without ever having once attended\nto his method of reasoning. Even those most versed in the dialectic\nart, repeatedly forget it; they perhaps follow it very correctly in\npractice, but they pay no express attention to any one of its rules.\n\n29. Ideologists have written whole volumes on the operations of\nour understanding, and the simple rustic performs these operations\nwithout thinking that he performs them. How much has been written on\nabstraction, generalization, and universals! Yet this is all well\nregulated in the mind of every man, ignorant as he may be of a science\nwhich examines it. In his language you will find the universal and the\nparticular expressed, and every thing occupying its proper place in his\ndiscourse: he encounters no difficulty in his direct acts. But call\nhis attention to these acts themselves, to abstraction for example;\nand what was in the direct act so clear and lucid, becomes a chaos the\nmoment it passes to the reflex order.\n\nThus we see that reflection, whose object is the act performed, is of\nvery little importance even in reasoning, its most reflective medium.\n\n30. Example of authority.\n\nAll civilized people know the existence of _England_, but most of them\nknow this only from having heard or read of it, that is, by authority.\nTheir certainty of the existence of England evidently is not surpassed\nby that of objects of their own vision; and yet how many of them have\never thought of analyzing the foundations of such a certainty? Yet\nis the certainty of those who have examined it greater than that of\nthose who have not examined it? In the present case, as in an infinity\nof others analogous to it, there is no intervention of reflex acts:\ncertainty is here formed instinctively, and needs no medium invented by\nphilosophers.\n\n31. These examples show that philosophers take a very different road\nto certainty from that taught by nature. He who created all things\nout of nothing, has provided them with all that is necessary to the\nexercise of their functions according to their respective positions in\nthe universe; and one of the first necessities of an intelligent being\nis the certainty of some truths. What would become of us, if before\nbeginning to receive impressions, and before the germination of primary\nideas in our understanding, we were obliged to perform the painful task\nof elaborating some system capable of saving us from uncertainty? Were\nit thus, our intellect would perish at its very birth, for no sooner\nwould it open its eyes to the light than it would be involved in the\nchaos of its own cavils, and it could never, with its scattered forces,\nsucceed in dissipating the clouds which would arise on all sides, and\nwhich would finally sink it in total darkness.\n\nIf the greatest philosophers, the most clear and acute intellects, the\nstrongest and most vigorous geniuses have labored to so little purpose\nto establish solid principles, such as might serve for the foundations\nof science, what would have happened had not the Creator succored us in\nthis necessity, and given certainty to the tender intellect, just as he\nprepared for the preservation of the body the milk that nourishes and\nthe air that vivifies it?\n\n32. If any part of science ought to be regarded as purely speculative,\nit is undoubtedly the part which concerns certainty; and this\nproposition, paradoxical as it may seem at first sight, is true, and\ncan be easily demonstrated.\n\n33. What does philosophy here propose to do? To produce certainty? But\nit exists independently of all philosophical systems, and mankind were\ncertain of many things before ever any one thought of such questions.\nMoreover, since the question was first raised, few, compared with the\nwhole human race, have examined it; so it is now, and so it will be;\nand all the theories invented on this point can have no effect upon the\nfact of certainty. What has been said of its production may be said of\nthe attempt to consolidate it. When have the generality of men had, or\nwhen will they have, time and opportunity to examine these questions?\n\n34. Philosophy could here have produced nothing but skepticism, for the\nvariety and opposition of systems were more calculated to create than\nto dissipate doubts. Happily nature is the most invincible opponent of\nskepticism; the sage's dreams pass not from his library to the every\nday uses of the life of ordinary men, or even of those who labor under\nor imagine them.\n\n35. Philosophy here can propose to itself no more reasonable object\nthan simply to examine the foundations of certainty, with the sole view\nof more thoroughly knowing the human mind, not of making any change\nin practice; just as astronomers observe the course of the stars,\ninvestigate and determine the laws to which they are subject, without\ntherefore presuming to be able to modify them.\n\n36. But even this supposition places philosophy in a very\nunsatisfactory position; for if we recollect what we have already\nestablished, we shall see that science observes a real and true\nphenomenon, but gives it a gratuitous explanation, by making an\nimaginary analysis of it.\n\nExperience has in fact shown our understanding to be guided by no one\nof the considerations made by philosophers; its assent, when it is\naccompanied by the greatest certainty, is a spontaneous product of a\nnatural instinct, not of combinations; it is a firm adhesion exacted\nby the evidence of the truth, the power of the internal sense, or\nthe impulse of instinct; not a conviction produced by a series of\nratiocinations. These combinations and ratiocinations therefore exist\nonly in the mind of philosophers, not in reality; when, therefore, they\nattempt to designate the foundations of certainty, we are told what\ncould or should have been, but not what is.\n\nIf philosophers would only be guided by their own systems, and would\nnot forget them nor set them aside as soon as, or even before, they\nhave finished explaining them, it might be said, that even if no reason\ncan be given for human certainty, one can be given for philosophical\ncertainty; but since these same philosophers make no use of these\nscientific means save when developing them _ex professo_, it follows\nthat their pretended foundations are a mere theory, having little or no\nconnection with the reality.\n\n37. This demonstration of the vanity of philosophical systems relating\nto the foundation of certainty, far from leading to skepticism, has a\ndirectly contrary tendency; for it makes us appreciate at their true\nvalue, the emptiness of our cavils, compares their impotence with the\nirresistible force of nature, and thus destroys that foolish pride\nwhich would make us superior to the laws imposed upon our understanding\nby the Creator himself; it places us in the channel through which\nthe torrent of humanity has for ages run; and it disposes us to\nreceive with sound philosophy what the laws of our nature force us to\naccept.(3)\n\n\n\n\nCHAPTER IV.\n\nEXISTENCE OF TRANSCENDENTAL SCIENCE IN THE ABSOLUTE INTELLECTUAL ORDER.\n\n\n38. Philosophers have sought a first principle of human knowledge; each\nhas assigned his own, and now after so much discussion it is doubtful\nwho is right, or even if any one is right.\n\nBefore inquiring what the first principle is, they ought to have\nascertained whether there be any such principle. We cannot suppose this\nlast question to be answered affirmatively; for it is, as we shall\nhereafter see, susceptible of different solutions, according to the\naspect under which it is seen.\n\nThe first principle of knowledge may be understood in either of two\nsenses; as denoting one first truth from which all others flow, or as\nexpressing a truth which we must suppose if we would not have all other\ntruths disappear. In the former sense it is a spring from which the\nwaters flow, which fertilize the intellect; in the second sense it is a\npoint whereon to rest a great weight.\n\n39. Is there any one truth from which all others flow? There is in\nreality, in the order of beings, in the universal intellectual order;\nbut in the human intellectual order there is none.\n\n40. There is in the order of beings one truth, the origin of all\ntruths; for truth is reality, and there is one Being, author of all\nbeings. This being is a truth,--truth itself,--the plenitude of\ntruth,--for he is being by essence, the plenitude of being.\n\nEvery school of philosophy has in some sense recognized this unity of\norigin. The atheist talks of the force of nature; the pantheist of\nan only substance, of the absolute, of the unconditioned; both have\nabandoned the idea of God, and now labour to replace it by something\nwhich may be made the origin of the existence of the universe, and of\nthe development of its phenomena.\n\n41. There is in the universal intellectual order one truth from which\nall others flow; it is, that the unity of origin of all truths is\nnot only found in realized truths, that is, in beings considered in\nthemselves, but likewise in the concatenation of ideas representing\nthese beings. And thus if our understanding could ascend to the\nknowledge of all truths, and embrace them in their unity and in all\nthe relations uniting them, it would see them after arriving at a\ncertain height, notwithstanding their dispersion and divergence as now\nperceived by us, converge to a centre, in which they unite, like rays\nof light in the luminous object from which they issued.\n\n42. The most profound philosophical doctrines often appear in the\ntreatises of theologians explaining the doctrines of the church.\nThus St. Thomas, in his questions on the understanding of angels,\nand in other parts of his works, has left us a very luminous and\ninteresting theory. According to him, spirits understand by a number\nof ideas smaller in proportion to the superiority of their order; and\nso the diminution goes on even to God, who understands by means of a\nsingle idea which is his own essence. And thus according to the holy\ndoctor, not only is there one being, author of all beings, but also\none infinite idea which includes all ideas. Whoever fully possesses\nthis idea will see every thing in it; but since this full possession,\ncalled comprehension in theology, is solely a property of the infinite\nintelligence of God, creatures, when in the other life they shall\nhave obtained the beatific vision, will see more or fewer objects in\nGod according to the greater or less perfection in which they possess\nit. How wonderful! The dogma of beatific vision well understood, is\nalso a truth which sheds much light upon philosophical theories.\nMalebranche's sublime dream about ideas was, perhaps, a reminiscence of\nhis theological studies.\n\n43. The transcendental science which embraces and explains them all,\nis a chimera to our mind so long as we inhabit this earth, but it is a\nreality to other spirits of a higher order, and it will also be so to\nus when, freed from this mortal body, we attain the regions of light.\n\n44. So far as we may conjecture from analogy, we have proofs of the\nexistence of this transcendental science, which includes all sciences,\nand is in its turn contained in one sole principle, or rather, in one\nonly idea, in one only intuition. If we observe the scale of beings,\nthe grades of distinction between individual intelligences, and the\nsuccessive progress of science, the image of this truth will be\npresented to us in a very striking manner.\n\nOne of the distinctive characteristics of our mind is its power of\ngeneralization, of perceiving the common in the various, of reducing\nthe multiplex to unity; and this power is proportional to its degree of\nintelligence.\n\n45. The brute is limited to its sensations and the objects causing\nthem. It has no power of generalization or of classification; nothing\nbeyond the impression received or the instinct of satisfying its wants.\nMan, however, as soon as he opens the eyes of his understanding,\nperceives unnumbered relations; he applies what he has seen in one\ncase to different cases; he generalizes and infolds very many ideas\nin a single idea. The child desires an object above his reach; he\nimmediately takes a chair or a stool, and improvises a ladder. A brute\nwill watch the object of its appetite whole hours when placed beyond\nits reach, without ever thinking of doing like the child, and forming a\nladder. If every thing be so disposed as to enable it to climb, it will\nclimb, but it is incapable of thinking that in similar circumstances it\nought to act in like manner. In the former case, we see a being having\nthe general idea of a _means_, and its relation to the _end_, of which\nit makes use when necessary: in the latter we see another being having\nindeed before its eyes the end and the means, but not perceiving their\nrelation, unable to go beyond the material individuality of objects.\n\nIn the former there is perception of unity; in the latter there is no\nbond to join the variety of particular facts.\n\nIt is seen by this simple example that the child will reduce all the\ninfinity of cases, in which an object may be placed beyond his reach,\nto this one case; he possesses, so to speak, the formula of this little\nproblem. True, he does not render himself an account of this formula,\nthat is, does not reflect upon it; but he has it in reality; and if you\ngive him an opportunity he will at once apply it, which proves that\nhe has it. Or speak to him of things placed too high for his reach,\nand point rapidly from one to another of the objects before him; he\nwill at all times instantly apply the general idea of an auxiliary\nmedium; he will avail himself perhaps of his father's arm, or that of a\nservant, a chair, if in the house, a heap of stones, if in the fields;\nhe discovers in all things _the relation of the means to the end_. When\nhe sees the end, he immediately turns his attention to the means of\nattaining it: the general idea seeks individualization in a particular\ncase.\n\n46. Art is the collection of rules for doing any thing well; and is\nthe more perfect in proportion as each rule embraces a greater number\nof cases, and consequently as the number of these rules is smaller.\nDoubtless, buildings that were solid, well proportioned, and adapted\nto the purpose for which they were destined, had been constructed\nbefore the rules of architecture were reduced to formulas; but the\ngreat progress of intelligence in the construction of buildings\nconsisted in ascertaining what there was common to all well-built\nhouses, in determining the cause of beauty and of solidity, in\nthemselves considered, by passing from the individual to the universal,\nthat is, by forming general ideas of beauty and solidity applicable to\nan indefinite number of particular cases, by simplifying.\n\n47. The same may be said of all other liberal and mechanical arts:\nthe progress of intelligence in all of them consists in reducing\nmultiplicity to unity, and including the greatest possible number of\napplications in the least possible number of ideas. This is why lovers\nof literature and the fine arts labor to discover an idea of beauty\nin general, in order to attain a type applicable to all literary and\nartistic objects. It is also obvious that those engaged in mechanical\narts always endeavor to govern their proceedings by a few rules, and he\nis held to be the most skilful who succeeds in combining the greatest\nvariety of results with the greatest simplicity of means, by making\nthat, which others connect with many ideas, depend upon one idea alone.\nWhen we see a machine produce wonderful effects by a very simple\nprocess, we praise the artificer not less for the means than for the\nend: this we say, is grand, and the simplicity with which it works is\nthe most astonishing.\n\n48. Let us apply this doctrine to the natural and exact sciences.\n\nThe merit of our actual system of numeration consists in including the\nexpression of all numbers in a single idea, making the value of each\nfigure ten times that to the right, and filling all intervals with\nzeros. The expression of infinite numbers is reduced to the simplicity\nof a single rule based upon a single idea; the relation of position\nwith a tenfold value. Logarithms have enabled arithmetic to make a\ngreat advance by diminishing the number of its fundamental operations,\nsince, with them it reduces multiplication and division to addition\nand subtraction. Algebra is only the generalization of arithmetical\nexpressions and operations, their simplification. The application of\nalgebra to geometry is the generalization of geometrical expressions;\nformulas of lines, figures, bodies, only the expression of their\nuniversal idea. In this idea as in a type, geometry preserves its first\nand generative idea, and it requires only the simplest applications\nin order to form an exact calculation of all lines belonging to the\nsame class, which can possibly be met with in practice. In the simple\nexpression dz/dx = A, called the differential coefficient, is contained\nthe whole idea of infinitesimal calculus. It originated in geometrical\nconsiderations, but so soon as its universality was conceived, it\npoured a flood of light upon every branch of mathematical and natural\nscience, and led to the discovery of a new world, whose confines are\nstill unknown. The prodigious fecundity of this calculus emanates from\nits simplicity, its prompt generalization of both algebra and geometry,\nand its uniting them in a single point which is the relation of the\nlimits of the differentials of any function.\n\n49. It is to this unity of idea that the human intellect in its\nambition aspires, and once obtained, it proves the cause of great\nprogress. The glory of the greatest geniuses is that they discovered\nit: the advance of science has consisted in profiting by it. Vieta\nexplained and applied the principle of the general expression of\narithmetical quantities; Descartes extended this to geometrical\nquantities. Newton established the principle of universal gravitation;\nand he, at the same time with Leibnitz, invented the infinitesimal\ncalculus; and the exact and natural sciences march, by the light of a\nvast flambeau, with gigantic strides along paths never before trodden.\nAnd all this because intelligence has approached unity, and become\npossessed of a generative idea, involving infinite other ideas.\n\n50. It is worthy of remark, that as we advance in science, we meet\nnumerous points of contact, close relations, which no one at first\nsight would have suspected. Ancient mathematicians discussed the conic\nsections, but were far from imagining that the idea of the ellipse\ncould be the basis of a system of astronomy: the foci to them were\nsimple points, the curve a line, and the relations of both the object\nof combinations at once profitless and without application. Ages pass\naway, and these foci are the sun, the curve the orbit of planets. The\nlines on the geometrician's table represented a world!\n\nThe intimate connection of mathematical and natural science cannot\nbe questioned; and who shall say to what extent both are connected\nwith ontological, psychological, theological, and moral science? The\nextended scale over which beings are distributed may at first sight\nseem to be an assemblage of unconnected objects, but seen with the\neyes of science, it is perceived to be a delicately worked chain,\nwhose links present, as we advance, greater beauty and perfection.\nWe see the different realms of nature united by close relations: the\nsciences, of which they are the objects, mutually borrow each other's\nlight, and enter on each other's territory. The complication of\nobjects among themselves involves this complication of science; and\nthe unity of the laws imposed upon different orders of beings makes\nall sciences approach, and tend to form, one only science. If it were\ngiven us to see the identity of their origin, the unity of the end\nand the simplicity of the means, we should come into the possession\nof the true transcendental science, the only science which involves\nall others, or more correctly speaking, the only idea in which every\nthing is represented as it is, and every thing seen without any\nnecessity of combination, or effort of any kind, just as a magnificent\nlandscape, its outlines, form, and colors are pictured on a perfectly\nclear mirror. In the meantime, we must rest satisfied with shadows of\nreality, and must see in the instinctive tendency of our understanding\nto simplify, to reduce every thing or make it approach as much as\npossible to unity, the announcement, the sign of this single science,\nthis intuition of the one infinite idea; just as in the desire for\nhappiness which agitates our heart, the thirst after enjoyment which\ntorments us we discover a proof that all is not ended here below, and\nthat our soul has been created for the possession of a good not to be\nattained in this mortal life.\n\n51. If we compare men with men, and pay attention to the character\nof genius, the most elevated point of human intelligence, we shall\nsee the truth of what has been said of the scale of human beings, and\nthe progress of science. Men of true genius are distinguished by the\nunity and extent of their conceptions. If they treat a difficult and\ncomplicated question, they simplify it, consider it from a high point\nof view, and determine one general idea which sheds light upon all the\nothers. If they have a difficulty to solve, they show the root of the\nerror, and with a word dispel all the illusion of sophistry. If they\nuse synthesis, they first establish the principle which is to serve as\nits basis, and with one dash trace the road to be followed in order to\nreach the wished-for result. If they make use of analysis, they strike\nin its secret resort the point where decomposition is to commence, they\nat once open the object, and reveal to us its most obscure mysteries.\nIf there is question of a discovery, while others are seeking here\nand there, they strike the ground with their foot, and exclaim, \"the\ntreasure is here.\" They make no long arguments, nor evasions; their\nthoughts are few but pregnant; their words are not many, but in each of\nthem is set a pearl of inestimable value.\n\n52. No doubt there is in the intellectual order a single truth from\nwhich all other truths emanate, one idea which includes all other\nideas. This philosophy teaches, and the efforts, the natural and\ninstinctive tendencies of every intelligence, toiling after simplicity\nand unity, show it: such also is the dictate of common sense, which\nconsiders that thought the highest and most noble which is the most\ncomprehensive and the most simple.(4)\n\n\n\n\nCHAPTER V.\n\nTRANSCENDENTAL SCIENCE IN THE HUMAN INTELLECTUAL ORDER CANNOT EMANATE\nFROM THE SENSES.\n\n\n53. In the human intellectual order, such as it is in this life, there\nis no one truth from which all others flow: philosophers have sought\none in vain; they have found none, for there was none to be found. In\nfact, where could it be found?\n\n54. Would it emanate from the senses?\n\nSensations are as various as the objects which produce them: by them we\nacquire knowledge of individual and material things; but no one truth,\nsource of all other truths, can be found in any one of these, or the\nsensations proceeding from them.\n\n55. If we observe our impressions received through sensation, we shall\nperceive that they are all equal so far as the production of certainty\nis concerned. We are just as certain of the sensation caused by any\nnoise whatever, as we are of that produced by an object which we see,\nan odorous body which we smell, a savory morsel which we taste, or any\nthing which strongly affects our sense of touch. There is no gradation\nin the certainty produced by these sensations: they are all equal; for\nif we speak of sensation itself, we experience it in such a manner as\nto leave no uncertainty; and if we speak of the relation of sensation\nwith the existence of the object causing it, we are just as certain\nthat the sensation called _sight_ corresponds to an external object\n_seen_, as we are that an external object _touched_ corresponds to the\nsensation called _touch_.\n\nHence we infer that no one sensation is the origin of the certainty\nof other sensations; in this they are all alike: and most men have no\nother reason than their experience why they should be sure of this\ncertainty. We are aware that what happens to individuals from whose\neyes cataracts have been removed, shows that simple sensation does not\nsuffice for the due appreciation of the object perceived, and that\none sense aids another: but this does not prove any one of them to be\npreferable; for as the blind man, whose sight was suddenly restored,\ndid not form an exact judgment as to the size and distance of objects\nseen by sight only, but required the assistance of touch; so is it\nvery probable that if a person of good eyesight had been deprived\nfrom his birth of the sense of touch, he would not be able, were this\nsense given him suddenly, to form an exact judgment concerning objects\ntouched, until, by the aid of sight, he had become accustomed to\ncombine the new and the old order of sensations, and learnt by practice\nto determine the relations of sensation with its object, or to know by\nsensation the properties of its object.\n\n56. This fact of the blind man is however contradicted by others which\nlead to a directly opposite result. The youth, upon whom the oculist,\nJean Janin, performed the same operation, and other persons blind from\ntheir birth, whose eyesight Luigi de' Gregori partly restored, did not,\nlike the blind man of Cheselden, deem these objects stuck to their\neyes, but that they saw them as things really external and separate.\nRosmini thus relates it,[3] although he gives the preference to the\nCheselden case, which he says was repeated in Italy by the professor\nGiacomo di Pavia with precisely the same results.\n\n[3] _Saggio sull' origine delle idee_, p. 5, c. iv., tr. 11, p. 285,\nwhere he cites the theoretico-chemical observations on the cataracts\nof those born blind, by Luigi de' Gregori, professor of chemistry and\nopthalmia, published at Rome in 1826.\n\n57. It is not easy to ascertain how this combination of one sensation\nwith another enables us to judge rightly of external objects; chiefly\nbecause the development of our sensitive and intellectual faculties is\ncompleted before we can reflect upon it: and thus we find ourselves\ncertain of the existence and properties of things before we have\nthought of certainty, and much less of the means of acquiring it.\n\n58. But even supposing us, after occupying ourselves with sensations\nand their relations with objects, to set aside the certainty which\nwe already have, and to act as if we sought it, we can find no one\nsensation the basis of the certainty of the other sensations. We should\nmeet in that all the difficulties to be encountered in the others.\n\n59. One of the chief difficulties upon this point is to determine the\nrelations of the sense of sight with that of touch, and how far the one\ndepends upon the other. We propose hereafter to examine these questions\nat some length, and we shall therefore now refrain from entering upon\nthem, as well because they are not of a character to be incidentally\ninvestigated, as because whatever their solution, it is not at all\nopposed to what we shall here establish.\n\n60. It would be of no advantage to us to know that the certainty of\nall sensations was, philosophically speaking, founded upon that of\nsome one sensation. Every sensation is a contingent, individual fact:\nhow then are we to draw from it light to guide us to necessary truths?\nNo matter under what aspect we consider sensation, it is only an\nimpression received through our organs. We are sure of the impression\nbecause it is intimately present to our mind; and its repetition aided\nby other sensations, whether of the same or another sense, makes us\ncertain of its relations with the object producing it: but every thing\nis done instinctively, with little or no reflection; and we are always\ncondemned, however much we reflect, to reach a point beyond which we\ncannot pass, for nature herself there stops us.\n\n61. Far then from finding in any sensation a fundamental fact on\nwhich to found a philosophical certainty, we discover a collection of\nparticular and mutually distinct facts, equal, however, so far as the\nproduction in us of that security which we call certainty is concerned.\nIt is of no use to decompose man, and reduce him first to an inanimate\nmachine, then allow him one sense, making him perceive different\nsensations, afterwards grant him another sense, making him combine the\nnew and the old sensations, and so on synthetically to the possession\nand exercise of them all. These things may do to entertain one's\ncuriosity, to nourish philosophical pretensions, or to give a show of\nprobability to imaginary systems; but they are in reality of little\nor no use; the evolutions which the observer imagines do not resemble\nthose of nature; and the true philosopher ought to examine what really\nis, not what is only in his conception.\n\nCondillac, animating his statue by degrees, and making the whole sum\nof human knowledge flow from one sensation, is like those priests who\ngot inside the statue of the idol, and thence emitted their oracles.\nIt is not the statue which receives animation, that speaks and thinks,\nit is Condillac from within it. Let us, however, grant to the sensist\nall he demands; let us allow him to regulate as he pleases the mutual\ndependence of sensations; for the instant we require him to make\nuse only of pure sensations in his discussions, he will be utterly\ndisconcerted, how much soever he may suppose them to be transformed.\nBut we reserve these questions to the place in which we shall examine\nthe nature and origin of ideas.\n\n62. Why are we sure that the agreeable sensation which we experience\nin our sense of smell proceeds from an object called a _rose_? Because\nwe recollect having experienced the same sensation on a thousand other\noccasions; because both sight and touch confirm the testimony of smell.\nBut how do we know that these sensations are something beside the\nimpressions received in our soul? Why may we not believe them to come\nfrom some cause or other, without relation to external causes? Is it\nbecause other men say the contrary? Are we certain that they exist? How\ndo they know what they tell us? How do we know that we hear rightly?\nThere is the same difficulty with the other senses as with that of\nhearing, and if we doubt the testimony of three senses, why shall we\nnot doubt that of four? Reasoning is here of no avail; it would lead us\nto cavils which would require an impassible doubt, and would tear from\nus a security, of which, notwithstanding all our efforts, we cannot\ndespoil ourselves.\n\nMoreover, if we appeal to the principles of reason, in order to prove\nthe truth of sensation, we leave the territory of sensations, and do\nnot place in them the primitive truth, origin of all other truths, nor\naccomplish what we undertook.\n\n63. Hence it follows: First, that there is no one sensation which is\nthe origin of the certainty of all others; this we have only indicated\nhere, reserving the demonstration of it to our treatise on sensations.\nSecondly, although such a sensation were to exist, it could not serve\nas the basis of any thing in the intellectual order, for with sensation\nalone it is impossible even to think. Thirdly, that sensations, so far\nfrom being able to serve as the basis of transcendental science, cannot\nserve of themselves alone to establish any science; because necessary\ntruths cannot flow from them, since they are contingent facts.(5)\n\n\n\n\nCHAPTER VI.\n\nTRANSCENDENTAL SCIENCE.--INSUFFICIENCY OF REAL TRUTHS.\n\n\n64. We have thought proper briefly to refute Condillac's system, not\non account of its intrinsic importance, or because it was not before\nin sufficiently bad repute, but in order to clear the field for higher\nand more strictly philosophical discussions. We should not omit to\nguard philosophy against the prejudice cast upon it by a system as vain\nas it is profitless. All that is most sublime in the science of the\nmind disappears with the _statue-man_ and transformed sensations: we\nvindicate the rights of human reason by showing that before entering\nupon more transcendental questions it is indispensable to discard\nCondillac's system; just as it is necessary before making a good road\nto clear away the brushwood which obstructs the passage.\n\n65. We come now to the proof that in the human intellectual order, such\nas it is in this life, there is no one truth the source of all truths;\nbecause no one truth includes them all.\n\nTruths are of two kinds, real and ideal. We call facts, or whatever\nexists, real truths; we call the necessary connection of ideas ideal\ntruths. A real truth may be expressed by the verb _to be_, taken\nsubstantively, or at least it supposes a proposition in which this verb\nhas been taken in this sense: an ideal truth is expressed by the same\nverb taken copulatively, as signifying the necessary relation of a\npredicate with a subject, abstracting it, however, from both. _We are_,\nthat is, _we exist_, expresses a real truth, a fact. _Whoever thinks\nexists_, expresses an ideal truth, for it does not affirm that there is\nany one who thinks or exists, but that if there is any one who thinks,\nhe exists; or, in other words, it affirms a necessary relation between\nthought and being. To real truths corresponds the real world, the world\nof existences; to ideal truths the logical world, that of possibility.\n\nThe verb _to be_, is sometimes taken copulatively, although the\nrelation expressed by it be not necessary: such is the case with all\ncontingent propositions, and when the predicate does not belong to\nthe essence of the subject. Sometimes the necessity is conditional,\nthat is, it supposes a fact; and then there is no absolute necessity,\nsince the supposed fact is always contingent. When we speak of ideal\ntruths, we refer to those that express an absolute necessary relation,\nabstracting it from all order of existence; and on the other hand,\nwe understand by real truths all those that suppose a proposition in\nwhich a fact has been established. To this class belong the truths of\nnatural science, for they all suppose some fact which is the object of\nobservation.\n\n66. No real finite truth can be the origin of all others. Truth of\nthis kind is the expression of a particular contingent fact, and\nconsequently can neither include other real truths or the world of\nexistences, nor ideal truths which refer only to necessary relations in\nthe world of possibility.\n\n67. Were we to see intuitively infinite existence, cause of all\nexistences, we should know a real truth, origin of all others; but\nas we know this infinite existence only by discursion and not by\nintuition, it follows that we do not know the fact of that existence\nin which the reason of all other existences is contained. Neither is\nit possible for us, after having by means of discursion reached this\ncognition, to explain from this point of view the existence of the\nfinite by the sole existence of the infinite; for if we abstract the\nexistence of the finite, the discursion, by which we attained to the\ncognition of the infinite, disappears, and then our whole scientific\nfabric tumbles to the ground. Demonstrate to a man by means of\ndiscursion the existence of God, and require him, setting aside the\npoint of departure, and depending upon the sole idea of the infinite,\nto explain not only the possibility, but also the reality of creation;\nand he cannot do it. If he only sets aside the finite all his reasoning\nfails, and no effort can prevent its failing; he is like an architect\nwho, after having built a superb cupola, is required to support it\nalthough the foundations of the edifice are removed.\n\n68. Take any real truth whatever, the plainest and most certain fact,\nand yet we can derive nothing from it if ideal truth comes not to\nfecundate it. We exist, we think, we feel; these are indubitable\nfacts, but science can deduce nothing from them; they are particular\ncontingent facts, whose existence or non-existence neither affects\nother facts nor reaches the world of ideas.\n\nThese truths are of the purely sensible order, have not of themselves\nany relation with the order of science, nor can they be elevated to it\nif not combined with ideal truths. Descartes, when he brought forward\nthe fact of thought and existence, driven as he was by his attempt\nto raise a scientific edifice, passed unawares from the real to the\nideal order. _I think_, he said; and had he stopped here he would have\nreduced his philosophy to a simple intuition of consciousness; but\nhe wished to go farther, he wished to reason, and then of necessity\navailed himself of an ideal truth: _whoever thinks exists_. Thus with\na universal and necessary truth he fecundated his individual and\ncontingent fact; and as he needed some rule to guide him in his onward\nmarch, he sought one in the admissibility of the evidence of ideas.\nAnd thus also we see how this philosopher, who so toiled in search\nof unity, came all at once in contact with triplicity: _a fact_, _an\nobjective truth_, _a criterion_: a fact in the consciousness of the\nsubject; an objective truth in the necessary relation of thought with\nexistence; a criterion in the admissibility of the evidence of ideas.\n\nWe may defy all the philosophers in the world to reason upon any fact\nwhatever without the aid of ideal truth. We shall find in all facts the\nsame sterility as in the fact of consciousness. This is no conjecture,\nbut a rigid demonstration. Only one existence contains the reason of\nall other existences; if, then, we do not immediately and intuitively\nknow it, we cannot discover any one real truth, origin of all others.\n\n69. Even supposing there to be in the order of creation a fact of such\na nature, that the whole universe is only a simple development of\nit, we should not therefore have found the real truth source of all\nscience, for it would not enable us to make any advance towards the\nworld of possibility, the ideal order, infinitely superior to that of\nfinite existences.\n\nIf we suppose the progress of natural science to lead to the discovery\nof a single, simple law, which presides over the development of\nall others, and the application of which, varied according to\ncircumstances, is a sufficient reason of all the phenomena now referred\nto many and very complicated laws; this would, without doubt, be an\nimmense progress in sciences the object of which is the visible world;\nbut what would it give us to know of the world of intelligences? What\nof the world of possibility?(6)\n\n\n\n\nCHAPTER VII.\n\nTHE PHILOSOPHY OF THE ME CANNOT PRODUCE TRANSCENDENTAL SCIENCE.\n\n\n70. The testimony of consciousness is sure and irresistible, but it\nhas no connection with that of evidence. The object of the one is a\nparticular and contingent fact; that of the other, a necessary truth.\nThat I now think, is to me absolutely certain; but this thought of\nmine is not a necessary but a decidedly contingent truth; for I might\nnever have thought, or even existed: it is a purely individual fact, is\nconfined to me, and its existence or non-existence in nowise affects\nuniversal truths.\n\nConsciousness is an anchor, not a beacon: it saves the understanding\nfrom shipwreck, but does not light it on its way; in the assaults\nof universal doubt, consciousness is at hand to shield it from\ndestruction; but if asked to direct us, it gives us only particular\nfacts.\n\nThese facts have no scientific value, except when made objective, or\nrather, when the mind, reflecting upon them, bathes them in the light\nof necessary truths.\n\nWe think, we feel, we are free; these are facts; but of themselves they\nare barren. If we would fecundate them, we must take them as a kind of\nmaterial of universal truths. Thought becomes immovable, it congeals,\nif deprived of the impulse of these ideas; sensation is common to us\nand the brutes; and liberty, without combination of motives presented\nby reason, has no object, no life.\n\n71. Here we discover the cause of the obscurity and sterility of German\nphilosophy since Fichte. Kant fixed himself upon the subject, without,\nhowever, destroying objectivity in the internal world; and therefore\nhis philosophy, although containing many errors, offers to the mind\nsome luminous points: but Fichte went farther, planted himself upon the\n_me_, and made no use of objectivity, save when it was necessary to the\nmore solid establishment of a fact of consciousness; and so he found\nonly realms of darkness and contradiction.\n\nMen of gifted minds have labored in vain to make some ray of light\nemanate from a point condemned to obscurity. The soul sees itself\nin its own acts; and that it presents immediately to itself facts\nconducing to its own cognition is the only title it has, more than\nother beings distinct from it, to be conceived by itself. What would\nit know were it not to perceive its own thought, its will, and the\nexercise of all its faculties? How is it to discuss its own nature, if\nnot from data furnished by the testimony of its own acts? The _me_ then\ndoes not see itself intuitively; is offered to itself only mediately,\nby its acts; that is, so far as it is known, it is in the same category\nas all other external beings, which are all known by their effects upon\nus.\n\nThe _me_ in itself considered, is not a luminous point; it supports\nthe fabric of reason, but is not the rule according to which it is\nto be constructed. The true light is found in objectivity, for it\nis properly the object of knowledge. The _me_ can neither be known\nnor thought, save inasmuch as it makes itself its own object, and\nconsequently places itself on a level with other beings subject to\nintellectual activity, which operates only by virtue of objective\ntruths.\n\n72. Intelligence cannot be conceived without at least internal objects;\nbut if the understanding do not conceive relations and consequently\ntruths in them, they will be sterile. These truths will have no\nconnection, will be isolated facts, if they involve no necessity;\nand even those relations which refer to particular facts furnished\nby experience will not be susceptible of any combination if they do\nnot, at least conditionally, involve some necessity. The brilliancy\nof the light in the room where I now write is in itself a particular,\ncontingent fact, and science, as such, cannot make it its object except\nby subjecting the movement of the light to geometrical laws, that is,\nto necessary truths.\n\nScience then may find a resting-point in the _me_ itself as subject,\nbut no point of departure. The individual is of no service to the\nuniversal, nor the contingent to the necessary. Assuredly there would\nbe no such thing as the individual A's science, if the individual\nA himself did not exist; but the science which stands in need of\nthe individual subject is not science properly so called, but the\ncollection of individual acts by which the individual perceives\nscience. This collection of acts is not the science perceived, which\nis something common to all intellects, and does not need this or that\nindividual: the fund of truths constituting science does not spring\nfrom this collection of individual acts, particular facts, which are\nlost like minutest drops in the ocean of intelligence.\n\nHow then can science be based solely upon the subjective _me_? How\ncan the object be made to spring from this subject? Consciousness has\nno connection with science, except in so far as it furnishes facts to\nwhich we may apply objective, universal, and necessary principles,\nindependent of all finite individuality, constituting the patrimony of\nhuman reason, but not requiring the existence of any man.\n\n73. No analysis of the facts of consciousness will produce the origin\nof the lights of science. Such an act would be either direct or\nreflex. If direct, its value is objective not subjective, the act does\nnot found science, but the truth perceived, not the subject but the\nobject, not the _me_, but that which is seen by the _me_. If reflex, it\nsupposes another previous act, to wit, the object of reflection, which\nis primitive, and not the act.\n\nNeither is the combination of the direct with the reflex act of any\nservice to science, except as connected with necessary and objective\ntruths, which are independent of the subject. An act individually\nconsidered, is an internal phenomenon, which, apart from objective\ntruths, teaches us nothing. It has, indeed, a scientific value, if\nconsidered under the general ideas of being, cause, effect, principle\nor product of activity, modification, or its relations with its\nsubject, which is the _substratum_ of other similar acts; that is, if\nit be considered as a particular case, comprised in the general ideas\nas a contingent phenomenon, to be appreciated by the help of necessary\ntruths, as an experimental fact to which a theory may be applied.\n\nThe reflex act is only a cognition of a cognition, feeling, or\nsome other internal phenomenon; and therefore all reflection upon\nconsciousness presupposes a prior direct act. The object of this\ndirect act is not the _me_; the fundamental principle of the cognition\ntherefore is not the _me_, as the object known, but only as the\nnecessary condition, since there cannot be thought without a thinking\nsubject.\n\n74. These considerations destroy the very foundations of the system\nof Fichte, and that of all who take the human me as their point of\ndeparture on the voyage of science. The me, in itself, is not presented\nto us; we know it only by its acts; and herein it participates of a\nquality of other objects, the essence of which is not immediately\noffered to us, but only what emanates from it by the exercise of their\nactivity upon us.\n\nThus guided by objective and necessary truths, which are the laws\nof our understanding, the type of the relations of beings, and\nconsequently a sure standard of them, we ascend by reasoning to the\ncognition of things themselves. We know that our mind is simple,\nbecause it thinks, whereas the composite, the multiplex cannot\nthink. It is thus we know the _me_. We are conscious of its thinking\nactivity, and this is the material furnished by the fact, but then\ncomes the principle, the objective truth to illumine the fact, and\nshow the repugnance between thought and composition, and the necessary\nconnection between simplicity and consciousness.\n\nUpon examination, this reasoning will be found to apply not only to the\n_me_, but to every thinking being; and this is why we can extend our\ndemonstration to all such beings: the _me_, therefore, which applies\nthis truth, does not create, it only knows it, and knows itself to be a\nparticular case comprised in the general rule.\n\n75. To pretend that truth has its source in the subjective _me_, is\nto begin by supposing the _me_ to be an absolute, infinite being, the\norigin of all truths, and the reason of all beings; which is equivalent\nto making philosophy commence by deifying the human understanding. But\nas one individual has no more right to this deification than another,\nto admit it is to establish a rational pantheism, which, as we shall\nhereafter see, is nearly, if not quite, identical with absolute\npantheism.\n\nIf we suppose individual reason to be only a phenomenon of the one\nabsolute reason, and consequently what we call spirits not to be\ntrue substances, but modifications of a single spirit, and each\nparticular consciousness to be only a manifestation of the universal\nconsciousness, we can then conceive why the source of all truth is\nsought in the _me_, and why we interrogate our own consciousness as\na kind of oracle through which the universal consciousness speaks.\nBut the difficulty is that such a supposition is gratuitous, and that\nthey who thus seek the reason of all truths, begin by establishing the\nmost incomprehensible and absurd of propositions. Who will persuade us\nthat our consciousness is only the modification of another? Who will\nmake us believe that what we call the _me_ is common to all men, to\nall intelligent beings, and that the only difference between them is\nthe difference of the modifications of one absolute being? Why, then,\nis not this absolute being conscious of every consciousness which it\ncomprises? Why does it not know that which it contains, and by which\nit is modified? Why does it believe itself multiplex, if indeed it\nbe one? Where is the bond of this multiplicity? If each particular\nconsciousness were only a modification, would it preserve its unity,\nand a connected series of all that happens to it, when this series,\nthis unity is wanting to the substance which it modifies?\n\n76. However this may be, not even by supposing pantheism, can the\nfriends of subjective philosophy at all advance their pretensions.\nWith pantheism they legitimate, so to speak, their pretension, but\ndo not realize it. They call themselves gods, and as such, have a\nreason for the source of truth being in them; but as there is in their\nconsciousness only one apparition of their divinity only one phase of\nthe orb of light, they can only see in it what it presents to them; and\ntheir divinity finds itself subjected to certain laws which make it\nimpossible for it to give the light demanded by philosophy.\n\n77. If we interrogate our consciousness upon necessary truths, we shall\nperceive that, far from pretending to found or to create them, it both\nknows and confesses them to be independent of itself. If, thinking\nof this proposition: \"It is impossible for a thing to be, and not be\nat the same time;\" we ask ourselves if the truth of this originates\nin our thought, consciousness at once answers that it does not. The\nproposition was true before our consciousness existed; and should it\nnow cease to exist, the proposition would still be true; true, also,\nwhen we do not think of it: the soul is as an eye which contemplates\nthe sun, but is not, therefore, necessary to the existence of the sun.\n\n78. Another consideration demonstrates the sterility of all philosophy\nwhich seeks in the _me_ alone the sole and universal origin of human\nknowledge. Every cognition requires an object; purely subjective\ncognition is inconceivable; although we suppose the subject and object\nto be identified, duality of relation, real or conceived, is still\nnecessary; that is, the subject as known must stand in a certain\nopposition,--opposition at least conceived,--with itself as subject\nknowing. Now, what is the object sought in the primitive act? Is it\nsomething not the subject? Then the philosophy of the subject falls\ninto the current of other philosophies, since in this something which\nis not the subject are objective truths. Is it the subject itself? Then\nwe ask, is it the subject in itself or in its acts; if the subject in\nits acts, then the philosophy is reduced to ideological analysis, and\nhas no special characteristic; if the subject in itself, we say it\nis not known intuitively, and least of all can they who call it the\n_absolute_ pretend to this cognition; it is for them even more than\nfor others a dark abyss. In vain will you stoop over this abyss, and\nshout for truth; the dull rumbling which reaches your ears is only the\necho of your own voice; the profound cavern rolls back to you only your\nown words still more hollow and mysterious.\n\n79. Eminent among the philosophers most given to empty cavils is the\nauthor of the _Doctrine of Science_, Fichte, of whose system Madame de\nSta\u00ebl ingenuously remarked, that it very much resembled the awakening\nof Pygmalion's statue from sleep, which, turning alternately to itself\nand to its pedestal said, _I am, I am not_.\n\nFichte says, in the beginning of his work entitled _Doctrine of\nScience_, that he proposes to seek the most absolute principle, the\nabsolutely unconditioned principle of all human knowledge. This his\nmethod is erroneous: he begins by supposing what is unknown, and does\nnot even suspect that there may be a true multiplicity in the basis\nof human cognitions. We believe that there may be, and that there\nreally is such a multiplicity, that the sources of our knowledge are\nvarious, and of different orders, and that we cannot reduce them to\nunity without leaving man and ascending to God. We repeat it, this\nequivocation has become exceedingly general, and its only result\nhas been uselessly to fatigue inquiring minds or to drive them to\nextravagant systems.\n\nFew philosophers have toiled harder than Fichte after this absolute\nprinciple; and yet, to speak plainly, he accomplishes nothing; he\neither repeats Descartes' principle, or amuses himself with a play\nupon words. We feel pity at seeing him labor so earnestly to so\nlittle purpose. We beg the reader to follow us with patience in our\nexamination of the German philosopher's doctrine, not with the hope of\nfinding a thread to serve as a clue to the D\u00e6dalus of philosophy, but\nin order to judge, with a knowledge of the cause, doctrines which have\nmade so much noise in the world.\n\n\"If this principle,\" says Fichte, \"is absolutely the first, it can\nneither be defined nor demonstrated. It must express the act, which\nneither is nor can be presented among the empirical determinations of\nour consciousness, but rather lies at the bottom of all consciousness,\nand alone makes consciousness possible.\"[4]\n\n[4] _Wissenschaftslehre, Th. 1, \u00a7 1_.\n\nWithout any antecedent, or any reason, without even taking the trouble\nto show on what he bases it, Fichte assures us that the first principle\nmust express an act. Why may it not be an objective truth? This, at\nleast, would have deserved some attention, for all preceding schools,\nthe Cartesian included, located the first principle among objective\ntruths, not among acts. Descartes himself needed an objective truth in\norder to establish the fact of thought and existence. \"Whoever thinks\nexists,\" or, in other words, \"whoever does not exist cannot think.\"\n\n80. This last remark shows one of the radical vices affecting the\ndoctrine of Fichte and other Germans, who attribute an altogether\nunmerited importance to subjective philosophy. They accuse others of\ntoo easily making the transition from the subject to the object, but\nforget that they, at the same time pass, unauthorised by any reason or\ntitle, from objective thought to the pure subject. Confining ourselves\nto the passage of Fichte just cited, what, we ask, will an act be which\nneither is nor can be presented among the empirical determinations\nof our consciousness? The principle in question is not exempted from\nbeing known because it is absolute; for if we do not know it, we cannot\nassert that it is absolute; and if it is not, and cannot be presented\namong the empirical determinations of our consciousness, it neither\nis nor can be known. Man knows not that which is not present in his\nconsciousness.\n\nThe absolute principle upon which all consciousness rests, and which\nmakes it possible, either does or does not belong to consciousness.\nIf the former, it is liable to all the difficulties affecting the\nother acts of consciousness; if the latter, it cannot be the object of\nobservation, and therefore we can know nothing of it.\n\nFichte confesses that in order to arrive at the primitive act, and\nseparate from it all that does not really belong to it, we must suppose\nthe rules of all reflection to be valid, and start with some one of the\nmany universally admitted propositions. \"Conceding us,\" he says, \"this\nproposition, you must, at the same time, concede as act that which we\ndesire to place as the principle of the whole _Doctrine of Science_;\nand the result of the reflection must be that this act is conceded to\nus as the principle together with the proposition. We take any fact\nof empirical consciousness, and strip it one after another of all its\nempirical determinations, until reduced to all its purity it contains\nthat only which thought cannot absolutely exclude, and from which\nnothing further can be taken.\"[5]\n\n[5] _Ibid._\n\nThese words show that the German philosopher proposed ascending to a\nperfectly pure and wholly indeterminate act of consciousness, which,\nhowever, is impossible. Either he takes the act in a very broad sense,\nand understands by it the _substratum_ of all consciousness, in which\ncase he only expresses in other words the idea of substance; or else\nhe speaks of an act properly so called, that is, of some exercise of\nthat activity, that spontaneity which we feel within ourselves; and\nin this sense the act of consciousness cannot be separated from all\ndetermination without destroying its individuality and existence. Man\ncannot think without thinking something, desire without desiring\nsomething, feel without feeling something, or reflect upon internal\nacts without fixing his reflection upon something. There is some\ndetermination in every act of consciousness: an act perfectly pure,\nabstracted from every thing, and wholly indeterminate, is impossible,\nabsolutely impossible; subjectively, because the act of consciousness,\nalthough considered in the subject, requires some determination;\nobjectively, because such an act is inconceivable as individual, and\nconsequently as existing, since it offers nothing determinate to the\nmind.\n\n81. Fichte's indeterminate act is only the idea of act in general. He\nimagined he had made a great discovery when he conceived nothing in the\ngroundwork but the principle of act, that is, the idea of substance\napplied to that active being whose existence consciousness itself makes\nknown to us.\n\nIf we may be allowed to say candidly what we think, our opinion is,\nthat Fichte, with all his analytical investigations, has not advanced\nphilosophy one step towards the discovery of the first principle. We\nsee from what has already been said how easy it is to stop him by\nsimply demanding an account of the suppositions made on the first page\nof his book. Still, wishing, as we do, to oppose him with all fairness,\nwe will not take up his ideas without allowing him to explain them\nhimself.\n\n\"Every one admits the proposition: A is A; just as that A = A, because\nsuch is the meaning of the logical copula; and indeed without the least\ndeliberation we perceive and affirm its complete certainty. Should any\none ask a demonstration of it, we should by no means give any, but\nshould maintain that the proposition is absolutely certain, that is,\nwithout any further foundation. Thus incontestibly proceeding with\ngeneral consent, we claim the right to _suppose something absolutely_.\n\n\"We do not, in affirming the preceding proposition to be certain\nin itself, suppose that A _is_. The proposition A is A, is not\nequivalent to this: A _is_, or, _there is an_ A. (_To be_ placed\nwithout a predicate has an entirely different meaning from _to be_\nwith a predicate, whereof more hereafter.) If we make A denote a\nspace contained between two straight lines, the proposition remains\nexact, although the proposition, A _is_, be evidently false. But, we\nassert: _if_ A _is_, A _is thus_. The question is in no wise whether\nA is in general or not. The question is not of the _contents_ of the\nproposition, but only of its _form_; not whereof we know something, but\nwhat we know of any object whatever.\n\n\"Consequently, by the above assertion, that the proposition is\nabsolutely certain, this is established, that between the _if_ and\nthe _thus_ there is a necessary connection; and it is this necessary\nconnection between both which is supposed _absolutely_ and _without\nother foundation_. I call this necessary connection provisionally = X.\"\n\nAll this show of analysis amounts only to what every logical student\nknows, that in every proposition the copula, or the verb _to be_,\ndenotes not the existence of the subject, but its relation to the\npredicate. There was no need of so many words to tell us so simple a\nthing, nor of such affected efforts of the understanding in treating of\nan identical proposition. But let us arm ourselves with patience, and\ncontinue to listen to the German philosopher:\n\n\"But to return to A itself, _whether_ A is or not; nothing is as yet\naffirmed thereon. The question then occurs: under what condition is A?\n\n\"X at least is supposed _in_ and _by_ the _me_, for it is the _me_\nwhich judges in the above proposition, and indeed judges by X as by a\nlaw, which consequently being given to the _me_, and by it established\nabsolutely and without other foundation, must therefore be given to the\n_me_ by the _me_ itself.\"\n\n82. What does all this Sanscrit mean? We will translate it into\nEnglish: in identical or equivalent propositions there is a relation\nwhich the mind knows, judges, and according to which it decides upon\nthe rest: this relation is given to our mind; identical propositions\nneed no proof in order to obtain assent. All this is very true, very\nclear, and very simple; but, when Fichte adds that this relation must\nbe given to the _me_ by the _me_ itself, he asserts what he neither\ndoes nor can know. Who told him that objective truths come to us from\nourselves? Is one of the principal philosophical questions, such as\nis that of the origin of truth, to be thus easily solved with a dash\nof the pen? Has he, perchance, defined his _me_, or given us any idea\nof it? Either his words mean nothing, or they mean this: I judge\nof a relation; this judgment is in me; this relation, as known and\nabstracted from real existence, is in me; all which may be reduced to\nDescartes' more natural and simple expression: \"I think, therefore I\nexist.\"\n\n83. Upon carefully examining Fichte's words, we clearly see that\nhe made no more progress than the French philosopher. He goes on:\n\"_Whether_ and _how_ A in general is supposed, we know not; but as\nX must mark a relation between an unknown supposition of A and an\nabsolute supposition of A under the condition of this supposition,\nin so far at least as that relation is supposed, A exists _in_ the\n_me_, and is supposed _by_ the _me_, just as X. X is possible only in\nrelation to an A: but X is really supposed in the _me_, therefore A\nalso must be supposed in the _me_ in so far as X is referred to it.\"\n\nWhat confusion and mystery in the expression of the commonest things!\nHow great Descartes appears beside Fichte! Each makes the fact of\nconsciousness revealing existence the beginning of his philosophy. The\none expresses his thoughts clearly, with simplicity and in a language\nwhich all the world does or may understand; the other, in order to\nseem an inventor, and to show that he has no master, envelops himself\nin a cloud of mystery, with darkness all around, whence in a hollow\nvoice he pronounces his oracles. Descartes says: \"I think, I cannot\ndoubt it, it is a fact attested to me by my internal sense; no one can\nthink without existing; therefore I exist.\" This is clear, simple, and\ningenuous; it manifests a true philosopher, one without affectation\nor pretension. Fichte says: \"Take any proposition whatever; for\nexample, A is A:\" and then goes on to explain how the verb _to be_ in\npropositions does not express the absolute existence of the subject,\nbut its relation with the predicate; the whole with a show of doctrine,\nwearisome in its form, and ridiculous in its sterility; and this too\nwhen he only wants to inform us that A is in the _me_, because the\nrelation of the predicate with the subject, that is, X, is possible\nonly in a being, since A denotes some being or other. Let us compare\nthe two syllogisms. Descartes says: \"No one can think without existing;\nbut I think; therefore I exist.\" Fichte says literally what follows:\n\"X is only possible in relation to an A; but X is really supposed in\nthe _me_; therefore A must also be supposed in the _me_.\" There is at\nbottom no difference at all, and the only difference in form is that\nwhich exists between the language of a vain man and that of a sensible\nman.\n\nAt bottom the syllogisms are not different, we repeat it. Descartes'\nmajor proposition is: \"Whatever thinks exists.\" He does not prove\nit, and admits that it cannot be proved. Fichte's major is: \"X is\npossible only in relation to an A,\" or, in other words, no relation\nof a predicate with a subject, in so far as it is known, is possible\nwithout a being which knows. \"X must mark a relation between an unknown\nsupposition of A and an absolute supposition of the same A, _at least\nin so far as that relation is supposed_,\" that is, inasmuch as it is\nknown. And how does Fichte prove a relative supposition to suppose an\nabsolute supposition, that is, a subject in which it is supposed? Like\nDescartes, he does not prove it at all. There is no relative A without\nan absolute A; what does not exist cannot think. This is clear and\nevident; farther than this neither Fichte nor Descartes goes.\n\nDescartes' minor is: \"_I think_;\" this he does not prove, but refers to\nconsciousness beyond which he confesses that he cannot pass. Fichte's\nminor is this: \"X is really asserted in the _me_;\" which is equivalent\nto saying: the relation of the predicate with the subject is really\nknown by the _me_; and as, according to Fichte himself, the proposition\nmay be selected at pleasure, to say that the relation of the predicate\nwith the subject is known by the _me_, is the same as to say that any\nrelation whatever is known by the _me_; which in clearer terms may be\nexpressed thus, _I think_.\n\n84. Here we would remark, that the difference, if any there be, is\naltogether in favor of the French philosopher, who understands by\nthought every internal phenomenon of which we are conscious. In order\nto establish this fact, he has no need of analyzing propositions,\nand confusing the understanding upon those very points where it most\nrequires clearness and precision. Fichte, to arrive at the same point,\ntakes a roundabout way. Descartes points his finger to it, and says:\n_this is it_. The one acts like a sophist, the other like a true man of\ngenius.\n\nHad the German philosopher confined his forms, little calculated as\nthey are to illustrate science, to what we have thus far examined,\ntheir greatest inconvenience would have been to weary both the author\nand his readers; but unfortunately his mysterious _me_, which makes its\nappearance at the very vestibule of science, and which, in the eyes of\nsound reason, can only be what it was to Descartes,--the human mind,\nknowing its existence by its own thought,--goes on dilating in Fichte's\nhands, like a gigantic spectre, which, beginning in a single point,\nends by hiding its head in the heavens and its feet in the abyss.\nThis _me_, absolute subject, is then a being which exists because it\nsupposed itself: it is a being which creates its own self, absorbs\nevery thing, is every thing, and is revealed in the human mind as in\none of the infinite phases of its infinite existence.\n\nWhat we have thus far said, suffices to show the tendencies of Fichte's\nsystem. We are here treating of certainty and its foundations; this,\nthen, is not the place to anticipate what we propose to say more at\nlength upon this system when we come to explain the idea of substance\nand refute pantheism: for this is one of the gravest errors of modern\nphilosophy; everywhere, and under all aspects, it must be combatted,\nbut to do this we must attack it in its roots. This is why we have\nexamined at such length Fichte's fundamental reflection in his\n_Doctrine of Science_, and stripped it of the importance which he\nclaimed for it, so as to make it the basis of a transcendental science;\nfor he flattered himself with being able to determine the absolutely\nunconditioned principle of all human knowledge.(7)\n\n\n\n\nCHAPTER VIII.\n\nUNIVERSAL IDENTITY.\n\n\n85. In order to give unity to science, some appeal to universal\nidentity; this, however, is not to discover unity, but to take refuge\nin chaos. Universal identity is not only an absurdity, but a groundless\nhypothesis. Excepting the unity of consciousness, we find in ourselves\nnothing that is one; but multiplicity of ideas, perceptions, judgments,\nacts of the will, impressions of various kinds; and in relation to\nexternal objects, we perceive multitude in the beings which surround\nus, or as some pretend, in their appearances. Where then are unity and\nidentity, for we can neither find them within nor without ourselves?\n\n86. If it be said that nothing is offered to us but phenomena, and\nthat we do not attain to the reality, the absolute and identical\nunity hidden beneath them, we can reply with this dilemma: either our\nexperience is confined to phenomena, or it reaches the very nature\nof things: if the former, we cannot know what is concealed under the\nphenomena, nor absolute and identical unity; if the latter, then nature\nis not one but multiplex, for we everywhere encounter multiplicity.\n\n87. It is curious to observe how easily men, the most skeptical in the\nsimplest things, suddenly become dogmatic at the very point where the\ngreatest motives of doubt are presented. With them the external world\nis either a pure appearance, or a being having no resemblance to the\nconception formed of it by the human race: the criterion of evidence,\nthat of consciousness, and that of common sense have little power to\ncommand assent: the crowd alone should be satisfied with such weak\nfoundations; the philosopher demands others far more solid. But strange\nas it may seem, the very philosopher who styled reality a deceitful\nappearance, and saw obscurity in what the human race considered\nluminous, so soon as he quitted the world of phenomena and arrived in\nthe dominions of the absolute, finds himself illumined by a mysterious\nsplendor, he requires no discussion, but by a most pure intuition, he\nsees the unconditioned, the infinite, the one in which every thing\nmultiplex is involved, the great reality, the basis of all phenomena,\nthe great All which re-unites in its breast all existences, re-assumes\nevery thing, and absorbs every thing into most perfect identity. He\nfixes his philosophic eye upon this focus of light and life, sees\nit roll out like the ocean of existence in vast billows, and thus\nexplains what is various by what is one, the composite by the simple,\nthe finite by the infinite. All these prodigies do not require him to\nleave himself; he has only to go on destroying all that is empirical,\nto ascend even to pure act by mysterious by-paths unknown to all\nexcept himself. This _me_, which may have believed itself an existence\nperishable and dependent on another superior existence, is astounded\nat finding itself so great; it discovers in itself the origin of all\nbeings, or, more correctly speaking, the only being, of which all\nothers are but phenomenal existences; it is the universe itself become\nby a gradual development conscious of itself: whatever is without\nitself, and at first appears distinct, is only itself, a reflection of\nitself, presented to its eyes, and unfolded under a thousand different\nforms like a magnificent panorama.\n\nLet not the reader think we have imagined a system for the sake of\ncombatting it; the doctrine which we have here exposed, is the doctrine\nof Schelling.\n\n88. One cause of this error is the obscurity of the problem of knowing.\nTo know, is an immanent action, having, at the same time, relation to\nan external object, excepting those cases in which the intelligent\nbeing becomes, by a reflex act, its own object. In order to know a\ntruth, whatever it may be, the mind does not quit itself; it does not\noperate beyond itself; its own consciousness tells it that it remains,\nand that its activity is developed, within itself.\n\nThis immanent action extends to objects the most distant in time and\nplace, and the most unlike in their nature. How is the mind to come in\ncontact with them? How is it to ascertain whether their representation\nconforms to reality? There can be no cognition without this\nrepresentation; without conformity, there is no truth, cognition is a\npure illusion to which nothing corresponds, and the human understanding\nis unceasingly the sport of vain appearances.\n\nUndeniably this problem is liable to very serious difficulties, which\nperhaps the science of man, while in this life, cannot solve. Here\narise all the ideological and psychological questions ever treated by\nthe most eminent metaphysicians. However, as it is not our intention\nto anticipate what is to be hereafter considered, we shall confine\nourselves to the point of view indicated by our present question of\ncertainty and its fundamental principle.\n\n89. Consciousness attests the fact of representation; without this\nthere is no thought; and the affirmation _I think_ is, if not the\norigin of all philosophy, at least its indispensable condition.\n\n90. Whence comes the representation? How is a being placed in such\ncommunication with other beings, and this not by a transient but by an\nimmanent act? How explain the conformity between the representation\nand the object? Does not this mystery indicate that there is unity,\nidentity, at the bottom of all things, that the being which knows, is\nthe very being known, which appears to itself under a distinct form,\nand that what we call realities are only phenomena of one and the\nsame being, always identical, infinitely active, which develops its\nstrength in various ways, and forms by its development what we call the\nuniverse? No! This neither is nor can be! It is an absurdity which the\nmost extravagant reason cannot accept: it is a resource as desperate as\nit is impotent to explain a mystery, if you will, but one a thousand\ntimes less obscure than the system which pretends to clear it up.\n\n91. Universal identity explains nothing, but greatly confuses\neverything; it does not dissipate the difficulty, but strengthens it,\nand renders it insolvable. It certainly is no easy matter to explain\nhow the mind obtains the representation of things distinct from itself;\nbut it is no easier to show how the mind can have the representation of\nitself. If there is unity, complete identity between the subject and\nthe object, how are the two presented to us as distinct things? How can\nduality proceed from unity, or diversity spring from identity?\n\nIt is a fact testified by experience, not the experience of external\nobjects, but that of consciousness, by that which is most hidden in\nour soul, that there is in every cognition a subject and an object,\nperception and the thing perceived, and without this difference the\nact is not possible. Even when by an effort of reflection, we take\nourselves for our own object, the duality appears; if it does not\nexist, we imagine it, for without this fiction we cannot think.\n\n92. Even in the most intimate and concentrated reflection, duality,\nupon careful examination, is to be found, not by fiction, as it might\nseem at first sight, but in reality. When the understanding turns\nupon itself, it does not see its own essence, for it has no direct\nintuition of itself: it sees its acts, and these it takes for its\nobject. The reflex act is not the act reflected. When I think that I\nthink, the first thought is distinct from the second, and so distinct\nthat one succeeds the other, for the reflective thought can exist only\nsubsequently to the thought reflected.\n\n93. This is confirmed by a profound analysis of reflection. Is\nreflection possible without an object reflected upon? Evidently not.\nWhat is this object in the present case? The thought itself: then this\nthought must have preceded the reflection. If it be supposed that they\nmust not of necessity follow in different instants of time, and that\nthe dependence is saved, notwithstanding the simultaneousness, still\nthe force of the argument is not lost; we grant, but do not concede,\nthat the simultaneousness is possible; but the dependence at least is\nnot possible without distinction. Dependence is a relation; relation\nsupposes opposition of extremes; and this opposition draws with it\ndistinction.\n\n94. That these acts are distinct, although simultaneous, may be\ndemonstrated in another manner. One of them, that reflected upon, may\nexist without the reflex act. We continually think, without thinking\nthat we think; and the same may be proved true of every reflection\nwhatever, whether it is occupied with the act thought, or it disappears\nand leaves only the direct act: these acts are, therefore, not only\ndistinct but separable; therefore, the duality of the subject and the\nobject exists not only in the external world, but also in that which is\nthe most intimate and pure in our soul.\n\n95. It avails not to say that the object of reflection is not any\ndeterminate act, but thought in general. This is in many cases false;\nfor we not only think that we think, but that we think a determinate\nthing. Moreover, although the object of reflection is sometimes thought\nin general, not even then does the duality disappear: in that case\nthe subjective act is an individual act, existing in a determinate\ninstant of time, and its object is thought in general, that is, an\nidea representative of all thought, an idea which involves a sort\nof confused recollection of all past acts, or of what is called\nactivity, intellectual force. The duality then exists more evidently,\nif possible, than when the object is a determinate thought. In one\ninstance at least two individual acts are compared; but in this case\nan individual act is compared with an abstract idea, a thing existing\nin one instant of time with an idea that either abstracts it, or\nconfusedly embraces all that has passed since the epoch when the\nconsciousness of the reflecting being commenced.\n\n96. These arguments have much greater weight when directed against\nthose philosophers who place the essence of the mind not in the power\nof thinking but in thought itself; who give to the _me_ no other\nexistence than what springs from its own knowledge, affirming that\nit exists only because it _supposes_ itself, by knowing itself, and\nonly in so far as it _supposes_ itself, that is, in so far as it knows\nitself. With this system there is duality, or rather plurality, not\nonly in the acts, but even in the _me_ itself; because this _me_ is an\nact, and acts follow like a series of fluxions developed to infinity.\nThus, far from saving the unity and identity of subject and object,\nplurality and multiplicity are established in the subject itself; and\nthe unity of consciousness itself, in danger of being broken by the\ncavils of philosophers, is forced to take refuge in the obscurity of\ninvincible nature.\n\n97. We have thus incontestably proved that there is in us a duality\nof subject and object, that without it knowledge is inconceivable,\nand that representation itself is a contradiction unless in one\nsense or another we admit things really distinct in the recesses of\nintelligence. We beg to observe that we have a sublime type of this\ndistinction in the august mystery of the Trinity, the fundamental dogma\nof our holy religion, covered, indeed, with an impenetrable veil, but\nwhich sends forth light to illustrate the profoundest questions of\nphilosophy. This mystery is not explained by feeble man, but is for him\na sublime explanation. Thus Plato availed himself of glimmerings from\nthis focus as a treasure of immense value to philosophical theories;\nthus the Holy Fathers and theologians, in endeavoring to throw some\nlight upon it by arguments of congruity, have illustrated the most\noccult mysteries of human thought.\n\n98. The upholders of universal identity, besides contradicting a\nprimitive and fundamental fact of consciousness, signally fail in\ntheir efforts to explain by it either the origin of intellectual\nrepresentation or its conformity to its object. Evidently no man has\nan intuition of the nature of the individual _me_, and still less of\nthe absolute being which these philosophers suppose as the _substratum_\nof whatever exists or appears. It is impossible for them to explain _a\npriori_, without this intuition, the representation of objects or their\nconformity to the representation. The fact, therefore, on which they\nwould base their whole philosophy, either does not exist, or is unknown\nto us: in neither case can it serve as the foundation of a system.\n\nWere this fact to exist, it could not be presented to our mind by\nany enunciation to which we could arrive by reasoning. It must be\nseen rather than known; either occupy the first place or none. If we\nbegin to reason without taking this fact for our basis, we start from\nthe apparent in order to attain to what truly is; we make use of an\nillusion to arrive at reality. Thus it evidently follows from the\nsystem of our adversaries that philosophy must either start with the\nmost powerful intuition, or else it cannot advance a single step.\n\n99. The schools distinguish between the principle of being and the\nprinciple of knowledge, _principium essendi et principium cognoscendi_;\nbut this distinction has no place in the system which we oppose; being\nis there confounded with knowledge; what exists, exists because it is\nknown, and it exists only in so far as it is known. To draw out the\nseries of cognitions, is to develop the series of existences. They\nare not even two parallel movements; they are but one movement; the\n_me_ is the universe, and the universe is the _me_; whatever exists\nis a development of the primitive fact, is the fact itself which is\ndisplayed under different forms, extending like an infinite ocean; its\nposition is unlimited space; its duration eternity.(8)\n\n\n\n\nCHAPTER IX.\n\nUNIVERSAL IDENTITY,--CONTINUED.\n\n\n100. These systems, as absurd as they are fatal, although under\ndistinct forms, and by various means, they tend to prepare the way for\npantheism, contain a profound truth which, disfigured by vain cavils,\nseems to be an abyss of darkness, whereas it is in itself a ray of most\nbrilliant light.\n\nThe human mind seeks that by reason to which it is impelled by an\nintellectual instinct; how to reduce plurality to unity, to re-unite,\nas it were, all the variety of existences in a point from which they\nall proceed, and in which they are all absorbed. The understanding\nknows that the conditioned must be included in the unconditioned, the\nrelative in the absolute, the finite in the infinite, the various in\nthe one. In this, all religions, all schools of philosophy agree. The\nproclamation of this truth belongs to no one of them exclusively; it is\nto be met with in all countries of the world, in primitive times, back\neven to the cradle of the human race. Beautiful, sublime tradition!\nPreserved through all generations, amid the ebb and flow of events,\nit offers us the idea of the Divinity presiding over the origin and\ndestiny of the universe.\n\n101. Yes! The unity sought by philosophers is the Divinity itself,--the\nDivinity whose glory the firmament declares, and whose august face of\nineffable splendor appears to us in our inmost consciousness. Yes! it\nis the Divinity which enlightens and guides the true philosopher, but\nblinds and confounds the proud sophist; it is what the true philosopher\ncalls GOD, and venerates and adores in the sanctuary of his soul, but\nwhat the insensate philosopher, with sacrilegious profanation, calls\nthe _me_. Considering its personality, its consciousness, its infinite\nintelligence, and its most perfect liberty, it is the foundation and\nthe copestone of religion: distinct from the world, it produced the\nworld from nothing, and preserves and governs it, and leads it by\nmysterious paths to the destiny assigned in its immutable decrees.\n\n102. There is then unity in the world; there is unity in philosophy.\nIn this all agree; the difference is that some separate, with the\ngreatest care, the finite from the infinite, the thing created from the\ncreative power, unity from multiplicity, and maintain the necessary\ncommunication between the free will of the omnipotent agent and finite\nexistences, between the wisdom of the sovereign intelligence and the\nfixed course of the universe: while others, affected with melancholy\nblindness, confound the effect with the cause, the finite with the\ninfinite, the various with the one, and reproduce in the domain of\nphilosophy the chaos of primeval times; but all scattering and in\nfrightful confusion, without any hope of order or union: the earth of\nthese philosophers is void, and darkness is upon the face of their\ndeep; the spirit of God has not moved over the waters to fecundate the\nchaos, and produce oceans of life and light out of darkness and death.\n\nThe absurd systems invented by philosophical vanity explain nothing;\nthe system of religion, which is that also of sound philosophy, and\nof all mankind, explains everything: the intellectual, as well as the\ncorporeal world, is a chaos to the human mind the instant it abandons\nthe idea of God: restore this and order reappears.\n\n103. The two capital problems: whence the intellectual representation,\nand whence its conformity to objects, have with us a most simple\nexplanation. Our understanding, although limited, participates in the\ninfinite light; this light is not that which exists in God himself, but\na semblance communicated to a being created according to his image.\n\nIllumined by this light, objects shine upon the eyes of our mind,\nwhether because they are in communication with it by means unknown to\nus, or because the representation is given to us directly by God, in\nthe presence of objects.\n\nThe conformity of the representation to the thing represented, results\nfrom the divine veracity. An infinitely perfect God cannot take\npleasure in deceiving his creatures. Such is the theory of Descartes\nand Malebranche, eminent thinkers, who took no step in the intellectual\norder, without looking to the Author of all light, and who never wrote\na page on which the name of God was not traced.\n\n104. As will hereafter be seen, Malebranche admitted that man sees\nevery thing in God, even in this life; but his system, far from\nidentifying the human _me_ with the infinite being, carefully\ndistinguishes them, not finding other means to sustain and enlighten\nthe former than by approximating and uniting it to the second. To read\nthe great metaphysician's immortal work is enough to convince one\nthat his system was not that of this pure, primitive intuition, which\nis an act required of all empiricism, and which seems to rise within\nthe limits of philosophy, from that intuition of the simple fact, the\norigin of all ideas and all facts, in which one of the dogmas of our\nreligion, the beatific vision, seems realized upon earth in the domain\nof philosophy. These are senseless pretensions, and as far from the\nmind as from the system of Malebranche.(9)\n\n\n\n\nCHAPTER X.\n\nPROBLEM OF REPRESENTATION: MONADS OF LEIBNITZ.\n\n\n105. The pretension to find a real truth, the fountain of all others,\nis dangerous in the extreme, however indifferent it may at first sight\nappear. Pantheism, and the deification of the _me_, two systems which\ncoincide at bottom, are a consequence not easy to be avoided if it be\nattempted to establish all human science upon one fact.\n\n106. The real truth or fact, which would serve as the basis of all\nscience, should be immediately perceived, otherwise it would lack the\ncharacter of origin and basis of other truths; because the medium by\nwhich it should be perceived would itself have the better right to\nthe title of first truth. If this intermediate fact were the cause of\nthe other, evidently this latter would not be primitive; and if the\npriority were given to the order of knowledge instead of the order of\nbeing, we should still have the same difficulty as now to explain the\ntransition from subject to object, or the legitimacy of the medium by\nwhich we perceive the primitive fact.\n\nSince then, the immediate presence, the intimate union of the\nunderstanding with the thing known is necessary, it is clear that as\nthe _me_ has this immediate presence only for itself and its own acts,\nthe fact sought for must be the _me_ itself. That which is immediately\npresent to us is the facts of consciousness; by them we place ourselves\nin communication with what is distinct from us. In case then that we\nmust find a primitive fact, the origin of all others, this fact must be\nthe _me_. If we deny this consequence, we must deny the possibility\nof finding any fact which may be the source of transcendental science.\nHere we see how the apparently most innocent philosophical pretensions\nlead to fatal results.\n\n107. There is here certainly very little chance for evasion, but there\nis one so specious as to merit an examination.\n\nThe fact, which is the scientific origin of all others, is not\nnecessarily their true origin. By distinguishing between the principle\nof being and the principle of knowledge, all difficulty seems to be\navoided. It is absurd and contrary to common sense, that the _me_ is\nthe origin of all that exists; but not that it is the representative\nprinciple of all that is or can be known. Representation is not\nsynonymous with causality. Ideas represent but do not cause the\nobjects represented. Why, then, is it not possible to admit a fact\nrepresentative of all that the human understanding can know? It is\ncertain that the perception of this fact must be immediate, that is, it\nmust be supposed intimately present to the understanding perceiving it;\nfor which reason, it can be nothing else than the _me_: this, however,\nis not to deify the _me_, but only to concede to it a representative\nforce, which may have been given to it by a superior being. It makes\nthe _me_ not an universal cause, but a mirror which reflects the\ninternal and external worlds.\n\nThis explanation reminds us of the famous system of _monads_ advanced\nby Leibnitz; an ingenious system indeed, the lofty flight of one of\nthe mightiest geniuses that ever honored the human race. The whole\nworld formed of invisible beings, all representative of the same\nuniverse, whereof they are a part, but by a representation adequate to\ntheir respective categories, and in conformity to their corresponding\npoint of view, according to the place which they occupy, unrolling\nthemselves in an immense series, which, commencing with the lowest\norder, goes on ascending to the very portal of infinity; and at the\nuppermost point of existences is the monad, which, in itself contains\nthe reason of all things, which has produced them from nothing, given\nto them their representative force, and distributed them into their\nproper categories, establishing among them a sort of parallelism of\nperception, will, action, and motion, in such a manner that, without\nany one communicating any thing to another, they all move on in most\nperfect conformity, in ineffable harmony. This is grand, beautiful, and\nwonderful; a colossal hypothesis which the genius of Leibnitz alone\ncould ever have conceived.\n\n108. Having paid this tribute of admiration to the eminent author of\nthe _Monadology_, we observe that its gigantic conception is only an\nhypothesis which all the talent of its inventor could never base upon\na single fact capable of giving to it an appearance of probability.\nOmitting the very serious difficulties, which this system, doubtless\nagainst the will of its author, opposes to the explanation of free\nwill, we shall confine ourselves to the examination of the bearings of\nthis system upon the question now before us.\n\nIn the first place, the representation of the monads, being a mere\nhypothesis, can serve to explain nothing, unless philosophy is to be\nmade the sport of ingenious combination. The _me_ is a monad, that is,\nan indivisible unity; of this there can be no doubt. The _me_ is a\nmonad representative of the universe: this is an absolutely gratuitous\nassertion, and until it is proved in some way or other, we have the\nright to ignore it.\n\n109. Now, suppose the representative force, as understood by Leibnitz,\nto exist in the _me_; this hypothesis does not impugn what has been\nsaid against the primitive origin of transcendental science. On close\ninspection, the hypothesis of Leibnitz will be found to explain the\norigin of ideas, but not their connection. Make the soul a mirror, in\nwhich, by an effect of the creative will, every thing is represented;\nstill it does not explain the order of these representations, show how\none of them springs from another, or assign to them any other bond\nthan the unity of consciousness. This system then is quite out of the\nquestion: we are not disputing on the manner in which representations\nexist in the soul, nor on their origin; but we are examining the\nopinion which pretends to found all science upon a single fact, and to\nunfold all ideas as simple modifications of that fact. This Leibnitz\nnever said, nor can any thing be found in any of his works to indicate\nsuch a thought. Moreover, the difference between this system of\n_Monadology_ and that of the German Philosophers, which we impugn, is\ntoo palpable to escape any one.\n\nI. So far is Leibnitz from advocating universal identity, that he\nestablishes an infinite plurality and multiplicity: his monads are\nbeings really different and distinct among themselves.\n\nII. The whole universe, composed of monads, proceeded, according to\nLeibnitz, from one infinite monad; and this procession was not by\nemanation, but by creation.\n\nIII. In the infinite monad, in God, Leibnitz places the sufficient\nreason of every thing.\n\nIV. Knowledge has been freely given by God himself to the monads.\n\nV. This knowledge, and the consciousness of it, belong to the monads\nindividually, and Leibnitz never even remotely took into consideration\nthis foundation of all things, which by its transformation ascends from\nnature to consciousness, or descends from the region of consciousness\nand is converted into nature.\n\n110. These differences so marked need no comments; they show most\nevidently that the philosophers of modern Germany cannot shield\nthemselves under the name of Leibnitz; although, in truth, these\nphilosophers have no failing of that kind: far from seeking guides,\nthey all aspire to originality, and this is one principal cause of\ntheir extravagance, Hegel, Schelling, and Fichte, all pretend to\nbe founders of a philosophy; and Kant was so governed by the same\nambition, that he made very important alterations in the second\nedition of his _Critic of Pure Reason_, lest he should be taken for a\nplagiarist from Berkeley's idealism.(10)\n\n\n\n\nCHAPTER XI.\n\nPROBLEM OF REPRESENTATION EXAMINED.\n\n\n111. All our knowledge is by representation, without which it would be\ninconceivable; and yet what is representation in itself considered? We\ncannot say: it enlightens us as to other objects, but not as to itself.\n\nIt is obvious that we do not attempt to conceal the very grave\ndifficulties which the solution of this problem offers: on the\ncontrary, we point them out with all clearness, in order to avoid that\nvain presumption which is as fatal to science as to every thing else.\nBut let it not be supposed that we intend to banish this question from\nthe arena of philosophy: for many and serious as are its difficulties,\nwe are yet of opinion that they allow of sufficiently probable\nconjectures.\n\n112. The representative force may emanate from any one of these three\nsources: identity, causality, or ideality. We will explain ourselves.\nA thing may represent itself; and this we call representation of\nidentity. A cause may represent its effect; and this is what we\nunderstand by representation of causality. A being, whether substance\nor accident, may represent another distinct from itself, which is not\nits effect; and this we call representation of ideality.\n\nWe do not see how it is possible to assign any other source of\nrepresentation: holding, therefore, the division to be complete, we\nwill examine its three points; and we beg to call the attention of the\nreader more especially to this matter, because it is one of the most\nimportant in philosophy.\n\n113. That which represents must have some relation to the thing\nrepresented: whether essential or accidental, inherent or communicated,\nthis relation must exist. Two beings, having absolutely no relation,\none of which nevertheless represents the other, are a monstrosity.\nThere is nothing without a sufficient reason; and there being no\nrelation between the thing representing, and that represented, there is\nno sufficient reason of the representation.\n\nIt is here to be borne in mind that, for the present, we abstract\nthe nature of this relation; we do not assert it to be either real\nor ideal; we only say that, between the thing representing and that\nrepresented, there must be some link, whatever that link may be. Its\nmysteries, its incomprehensibility, do not destroy its existence.\nPhilosophy perhaps may be unable to explain the enigma; but it\ncan demonstrate the existence of the link. Thus, abstracting all\nexperience, it is possible to demonstrate _a priori_, that there is a\nrelation between the _me_ and other beings, by the mere fact of their\nrepresentation existing in the _me_.\n\nThe incessant communication of intelligences with each other, and with\nthe universe, proves that there is a point of union for them all.\nRepresentation, alone, is a convincing proof of this: so many beings,\napparently dispersed and unconnected, are intimately united in some\ncentre, so that the simple phenomenon of intelligence leads us to\naffirm the common link, the unity in which plurality is joined. This\nunity, with pantheists, is universal identity; with us, it is God.\n\n114. Here observe that this relation between the thing representing and\nthat represented, is not necessarily direct or immediate; it suffices\nthat it be with a third object: thus, they who explain representation\nby identity, and they who account for it by intermediate ideas, must\nequally admit it; for, on the present matter, there is no difference\nbetween those who hold these ideas to be produced by the action of\nobjects upon our mind, and those who make them proceed immediately from\nGod.\n\n115. Whatever represents any thing, contains in some sense the thing\nrepresented; for an object cannot be represented unless it is in some\nmanner or other in the representation. It may be the object itself,\nor its image; but this image cannot represent the object, unless it\nis known to be its image. Every idea then involves the relation of\nobjectivity; otherwise it could not represent the object, but only\nitself. The act of intelligence is immanent, but in such a manner, that\nthe intellect does not need to go out of itself to attain its object.\nWhen we think of a star a million leagues distant, our mind certainly\ndoes not go to the point where the star is; but by means of the idea,\nit destroys in an instant this immense distance, and unites itself with\nthe star. What it perceives is not the idea, but its object: if this\nidea did not involve a relation to the object, it would cease to be an\nidea to the mind, and would represent nothing except itself.\n\n116. There is then, in every perception, a connection of the being\nthat perceives with the thing perceived. When this perception is not\nimmediate, the medium must be such as to contain a necessary relation\nto the object; it must conceal itself in order to offer to the eye of\nthe mind only the thing represented. From the instant that it presents\nitself, and is seen, or even noticed, it ceases to be an idea and\nbecomes an object. The idea is a mirror, which is most perfect when it\ncreates the most perfect illusion. It must necessarily present only the\nobjects, and project them at the proper distance, without allowing the\neye to see the crystalline plane which reflects them.\n\n117. This union of the thing representing, with that represented, of\nthe intellect with its objects, may, in some instances, be explained\nby identity. In general, no contradiction is discovered in any thing\nrepresenting itself to the eye of the understanding, if we suppose\nthem to be united in some way or other. In case then that the thing\nknown is itself intelligent, we see no difficulty in its being its\nown representation, and consequently none in confounding ideality\nand reality in the same being. If an idea can represent an object,\nwhy may it not represent itself? If an intelligent being can know an\nobject through the medium of an idea, why may it not know that object\nimmediately? The union of the thing known with the intellect is to\nus a mystery, it is true; but is the union effected by the medium of\nan idea less so? To the idea may be objected all that can be brought\nagainst the thing itself; and it is even more inexplicable how one\nthing represents another, than how it represents itself. The thing\nrepresenting and that represented, have between them a sort of relation\nof containing and contained. It is easily conceived that the identical\ncontains itself, since identity expresses much more than to contain;\nbut it is not so easily conceived how the accident can contain the\nsubstance, the transitory the permanent, the ideal the real. Identity\nis then a true principle of representation.\n\n118. We would here make the following remarks necessary to avoid\nequivocations.\n\nI. We do not assert a necessary relation between identity and\nrepresentation; for this would make every being representative, since\nevery being is identical with itself. We establish this proposition:\nidentity may be the origin of representation; but we deny the two\nfollowing: identity is the necessary origin of representation;\nrepresentation is a sign of identity.\n\nII. We determine nothing as to the application of the relations between\nrepresentation and identity, so far as finite beings are concerned.\n\nIII. We abstract the duality which results from supposing only subject\nand object, and enter into no question on the nature of this duality.\n\n119. These ideas being fixed, we may observe that we have an\nincontestable proof that there is no intrinsic repugnance between\nidentity and representation in two dogmas of the Catholic religion: the\nbeatific vision and the divine intelligence. The dogma of the beatific\nvision teaches us that the human soul in the mansion of the blessed\nis intimately united to God, and sees him face to face in his very\nessence. No one ever said that this vision was made by the medium of an\nidea, but theologians, and among them St. Thomas, expressly teach the\ncontrary. We have then identity united with representation, that is,\nthe divine essence representing, or rather presenting, itself to the\neyes of the human mind. The dogma of divine intelligence teaches that\nGod is infinitely intelligent. God does not need to go out of himself,\nnor employ distinct ideas in order to understand; he sees himself in\nhis essence. Here, too, identity is united with representation, and the\nintelligent being identified with the thing understood.(11)\n\n\n\n\nCHAPTER XII.\n\nIMMEDIATE INTELLIGIBILITY.\n\n\n120. Neither active nor passive representation can be predicated of\nall things; we mean to say, that there are some beings which are not\nendowed with intellectual activity, and cannot be even passively the\nobject of the acts of the intellect.\n\nAs regards the power of active representation, which is at bottom\nonly the faculty of intelligence, it is evident that many beings are\ndestitute of it. There may be greater difficulty with regard to passive\nrepresentation, or the fitness to be the immediate object of the\nintellect.\n\n121. An object cannot be known immediately, that is, without the\nmediation of an idea, if it do not itself perform the functions of this\nidea, and unite itself to the intellect which is to know it. This alone\ntakes from all material objects the character of being _immediately\nintelligible_: so that if a mind be imagined having no idea of the\ncorporeal universe, it could know nothing of it, although for all\neternity in the midst of it.\n\nHence it follows that matter neither is, nor can be, intelligent or\nintelligible: the ideas which we have of it come from another source;\nwithout them we might be united to matter, and never know or even\nsuspect its existence.\n\n122. An opportunity is here presented of explaining an exceedingly\ncurious doctrine of St. Thomas. This eminent metaphysician was\nof opinion that it required greater perfection to be immediately\nintelligible than to be intelligent; so that the human mind, although\nendowed with intelligence, does not possess intelligibility.\n\nIn his _Summa Theologica_,[6] the holy Doctor asks if the soul knows\nitself by its essence, and answers that it does not, and thus defends\nhis position:\n\n[6] P. 1^a, Q. 87^a, A. 1^o.\n\n\"Things are intelligible accordingly as they act, and not as they have\nthe power to act, as is said in the ninth book of Metaphysics (tex. 20\ntr. 3). For any thing that comes under knowledge is being, is the true,\nin so far as it is in act, and this is manifestly apparent in sensible\nthings. Thus the sight does not perceive that which may be colored,\nbut that only which actually is colored. And in the same manner as is\nmanifest, the intellect, in so far as it knows material things, knows\nthat only which is in act.... Hence, also, in immaterial substances,\neach one is intelligible by its essence, accordingly as it is in act\nby its essence. Therefore, the essence of God, which is a pure and\nperfect act, is absolutely and perfectly intelligible by itself; thus\nGod knows, by his essence, not only himself but also all other things.\nBut the essence of the angel belongs to the class of intelligible\nbeings as an act, but not as a pure and complete act, wherefore his\nunderstanding is not completed by his essence. For, although the\nangel knows himself by his essence, he cannot know all things by his\nessence, but knows those distinct from himself only by their images.\nBut the human intellect in the class of intelligible beings is only\na possible being.... Therefore, considered in its essence, it is an\nintelligent power; hence of itself it has the faculty of understanding,\nbut not of being understood, except inasmuch as it acts. On this\naccount the Platonists placed the order of intelligible beings above\nthe order of intellect; because the intellect understands only by\nparticipation of the intelligible; but according to them, that which\nparticipates is beneath that of which it participates. If, then, the\nhuman intellect places itself in act by the participation of separate\nintelligible forms, as the Platonists held, it would know itself by\nthis participation of incorporeal things. But as it is natural to our\nintellect in the present life to look to material and sensible things,\nit follows that our intellect knows itself only as it is placed in act\nby the species (ideas) abstracted from sensible things by the light\nof the intellect acting, which is the act of the intelligible things\nthemselves.... Therefore our intellect does not know itself by its\nessence but by its acts.\"\n\nSuch is the doctrine of St. Thomas. Cardinal Cajetan, one of the most\npenetrating and subtile minds that ever existed, has a commentary on\nthis passage, worthy of the text. These are his words: \"Two things\nexpressly follow, from what is said in the text. The first is, that our\nintellect has of itself the faculty of understanding. The second is,\nthat our intellect has not of itself the faculty of being understood.\nHence the order of intellect is below the order of intelligible beings.\nFor if the perfection, which our intellect has of itself, is sufficient\nto understand, but not to be understood, it necessarily follows that\ngreater perfection is required in a thing to be understood than to\nunderstand. And because St. Thomas saw this consequence, which at\nfirst sight does not seem true, and might even be objected to him, he\nexcludes this apprehension, by showing that this must be admitted to be\ntrue not only by the Peripatetics, from whose doctrine it results, but\nalso by the Platonists.\"\n\nBut afterwards, in answer to an objection brought by Scotus, called\nthe Subtle Doctor, he adds: \"But because in order to understand an\nintellect and an intelligible object are required, and the relation of\nthe intellect to the intelligible, is the relation of the perfectible\nto its perfection, since the intellect in act consists in its being\nitself the intelligible thing, as is evident from what has been said\nabove; it follows that immaterial beings are divided into two orders,\nintellects, and things intelligible. And as the intelligible consists\nin perfective immateriality, it follows that any thing is intelligible\ninasmuch as it is immaterially perfective. That intelligibility\nrequires immateriality is shown by this, that no material thing is\nintelligible, unless, inasmuch as it is abstracted from matter.... It\nhas already been shown that any thing is intelligible by this, that not\nonly itself, but others, also, are in the intelligible order, either in\nact or in potentiality; it is thus nothing more than to be perfected or\nperfectible by the intelligible.\"\n\n123. This theory may be more or less solid, but it is in either case\nsomething more than ingenious; it raises a new problem in philosophy of\nthe highest importance: to assign the conditions of intelligibility. It\nhas moreover the advantage of being in accordance with a fact attested\nby experience; this fact is the difficulty experienced by the mind in\nknowing itself. If it is immediately intelligible, why does it not\nknow itself? What condition is wanting? Its intimate presence? It has\nnot only presence but identity. Perhaps the effort to know itself? But\nthe greater part of philosophy has no other end than this knowledge.\nBy denying immediate intelligibility to the soul, we can explain why\nso great a difficulty is involved in ideological and psychological\ninvestigations, by showing the reason of the obscurity experienced in\npassing from direct to reflex acts.\n\n124. The opinion of St. Thomas is not a mere conjecture: we may, in\norder to establish it in some manner upon fact, assign a reason which\nseems to us greatly to strengthen it, and which may be regarded as\nmerely an extension of the one already given.\n\nA thing to be intelligible must have two qualities: immateriality,\nand the activity necessary to operate upon the intelligent being.\nThis activity is indispensable, for in the act of intelligence, the\nintellect is in some sense passive. When the idea is present, the\nintellect cannot but know it: when it is wanting, it is impossible for\nthe intellect to know it. The idea, therefore, enables the intellect to\nact; without it the intellect can do nothing. Consequently, if we admit\nthat any being can serve as idea to the intellect, we must concede that\nbeing an activity to excite intellectual action; and so far we make it\nsuperior to the intellect excited.\n\nThus we explain why our intellect, in this life at least, does not\nknow itself by itself. Experience shows that its activity needs to\nbe excited. Left to itself it is like one asleep; and this want of\nactivity in our mind, in the absence of exciting influences, is one of\nthe most constant of psychological facts.\n\nThis is not, however, to say that we have no spontaneity, and that no\naction is possible without an external determining cause; but only\nthat this same spontaneous development would not exist, if we had not\npreviously been subjected to the influence of causes which brought out\nour activity. We may learn things not taught us; but we could learn\nnothing, if teaching had not presided over the first development of\nour mind. There are, it is true, many ideas in our mind, which are not\nsensations, and which cannot have emanated from them; but it is equally\ntrue that a man, deprived of all his senses, could not think, because\nhis mind would want the exciting cause.\n\n125. We have dwelt thus long upon the explanation of the problem of\nintelligibility, because we consider it of scarcely less importance\nthan that of intelligence, although we do not find it treated in\nphilosophical works as it merits. We will now reduce this doctrine\nto clear and simple propositions, so that the reader may form a\nmore complete conception of it; and also, in order to deduce some\nconsequences which have been only slightly indicated in our exposition:\n\nI. A thing must be immaterial in order to be immediately intelligible.\n\nII. Matter cannot be intelligible by itself.\n\nIII. The relations of spirits to bodies, or the representation of the\nlatter in the former, cannot be purely objective.\n\nIV. Some other class of relations must necessarily be admitted to\nexplain the representative union of the world of intelligences with the\ncorporeal world.\n\nV. Immediate objective representation supposes activity in the object.\n\nVI. The power of an object to represent itself to the eyes of an\nintelligence, supposes in it a faculty of acting on that intelligence.\n\nVII. This faculty necessarily produces an effect, and consequently\ninvolves a kind of superiority of the object over the intelligence.\n\nVIII. An intelligent being is not necessarily immediately intelligible.\n\nIX. Immediate intelligibility seems to require greater perfection than\nintelligence.\n\nX. Although not every intelligent being is intelligible, yet every\nintelligible being is intelligent.\n\nXI. God, who is in every sense infinite activity, is infinitely\nintelligent and infinitely intelligible by himself.\n\nXII. God is intelligible by all created intellects, provided it be his\nwill to present himself immediately to them, and strengthen and elevate\nthem as may be necessary.\n\nXIII. There is no repugnance in immediate intelligibility being\ncommunicated to some beings, which are consequently intelligible by\nthemselves.\n\nXIV. Our soul, while united to our body, is not immediately\nintelligible, and we know it only by its acts.\n\nXV. In this want of immediate intelligibility is found the reason\nof the difficulty of ideological and psychological studies, and\nthe obscurity which we experience in passing from direct to reflex\nknowledge.\n\nXVI. Therefore, the philosophy of the _me_, or that which seeks to\nexplain the internal and external world by starting from the _me_, is\nimpossible; it commences by denying one of the fundamental facts of\npsychology.\n\nXVII. Therefore, the doctrine of universal identity is also absurd,\nsince it gives both intelligence and immediate intelligibility to\nmatter, which can have neither.\n\nXVIII. Spiritualism, therefore, is a truth which springs as well from\nsubjective as from objective philosophy, from intelligence as from\nintelligibility.\n\nXIX. We must, therefore, go beyond ourselves, and even rise above\nthe universe to find the origin of either subjective or objective\nrepresentation.\n\nXX. Therefore, we must ascend to a primitive, infinite activity, which\nplaces intelligences in communication among themselves and with the\ncorporeal world.\n\nXXI. Therefore, purely ideological and psychological philosophy leads\nus to God.\n\nXXII. Therefore, philosophy cannot commence by a single fact, the\norigin of all other facts, but must, and does end with this supreme\nfact, the infinite existence, which is God.(12)\n\n\n\n\nCHAPTER XIII.\n\nREPRESENTATION OF CAUSALITY AND IDEALITY.\n\n\n126. Besides the representation of identity, there is what I have\ncalled the representation of causality. A being may represent itself,\na cause its effect. Productive activity is inconceivable, if the\nprinciple of the productive act does not in some manner contain the\nthing produced. Therefore we say that God, the universal cause of all\nthat does or can exist, contains in his essence all real and possible\nbeings in a virtual or eminent manner. A being can just as well present\nwhatever it contains in itself, as it can represent itself; causality,\ntherefore, under the conditions above explained, may be an origin of\nrepresentation.\n\n127. And here we would remark how profound a philosopher St. Thomas\nshows himself to be, when he explains the manner in which God knows\nhis creatures. In his _Summa Theologica_,[7] he asks if God knows\nthings distinct from himself, and answers in the affirmative; not that\nhe regards the divine essence as a mirror, but that by recourse to a\nmore profound consideration he seeks the origin of this knowledge in\ncausality. This is his doctrine in a few words: It is manifest that\nGod knows himself perfectly; therefore he knows all his power, and\nconsequently all the things to which it extends. Another reason, or\nrather enlargement of the same reason, is, that the being of the first\ncause is its intellect: all effects pre-exist in God as in their cause;\nthey must, therefore, be in him in an intelligible manner, since they\nare his intellect itself. God then sees himself by his essence; but he\nsees other things not in themselves, but in his essence, inasmuch as\nhis essence contains the similitude of everything.\n\n[7] P. 1^a, Q. 14^a, A. 5^o.\n\nThe same doctrine is found in another place,[8] where he asks if they\nwho see the divine essence see all things in God.\n\n[8] Q. 12^a, A. 8^o.\n\n128. Representation of ideality is that which neither proceeds from the\nidentity of the thing representing with that represented, nor from the\nrelation of cause and effect. Our ideas are of this class, for they\nare neither identical with their objects nor do they cause them. It is\nimpossible for us to know whether, besides this representative force\nwhich we experience in our ideas, there are finite substances capable\nof representing things distinct from, and not caused by, themselves.\nLeibnitz maintains that there are such substances; but, as we have\nseen, his system of monads must be regarded as merely hypothetical.\nIt is better to say nothing than to make conjectures which lead to no\nresult; we shall therefore content ourselves with establishing the\nfollowing propositions:\n\nI. If any being represent another which is not its effect, it has not\nthis representative force of itself, but has received it from another.\n\nII. The communication of intelligences can only be explained by\nrecurring to a first intelligence, which, being the cause of the\nothers, can give them the force to act upon one another, and\nconsequently to produce representation.\n\n129. Causality may be a principle, but is not a sufficient reason, of\nrepresentation.\n\nIn the first place, a cause cannot represent its effect unless\nintelligible in itself. Thus, although we attribute to matter an\nactivity of its own, we cannot concede it the power to represent\nits effects, for want of the indispensable condition of immediate\nintelligibility.\n\n130. In order that effects may be intelligible in their cause, it must\nof necessity possess the character of cause in its fulness, by uniting\nall the conditions and determinations requisite to the production of\nthe effect. Free causes do not represent their effects, because these\neffects with relation to their causes are found only in the sphere of\npossibility. The production may be realized, but is not necessary; and\nthus the possible, but not the real, is seen in the cause. God knows\nfuture contingencies, which depend upon the human will, not precisely\nbecause he knows the activity of man, but because he sees in himself,\nwithout succession of time, not only all that may, but all that will\nhappen; since nothing can exist in the present or in the future without\nhis will or permission. He also knows future contingencies dependent\nsolely on his own will, because he knows from all eternity what he has\nresolved, and his decrees are indefectible and immutable.\n\n131. Even if we refer to the necessary order of nature, and suppose\none or more second causes to be known, it is not possible to see in\nthem all their effects with entire security, unless the cause act in\nisolation, or all the others are known together with it. As experience\nshows us that all the parts of nature are in intimate and reciprocal\ncommunication, we cannot suppose the above isolation, and consequently\nthe action of every second cause is subjected to the combinations\nof others, which may either impede or modify its effect. Hence the\ndifficulty of establishing general, and at the same time, perfectly\nsafe laws in all that concerns nature.\n\n132. The preceding considerations, it is to be observed, demonstrate\nanew the impossibility of transcendental science based upon a fact\nfrom which all other facts proceed. Intellectual representation is\nnot explained by substituting necessary emanation for free creation.\nEven supposing the variety of the universe to be purely phenomenal,\nand at bottom only a being always one, identical, and absolute, it\ncannot be denied that the phenomena are governed by certain laws, and\nsubject to various conditions. Either the human intellect can see the\nabsolute in such a way as to discern by a simple intuition whatever is\ncontained in it, all that it is or can be, under all possible forms;\nor else it is condemned to follow the unfolding of the unconditioned,\nthe absolute, and the permanent, through its conditioned, relative, and\nvariable forms. The former, which is a sort of ridiculous plagiarism\nfrom the dogma of beatific vision, is, in treating of the intellect in\nits present state, so palpable an absurdity, as to merit neither debate\nnor refutation. The latter subjects the intellect to all the fatigue of\ninvestigation, and destroys at one blow all the illusory promises of\ntranscendental science.\n\n133. The understanding is, in its acts, subject to a law of succession,\nor the idea of time. The same thing obtains in nature, whether it is so\nverified in reality, or time is considered as a subjective condition\nwhich we transfer to objects; be this doctrine of Kant, which we shall\nin due time examine, as it may, it is certain that succession, at\nleast for us, exists, and that we cannot ignore it. In this hypothesis\nan infinite evolution can be known to us only in an infinite time.\nThus, by a metaphysical necessity, we are unable to know not only the\nfuture evolution of the absolute, but also the present and the past.\nThis evolution being absolutely necessary, according to the doctrine\nto which we have reference, an infinite succession must have preceded\nus; thus the present organization of the universe must be regarded as\none round of an unlimited ladder, which in the past as in the future,\nhas no measure but eternity. We can know the present state of the\nworld solely by observation, and then only to a very limited degree; we\nmust, therefore, of necessity, deduce it from the idea of the absolute,\nby following it in its infinite evolution. Were this not, however,\nin itself radically impossible, it would, nevertheless, labor under\nthe inconvenience of being too long a task to be accomplished in the\nlife-time of any one man, or even in that of all men who have ever\nlived, taken collectively.\n\n134. But let us return to the representation of causality. The ideal\nrepresentation may be reduced to that of causality; for since a spirit\ncan have no idea of an object not produced by it, unless communicated\nto it by another spirit, the cause of the thing represented, we infer\nthat all purely ideal representations proceed either directly or\nindirectly, mediately or immediately, from the cause of the objects\nknown. And since, on the other hand, as we have already seen, the first\nbeing knows things distinct from himself only, as he is their cause; we\nhold the representation of ideality to be reduced to that of causality,\nthus in part verifying the principle of Vico, the profound Neapolitan\nthinker: \"the intellect only knows what it does.\"\n\n135. From this doctrine flow two consequences of which we must take\nnote:\n\nI. There are only two primitive sources of intellectual representation:\nidentity and causality. That of ideality is necessarily derived from\nthat of causality.\n\nII. In the real order, the principle of being is identical with the\nprinciple of knowledge. That only which gives being can give knowledge.\nThe first cause can give knowledge only in so far as it gives being: it\nrepresents because it causes.\n\n136. The representation of ideality, although connected with that\nof causality, is yet really distinct from it. The explanation of\nits nature belongs indeed to the treatise on ideas; but we cannot\nrelinquish, without an illustration, a point so closely connected with\nthe problem of intellectual representation.\n\nSome conceive ideas to be a sort of image or copy of the object;\nbut this is true only with respect to the representations of the\nimagination, that is, the purely corporeal; and even here it is\nnecessary to suppose the external world to be such as the senses\npresent it, which, however, under many aspects, is not true. To be\nconvinced how illusory is the theory founded on the likeness of\nsensible things, we have only to ask, what the image of a relation\nis, or, how causality, substance, and being are portrayed. In the\nperception of these ideas, there is something more profound than any\nthing apparent in sensible things, something of an entirely different\norder. Necessity has led us to compare the understanding to an eye\nwhich sees, and the idea to an image present; but this is only a\ncomparison; the reality is something more mysterious, more secret, more\nintimate: there is an ineffable union between the perception and the\nidea: man cannot explain it, but he experiences it.\n\n137. Our consciousness attests that there is in us unity of being, that\nthe soul is at all times identical with itself, and that it remains\nconstant notwithstanding the variety of ideas and of acts which pass\nover it, like waves over the surface of a lake. Ideas are a mode of\nbeing of the mind: but what is this mode? In what does it consist?\nDoes the production and reproduction of ideas proceed from a distinct\ncause which continually acts upon our soul, and produces immediately\nthose modes of being which we call representations, or ideas? Or must\nwe admit that there has been given to the mind an activity to produce\nthese representations, subject, however, to the determination of\nexciting causes? These are questions which, for the present, we shall\nonly indicate.(13)\n\n\n\n\nCHAPTER XIV.\n\nIMPOSSIBILITY OF FINDING THE FIRST PRINCIPLE IN THE IDEAL ORDER.\n\n\n138. We shall in vain seek in the region of ideas for that which we\ncould not find in that of facts, for there is no ideal truth, the\norigin of all other truths.\n\nIdeal truth only expresses the necessary relation of ideas, abstracting\nthe existence of the objects to which they relate: hence it follows,\nfirst of all, that ideal truths are absolutely incapable of producing\nthe knowledge of reality.\n\nNo ideal truth can lead to any result in the order of existences,\nunless there be some fact to which it applies. Otherwise, however\nfruitful it may be in the order of ideas, it will be absolutely sterile\nin that of facts. The fact without the ideal truth remains in its\nisolated individuality, incapable of producing any thing more than\ncognition of itself: but in return, the ideal truth, apart from the\nfact, remains purely objective in the logical world, and has no means\nof descending to that of existences.\n\n139. Let us apply this doctrine to the most certain and most evident\nideal principles, to those which contain the most general ideas, and\nwhich ought, therefore, to possess the fecundity in question, if,\nindeed, it be anywhere to be encountered.\n\n\"It is impossible for the same thing to be and not be at the same\ntime.\" This is the famous principle of contradiction, which may\nundoubtedly claim to be regarded as one source of truth to the human\nunderstanding. The ideas contained in it are the clearest and most\nsimple conceivable; in it is affirmed the repugnance of being to\nnot-being, and of not-being to being, at the same time, which is most\nevident. But what advance can we make with this principle alone?\nPresent it to the most penetrating mind, to the most powerful genius;\nleave them alone with it, and there will result only a sterile,\nalthough pure and most clear intuition. Since it does not affirm that\nany thing is or is not, nothing can be inferred either for or against\nany existence: it only offers to the mind this conditional relation:\nthat if any thing does exist, it is repugnant for it not to exist at\nthe same time that it exists, or to exist at the same time that it does\nnot exist. But if the condition of existence or non-existence be not\ngiven, _yes_ and _no_ in the real order are indifferent; nothing is\nknown concerning them, however great the evidence in the ideal order.\n\nTo pass from the logical world to that of reality, all that is required\nis a fact to serve as a bridge. If this fact be offered to the\nunderstanding, the two banks are joined, and science commences. I feel,\nI think, I exist: these are facts of consciousness; combine any one of\nthem with the principle of contradiction, and what before were sterile\nintuitions become prolific ratiocinations, embracing at once the world\nof ideas, and that of reality.\n\n140. Even in the purely ideal order, the principle of contradiction\nis sterile unless joined with particular truths of the same order. In\ngeometry, for example, it is often argued thus: such a quantity is\neither greater or less than another, or equal to it; for otherwise it\nwould be both greater and less, equal and unequal, at the same time,\nwhich is absurd. Here the principle of contradiction is effectively\napplied, not alone, but together with a particular truth which makes\nsuch an application available. Thus, in the above argument, no use\ncould be made of the principle of contradiction, to prove equality or\ninequality were not the existence or non-existence of one of the two\npreviously proved or supposed: since this neither does nor can result\nfrom the principle of contradiction which includes, not a particular\nidea, but the most general ideas presented to the human mind.\n\n141. General truths, of themselves, even in the purely ideal order,\nlead to nothing, because of the indeterminateness of the ideas which\nthey contain; and, on the other hand, particular truths of themselves\nproduce no result, because they are limited to what they are, making\nreasoning, which cannot take one step without the aid of general ideas\nand propositions, impossible. Light results from the union of one with\nthe other; separated they afford only an abstract and vague intuition,\nor the contemplation of a particular truth, which, limited to a\ncontracted sphere, can give no knowledge of beings considered under a\nscientific aspect.\n\n142. We shall see when we come to treat of ideas, that our mind has\ntwo very distinct classes of them; the one supposes space, and cannot\nabstract it, such are all geometrical ideas: the other does not relate\nto space, and includes all non-geometrical ideas. These two orders of\nideas are separated by an impassable abyss, if the two orders are not\napproximated by a simultaneous use of both. The ideal order is not\ncomplete without this approximation; and the real order of the universe\nis turned into a chaos, or rather disappears, if real and ideal truths\nare not combined, in both the geometrical and non-geometrical orders.\nFrom all geometrical ideas imaginable, considered in all their ideal\npurity, nothing would result for the ideal non-geometrical order, for\nthe world of material, much less of immaterial realities; and, on the\nother hand, from non-geometrical ideas alone we could not get so much\nas the idea of a right line. This observation shows that there is for\nus in the ideal order no one truth, the origin of all other truths; for\nif we take the geometrical order, we are limited to those combinations\nwhich do not go out of it; if the non-geometrical order, we lack the\nidea of space, without which we lose even the possibility of conceiving\nthe corporeal world.(14)\n\n\n\n\nCHAPTER XV.\n\nTHE INDISPENSABLE CONDITION OF ALL HUMAN KNOWLEDGE.--MEANS OF\nPERCEIVING TRUTH.\n\n\n143. We have not been able to discover, either in the real or the ideal\norder, a truth, the origin of all other truths to our intellect while\nin this life. Therefore it stands proved that transcendental science\nproperly so called is for us a chimera. Our cognitions must, doubtless,\nhave some resting-point, and this we shall now investigate.\n\nFor the better understanding of the subject now before us, we will\nrecall the true state of the question. We do not seek a first\nprinciple, which of itself alone illumines or produces all truths;\nbut we seek a truth which shall be the indispensable condition of\nall knowledge; for this reason, we do not call it an origin, but a\nresting-point. The edifice does not originate in the foundation,\nbut rests upon it. We must consider the principle sought for as\na foundation, just as in the preceding chapters, we treated of\ndiscovering a seed. These two images _seed_ and _foundation_, perfectly\nexpress our ideas, and exactly trace the limits of the two questions.\n\n144. Is there a resting-point of all science, and of all knowledge,\nscientific or not scientific? If there is, what is it? Are there many,\nor only one? Evidently there must be a resting-point. If asked the\nreason of an assent, we must at last come to a fact or a proposition,\nbeyond which we cannot go; for we cannot admit the process _ad\ninfinitum_. This is the point where we must of necessity stop, and\nconsequently the resting-point of certainty.\n\n145. Starting with a given assent, we may, perhaps, arrive at different\nprinciples, independent one of the other, all equally fundamental, as\nregards our mind: in this case there will be not only one, but many\nresting-points.\n\nWe do not believe it possible to determine _a priori_, whether there\nis unity or plurality for our intellect in this matter. That human\nscience must be reduced to a single principle is a proposition that\nhas been asserted, but never yet proved. Since the source of all\ntruth, as has been shown in the preceding chapters, is not in man, it\nis evident that the principles, on which his knowledge is founded,\nmust be communicated. Who shall assure us that they are not many in\nnumber, and of different orders? Nothing then in the present question\ncan be resolved _a priori_, and we must descend to ideological and\npsychological observations.\n\n146. Our mind acquires truth, or at least the appearance of truth; that\nis to say, that in one way or another, it performs those acts which we\ncall perception and sensation. Whether the reality does or does not\ncorrespond to the acts of our soul, is at present of no consequence, is\nnot what we now seek: we place the question on a ground accessible to\nthe most skeptical; for even they do not deny perception and sensation;\nalthough they destroy reality, they admit appearance.\n\n147. The means by which we perceive truth are of different orders; and\nthis is why truths perceived correspond equally to different orders,\nparallel, so to speak, with the respective means of perception.\n\nConsciousness, evidence, and intellectual instinct or common sense, are\nthe three means; to which correspond truths of consciousness, necessary\ntruths, and common-sense truths. These are distinct, different, and\nin many cases unconnected with each other; and he, who seeks to\nacquire complete and accurate ideas upon matters relating to the first\nprinciple of human knowledge, must mark out their limits with great\ncare.\n\n148. That means which we have called consciousness, or the intimate\nsense of that which passes within us, that which we experience, is\nindependent of all the others. Destroy evidence, destroy intellectual\ninstinct, yet consciousness remains. In order to feel, and to be sure\nthat we feel, and what we feel, we need only experience. If we suppose\nthe principle of contradiction to be doubtful, still it will not shake\nour certainty that we suffer when we suffer, that we rejoice when we\nrejoice, that we think when we think. The presence of the act, or the\nimpression at the bottom of our soul, is intimate, immediate to us,\nand of irresistible efficacy to place us above all doubt. Sleeping or\nwaking, sane or insane, the testimony of consciousness is the same;\nthere may be an error in the object, but there can be none in the\ninternal phenomenon. The lunatic who believes that he counts numberless\nbags of dollars, certainly does not count them, and in this he is\ndeceived; yet he has in his mind the consciousness of what he does, and\nin this he is infallible. A man who dreams that he has fallen into the\nhands of robbers, is deceived as to the external object, but not as\nregards the act by which he believes it.\n\nConsciousness is independent of all extrinsic testimony; its necessity\nis inevitable, its force irresistible in producing certainty; it is\ninfallible in what concerns only itself; if it exist it must give\ntestimony of itself; if it does not exist it cannot give it. In it\nreality and appearance are confounded; it cannot be apparent without\nbeing real; the appearance alone is already a true consciousness.\n\n149. We include in the testimony of consciousness all that which we\nexperience in our soul, all that which affects what some call the human\n_me_, ideas, thoughts of every class, acts of the will, sentiments,\nsensations; in a word, every thing of which we can say: I experience it.\n\n150. Manifestly the truths of consciousness are rather facts to be\npointed out, than combinations to be enunciated. This is not to say\nthat they cannot be enunciated, but that in themselves they abstract\nall intellectual form, are simple elements, in ordering and comparing\nwhich the intellect may occupy itself, but which of themselves give no\nlight, _represent_ nothing, but only _present_ what they are; that they\nare mere facts, beyond which we cannot go.\n\n151. The habit of reflecting upon consciousness, and of joining purely\nintellectual operations with facts of simple internal experience, makes\nit difficult to conceive this isolation, in which every thing purely\nsubjective is by its nature found. We endeavor to abstract reflection,\nbut we reflect upon our very effort to abstract it. Our intellect is\na fire, which, extinguished on one side, burns on the other; the very\neffort to extinguish it ordinarily makes it burn brighter. Hence the\ndifficulty of distinguishing the two characters of purely subjective\nand purely objective, to mark the dividing line between evidence and\nconsciousness, between the known and the experienced. Nevertheless,\nthe separation of two such different elements may be made easy, by\nconsidering that brutes are, in their own way, conscious of what they\ninwardly experience; not supposing them to be mere machines, we must\nallow them consciousness, or the intimate presence of their sensations.\nWithout this even sensation is inconceivable, for that can have no\nsensation which does not perceive that it feels. Brutes reflect not\non what passes within themselves; they experience it, but nothing\nmore. Sensations succeed one another in their soul, connected only\nby the unity of the being experiencing them; but they do not take\nthem for objects and consequently, do not combine or transform them\nin any manner; they leave them as they are, simple facts. From this\nwe may derive some light for the conception of what the simple facts\nof consciousness are in us when abandoned to themselves, perfectly\nisolated, separated from purely intellectual operations, and under no\nsubjection to reflective activity, which, combining them in various\nways, and elevating them to the region of the purely ideal, presents\nthem to us in such a manner as to make us forget their primitive purity.\n\nAn effort is necessary in order clearly to perceive what the facts\nof consciousness are, and what its testimony is; for without this it\nis impossible to advance one step in the investigation of the first\nprinciple of human knowledge. Confusion on this point makes us fall\ninto transcendental equivocations. We shall hereafter have occasion to\nobserve this, and we have already encountered lamentable examples of\nsuch deviations in the errors of the philosophy of the _me_.\n\n152. Evidence is usually called an intellectual light. This is a\nvery happy metaphor, and even exact; but, like all metaphors, it has\nthe defect of being of but little service to explain the mysteries\nof philosophy. We also find intellectual light in many acts of\nconsciousness. There is also a sort of clear light in that intimate\npresence by which an operation or an impression is offered to the mind;\nit shines upon the eye of the soul, and makes it see what is before\nit. If, then, we define evidence only by calling it the light of the\nintellect, we confound it with consciousness, or, at least, by the use\nof ambiguous language, give others occasion of confounding them.\n\nLet us not be thought to blame those who have used the metaphor of\nlight, or to flatter ourselves with being able to define evidence\nwith all exactness; for who can express in words this phenomenon of\nour mind? If we are to have any metaphor, that of the intellectual\nlight seems to be the most adequate. For, in truth, when we fix our\nattention upon evidence, in order to examine its nature and its effects\non the mind, it very naturally presents itself under the image of a\nlight, whose splendor illumines the objects, and enables the mind to\ncontemplate them: but this, we repeat, is not enough. We will, then,\nalthough we do not undertake exactly to define it, point out a mark to\ndistinguish it from every thing else.\n\n153. Evidence is always accompanied by the necessity, and consequently,\nby the universality, of the truths which it attests. There is no\nevidence of the contingent, except in so far as subjected to a\nnecessary principle.\n\nLet us explain this doctrine by comparing examples taken respectively\nfrom consciousness and evidence.\n\nThat there is in me a being which thinks, I know, not by evidence,\nbut by consciousness. That whatever thinks exists, I know, not by\nconsciousness, but by evidence. In both cases the certainty is\nabsolute, irresistible; but in the first it rests upon a particular,\ncontingent fact; in the second upon a universal and necessary truth.\nThat I think is certain for me, but not necessarily so for others;\nthe disappearance of my thought does not overturn the world of\nintelligences; if my thought should now cease to exist, truth in itself\nwould suffer no change; other intellects might and would continue to\nperceive truth; and neither in the real nor in the ideal order would\nthere be less concert and harmony.\n\nI ask myself if I think, and in the bottom of my soul I read that I do\nthink: I ask myself if this thought is necessary, and not only does\nexperience tell me that it is not, but I can find no reason why it\nshould be necessary. Even supposing that my thought ceases to exist,\nI perceive that I continue to reason in due form. Thus I examine what\nwould have happened if I had not existed, or what may hereafter happen\nif I cease to exist; and I assent to principles and draw conclusions\nwithout transgressing any law of the intellect. The ideal world and\nthe real world are presented to my eyes as a magnificent spectacle\nat which I indeed assist, but from which I may withdraw without the\nrepresentation undergoing any change, except that I should leave vacant\nthe imperceptible place which I now occupy. But it is very different\nwith the truths which are the object of evidence. It is not necessary\nfor me to think; but it is so necessary for whatever thinks to exist,\nthat no efforts of mine could suffice to abstract this necessity for\none moment. If, taking an absurd position, I suppose the contrary,\nand imagine for an instant the relation between thought and being\nto be cut short, I break the chain which supports the order of the\nentire universe; every thing is reversed, thrown into confusion;\nand I know not if what I see be chaos or nonentity. What has taken\nplace? The intellect has only suffered a contradiction, at the same\ntime affirming and denying thought, because it affirmed a thought to\nwhich it denied existence. It has violated a universal and absolutely\nnecessary law, the violation of which throws every thing into chaos.\nNot the certainty of the soul's existence, supported by the testimony\nof consciousness, suffices to prevent the confusion: the intellect by\ncontradicting itself has denied itself; from its insensate words, not\nbeing, but nonentity has resulted, not light, but darkness; and this\ndarkness cast over whatever exists or is possible turns back upon it\nand involves it in eternal night.\n\n154. We have here fixed and defined the conditions of consciousness and\nevidence. The object of the former is the individual, the contingent;\nthat of the latter the universal and the necessary. Only in God, the\nsource of all truth, the universal and necessary principle of being\nand of knowledge, is consciousness identified with evidence; and it is\nnot possible to abstract the testimony of his consciousness, without\nannihilating everything. What would remain in the world were I to\ndisappear? the creature asks itself, and answers: _everything except\nmyself_. Were God to ask himself this question, he would answer:\n_nothing_.\n\n155. We have given the name of intellectual instinct to the impulse\nwhich in many cases produces certainty without the aid of the testimony\neither of consciousness or of evidence. If you show a man a target,\nthen blindfold his eyes, and turn him around at random several times,\nand, after this, place a bow in his hands, and assure him that the\narrow will strike the precise centre of the target, he will say that\nthis is impossible; and nothing can induce him to believe so great an\nabsurdity. And why not? Because of the testimony of consciousness? No!\nFor the question is now of external objects. Neither does he depend on\nevidence; for the objects of evidence are things necessary, and it is\nnot intrinsically impossible for the arrow to hit the mark assigned.\nOn what then rests his profound conviction that this is not possible?\nIf we suppose him to know nothing of theories, of probabilities, and\ncombinations, to have no knowledge of this science, and never to have\nso much as thought of such things, his certainty is just as great as\nit would be were he able to base it upon some sort of calculation. All\nthe bystanders, whether rude or cultivated, ignorant or learned, need\nno reflection to be equally certain; all will say, or think, \"this is\nimpossible; it cannot happen.\" We again ask, what is the foundation\nof so strong a conviction? Not springing from consciousness, or from\neither mediate or immediate evidence, it manifestly can have no other\norigin than that internal force which we call intellectual instinct,\nand which may be called common sense, or anything else, so long as the\nfact itself is recognized. It is a precious gift, which the Creator has\ngiven to us, to make us reasonable even before we reason, and to enable\nus rightly to govern our conduct when we lack time to examine motives\nof prudence.\n\n156. This intellectual instinct embraces many objects of different\norders; it is the guide and the shield of reason: the guide, because it\nprecedes and shows the way; the shield, because it defends reason from\nher own cavils, and because sophistry becomes dumb in its presence.\n\n157. The testimony of human authority, equally necessary to the\nindividual and to society, commands our assent, by means of an\nintellectual instinct. Man believes man, believes society, even before\nthinking of the motives of his faith; few examine them at all, and yet\nthis faith is universal.\n\nWe do not here inquire if intellectual instinct sometimes deceives,\nor why, or in what cases it deceives; at present we only seek to\nestablish its existence; and with regard to the errors to which it\nleads, we shall simply remark, that in a weak being, such as man, the\nrule is continually changing, and as it is not possible to find a man\ngood, without any admixture of evil, so is it impossible to find truth\nwithout some admixture of error.\n\n158. We make sensations objective only by virtue of an irresistible\ninstinct. Nothing is more certain, more evident to the eyes of\nphilosophy, than the subjectivity of all sensations; that is,\nsensations are immanent phenomena, are within us, and do not go out\nof us; and yet nothing is more constant than the transition made by\nthe whole human race from the subjective to the objective, from the\ninternal to the external, from the phenomenon to the reality. On\nwhat is this transition grounded? If the most eminent philosophers\nexperienced so much difficulty in finding the bridge, which unites\nthe two opposite banks; if some of them, wearied with investigation,\nresolutely asserted that it was not possible to discover it, will the\ncommonalty of mankind discover it from their very childhood? Evidently,\nmotives of reasoning do not explain the transition; appeal must be made\nto the instinct of nature. There is then an instinct, which by itself\nassures us of a truth demonstrated with difficulty by the most abstruse\nphilosophy.\n\n159. Here I shall notice the errors of those methods which isolate\nman's faculties, and, in order better to know the mind, disfigure\nand mutilate it. One of the most constant and fundamental facts of\nideological and psychological science, is the multiplicity of acts\nand faculties of the soul, notwithstanding its simplicity attested by\nthe unity of consciousness. There is in man, and in the universe, an\nassemblage of laws, the effects of which are simultaneously evolved\nwith harmonious regularity; to separate them, is often equivalent to\nplacing them in contradiction; for, no one of them being capable of\nproducing its effect if isolated, but requiring to be combined with\nthe others, they produce, when made to operate alone, instead of their\nregular effects, the most hideous monstrosities. If you retain in the\nworld only the law of gravitation not combined with that of projection,\nevery thing will be precipitated towards one centre; instead of that\ninfinity of systems which adorn the firmament, you will have only a\nrude and indigested mass. If you destroy gravitation, and preserve the\nforce of projection, all bodies will be decomposed into imperceptible\natoms, and be dispersed, like most subtle ether, through regions of\nimmensity.(15)\n\n\n\n\nCHAPTER XVI.\n\nCONFUSION OF IDEAS IN DISPUTES ON THE FUNDAMENTAL PRINCIPLE.\n\n\n160. There are, in our opinion, various principles, which, with regard\nto the human intellect, may be called equally fundamental, both because\nthey serve as foundation in the common and scientific orders, and\nbecause they do not rest upon any other, since it is impossible to\nassign any one which enjoys this quality as an exclusive privilege.\nIn seeking the fundamental principle, it is customary in the schools\nto observe that they do not endeavor to find a truth from which all\nothers emanate, but an axiom the destruction of which draws with it\nthat of all other truths, and the firmness of which sustains them,\nat least indirectly, in such manner that whoever denies them may be\nrefuted by indirect demonstration, or reduction _ad absurdum_; that is,\nadmitting the above axiom, it may follow that whoever denies the others\nwill be convicted of being in opposition to one which he himself has\nacknowledged to be true.\n\n161. It has been much disputed whether this or that principle merit\nthe preference. We believe that there is here a confusion of ideas,\nproceeding in great part from not sufficiently marking the limits of\ntestimonies so distinct as those of consciousness, of evidence, and of\ncommon sense.\n\nDescartes' famous principle, _I think, therefore I am_; that of\ncontradiction, _it is impossible for a thing to be and not to be at\nthe same time_; and what is called the principle of the Cartesians,\n_whatever is contained in the clear and distinct idea of anything, may\nbe affirmed of it with all certainty_; are the three principles that\nhave divided the schools. In favor of each, reasons the most powerful,\nand even conclusive against the others, considering the ground on which\nthe question was placed, have been brought forward.\n\nIf you are not certain that you think, argues the partisan\nof Descartes, you cannot be certain even of the principle of\ncontradiction, or know the criterion of evidence to be valid; for\nboth, it is necessary to think; whoever affirms or denies anything,\nthinks; without thought, neither affirmation nor negation is possible.\nBut let us admit thought: we have already a foundation, and one of\nsuch a nature that we find it in ourselves, attested by consciousness,\nirresistibly forcing upon us the certainty of its existence. The\nfoundation once laid, we see how the edifice can be raised; for this\nwe need not go out of our own thought; there is the luminous point to\nconduct us in the path to truth; let us follow its splendor, and having\nestablished an immovable point, let us draw from it the mysterious\nthread to guide us in the labyrinth of science. Thus our principle is\nthe first, the basis of all others; it has sufficient power to sustain\nitself, sufficient also to impart firmness to others.\n\nThis language is certainly reasonable; but it has this fault, that the\nconviction which it is intended to produce, is neutralized by the not\nless reasonable language of those who hold a directly contrary opinion.\nOne who maintains the principle of contradiction may reason thus: if\nyou do not admit it to be impossible for the same thing to be and not\nbe at the same time, it may be possible that you think and do not think\nat the same time; your assertion, then, _I think_, is of no weight,\nfor its opposite, _I do not think_, may, at the same time, be true. In\nthis case, the conclusion of existence is invalid; for, even admitting\nthe legitimacy of the consequence, _I think, therefore I am_, as we\nknow on the other hand that this other premise, _I do not think_, is\npossible, the deduction cannot be made. Nor is the other principle:\n_whatever is contained in the clear and distinct idea of anything,\nmay he affirmed of it with all certainty_, of any more value without\nthe principle of contradiction; because if being and not-being are\npossible at the same time, an idea may be clear and obscure, distinct\nand confused; a predicate may be contained and not contained in the\nsubject; we may be certain and uncertain, affirm and deny; therefore it\nis of no service.\n\nHe who argues thus seems quite reasonable; but strangely enough, the\nadvocate of the third principle brings equally strong arguments against\nhis two adversaries. How is it known, he asks, that the principle of\ncontradiction is true? Only because we see in the idea of being the\nimpossibility of its being and not being at the same time, and _vice\nversa_; therefore, we are sure of the principle of contradiction\nonly from the application of the principle: _whatever is contained\nin the clear and distinct idea of anything, may he affirmed of it\nwith all certainty_. If nothing can be sustained without relying\nupon the principle of contradiction,--and this is based upon our\nprinciple,--ours is the foundation of them all.\n\n162. They are all three right, and all three wrong. They are right\nin asserting that the denial of their respective principles is the\nruin of the others. They are all wrong in pretending that the denial\nof the others is not the ruin of their own. Whence then the dispute?\nFrom the confusion of ideas, by which they compare principles of very\ndifferent orders, all indeed very true, but not to be compared with\neach other for the same reason that we cannot compare the white and\nthe warm, and dispute whether a thing has more degrees of heat or\nwhiteness. Comparison requires not only opposition in the extremes, but\nalso something in common; if things are totally unlike, comparison is\nimpossible.\n\nDescartes' principle is the enunciation of a simple fact of\nconsciousness; that of contradiction is a truth known by evidence;\nand that of the Cartesians is an assertion that the criterion of\nevidence is valid, and that it is a truth of reflection expressing the\nintellectual impulse by which we are borne to believe the truth of what\nwe know by evidence.\n\nThe importance of this question requires a special examination of each\nof the three principles, which we shall make in the next chapters.(16)\n\n\n\n\nCHAPTER XVII.\n\nTHOUGHT AND EXISTENCE.--DESCARTES' PRINCIPLE.\n\n\n163. Am I certain that I exist? Yes. Can I prove it? No. Proof supposes\nreasoning; there is no solid reasoning without a firm principle on\nwhich to rest it; and there is no firm principle unless we suppose the\nexistence of the reasoning being.\n\nIn effect, if he who reasons is not certain of his own existence,\nhe cannot be certain of his own reasoning, since there will be no\nreasoning if there be no one to reason. Therefore there are, unless\nwe suppose this, no principles on which to rest; there is nothing but\nillusion, or rather there is neither any illusion, for there can be\nnone where there is no one illuded.\n\nOur existence cannot be demonstrated: we have so clear and strong\na consciousness of it that it leaves us no uncertainty; but it is\nimpossible to prove it by reasoning.\n\n164. It is a prejudice and a fatal error to believe ourselves able to\nprove everything by the use of reason; the principles on which it is\nfounded are prior to its use; the existence of reason, and that of the\nbeing that reasons, are prior to both.\n\nNot only are not all things demonstrated, but it may even be\ndemonstrated that some things are indemonstrable. Demonstration\nis a ratiocination in which we infer from evident propositions, a\nproposition evidently connected with them. If the premises are of\nthemselves evident, they do not admit of demonstration; if we suppose\nthem in their turn demonstrable, we shall have the same difficulty with\nrespect to those on which the new demonstration is founded; therefore\nwe must either stop at an indemonstrable point, or proceed to infinity,\nwhich would be never to finish the demonstration.\n\n165. And it is to be remarked that indemonstrability does not belong\nsolely to certain premises; it is found, in some measure, in every\nargument by its very nature, abstracting the propositions which compose\nit. We know that the premises A and B are certain; from them we infer\nthe proposition C. By what right? Because we see that C is connected\nwith A and B. But how do we know this? If by immediate evidence,\nby intuition, here is something else that cannot be demonstrated,\nthe connection of the conclusion with the premises. If by argument,\nratiocination, establishing ourselves on the art of reasoning, there\nare two considerations, both tending to demonstrate indemonstrability.\nI. If the principles of the art are indemonstrable, we have at once\nsomething indemonstrable; if they are demonstrable, we must make use\nof others which serve as their basis, and at last either come to one\nwhich does not admit of demonstration, or else proceed to infinity.\nII. How do we know the principles of reasoning to be applicable to\nthis case? By another act of reasoning? Then we shall encounter the\nsame difficulty as in the other case. Is it because we see that it\nis so? because it is immediately evident? Then here again we have an\nindemonstrable point. These reflections will clearly show that to\ndemand proof of everything is to demand what is impossible.\n\n166. A being which does not think has no consciousness of itself: the\nstone exists, but does not know that it exists, neither would man\nhimself in a similar case, were all his intellectual and sensible\nfaculties in complete inaction. We easily conceive the difference of\nthese two states by calling to mind what occurs, when from waking we\npass into a profound sleep, and again when we awake from it. The first\nstarting-point of our cognitions is this intimate presence of our\ninternal acts, abstraction made of the questions which may be raised\nupon their nature. If every thing existed as at present, and there also\nexisted, besides the world which we see, infinite other worlds, not\neven then would any thing exist for us, had we not those internal acts\nof which we are speaking. We should be like an insensible body placed\nin the immensity of space, which would suffer no mutation were every\nthing around it to disappear, and would perceive no change even if it\nwere itself to sink into the abyss of nothing. On the other hand, if\nwe suppose every thing to be annihilated except this being within us\nwhich feels, thinks, and wills, there still remains a point whereon\nto base the edifice of human cognitions: this being, though alone in\nimmensity, would render itself an account of its own acts to the\nextent of its ability, and might go into numberless combinations having\nfor their object the possible though not the real.\n\n167. The famous principle of Descartes, _I think, therefore I am_,\nhas been often attacked, and justly and conclusively so, if this\nphilosopher really understood his principle in the sense which the\nschools are accustomed to give it. If Descartes presented it as a\ntrue argument, as an enthymema with an antecedent and a consequent,\nthe argument was clearly defective in its foundation. For when he\nsaid, \"I am going to prove my existence with this enthymema: I think,\ntherefore I am:\" this objection might have been made; your enthymema is\nequivalent to a syllogism in this form: whatever thinks, exists; but\nI think; therefore, I exist. This syllogism, in the supposition of a\nuniversal doubt, excluding even the supposition of existence itself, is\ninadmissable in its propositions and in their connection. In the first\nplace, how do you know that whatever thinks exists? Because nothing can\nthink without existing. How do you know that? Because what does not\nexist, does not act. But how in its turn do you know this? Supposing\nevery thing to be doubted, nothing to be known, these principles are\nnot known; otherwise we fall short of the supposition of universal\ndoubt, and consequently go out of the question. If any one of these\nprinciples must be admitted without proof, it is just as well to admit\nyour own existence and save yourself the trouble of proving it with an\nenthymema.\n\nIn the second place, how do you know that you think? Your argument may\nbe retorted, as dialecticians say, in the following manner: nothing can\nthink without existing; but your existence is doubtful, for you are\ntrying to prove it; therefore you are not sure that you think.\n\n168. Manifestly, then, Descartes' principle, taken as a true argument,\ncannot be defended; and it is so easy to see its defect, that it seems\nimpossible for so clear and penetrating an intellect to have overlooked\nit. It is therefore probable that Descartes understood his principle in\na very different sense; and we will now briefly show what meaning, in\nour judgment, the illustrious philosopher must have given to it.\n\nSupposing himself for a moment in universal doubt, without accepting\nfor certain anything that is known, he concentrated himself on himself,\nand in the depth of his soul sought a point whereon to base the edifice\nof human cognitions. Although we abstract all around us, we clearly\ncannot abstract ourselves, our mind, which is present to its own eyes,\nonly the more lucidly, the greater the abstraction in which we place\nourselves with respect to eternal objects. Now in this concentration,\nthis collection of himself within himself, this withdrawal from every\nthing for fear of error, and asking himself if there be any thing\ncertain, if there be any foundation and starting-point in the career\nof knowledge; first of all is presented to him the consciousness of\nthought, the very presence of the acts of his mind. If we mistake\nnot, this was Descartes' thought: I wish to doubt of every thing; I\nrefrain from affirming as from denying any thing; I isolate myself from\nwhatever surrounds me, because I know not if it be any thing more than\nan illusion. But in this very isolation, I meet with the intimate sense\nof my internal acts, with the presence of my mind; I think, therefore\nI am; this I feel in a manner that leaves no room for doubt or\nuncertainty; therefore, I am; that is to say, this sense of my thought\nmakes me know my existence.\n\n169. This explains why Descartes did not present his principle as a\nmere enthymema, as an ordinary argument, but as determining a fact\npresented to him and first in the order of facts: even if he inferred\nexistence from thought, it was not by deduction, properly so called,\nbut as one fact contained in another, or rather identified with it.\n\nWe say _identified_, because it really is so in Descartes' opinion;\nand this confirms what we have already advanced, that this philosopher\ndid not offer an argument, but laid down a fact. According to him,\nthe essence of the soul consists in thought; and as other schools of\nphilosophy distinguish between substance and its acts, considering\nthe mind in the first class, and thought in the second, so Descartes\nheld that there was no distinction between mind and thought, that\nthey were the same thing, that thought constituted the essence of the\nsoul. \"Although one attribute,\" he says, \"suffices to make us know the\nsubstance, there is, nevertheless, in every substance one attribute,\nwhich constitutes its nature and its essence, and on which all the\nothers depend. Extension in length, breadth, and depth, constitutes the\nessence of corporeal substance; and thought constitutes the nature of\nthe substance which thinks.\"[9] From this it follows that Descartes, in\nlaying down the principle, _I think, therefore I exist_, only declared\na fact attested by consciousness; and so simple did he consider it, and\nso unique, that in evolving his system, he identified thought with the\nsoul, and its essence with its existence. He was conscious of thought,\nand said: \"this thought is my soul; I am.\" It is not now our purpose\nto weigh the value of this doctrine, but only to explain in what it\nconsists.(17)\n\n[9] Descartes. _Principes de la Philosophie_, 1^{i\u00e8re} partie.\n\n\n\n\nCHAPTER XVIII.\n\nTHE PRINCIPLE OF DESCARTES, CONTINUED.--HIS METHOD.\n\n\n170. Descartes did not always express himself with, sufficient accuracy\nwhen announcing and explaining his principle; and hence his words have\nbeen misinterpreted. In the passage where he establishes consciousness\nof our own thought and existence as the foundation whereon all our\ncognitions must rest, he uses terms from which it can be inferred that\nhe not only means to declare a fact, but that he also intends to afford\na true argument. Nevertheless, if we read his words attentively, and\ncompare them with one another, it will be evident that such was not\nhis idea, although we should not sometimes be wrong in saying that he\ndid not make sufficient account of the difference, which we have just\npointed out, between an argument and the simple declaration of a fact;\nand that, when concentrating himself on himself, he did not have a\nsufficiently clear _reflex_ knowledge of the manner in which he rested\nupon his fundamental principle. To convince ourselves of this, let us\nexamine his own words: \"While we thus reject every thing of which we\ncan have the least doubt, and even _feign_ that it is false, we easily\nsuppose that there is no God, no heaven, no earth; that we have not\na body: but we cannot in like manner suppose that we are not whilst\nwe doubt the truth of all these things; for we experience so great\nrepugnance to conceive that what thinks is not at the same time that it\nthinks, that notwithstanding all the most extravagant suppositions, we\ncannot help believing this conclusion, _I think, therefore I am_, to be\ntrue, and consequently the first and most certain to present itself to\nhim who orders well his thoughts.\"[10]\n\n[10] Descartes. _Principes de la Philosophie_, 1^{i\u00e8re} partie, N. 7.\n\nIn this passage we detect a true syllogism: whatever thinks, exists;\nbut I think; therefore I exist. \"We have,\" says Descartes, \"so great\nrepugnance to conceive that what thinks is not at the same time that\nit thinks;\" which is the same as to say, whatever thinks, exists; and\nthis, in scholastic terms, is to establish the major. He then says:\n\"notwithstanding all the most extravagant suppositions, we cannot help\nbelieving this conclusion, _I think, therefore I am_, to be true;\"\nwhich is equivalent to proving the minor, and the conclusion of the\nsyllogism. We know that Descartes was somewhat taken up with the idea\nof proving at the same time that he was engaged in declaring. This was\nthe general tendency of his age, and even the most ardent reformers\nwith difficulty preserved themselves from the surrounding atmosphere.\nWe encounter this same spirit throughout his meditations, admirably\njoined, however, with the spirit of observation.\n\nBut through these obscure or ambiguous explanations, what thought do\nwe discover at the bottom of Descartes' system when we abstract his\nhaving, or not having, rendered himself an exact account of what he\nexperienced? This thought: \"By an effort of my mind I can doubt the\ntruth of everything; but this effort has a limit in myself. When I\nturn my attention upon myself, upon the consciousness of my internal\nacts, upon my existence, doubt is at an end; it cannot extend so far:\nI find _so great repugnance_ that the most extravagant suppositions\ncannot overcome it.\" This his very words show: besides declaring this\nfact, he rises to a general and undoubtedly true proposition; he draws\na conclusion also very legitimate; but neither of these was at all\nnecessary to the present case; neither seemed to explain well his\nopinion, but either served to confuse it.\n\n171. Descartes did nothing more in this point than what all\nphilosophers do; and strange as it may seem, he did not differ from\nthe chiefs of the metaphysical school diametrically opposed to his\nown, that of Locke and Condillac. That man, in seeking to examine the\norigin of his cognitions, and the principles on which his certainty is\nbased, encounters the fact of consciousness of his internal acts, that\nthis consciousness produces a firm certainty, and that we can conceive\nnothing more certain, is a fact on which all ideologists agree, and\nwhich all establish, although not in the same words. The more we\nreflect on these matters, the more we discover in them the realization\nof a principle confirmed by reason and experience, that many truths are\nnot new, but only presented under a new form, and that many systems are\nnot new, but only expressed in new formulas.\n\n172. Even the universal doubt of Descartes, rightly understood, is\npractised by every philosopher; whence we see that the basis of his\nsystem, opposed by many, is in fact adopted by all. In what does his\nmethod consist? It may all be reduced to these two points: I. I wish to\ndoubt of everything: II. When I wish to doubt of myself, I cannot.\n\nLet us examine these points, and we shall see that they are common to\nall philosophers with Descartes.\n\nWhy does Descartes wish to doubt of everything? Because he proposes\nto examine the origin and certainty of his cognitions, his whole\nknowledge; and therefore he cannot help supposing nothing to be true.\nIf then he supposes anything, he does not examine the origin and\nmotives of the certainty of everything, since he excepts that which\nhe supposes to be true. He must suppose nothing to be true, that he\nknows nothing of anything; otherwise he cannot say that he examines\nthe foundation of everything. Either there is no such philosophical\nquestion, although one is found in all books of philosophy, or else\nDescartes' method must of necessity be followed.\n\nBut in what does this doubt consist? Can it, rationally speaking, be a\nreal and true doubt? No! that is absolutely impossible. Man does not,\nbecause a philosopher, destroy his nature; and nature is invincibly\nopposed to this doubt taken in a strict sense.\n\n173. What then is this doubt? Nothing more than a _supposition_,\na _fiction_; a supposition and fiction such as we make at every\nstep in all science, and which, in reality, is only non-attention\nto a conviction of our own. Use is made of this doubt in order to\ndiscover the first truth on which our understanding rests; and this\nonly requires a fictitious doubt: there is no necessity of its being\npositive, for it will evidently make no difference whether we really\ndoubt of everything, admit absolutely nothing, or say: I suppose that\nI have nothing for certain, know nothing, admit nothing. An example\nwill make this explanation more evident. Whoever knows the rudiments\nof geometry, knows that in a triangle, the greater angle is opposite\nto the greater side, and he is absolutely certain of the truth of this\ntheorem; but if he propose to demonstrate it to another, or repeat the\ndemonstration to himself, he abstracts the said certainty, and proceeds\nas though he had it not, in order to show that it is founded upon\nsomething.\n\nIn all our studies, at every step, we do the same. Such expressions as\nthese are common: \"This is so, it is evident; but _let us suppose_ that\nit is not; what will be the result?\" \"This demonstration is conclusive,\nbut let us set it aside and suppose that we have it not; how shall we\ndemonstrate what we desire?\" Arguments _ad absurdum_, so much in use\nin every science, more especially in mathematics, consist not only in\nabstracting what we know, but in supposing something directly contrary.\n\"If the line A,\" says continually the geometrician, \"is not equal to B,\nit is either greater or less: let us suppose it to be greater, etc.\"\nThus to investigate truth, we frequently abstract what we know, and\neven suppose the contrary. Apply this system to the investigation of\nthe fundamental principle of our cognitions, and Descartes' universal\ndoubt will follow, in the only sense admissible at the tribunal of\nreason, and possible to human nature.\n\nIt is probable that the illustrious philosopher understood it in the\nsame sense, although we must confess that his words are ambiguous.\nWe cannot conceive what object he could have had in understanding\nit differently, supposing, as we do, that he had no other purpose\nthan to pave the way for the investigation of truth. By his manner\nof expressing himself, he gave occasion to disputes, which greater\nclearness would have prevented.\n\nAs he did not express himself with sufficient clearness, so his\nadversaries did not press him with all the precision and energy\npossible. To settle this whole matter, it would have sufficed to\nask him this question: Do you mean to say that, in commencing our\nphilosophical investigations, there is a moment in which we _really_\nand _actually_ doubt of every thing; or do you deem it sufficient\nto abstract certainty, and to suppose that we have it not, as is\nfrequently done in other studies?\n\n174. Descartes was like all reformers who are ruled by one idea, and\nexpress it so strongly as to seem to admit no other beside it. In\ntheir language every thing is absolute, exclusive. They anticipate the\ncombat which they must sustain, perhaps already experience it, and so\nthey concentrate all their strength on the idea whose triumph they\npropose, and lose sight of every thing else. It cannot be inferred\nfrom this that they have no others which notably modify the principal;\nbut to oppose their adversaries, who say, \"This is absolutely false,\"\nthey assert that it is absolutely true. History and experience furnish\ninnumerable examples of such exaggerations.\n\nThe dominant idea of Descartes was to demolish the philosophy which at\nthat time reigned in the schools; and he gave it so rude a shock as\nto make the world tremble. See how he expressed his contempt for many\ncalled philosophers: \"Experience shows that they who make profession of\nbeing philosophers are often less wise and less reasonable than they\nwho never applied themselves to this study.\"[11]\n\n[11] _Les Principes de la Philosophie._ Preface, p. 13.\n\n175. The second part of Descartes' method consists in taking thought\nfor the point of departure, and in declaring that in trying to doubt of\nevery thing man finds a limit in the consciousness of his thought, his\nexistence. This is evidently the phenomenon which remains in the mind\nof the observer after doubting of every thing else; at least he cannot\ndoubt that he doubts, and consequently that he thinks; for it must be\nremarked that this is an argument which has always been used against\nskeptics, which is equivalent to Descartes' method, and establishes\nas an undeniable phenomenon a certainty superior to all sophisms, the\nconsciousness of one's self.\n\nWhen Descartes said, _I think_, he meant by this word every internal\nact, every phenomenon immediately present to the soul; he spoke not of\nthought taken in a purely intellectual sense, but included in it all\nthat of which we have immediate consciousness. \"By the word _thought_,\"\nhe says, \"I understand all that is done within us, in such a manner\nthat we perceive it immediately by ourselves: this is why not only to\nunderstand, to will, to imagine, but also to feel, are here the same\nthing as to think. For if I say that I see, or that I walk, and thence\nI infer that I am; if I mean to speak of the action performed with my\neyes or with my feet, this conclusion is not so infallible that I have\nno reason to doubt it; because it may be that I think I see, or walk,\nalthough I do not open my eyes or stir from my seat; for this sometimes\nhappens when I am asleep, and the same might also happen even if I had\nno body; but if I mean to speak only of the action of my thought or of\nthe feeling, that is to say, the knowledge that I possess, which makes\nit seem to me that I see, or that I walk, this same conclusion is so\nabsolutely true that I cannot doubt it; because it relates to the soul,\nwhich alone has the faculty of feeling, or of thinking, in any other\nmanner whatever.\"[12]\n\n[12] _Les Principes de la Philosophie._ 1^{i\u00e8re.} partie, N. 9.\n\n176. This passage shows very clearly Descartes' ideas; he destroyed\nevery thing by doubt, excepting one thing which defied all his\nefforts, the consciousness of himself; and this consciousness he took\nfor the basis, on which, with full certainty, he might build anew\nthe edifice of science. Locke and Condillac did nothing else; they\nfollowed, indeed, a different path, but their point of departure was\nat all times the same. Locke says: \"First, I shall inquire into the\n_original_ of those _ideas_, notions, or whatever else you please to\ncall them, which a man observes, and is conscious to himself he has in\nhis mind; and the ways whereby the understanding comes to be furnished\nby them.\"[13] \"Since the mind, in all its thoughts and reasonings, hath\nno other immediate object but its own _ideas_, which it alone does or\ncan contemplate, it is evident that our knowledge is only conversant\nabout them.\"[14] \"Whether, to speak metaphorically,\" says Condillac,\n\"we ascend even to the heavens, or descend into the abysses, we do\nnot go out of ourselves, and it is always our own thought that we\nperceive.\"[15]\n\n[13] _Essay on the Human Understanding._ Prologue.\n\n[14] _Essay on the Human Understanding._ Book iv., Chap. I., \u00a7 1.\n\n[15] _Essai sur l'Origine des Connaissances._ Premi\u00e8re partie, C. 1., \u00a7\n1.\n\n177. All ideological labors commence then by establishing the fact of\nconsciousness of our ideas; and it cannot be otherwise with respect to\ntheir certainty. Man, although he overthrow and destroy every thing,\nstill encounters himself, the one who overthrows and destroys every\nthing. When he has gone so far as to doubt the existence of God, the\nworld, his fellow-beings, his own body, he still, in the midst of this\nimmense solitude, encounters himself. The effort to conceal himself\nfrom his own eyes serves only to render him more visible: he is a\nspirit to be killed by no blow, and rays of light flow from every\nwound inflicted on him. If he doubts that he feels, he at least feels\nthat he doubts; if he doubts of this doubt, he feels that he doubts\nof doubt itself; thus, in doubting of direct acts, he enters into an\ninterminable series of reflex acts, necessarily linked one with the\nother, and unrolled to the internal view like folds of a scarf which\nhas no end.(18)\n\n\n\n\nCHAPTER XIX.\n\nVALUE OF THE PRINCIPLE, I THINK: ITS--ANALYSIS.\n\n\n178. We have already seen that Descartes' principle, considered as an\nenthymema, cannot aspire to be fundamental. In every argument there are\npremises and a consequence; and to be conclusive, the premises must be\ntrue, and the consequence legitimate. To say that an argument may be a\nfundamental principle, is a manifest contradiction.\n\nBut if we take Descartes' principle in the sense above explained,\nthat is, not as an argument but as the declaration of a fact, the\ncontradiction ceases, and it is a question, worthy to be examined,\nwhether it merits the title of fundamental principle or not, and in\nwhat sense. We have already somewhat illustrated this matter, but not\nyet sufficiently cleared it up; we have made some preliminary remarks\nin order to show the state of the question, but have not yet completely\nsolved it.\n\n179. The proposition, _I think_, as we have remarked, expresses\nsomething more than merely thought, strictly so called: it embraces\nacts of the will, sentiments, sensations, acts, and expressions of\nall kinds which are realized within us; it includes all phenomena\nimmediately present to our mind, and attested by consciousness.\n\nNothing that distinguishes between various acts and impressions can\nbe a fundamental principle: such a distinction supposes analysis, and\nanalysis requires reflection. We do not reflect without rules and\nobjects already known; consequently, to admit classifications in the\nfirst principle, is to divest it of its character and to contradict\nourselves.\n\n180. We must not confound what is expressed by the proposition _I\nthink_ with the proposition itself. The thing itself and the form\nare here very different: the nature of the form may make us conceive\nambiguous ideas of the thing itself: the thing itself is a most\nsimple fact; the form is a logical combination, and includes very\nheterogeneous elements. This demands explanation.\n\nThe fact of consciousness, in itself considered, abstracts all\nrelations; it is nothing but itself, leads to nothing but itself; it\nis the presence of the act or impression, or rather it is the act,\nthe impression itself, which is present to the mind. There is no\ncombination of ideas, no analysis of conceptions; when it comes to\nthis latter, it leaves the territory of pure consciousness, and enters\nthe objective regions of intellectual activity. But as language is to\nexpress the products of this activity, and as it is cast, so to say,\nnot in the mould of consciousness, but in that of the intellect, it is\nimpossible for us to speak without some logical or ideal combination.\nWere we seeking an expression of pure consciousness, unmixed with\nintellectual elements, we should seek it not in language, but in the\nnatural sign of grief, joy, or some other passion; in this alone is\nit expressed spontaneously and uncombined with foreign elements, that\nsomething passes in our mind, that we are conscious of something;\nbut the instant that we speak, we express something more than pure\nconsciousness: the external world indicates the internal, the product\nof intellectual activity, its conception; and this involves a subject\nand an object, and therefore pertains to an order far superior to that\nof consciousness.\n\n181. To demonstrate the truth of what we have just said, let us examine\nthe expression, _I think_. This is a true proposition, and it may,\nwithout being in the least changed, be presented under a strictly\nlogical form, _I am thinking_. Here we have a subject, a predicate,\nand a copula. The subject is _I_; that is to say, we at once find the\nidea of a being, the subject of acts and impressions, the possessor of\nan activity expressed in the predicate. This _I_ is then presented to\nus as something far superior to the order of pure consciousness; it is\nnothing less than the idea of substance. We will analyze more at length\nwhat is contained under it.\n\nWe have, in the first place, the idea of unity: the _I_ has no\nmeaning, if it do not denote that something is one and identical,\nnotwithstanding the plurality and diversity realized in it. The\nexperimental unity of consciousness draws with it, as a rigid\nconsequence, the unity of the being possessing it. This being is the\nsubject; and in it are realized the variations without which it would\nbe impossible to say _I_. We hold then that in so simple an expression\nthe ideas of unity and its relation to plurality, of substance and its\nrelations to accidents, are contained; that is, the idea of the soul,\nalthough expressive of a most simple unity, is, under the logical\naspect, composite, and contains many things pertaining to the ideal\norder, and not to be found in pure consciousness. The idea of the soul,\nstrictly speaking, although in a certain sense common to all men, is in\nitself highly philosophical, for it involves a combination of elements\nbelonging to the intellectual order.\n\n182. The predicate _thinking_ is the expression of a general idea,\ncomprehending not only all thought, but also all phenomena which\nimmediately affect the mind. These phenomena, considered in what they\nhave in common, under the general idea of present to the mind, are\nexpressed in the word thinking.\n\nThe relation of the predicate with the subject, or the agreement\nof _thinking_ with the soul, also expresses an analysis worthy of\nattention. We at once detect a decomposition of the conception of the\nsoul into two ideas; that of the subject of various modifications, and\nthat of thinking. Otherwise the proposition has no meaning, or rather\nits expression becomes impossible. The idea of subject involves the\nideas of unity and substance, and that of thinking involves the idea of\nactivity, or of passivity, so to speak, accompanied by consciousness.\n\n183. To render the proposition possible, we must suppose the\ndecomposition of the ideas to commence at some point, that is, either\nin the idea of the soul we find that of _thinking_, or in that of\n_thinking_ we find that of the soul. Fixing ourselves in the soul,\nand abstracting _thinking_, we meet with the idea of subject, or of\nsubstance in general; and there, however much we cavil, we shall never\nfind the idea of _thinking_. The soul in itself is not manifested to\nus; we know it by thought; in thought therefore we must fix the point\nof departure, not in the soul; wherefore in the above proposition, what\nis primitively known is rather the predicate than the subject; and of\nthe two conceptions, that of subject has rather the character of a\nthing contained, than of a thing containing.\n\nThe soul by itself, so to speak, springs up with the presence of\nthought. If the intellectual activity is concentrated in search of its\nfirst basis, it finds it, not in the pure subject, but in its acts,\nthat is, in its thoughts. These last are then the first object of\nreflective intellectual activity, its first element of combination,\nits first _datum_ for the solution of the problem. Fixing its sight\non this element, it discovers a unity in the midst of plurality, a\nbeing that remains the same through the ebb and flow of the phenomena\nof consciousness; and this identity is incontestably asserted by\nconsciousness itself. The idea of the soul then is taken from that\nof thought, and consequently the subject springs from the predicate,\nrather than the predicate from the subject.\n\n184. The thought from which we derive the idea of the soul is not\nthought in general, but thought realized, existing in ourselves. But\nthis reality is sterile unless offered to the mind under a general\nidea; for it is evident that the soul does not come from one single\nact, since it is unity, the subject of plurality. To arrive at the idea\nof the soul we require unity of consciousness, and this we know only as\nwe have experienced it, that is, so far as we perceive the relation of\nthe one to the multiple, of a subject to its modifications.\n\nSuch elaboration is necessary to the production of so simple an\nexpression as _I think_; and here we see how much reason there\nis to distinguish between the thing itself and the form, and how\ninconsiderately they act who confound things so different. Thus, from\nwant of due analysis, they take in philosophy immense strides from one\norder to another, confound ideas and entangle matters.\n\n185. To completely illustrate this matter, we will examine the\nrelations of existence to thought; a very easy examination, if we bear\nin mind the observation just made.\n\nIt is certain that we conceive existence before thought: nothing can\nthink without existing: existence is an indispensable condition to\nthought: to think and not to exist is a manifest contradiction. But\nwhat is first offered to our mind is not existence, but thought,\nand this not in the abstract, but determinate, experimental, or as\nthe expression now is, empyrical. The idea of existence is general,\nincludes all beings, and consciousness cannot commence with it. At\none time we obtain this idea by abstraction; at another, it is a form\npre-existing in our mind, not the first that occurs to us, or to speak\nmore exactly, not the last point to be attained when we follow back the\nthread of our cognitions in order to discover their starting-point.\nThis consciousness, when made objective, and when the conception\nwhich it offers is analyzed, presents to us the idea of existence as\ncontained in itself.\n\nHence we infer that the _therefore I exist_ is not, strictly speaking,\na consequence of the _I think_, but the intuition of the idea of\nexistence in that of thought. There are here two propositions _per\nse not\u00e6_, as the scholastics say: the one general, _the thinking is\nexisting_; the other particular, _I thinking am existing_. The first\nbelongs to the purely ideal order, and is intrinsically evident,\nindependently of all particular consciousness; the second participates\nof the two orders, the real and the ideal; the real, in so far as it\nincludes the particular fact of consciousness; the ideal, in so far as\nit includes a combination of the general idea of existence with the\nparticular fact; since thus only is the union of the predicate with the\nsubject conceivable.\n\n186. It will now be very easy to solve all the questions discussed in\nthe schools.\n\nFirst question. Does the principle _I think_ depend on another? We\nanswer with a distinction. If by this principle is meant the simple\nfact of consciousness, it evidently does not. For our understanding\nthere is nothing prior to ourselves; whatever we know so far forth as\nknown by us, supposes our consciousness; if we suppress it, we destroy\nevery thing, and although we attempt to destroy every thing, it still\nremains indestructible, since it depends on nothing, presupposes\nnothing.\n\nIf by the principle _I think_ is meant a proposition, it can only have\nproceeded from reasoning or analysis, and so cannot be the fundamental\nprinciple of our cognitions.\n\n187. Second question. When the other principles are wanting, is this\none also wanting? We must apply the same distinction here: as a simple\nfact? No! as a proposition? Yes! Deny every thing, even the principle\nof contradiction, and consciousness still subsists; but deny the\nprinciple of contradiction, and every proposition is destroyed, every\ncombination becomes absurd: analysis, and the relation of the predicate\nwith the subject, are unmeaning words.\n\n188. Third question. Admitting the principle _I think_, can he who\ndenies the others be reduced at least indirectly to truth? We again\ndistinguish: you speak of reducing him either by reasoning or by\nobservation; that is, either you wish to convince him by arguments,\nor else to turn his attention to himself, as is done with a man\ndistracted, or one suffering mental derangement. The second is\npossible, but not the first. Whoever denies all principles, that of\ncontradiction included, makes all argument impossible; in vain then\nwill you reason with him. Let us see.\n\nYou think, one may say to him, at least you so assert, when you admit\nthe principle _I think_. True. Then you must also admit the principle\nof contradiction. Why so? Because otherwise you could think and not\nthink at the same time. Very well. But then you destroy your own\nthought. How? Is it not true that you think? Certainly. According to\nyourself it is possible that at the same time you do not think. I agree\nwith you. Therefore, you destroy your thought; for if you do not think,\nthe _I think_ is destroyed, and, as all this is simultaneous, you\ndestroy your own thought.\n\nNot at all. What I object to in your system is that you suppose true\nthe very thing which I deny, and so fall into the sophism named by\nlogicians _petitio principii_. By the very fact of my denying the\nprinciple of contradiction, I deny that not-being destroys being, and\nthat being destroys not-being; consequently, I do not admit that the\n_I do not think_ destroys the _I think_. When you argue against me\nin this way, you suppose the very point in question, and attack me\nwith principles which I do not admit. In your system, in which being\ndestroys not-being, and _vice versa_, it is certain that to think,\nand not think, are incompatible; but on my principles, it is a very\nsimple thing; since, according to them, it is not impossible for the\nsame thing to be and not be at the same time, when I do not think, I\ndo not cease to think. This is indeed absurd, but not illogical; deny\nthe principle, and the deduction is necessary. And if it be said that\nin such a case he cannot reason, as he just has reasoned, he may reply\nthat neither can his adversaries reason; or, if you choose, he sees no\ndifficulty in their both reasoning and not reasoning.\n\nObservation is the only means of bringing back one who has thus strayed\naway; such a one has departed from reason, and cannot be brought back\nto it by means of reason. Observations directed to him must be more\nof a call, a sort of alarm to arouse reason, not a combination to\nre-construct it: he is as a man asleep, or one in a swoon, and we must\ncall him, and shake him, in order to arouse him; we must not dispute\nwith him as with an adversary.(19)\n\n\n\n\nCHAPTER XX.\n\nTRUE SENSE OF THE PRINCIPLE OF CONTRADICTION.--KANT'S OPINION.\n\n\n189. Before examining the value of the principle of contradiction as\na basis for our cognitions, it will be well to fix its true and exact\nsense. This renders necessary some considerations upon an opinion\nof Kant, advanced in his _Critic of Pure Reason_, when treating of\nthe form in which the principle of contradiction has hitherto been\nenunciated in all schools of philosophy. The German metaphysician\ngrants, that whatever may be the matter of our cognitions, and in\nwhatever manner they may relate to their object, it is a general,\nalthough a purely negative, condition of all our judgments, that they\nshould not mutually contradict each other; otherwise, even without\nreference to their object, they are nothing in themselves. This\ndoctrine established, he observes that what is called the principle\nof contradiction is the following: \"A predicate that is opposed to a\nsubject does not belong to it;\" and then goes on to say, that this is\na universal, although purely negative criterion of all truth; that\nit moreover belongs exclusively to logic, since it is of use to pure\ncognitions as to cognitions in general, without relation to their\nobject, and he declares that the contradiction makes them completely\ndisappear. \"But of this celebrated principle, although stripped of\nall contents, and purely formal,\" he continues, \"there is still a\nformula containing a synthesis, which has inadvertently, and quite\nunnecessarily, been mixed up therein. It is this: _It is impossible\nfor the same thing to be and not be at the same time._ Not only has\nthe apodictic certainty (by the word _impossible_) been unnecessarily\nadded, which certainty would have been of itself understood from the\nproposition; but the proposition is affected by the condition of time,\nand says, as it were: a thing = A, which is something = B, cannot at\nthe same time be not B, but it can very well be both (B as well as not\nB) in succession. For example: a man who is young, cannot at the same\ntime be old; but the same person may very well be young at one time, at\nanother not young, that is, old. Now, the principle of contradiction,\nas a mere logical principle, must not at all restrict its meaning\nto the relations of time, and consequently, such a formula is quite\nopposed to its intention. The misapprehension arises simply from this:\nthat we first separate the predicate of a thing from its conception,\nand afterwards unite its opposite with this predicate, which never\ngives a contradiction with the subject, but only with its predicate,\nwhich is synthetically joined with that subject, and that only when\nthe first and second predicates are asserted at the same time. If I\nsay a man who is unlearned is not learned, the condition, _at the same\ntime_, must be expressed; for he who is unlearned at one time may very\nwell be learned at another. But if I say no unlearned man is learned,\nthe proposition is analytic, since the sign (the unlearnedness) now\nconstitutes the conception of the subject, and then the negative\nproposition is evident immediately from the principle of contradiction,\nwithout it being necessary for the condition, _at the same time_, to be\nadded. This is also the cause why I have so changed the formula of this\nprinciple, that the nature of an analytic proposition might be clearly\nexpressed.\"[16]\n\n[16] _Transcendental Logic_, B. ii., C. 2, Sect. 1, pp. 140-141. Ed.\nLeipsic. 1828.\n\n190. The reader will not easily comprehend the meaning of this passage,\nnot very clear of itself, unless he knows what Kant understands by\nanalytic and synthetic propositions. We will explain this. In all\naffirmative judgments, the relation of a predicate to a subject is\npossible in two manners: either the predicate belongs to the subject\nas contained in it, or is completely extraneous to it although joined\nwith it. In the former case, the judgment is analytic; in the latter,\nit is synthetic. Analytic affirmative judgments are those in which the\nunion of the predicate with the subject is conceived by identity: those\nare called synthetic in which this union is conceived without identity.\nKant illustrates his idea by the following examples: \"When I say all\nbodies are extended, I express an analytic judgment; for I need not go\nout of the conception of body in order to find that of extension, which\nI connect with it, but I have only to analyze the conception of body,\nthat is, to become conscious of the diversity which I always think in\nthis conception, in order to find the predicate. It is, therefore, an\nanalytic judgment. But when I say, all bodies are heavy, the predicate\nheaviness is by no means included in my conception of the subject, that\nis, of body in general. It is a conception added to the conception of\nbody. The addition in this way of the predicate to the subject gives a\nsynthetic judgment.\"[17]\n\n[17] _Critic of Pure Reason._ Introduction, Sect. 4., p. 9.\n\nIt is easy to see the reason of the new nomenclature employed by the\nGerman philosopher. He calls those judgments analytical, in which\nit suffices to decompose the subject to find therein the predicate,\nwithout the necessity of adding any thing not already thought, at\nleast obscurely, in the very conception of the subject; and he calls\nsynthetic those in which it is necessary to add something to the\nconception of subject, since the predicate is not found in this\nconception however much we decompose it.\n\n191. This division of judgment, into analytic and synthetic, is much\nused in modern philosophy, above all among the Germans; certainly there\nare some who may imagine this to be a discovery made by the author of\nthe _Critic of Pure Reason_; and the very novelty of the name may give\noccasion to equivocation. Yet, in all the scholastic writers who lie\nforgotten, and covered with dust, in the recesses of libraries, we find\nanalytic and synthetic judgments, though not under these names. They\nsaid there were two kinds of judgments; some, in which the predicate\nwas contained in the idea of subject, and others, in which it was not.\nThey called the propositions which expressed judgments of the former\nclass, _per se not\u00e6_, or known by themselves, because, the meaning of\nthe terms being understood, the predicate was seen to be contained in\nthe idea, or the conception of the subject. They also called them first\nprinciples, and the perception of them, _intelligence_, _intellectus_,\nto distinguish them from _reason_, which is conversant about the\ncognitions of mediate evidence, or ratiocination.\n\nSee if the following texts of St. Thomas leave any thing to be desired\nin clearness or precision: \"A proposition is known by itself, _per\nse not\u00e6_, when the predicate is contained in the subject, as; _man\nis an animal_; for animal is of the essence of man. If, then, it is\nknown to all, what the subject and the predicate are, that proposition\nwill be known by itself to all, as is seen in the first principles\nof demonstration, which are certain, common things, not unknown to\nany one, as being and not-being, the whole, the part, and others\nsimilar.\"[18]\n\n[18] _Summa Theologica._ P. 1^a, Q. 2^a, A. 1^o, in corp.\n\n\"Any proposition the predicate of which is of the essence of the\nsubject, is known by itself, although such a proposition is not known\nby itself for any one who is ignorant of the definition of the subject.\nThus this proposition, _man is rational_, is by its nature known by\nitself, because _whoever says man, says rational_.\"[19]\n\n[19] 1^a 2^{dae}, Q. 94^a, A. 2^o, in corp.\n\n192. By these, and many other examples, which it would be easy to\nadduce, it is seen that the distinction between analytic and synthetic\njudgments was common in the schools centuries before Kant flourished.\nAnalytic judgments were all those formed by immediate evidence; and\nsynthetic, those resulting from mediate evidence, whether of the\npurely ideal order, or in some sense depending on experience. It\nwas well known that there were conceptions of the subject, in which\nthe predicate was thought, at least confusedly; and thus union, or\nidentity, was explained by saying that the propositions, in which it\nwas found, were _per se not\u00e6 ex terminis_. In analytic judgments, the\npredicate is in the subject; nothing is added, according to Kant, it is\nonly unfolded. _Whoever says man says rational_, are the words of St.\nThomas: the idea is the same as that of the German philosopher.\n\n193. But let us see if it is necessary to change the formula by which\nthe principle of contradiction has hitherto been expressed.\n\nThe first observation of Kant refers to the word _impossible_, which he\nconsiders unnecessarily added, since the apodictic certainty, which we\nwish to express, should be contained in the proposition itself. Kant's\nformula of the principle is this: \"a predicate which is _opposed_ to\na subject, does not belong to it.\" What is the meaning of the word\n_impossible_? \"Possible and impossible absolutely, are said in relation\nto the terms. Possible, because the predicate is not opposed to the\nsubject; impossible, because the predicate is opposed to the subject;\"\nsays St. Thomas,[20] and with him agree all the schools. Therefore,\nimpossibility is the opposition of the predicate to the subject, and to\nbe repugnant is the same thing as to be impossible, and Kant uses the\nvery language which he blames in others. The common formula might be\nexpressed in this manner: \"there is opposition in the same thing being\nand not-being at the same time,\" or, \"being is opposed to not-being,\"\nor, \"being excludes not-being,\" or, \"every thing is equal to itself;\"\nand Kant expresses nothing more when he says: \"a predicate which is\nopposed to a subject does not belong to it.\"\n\n[20] P. 1^a, Q. 25^a, A. 3.\n\n194. As a universal criterion, there is more exactness in the common\nformula than in that of Kant. The latter restricts the principle\nto the relation of predicate and subject, and consequently to the\npurely ideal order, making it of no value for the real, unless by\na sort of enlargement. This enlargement, although legitimate and\neasy, is not needed in the common formula: by saying being excludes\nnot-being, we embrace the ideal and the real, and present to the mind\nthe impossibility, not only of contradictory judgments, but also of\ncontradictory things.\n\nKant admits that the principle is the condition _sine qua non_ of\nthe truth of our cognitions, so that we must take care not to place\nourselves in contradiction with it, under pain of annihilating all\ncognition. Let us put this to the proof. Give a man, unacquainted with\nthese matters, although not ignorant of what is meant by predicate and\nsubject, these two formulas; which will appear to him the best for all\nuses in the external as in the internal? Certainly not that of Kant.\nHe sees in an instant, in all its generality, that a thing cannot\nboth be and not be at the same time; and he applies the principle to\nall uses as well in the real as in the ideal order. Treating of an\nexternal object, he says, this cannot both be and not be at the same\ntime; treating of contradictory judgments, of ideas which exclude one\nanother, he says, without any difficulty, this cannot be, because it\nis impossible for the same thing to be and not be at the same time.\nBut it is not so easily and so readily seen how transition is made\nfrom the ideal to the real order, or how the purely logical ideas of\npredicate and subject can be used in the order of facts. The common\nformula, then, besides being fully as exact as that of Kant, is more\nsimple, more intelligible, and more easy of application. Are there any\nqualities more desirable than these in a universal criterion, in the\ncondition _sine qua non_ of the truth of our cognitions?\n\n195. We have thus far supposed Kant's formula really to express the\nprinciple of contradiction; but this supposition is far from being\nexact. Undoubtedly there would be a contradiction, were a predicate\nopposed to a subject, and yet to belong to it; and in this sense it\nmay be said that the principle of contradiction is in some manner\nexpressed in Kant's formula. But this is not enough; for we should\nthen be obliged to say that every axiom expresses the principle of\ncontradiction, since no axiom can be denied without a contradiction.\nThe formula of the principle must _directly_ express reciprocal\nexclusion, opposition between being and not-being; this is what\nwas intended, and nothing else was ever meant by the principle of\ncontradiction. Kant, in his new formula, does not directly express\nthis exclusion: what he expresses is, that when the predicate is\nexcluded from the idea of the subject, it does not belong to it. So\nfar from expressing the principle of contradiction, it is the famous\nprinciple of the Cartesians: \"whatever is contained in the clear and\ndistinct idea of any thing may be affirmed of it with all certainty.\"\nIn substance the two formulas express the same thing, and are only\ndistinguished by these purely accidental differences: first, that\nKant's formula is the more concise; second, that it is negative, and\nthat of the Cartesians affirmative.\n\n196. Kant says: \"whatever is _excluded_ from the clear and distinct\nidea of any thing, may be denied of it.\" A _predicate which is opposed_\nto a subject \"is the same thing as that which is _excluded_ from\nthe idea of any thing;\" \"does not belong to it\" is the same as \"may\nbe denied of it.\" And as, on the other hand, the principle of the\nCartesians must be understood in both senses, the affirmative and the\nnegative, because when they say that whatever is contained in the clear\nand distinct idea of any thing may be affirmed of it, they mean also\nthat when any thing is excluded, it may be denied; it follows that\nKant says the same thing as the Cartesians; and thus, in attempting to\ncorrect all the schools, he has fallen into an equivocation not of a\nnature to acquire him any great credit for perspicacity.\n\nIt is clear that Kant's formula implies this: the predicate contained\nin the idea of a subject belongs to it. This condition is equally\nthe condition _sine qua non_ of all analytic affirmative judgments;\nfor these disappear if that does not belong to the subject which is\ncontained in its idea. In this case there is not even an apparent\ndifference between Kant's formula and that of the Cartesians; the only\ndifference is in terms; the propositions are exactly the same. Hence we\nsee that instead of affirming that the schools expressed themselves\ninaccurately in the clearest and most fundamental point of human\nknowledge, we ought to proceed with great circumspection; witness the\noriginality of Kant's formula.\n\n197. The author of the _Critic of Pure Reason_ was not more fortunate\nin censuring the condition, _at the same time_, which is generally\nadded to the formula of the principle of contradiction. Since he\ntook the liberty of believing that no philosopher before himself had\nexpressed this formula in the proper manner, we beg to say that he did\nnot himself well understand what the others intended to express, and\nwe do not, in saying this, deem ourselves guilty of a philosophical\nprofanation. If Kant is an oracle for certain persons, all philosophers\ntogether and all mankind are also oracles to be heard and respected.\n\nAccording to Kant, the principle of contradiction is the condition\n_sine qua non_ of all human cognitions. If, then, this condition is\nto serve as their object, it must be so expressed as to be applicable\nto all cases. Our cognitions are not composed solely of necessary\nelements, but admit, to a great extent, ideas connected with the\ncontingent; since, as we have seen, purely ideal truths lead to nothing\npositive, unless brought down to the ground of reality. Contingent\nbeings are subject to the condition of time, and all cognitions\nrelating to them must always depend on this condition. Their existence\nis limited to a determinate space of time; and it is necessary to think\nand speak of it conformably to this determination. Even their essential\nproperties are in some manner affected by the condition of time;\nbecause if abstracted from it, and considered in general, they are\nnot as they are when realized; that is, when they cease to be a pure\nabstraction, and become something positive. Here, then, is the reason,\nand a very profound and cogent reason, why all the schools joined the\nidea of time to the formula of the principle of contradiction: the\nreason, we repeat, is very profound, and it is strange how it escaped\nthe German philosopher's penetration.\n\n198. The importance of this subject requires still further explanation.\nWhat is essential to the principle of contradiction, is the exclusion\nof being by not-being, and of not-being by being. The formula must\nexpress this fact, this truth, which is presented by immediate\nevidence, and is contemplated by the intellect in a most clear\nintuition, admitting neither doubt nor obscurity of any kind.\n\nThe word _being_ may be taken in two senses: _substantively_, inasmuch\nas it signifies existence; and _copulatively_, as it expresses the\nrelation of predicate to subject. Peter _is_: here the verb _is_\nsignifies the existence of Peter, and is equivalent to this: Peter\nexists. The equilateral triangle is equiangular: here the verb _is_\nis taken copulatively, since it is not affirmed that any equilateral\ntriangle exists; merely the relation of equality of angles to equality\nof sides is established absolutely, abstraction made from the existence\nof either.\n\nThe principle of contradiction must extend to the cases in which\n_being_ is copulative, and to those in which it is substantive; for\nwhen we say it is impossible for the same thing to be and not be,\nwe speak not only of the ideal order, or of the relations between\npredicates and subjects, but also of the real order. Were no reference\nmade to this last, we should hold the entire world of existences\nto be deprived of this indispensable condition of all cognitions.\nMoreover this condition is not only necessary to every cognition, but\nalso to every being in itself, abstracting its being known, or being\nintelligent. What would a being be that could both be and not be? What\nis the meaning of a contradiction realized? The principle must extend\nto the word being, not only as copulative, but also as substantive.\nAll finite existences, our own included, are measured by a successive\nduration; therefore, if the formula of the principle of contradiction\nis to be applicable to whatever we know in the universe, it must be\naccompanied by the condition of time. All finite things, which now\nexist, at one time did not exist, and it may again be true that they\ndo not exist. Of no one can it be truly said that its non-existence\nis impossible; this impossibility springs from existence in a given\ntime, and can only be asserted with respect to that time. Therefore,\nthe condition of time is absolutely necessary in the formula of the\nprinciple of contradiction, if this formula is to serve for the\nexistent, that is, for that which is the real object of our cognitions.\n\n199. Let us now see what happens in the purely ideal order, where the\nword _being_ is taken copulatively. Propositions of the purely ideal\norder are of two classes; in the first, the subject is a generic idea,\nwhich, by the union of the specific difference, becomes a determinate\nspecies; in the second, the subject is this determinate species, or the\ngeneric idea joined with the difference. The word _angle_ expresses\nthe generic idea comprehending all angles, which, united with the\ncorresponding difference, constitutes the species of acute, obtuse,\nor right angle. At every step we modify the generic idea in various\nways, and as a succession, in which are represented to us distinct\nconceptions, all having for their basis the generic idea, necessarily\nenters into it, it follows that we consider this idea as a being which\nis successively transformed. To express this succession, which is\npurely intellectual, we employ the idea of time; and here is one of\nthe reasons which justify the use of this condition even in the purely\nideal order. Thus we say, an angle cannot at the same time be both\na right angle and a not-right angle; for the idea of angle may be\nsuccessively determined by the difference which constitutes it a right\nangle, and a not-right angle; but these determinations cannot co-exist\neven in our conception, for which reason we do not assert the union of\nthe difference with the genus to be absolutely impossible, but limit\nthe impossibility to the condition of simultaneousness.\n\nIn this proposition, a right angle cannot be obtuse; the subject is not\nthe generic idea alone, but is united with the difference expressed by\nthe word _right_. In the conception formed of these two ideas, right\nand angle, we see the impossibility of uniting the idea _obtuse_ with\nthem. This is without any condition of time, and here there is none\nexpressed. We frequently say, an angle cannot be at the same time right\nand obtuse; but we never say, a right angle can never _at the same\ntime_ be obtuse, but, absolutely, a right angle cannot be obtuse.\n\n200. Kant observes that the equivocation proceeds from commencing by\nseparating the predicate of a thing from the conception of this thing,\nand afterwards joining to this same predicate its opposite, which\nnever makes a contradiction to the subject, but to the predicate,\nwhich is synthetically united with it; a contradiction which happens\nonly when the first and second predicates are supposed at the same\ntime. This observation of Kant is at bottom very true, but it has its\ndefects: first, it pretends to be original, when it only says things\nalready well known; and secondly, it is used to combat an equivocation\nexisting only in the mind of the philosopher who wants to free others\nfrom it. The two propositions analyzed in the last paragraph confirm\nwhat we have just said. An angle cannot be both right and not right.\nHere the condition of time is necessary, because the opposition is not\nbetween the predicate and the subject, but between the two predicates.\nThe angle may be right or not right, only at different times. A\nright angle cannot be obtuse; here the condition of time must not be\nexpressed, because the idea _right_ entering into the conception of the\nsubject, entirely excludes the idea obtuse.\n\n201. If the principle of contradiction were to serve only for analytic\njudgments, that is, for those in which the predicate is contained\nin the idea of the subject, the condition of time should never be\nexpressed; but as this principle is to guide us in all other judgments,\nit follows that, in the general formula, we cannot abstract a condition\nabsolutely indispensable in most cases. In the present state of our\nunderstanding, while we are in this life, non-abstraction of time is\nthe rule, abstraction the exception; and would you have a general\nformula conform to the exception and neglect the rule?\n\n202. We cannot conceive what reason Kant had to illustrate this\nsubject with the examples above cited. Nothing can be more common\nand inopportune than what he adds in illustration of this matter\nby examples. \"If I say a man who is unlearned is not learned, the\ncondition _at the same time_ must be understood; for he who is\nunlearned at one time, may very well be learned at another.\" This is\nnot only very common and inopportune, but it is exceedingly inexact.\nIf the proposition were: a man cannot be ignorant and instructed; then\nthe condition _at the same time_ should be added, because not giving\npreference to either predicate over the other indicates the manner\nof the opposition, which is of predicate to predicate, and not of\npredicate to subject. But in the example adduced by Kant, \"the man that\nis ignorant is not instructed.\" The subject is not man alone, but an\nignorant man; the predicate _instructed_ devolves on man modified by\nthe predicate _ignorant_, and, consequently, the expression of time is\nnot necessary, nor is it used in ordinary language.\n\nThere is a great difference between these two propositions: a man that\nis ignorant _is not_ instructed; and a man that is ignorant _cannot\nbe_ instructed. The condition of time must not be expressed in the\nformer, for the reason already given; it must be in the latter, because\nspeaking of the impossibility in an absolute manner, we should deny the\nignorant man even the _power_ to be instructed.\n\n203. Kant's other example is the following: \"But if I say no unlearned\nman is learned, the proposition is analytical, since the sign of\nunlearnedness now constitutes the conception of the subject, and then\nthe negative proposition is immediately evident from the principle\nof contradiction, without it being necessary for the condition _at\nthe same time_ to be added.\" We cannot see why Kant makes so great\ndifference between these two propositions: a man who is unlearned is\nnot learned, and no unlearned man is learned; in both, the predicate\nrelates not only to man, but to an unlearned man; and it is the same\nto say, a man that is unlearned, as, an unlearned man. If, then, the\nexpression of time is not necessary in the one, neither is it in the\nother.\n\nIf the idea of unlearned affects the subject, the predicate is\nnecessarily excluded, because the ideas, learned and unlearned, are\ncontradictory; and we encounter the rule of logic, that in necessary\nmatters, an indefinite is equivalent to a universal proposition.\n\nThe principle of contradiction must, therefore, be preserved as it is;\nthe condition of time must not be suppressed, for this would render the\nformula, in many cases, inapplicable.(20)\n\n\n\n\nCHAPTER XXI.\n\nDOES THE PRINCIPLE OF CONTRADICTION MERIT THE TITLE OF FUNDAMENTAL; AND\nIF SO, IN WHAT SENSE?\n\n\n204. Having cleared up the true sense of the principle of\ncontradiction, let us now see whether it merits to be called\nfundamental, whether it possesses all the characteristics requisite to\nsuch a dignity. These characteristics are three in number: first, that\nit depend on no other principle; secondly, that its fall involve the\nruin of all others; thirdly, that it may, while it remains firm, be\nconclusively urged against all who deny the others, and be of avail to\nbring them back to the truth by a demonstration at least indirect.\n\n       *       *       *       *       *\n\n205. In order completely to solve all questions depending on the\nprinciple of contradiction, we shall state a few propositions, and\naccompany them with their proper demonstrations:\n\n\nFIRST PROPOSITION.\n\nIf the principle of contradiction be denied, all certainty, all truth,\nand all knowledge are at an end.\n\n_Demonstration._--If a thing may be and not be at the same time,\nwe may be certain and not certain, know and not know, exist and\nnot exist; affirmation may be joined with negation, contradictory\nthings united, distinct things identified, and identical things\ndistinguished: the intellect is a chaos to the full extent of the word;\nreason is overturned; language is absurd; subject and object clash\nin the midst of frightful darkness, and all intellectual light is\nfor ever extinguished. All principles are involved in the universal\nwreck, and consciousness itself would totter, were it not, when this\nabsurd supposition is made, upheld by the invincible hand of nature.\nConsciousness, indeed, in this absurd hypothesis, does not perish, for\nthis is impossible, but it sees itself carried away by this violent\nwhirlwind, which precipitates it and every thing else into chaotic\ndarkness. In vain does it strive to save its ideas; they all vanish\nbefore the force of contradiction: in vain does it generate new ideas\nto be substituted for those it loses; these also disappear: in vain\ndoes it seek new objects, for they, too, disappear in like manner, and\nit endures only to feel the radical impossibility of all thought, and\nsee contradiction lording it over the intellect, and destroying, with\nirresistible might, whatever would germinate there.\n\n\nSECOND PROPOSITION.\n\n206. It is not enough not to suppose the principle of contradiction\nfalse; we must suppose it to be true, if we would not have all\ncertainty, all knowledge, all truth to perish.\n\n_Demonstration._--The reasons given for the first proposition avail\nalso to prove this. In the one case the principle of contradiction is\nsupposed to be denied; in the other, it is neither supposed true nor\nfalse; but this evidently is not enough, for, until the principle of\ncontradiction is placed beyond all doubt, we remain in darkness, and\nmust doubt of every thing. We do not mean to say that it is impossible\nfor us to have certainty of any thing, if we do not think explicitly\nof this principle; but that it must be so firmly established, that we\ncannot raise the least doubt concerning it, and that, when we see any\nthing connected with it, we must, of necessity, consider that thing as\nfounded upon an immovable basis: the least vacillation, the least doubt\nof this principle utterly destroys it; the possibility of an absurdity\nis itself an absurdity.\n\n\nTHIRD PROPOSITION.\n\n207. The certainty of the principle of contradiction rests upon no\nother principle.\n\n_Demonstration._--It is, as we have seen, necessary in every\ncognition to suppose the truth of the principle of contradiction;\ntherefore, no one can avail to demonstrate it. Every argument, made\nto demonstrate this, necessarily involves a vicious circle; the\nprinciple of contradiction is proved by another principle, which,\nin its turn, supposes that of contradiction; and so we shall have a\nsuperstructure resting upon a foundation, which foundation rests upon\nthe superstructure itself.\n\n\nFOURTH PROPOSITION.\n\n208. Whoever denies the principle of contradiction can neither directly\nnor indirectly be refuted by any other.\n\n_Demonstration._--It would be amusing to hear the arguments directed\nagainst a man who admits both affirmation and negation to be at the\nsame time possible; although forced to admit the affirmative, he will\nstill hold the negative, and _vice versa_. It is impossible not only to\nargue, but even to speak, or to think on such a supposition.\n\n\nFIFTH PROPOSITION.\n\n209. It is not exact to say, as is generally said, that by the\nprinciple of contradiction, we may argue conclusively against whoever\ndenies the others.\n\nHere take notice that we only say _it is not exact_, for we believe\nit at bottom to be true, although not free from inexactness. To show\nthis, let us examine the weight of the demonstration ordinarily given.\nThe reasons, arguments, and replies may be presented most clearly and\nstrongly in the form of a dialogue. Let us suppose some one to deny\nthis axiom: the whole is greater than its part.\n\nIf you deny this, you admit that the same thing may both be and not be\nat the same time. This is what you have to prove. With you the whole is\nthe whole and not the whole, and the part the part and not the part.\nWhy so? First, it is the whole by supposition. Admitted. And at the\nsame time it is not. Denied. It is not the whole because it is not\ngreater than its part. An excellent way of arguing! This is a _petitio\nprincipii_. I commence by asserting that the whole is not greater than\nits part, and you argue on the contrary supposition; for you tell me\nthe whole would not be the whole were it not greater than its part. If\nI had conceded that the whole is greater than its part, and then denied\nthis property, I should indeed fall into a contradiction, making that\na whole, which, according to my principles, is not a whole; but as I\nnow deny that the whole must be greater than its part, I must also deny\nthat it ceases to be a whole by not being greater than its part.\n\n210. What will you reply to one reasoning thus. Certainly nothing in\nthe form of an argument: all that you can do is to call his attention\nto the absurdity of his position; but this is to be done not by\nargument, but by exactly determining the meaning of the words and\nanalyzing the conceptions which they express. This is all that can\nor should be done. The contradiction exists; this is certain; but\nwhat is wanted is, that he see that he has fallen into it; and if the\nexplanation of the terms, and the analysis of the conceptions do not\nsuffice, nothing else will.\n\nLet us see how this may be done in the same example. The whole is\ngreater than its part. What is the whole? The collection of the parts,\nthe parts themselves united. The idea of the parts then enters into the\nidea of the whole. What is the meaning of greater? One thing is said to\nbe greater than another, when, besides containing an equal quantity,\nit also contains something else. Seven is greater than five, because,\nbesides the same five, it contains also two. The whole contains one\npart and also the other parts; therefore, the idea of _greater than\nits part_ enters into the idea of whole. Thus it is that we must\nrefute whoever denies this principle; and this method, better than\nthat of argumentation, may be said to explain the terms and analyze\nthe conceptions, for it clearly does nothing but define the former and\ndecompose the latter.\n\n\nSIXTH PROPOSITION.\n\n211. The principle of contradiction is known only by immediate evidence.\n\n_Demonstration._--Two things are here to be proved: that the knowledge\nis by evidence, and that the evidence is immediate. As regards the\nformer we will remark that the principle of contradiction is not a\nsimple fact of consciousness, but a purely ideal truth. Every fact of\nconsciousness involves reality, and cannot be expressed without the\nassertion of some existence: the principle of contradiction neither\naffirms nor denies any thing positive; that is, it does not say that\nany thing exists or does not exist; it only expresses the opposition of\nbeing to not-being, and of not-being to being, abstraction made from\nour taking the word being copulatively or substantively.\n\n212. Every fact of consciousness is not only something existent, but\nsomething determinate; it is not a thought in the abstract, but is\nthis or that thought. The principle of contradiction contains nothing\ndeterminate; it abstracts not only the existence, but also the essence\nof things, since it relates not only to existing things, but also to\nthings possible: it distinguishes no species among them, but embraces\nthem all in their greatest generality. When we say, \"it is impossible\nfor the same thing to be and not be,\" the word _thing_ does not at all\nrestrict the meaning; it expresses being in general, in its greatest\nindeterminateness. In the _to be_ or _not be_, the word _be_ expresses\nnot only existence, but also every class of essences in their most\ncomplete indeterminateness. Thus the principle is equally applicable\nin these two propositions: it is impossible for the moon to be and not\nbe; it is impossible for a circle to be and not be a circle; although\nthe first is in the real order, and there the word _be_ expresses\nexistence, and the second is in the ideal order, and the word _be_\nexpresses only the relation of predicate to subject.\n\n213. Every fact of consciousness is individual; the principle of\ncontradiction is the most universal imaginable: every fact of\nconsciousness is contingent; the principle of contradiction is\nabsolutely necessary, a necessity which is a mark of truths known by\nevidence.\n\n214. The principle of contradiction is a law of all intelligence; it is\nof absolute necessity for the finite as for the infinite; not even the\ninfinite intelligence is beyond this necessity, for infinite perfection\ncannot be an absurdity. Every fact of consciousness as purely\nindividual, relates only to the being that experiences it; neither the\norder of intelligences, nor that of truth suffers any mutation from my\nexistence or non-existence.\n\n215. The principle of contradiction, besides the marks of necessity and\nuniversality, which distinguish truths of evidence, possesses also that\nof being seen with that immediate, intellectual clearness, of which we\nhave already treated. In the idea of being we see most clearly the\nexclusion of not-being.\n\nHence the proof of the second part of the proposition: because there\nis immediate evidence of the relation of the predicate to the subject,\nwhen the sole idea of the subject, without the necessity of combination\nwith other ideas, enables us to perceive this relation: this is so\nin the present case, for not only no combination is needed, but all\ncombinations are impossible if the truth of this principle be not\nsupposed.(21)\n\n\n\n\nCHAPTER XXII.\n\nTHE PRINCIPLE OF EVIDENCE.\n\n\n216. Among the principles which, by their pretensions to the title\nof fundamental, have most figured in the schools, is one called the\nprinciple of the Cartesians: \"whatever is contained in the clear and\ndistinct idea of any thing, may be affirmed of it with all certainty.\"\nWe have already seen Kant resuscitate this principle, although in other\nwords, equivocally taking it as synonymous with that of contradiction.\nUpon close examination we shall easily perceive that the formula of\nthe Cartesians, like that of Kant, only expresses the legitimacy of\nthe criterion of evidence. Both may be simplified to this: evidence\nis a criterion of truth; or, whatever is evident is true. As we shall\nhereafter use this transformation to distinguish ideas which we\nconsider very confused, we will show the reason of the equality of the\ntwo expressions.\n\n217. To say that any thing is contained in the clear and distinct idea\nof another thing, is the same as to say that there is evidence that a\npredicate belongs to a subject; the words have, and can have, no other\nmeaning. To be contained in a clear and distinct idea, is equivalent to\nseeing one thing in another by that intellectual light which we call\nevidence; therefore, this expression, \"whatever is contained in the\nclear and distinct idea of any thing,\" is exactly equivalent to this,\n\"whatever is evident.\"\n\nTo say, that any thing may be affirmed of another with all certainty,\nis the same as to say, \"this thing is true, and we may be perfectly\ncertain of it.\" It is the truth that is affirmed, and the truth only;\ntherefore, this expression, \"may be affirmed of it with all certainty,\"\nis exactly equivalent to this, \"it is true.\"\n\nThus the expression of the Cartesians may be transformed into this:\n\"Whatever is evident is true,\" or its equivalent, \"evidence is a sure\ncriterion of truth.\"\n\n218. \"A predicate that is opposed to a subject does not belong to it,\"\nis Kant's formula. The opposition here meant is that founded on ideas,\nwhen the predicate is necessarily excluded by intrinsic _opposition_\nfrom the idea of the subject. The expression, then, \"a predicate that\nis opposed to a subject,\" is equivalent to this: \"when the predicate is\nclearly seen excluded from the idea of the subject,\" which last is in\nits turn equivalent to this: \"the exclusion, or the opposition between\nthe subject and the predicate, is evident.\"\n\n\"Does not belong to it,\" means the same as, \"it is true that it does\nnot belong to it;\" and since these formulas have two values, one for\naffirmative, another for negative cases, if we say the predicate that\nis opposed to a subject does not belong to it, we may with equal reason\nsay, the predicate contained in the idea of a subject belongs to it;\nwherefore, Kant's formula exactly coincides with this: \"whatever is\nevident is true.\"\n\n219. This transformation gives us greater simplicity and generality;\nsimplicity by the very expression, and generality, because affirmative\nas well as negative cases are included. The words, \"whatever is\nevident,\" embrace affirmations as well as negations, for the inclusion\nof a predicate in a subject may be just as evident as their mutual\nopposition. Thus, we may see one thing contained in the idea of\nanother, just as we may see it excluded from that idea. Under all\nconceptions the formula, \"whatever is evident is true,\" is preferable;\nand if we would express it not as a principle, but as a rule to be\napplied, it may be converted into this: \"evidence is a sure criterion\nof truth.\"\n\n220. This transformation must not be supposed to be the only object\nof the preceding analysis; although in these matters clearness and\nprecision should be carried to the highest possible point, we should\nnevertheless have abstained from these considerations, had we only\nproposed to make an innovation, and one perhaps of little practical\nconsequence; the same thing is expressed in both formulas, and he who\ndoes not understand the first will not understand the second. Our\nprincipal object was not, however, to make this innovation, but to\nshow into what a confusion of ideas those fall who inquire whether the\nprinciple involving the legitimacy of the criterion of evidence ought,\nor ought not, to be considered as fundamental, and be preferred to the\nprinciple of contradiction, as also to that of Descartes.\n\n221. We begin by establishing a proposition which may seem a most\nstrange paradox, but is far from being so: _the principle of evidence\nis not evident_.\n\n_Demonstration._--This principle in its simplest form is this: the\nevident is true. This proposition, we say, is not evident. When is\na proposition evident? When we see the predicate in the idea of\nthe subject; and here this does not occur. _Evident_ is the same\nthing as _clearly seen_, as offered to the intellect in a most lucid\nmanner. _True_ is the same as conformity of the idea with the object.\nWe now ask, can you, however much you analyze this idea, \"seen with\nclearness,\" ever find this other, \"conformed to the object?\" No. This\nis an immense leap: we pass from subjectiveness to objectiveness; we\naffirm subjective to be the reflex of objective conditions; we go from\nthe idea to its object, and this transition is the most transcendental,\ndifficult, and obscure problem of philosophy. Let the reader now decide\nif we had not ground to assert that the proposition, \"the principle of\nevidence is not evident,\" was not a paradox.\n\n222. What, then, shall we say of this proposition: \"Whatever is evident\nis true?\" It is not an axiom, for the predicate is not contained in\nthe idea of the subject; it is not a demonstrable proposition, for all\ndemonstration rests on evident principles, and consists in deducing\nfrom them a consequence evidently connected with them; this cannot take\nplace unless we presuppose the legitimacy of evidence, that is to say,\nthat which is the object of the demonstration. At the commencement of\nthe argument, it might be asked, how do you know the principle on which\nyour argument is based? How do you know it to be true? By evidence.\nBut recollect you are proving that whatever is evident is true, and,\ntherefore, you beg the question. The truth of the laws of logic, to\nwhich every argument must conform, is known only by evidence; therefore\nif we do not suppose whatever is evident to be true, we cannot argue at\nall.\n\n223. We hold then that the principle of evidence can be based on no\nother principle, and that, consequently, it has the first mark of the\nfundamental principle. If it fails, all other principles,--that of\ncontradiction, known like the others only by evidence, included,--fail\nwith it; this is another mark of the fundamental principle. Let us see\nif it has the third, by aid of which, whoever denies the rest may be\nrefuted.\n\nRarely does any one deny the principle of contradiction, and admit that\nof evidence; yet, making this extravagant supposition, this principle\nalone would be of avail, because the question would be reduced to\nthis: does he admit the principles to be evident? If he does not, his\nintellect is unlike that of other men; if he does, the argument brought\nagainst him is conclusive. You admit that whatever is evident is true;\nsuch or such a principle is evident for you, therefore it is true. The\npremises are evident of themselves; the legitimacy of the consequence\nis also evident; and he must consequently admit it, since he admits the\ncriterion of evidence to be a general rule.\n\n224. Whence then the singularity we have noticed in this principle?\nIt is neither evident, nor demonstrable; it is necessary to all\nothers, and whoever denies them is refuted by it. Whence, then,\nsuch a singularity? It has a very simple cause; it is, that the\nprinciple of evidence expresses no objective truth, and therefore\nis not demonstrable: it is not a simple fact of consciousness, for\nit expresses the relation of the subject to the object, for which\nreason it cannot be limited to the purely subjective; it is a\nproposition known by a reflex act, and it expresses the primary law\nof all our objective cognitions. These are founded on evidence; this\nwe experience: but when the mind asks why we trust evidence, we can\nmake no other answer than that whatever is evident is true. What\nis the foundation of this proposition? Ordinarily it has none; we\nconform to it without ever thinking of it; but if we take the pains to\nreflect, we find three motives for assenting to it: the first is an\nirresistible instinct of nature; the second is the destruction of all\nour cognitions and the impossibility of thought, if we do not admit\nthe legitimacy of the criterion; the third is the perceiving that,\nadmitting this criterion, every thing is co-ordinated in the intellect,\nthat an ideal universe admirably harmonized, takes the place of chaos,\nand that we feel possessed of the means necessary to reason and to\nconstruct a scientific edifice in the real universe, the knowledge of\nwhich we have from experience.(22)\n\n\n\n\nCHAPTER XXIII.\n\nTHE CRITERION OF CONSCIOUSNESS.\n\n\n225. Having established the worth of the principles of consciousness,\nof evidence, and of contradiction, in relation to the dignity of\nfundamental, we will now examine the intrinsic value of the different\ncriteria. And here the doctrine of the preceding chapters, of which the\nfollowing are the development and complement, furnishes much light. We\nwill begin with consciousness, or the internal sense.\n\nThe testimony of consciousness includes all phenomena, either actively\nor passively, realized in our soul. It is by its nature purely\nsubjective; so that in itself considered, apart from the intellectual\ninstinct and the light of evidence, it testifies nothing with respect\nto objects. By it we know what we experience, not what is; we perceive\nthe phenomenon, not the reality; what authorizes us to say: such a\nthing appears to me; but not, such a thing is.\n\nThe transition from subject to object, from the idea representing to\nthe thing represented, from the impression to the cause impressing,\nbelongs to other criteria: consciousness is limited to the interior,\nor rather, to itself, which is nothing but an act of our soul.\n\n226. We must distinguish between direct and reflex consciousness: the\nformer accompanies every internal phenomenon; the latter does not: the\nformer is natural; the latter philosophical: the former abstracts the\nact of reason; the latter is one of these acts.\n\nDirect consciousness is the presence of the phenomenon to the mind,\nwhether that phenomenon be a sensation or an idea, an act or an\nimpression, in the intellectual or the moral order.\n\nThis distinction shows that direct consciousness accompanies every\nexercise, whether active or passive, of the faculties of our soul. It\nis a contradiction to say that these phenomena exist in the soul, and\nare not present to it.\n\nThese phenomena are not modifications like those which occur in\ninsensible things; we here treat of living modifications, so to speak,\nin a living being; in the idea of these modifications is contained\ntheir presence to the mind.\n\nIt is impossible for us to have a sensation without experiencing\nit; for whoever says he has a sensation, says that he experiences a\nsensation: this experience is its presence; an experienced sensation is\na present sensation.\n\nThought is by its essence, a representation that can neither exist nor\nbe conceived without presence; the name itself shows this, and the idea\nwhich we join with it confirms the meaning of the word. When we speak\nof representation, we understand that there is some real or imaginary\nobject, which mediately or immediately offers itself to the subject.\nThere is then presence in every representation, and consequently in\nevery thought.\n\nIf, from what is passive, like sensations and representations, we\npass to the active, that is, to the phenomena when the soul freely\nevolves its force in the intellectual or moral order, _in combining or\nwilling_, this presence is, if possible, yet more evident. The being\nthat thus acts, does not obey a natural impulse, but motives which it\nproposes to itself, and to which it may or may not attend. To make\nintellectual combinations and to exercise acts of the will, without\neither being present to the soul, are contradictory assertions.\n\n227. Reflex consciousness, called by the French _aperception_, from\nthe verb _s'apercevoir_, and denoting perception of the perception,\nis the act whereby the mind explicitly knows any phenomenon which is\nrealized in it. Thus, I hear a noise: the simple sensation, present\nto and affecting my mind, constitutes what we have called direct\nconsciousness; but if besides hearing, I also _aperceive_, to use a\nGallicism, that I hear; then I not only hear, but also think that I\nhear: this we call reflex consciousness.\n\n228. It is clear from this example, that direct and reflex\nconsciousness are not only distinct but separable. I may hear without\nthinking that I hear; and this is very often the case.\n\n229. Most men have little reflex consciousness, and the greatest\nintellectual force operates directly. This ideological fact is\nconnected with moral truths of the utmost importance. The human mind\nwas not born to contemplate itself, to think that it thinks: its\naffections were not given as an object of reflection, but as impulses\nwhich elevate it to what it is called to: the principal object of its\nintelligence and love is, in this life as in the other, the infinite\nbeing. The worship of itself is an aberration of pride; its punishment\nis darkness.\n\n230. All great scientific discoveries lie in the objective, not in\nthe subjective order. The exact sciences, natural as well as moral,\nhave emanated not from reflexion of the subject upon itself, but from\nknowledge of objects and their relations. Even the metaphysical\nsciences, in all that is most solid in them, ontology, cosmology,\nand theology, are purely objective: ideology and psychology which\nconsider the subject, are full of the obscurity inherent in all that is\nsubjective; ideology scarcely does more than merely observe internal\nphenomena,--an observation, we may remark, generally very defective,\npoorly made, and bewildered with vain cavils; and what has psychology\nitself, truly demonstrated, except the simplicity of the soul, the\nnecessary consequence of the unity of consciousness? In all else it\nresembles ideology, and to a certain point, is confounded with it; it\nobserves phenomena, and afterwards defines and classifies them better\nor worse, but fails to explain their mysterious nature.\n\n231. Consciousness is the foundation of the other criteria, not as\na proposition which serves as their basis, but as a fact which is a\nnecessary condition of them all.\n\n232. Consciousness tells us that we see the idea of one thing contained\nin the idea of another: thus far there is nothing but appearance;\nthe formula, to express its testimony would be: _it appears to me_;\nwhich denotes a purely subjective phenomenon. But this phenomenon is\naccompanied by an intellectual instinct, an irresistible impulse of\nnature, which makes us assent to the truth of the relation, not only\nso far as it is in us, but as it is formed without us, in the purely\nobjective order, whether in the sphere of reality or possibility.\nThus it is explained how evidence is founded on consciousness, not as\nidentified with it, but as resting upon it as a fact from which it\ncannot be abstracted, and as also containing the intellectual instinct\nwhich makes us believe whatever is evident to be true.\n\n233. Sensation, in itself considered, is a fact of pure consciousness,\nsince it is immanent in us: so far is it from being an act whereby\nthe mind passes beyond itself, translates itself to the object, that\nit ought rather to be regarded as a passion than an action, and this\naccords with the common mode of speaking, which ascribes it to a\npassive rather than to an active faculty. Nevertheless on this mere\nfact of consciousness is in some sense founded what is called the\ntestimony of the senses, and consequently all knowledge of the external\nworld, its properties, and relations.\n\nIn the sensation whereby we see the sun, there are two things: the\nsensation itself, that is, the representation which I experience\nin myself, and which I call sight; and the correspondence of this\nsensation to the external object which I call the sun. Evidently,\nthese are two very distinct things, and yet we always unite them.\nConsciousness is certainly the first basis of the formation of\njudgment; but alone it does not suffice, for it only testifies that\nthe sensation is, not what it is. How is the judgment completed? By\nmeans of a natural instinct which makes us render sensations objective,\nthat is, makes us believe in an external object corresponding to\nthe internal phenomena. Thus the testimony of the senses is in some\nmanner founded on consciousness; it does not, however, proceed from\nconsciousness alone, but requires the natural instinct, by means of\nwhich we form our judgments in perfect security.\n\n234. We must here remark that evidence has nothing to do with the\ntestimony of the senses, even in their intellectual part, wherein we\njudge that an external object corresponds to the sensation. The idea\nof the existence or possibility of an external object does not enter\ninto the idea of the sensation as purely subjective, and without\nthis indispensable condition there can be no evidence. Not only is\nthis clear of itself, but it is confirmed by daily experience. We\ncontinually have the representation of the external subjectively\nconsidered, as a pure phenomenon in our soul, although no real object\ncorresponds to it; more or less clear when we are awake, but most\nvivid, even so as to produce a perfect illusion, when we are asleep.\n\n235. With this exposition, the value and extent of consciousness may be\nexactly determined: this we shall see in the following propositions, in\nall of which, we would observe, we treat only of direct consciousness.\n\n\nFIRST PROPOSITION.\n\nThe testimony of consciousness extends to all the phenomena that are\nrealized in our soul, regarded as an intellectual and sensitive being.\n\n\nSECOND PROPOSITION.\n\n236. If there exist in our soul phenomena of a different order, that\nis to say, if it may in some sense be modified in non-representative\nfaculties, the testimony of consciousness does not extend to such\nphenomena.\n\nWe do not advance this proposition without a solid reason. It is\nprobable, and even very probable, that our soul has active faculties,\nof the exercise of which it is not conscious; otherwise how explain\nthe mysteries of organic life? The soul is united to the body, and is\nfor it the vital principle, the separation from which causes death,\nmanifested in complete disorganization and decomposition. This activity\nis exercised without consciousness, either of the mode or of the fact\nof its existence.\n\nIt may be said that there is here a series of those confused\nperceptions of which Leibnitz speaks in his _Monadologie_; or that\nthese perceptions are so slight, so wan, as to leave no trace in the\nmemory, nor be an object of reflection: but these are only conjectures.\nIt is hard to persuade one's self that the f\u0153tus in the mother's womb\nhas any consciousness of the activity exercised for the development of\nits organization: it is also hard to persuade one's self that even\nin adults there is any consciousness of that same activity producing\ncirculation of the blood, nutrition, and other phenomena which\nconstitute life. If these phenomena are produced, as they certainly\nare, by the soul, there is in it, an exercise of activity of which it\neither has no consciousness, or one so weak and confused that it is as\nif it were not.\n\n\nTHIRD PROPOSITION.\n\n237. The testimony of consciousness, in itself considered, is so\nlimited to the purely internal, that it is _of itself_ worth nothing in\nthe external order, either for the criterion of evidence or that of the\nsenses.\n\n\nFOURTH PROPOSITION.\n\nThe testimony of consciousness is the foundation of the other criteria,\ninasmuch as it is a fact which they all require, and without which they\nare impossible.\n\n\nFIFTH PROPOSITION.\n\n238. From the combination of consciousness with intellectual instinct\narise all the other criteria.(23)\n\n\n\n\nCHAPTER XXIV.\n\nTHE CRITERION OF EVIDENCE.\n\n\n239. There are two species of evidence, mediate and immediate. We\ncall immediate evidence that which requires only understanding of the\nterms; and mediate evidence that which requires reasoning. That the\nwhole is greater than its part is evident by immediate evidence;\nthat the square of the hypothenuse is equal to the sum of the squares\nof the other two sides, is known by mediate evidence, that is, by\ndemonstrative reasoning.\n\n240. We have said that one of the distinctive characteristics of\nevidence is the necessity and universality of its object. This is a\ncharacteristic as well of mediate as of immediate evidence.\n\nBesides this characteristic there is another, called with more reason\nessential, notwithstanding some doubt as to whether it extends to\nmediate evidence or not; it is that the idea of the predicate is\nfound contained in that of the subject. This is the most complete\nessential notion of the criterion of immediate evidence, by which it is\ndistinguished from the criteria of consciousness and common sense.\n\nWe have said there is some doubt as to this characteristic extending\nto mediate evidence; by this we mean that also in mediate evidence\nthe idea of the predicate may be contained in that of the subject. In\nthis it is not our intention to ignore the difference between theorems\nand axioms, but to call the reader's attention to a doctrine which we\npropose to develop, while treating of mediate evidence. In the present\nchapter we shall only treat of evidence in general, or of immediate\nevidence alone.\n\n241. Evidence involves relation, for it implies comparison. When\nthe understanding does not compare, it has no evidence, but only a\nperception, which is a pure fact of consciousness; and this evidence\ndoes not refer to perception alone, but always supposes or produces a\njudgment.\n\nWe find two things in every act where there is evidence: the pure\nintuition of the idea, and the decomposition of this idea into various\nconceptions accompanied with the perception of their mutual relations.\nThis we will explain by an example from geometry. The triangle has\nthree sides: this is an evident proposition, for in the very idea of\ntriangle, we find the three sides; and in conceiving the triangle, we\nin some sense conceive the three sides. Had we limited ourselves to\nthe contemplation of the simple idea of triangle, we should have had\nintuition of the idea, but not evidence, which begins only when we\nfind, in decomposing the conception of triangle, and considering in it\nthe idea of figure in general, of side, and of the number three, these\nall contained in the primitive conception. Evidence consists in the\nclear conception of this.\n\nSo true is this that the very nature of things makes common language\nphilosophical. We do not say, an idea is evident, but a judgment is: no\none calls a term evident, but a proposition only. And why? Because the\nterm simply expresses the idea without any relation, or decomposition\ninto its partial conceptions; whereas the proposition expresses the\njudgment, that is, affirms or denies that one conception is contained\nin another, which, in the present matter, supposes decomposition of the\nentire conception.\n\n242. Immediate evidence is the perception of identity between various\nconceptions, separated by the analytical power of the intellect.\nThus identity combined in a certain way with diversity is not a\ncontradiction, as it might at first sight seem, but something very\nnatural, if we observe one of the most constant facts of our intellect,\nthe faculty of analyzing the most simple conceptions, and of seeing\nrelations between identical things.\n\nWhat are all axioms? What are all propositions _per se not\u00e6_? Nothing\nbut expressions, in which it is affirmed that a predicate belongs to\nthe essence of the subject, or is contained in its idea. The mere\nconception of the subject includes the predicate: the term which\ndenotes the first also denotes the second; yet the intellect, with a\nmysterious power of analysis, distinguishes between identical things,\nand then compares them in order to make them again identical. Whoever\nsays triangle, expresses a figure composed of three sides and three\nangles; but the intellect may take this idea and consider in it the\nideas of the number three, side, and angle, and compare them with the\nprimitive conception. In this distinction there is no deception; there\nis only the exercise of the faculty, which regards the thing under\ndifferent aspects, in order to arrive at the intuition and affirmation\nof the identity of the very things it had before distinguished.\n\n243. Evidence is a sort of calculation of the intellect, whereby it\nfinds in the conception analyzed whatever was placed in the principle\nor was contained in it. Hence the necessity and universality of the\nobject of evidence, inasmuch as, and in the manner, in which it is\nexpressed by the idea. To this there are no exceptions. Either a\npredicate is or is not placed in a primitive principle: if it is, it is\nthere, according to the principle of contradiction. Either it was or\nwas not excluded from the conception; if the conception itself excludes\nor denies it, this it does by virtue of the principle of contradiction.\n\nThus the more fundamental of the two characteristics of evidence given\nabove is, that the idea of the predicate is contained in the idea of\nthe subject. Hence the necessity and universality; since, in verifying\nthis condition, it is impossible for the predicate not to belong\n_necessarily to all the subjects_.\n\n244. Thus far we have encountered no difficulty, because we have\ntreated only of evidence subjectively considered, that is, as relating\nto pure conceptions; but the intellect does not stop with the\nconception, but extends to the object, and says not only that it sees\nthe thing, but that the thing is as it sees it. Thus the principle of\ncontradiction, considered in the purely subjective order, means that\nthe conception of being is opposed to that of not-being, which destroys\nit, just as the conception of being destroys that of not-being; it\nmeans, that in endeavoring to conceive jointly these two things, and\nto make them co-exist, a sort of struggle of thoughts, reciprocally\nannihilating each other, takes place in the depths of our soul,--a\nstruggle which the understanding is condemned to witness without hope\nof establishing peace between the combatants. If we confine ourselves\nto this phenomenon, no objection can be made. We experience it, and\nthere is no further question about it; but in announcing the principle,\nwe would announce something more than the incompatibility of the\nconceptions; we would transfer this incompatibility to the things\nthemselves, and assert that not only our own conceptions, but also\nall real and possible beings are subjected to this law. Whatever be\nthe object of which we treat, whatever the conditions under which we\nsuppose it existent or possible, we say that while it is, it cannot\nnot be; and while it is not it cannot be. We affirm, then, the law of\ncontradiction, not only for our own conceptions, but also for things\nthemselves; the intellect applies to every thing the law which it finds\nnecessary to itself.\n\nBy what right? An incontestible right, for it is the law of necessity.\nWith what reason? With none, for we are now at the foundation of\nreason; this is the _ne plus ultra_ of the human understanding;\nphilosophy can go no farther. Let us not, however, be thought to\nabandon the field to skeptics, or to entrench ourselves in necessity,\ncontented with pointing out a fact of our nature. The question is\nsusceptible of different solutions, which may not, indeed, go beyond\nthe _ne plus ultra_ of our mind, but which yet leaves the cause of\nskepticism in great straits.\n\n245. To ask why the criterion of evidence is legitimate, is to ask why\nthis proposition is true: \"whatever is evident is true;\" it is to raise\nthe question of the objectiveness of ideas. The fundamental difference\nbetween dogmatists and skeptics, is not that the latter deny the facts\nof consciousness,--the most refined skepticism has not come to this,\nand both agree in recognizing the purely subjective appearance of\nphenomena; but it is that dogmatists found science on consciousness,\nand skeptics maintain that this is an illegitimate transition, and that\nwe must despair of science, and confine ourselves to mere consciousness.\n\nAccording to this doctrine, ideas are empty forms of the understanding,\nmean nothing, and can lead to nothing; although they entertain the\nunderstanding, and offer to it an immense field for combinations, the\nworld they present to it is purely illusory, and can serve for nothing\nin the real order. In contemplating these entirely empty forms, the\nintellect is the sport of fantastic visions, from the union of which\nresults the spectacle which seems now to belong to reality, and now to\npossibility; either it is a mere nonentity, or something, and if so, it\ncan never make us sure of the reality it possesses.\n\n246. It is difficult to fight skepticism when it takes this ground:\nsituated beyond the domains of reason, the decisions of reason cannot\nreach it. It will appeal from them all, for it begins by denying the\ncompetency of the judge. But as these skeptics admit consciousness, it\nis right that they should defend it against whoever attempts to deprive\nthem of it. We believe that if the objectiveness of ideas be denied,\nnot only all science, but also all consciousness is annihilated;\nand here skeptics are guilty of an inconsequence; for, while they\ndeny the objectiveness of some ideas, they admit that of others. No\nconsciousness, properly so called, can exist, if this objectiveness be\nabsolutely destroyed. We beg the reader to follow us in a brief, but\nsevere analysis of the facts of consciousness, in their relations with\nthe objectiveness of ideas.(24)\n\n\n\n\nCHAPTER XXV.\n\nTHE OBJECTIVE VALUE OF IDEAS.\n\n\n247. The transition from subject to object, from subjective appearance\nto objective reality, is a problem which vexes fundamental philosophy.\nConsciousness will not permit us to doubt that certain things _appear_\nto us in such a manner; but _are_ they in reality what they appear to\nus? How are we to know this? What shall assure us of this conformity of\nthe idea with the object?\n\nThe question does not relate solely to sensations; it also extends to\npurely intellectual ideas, even to those inundated with that internal\nlight which we call evidence. \"What I evidently see in the idea of a\nthing, is as I see it,\" philosophers have said, and all mankind with\nthem. No one doubts what is presented to him as evidently true. But how\nprove that evidence is a legitimate criterion of truth?\n\n248. \"God is truthful,\" says Descartes, \"and could not have deceived\nus; He could not have taken pleasure in making us the victims of\nperpetual illusions.\" All this is true. But the skeptic will ask how\nwe know that God is truthful, or even that he exists. If we found\nthe veracity of God on the idea of an infinitely perfect being, as\nDescartes does, there is still the same difficulty with respect\nto the correspondence of the idea with the object. If we draw the\ndemonstration of the veracity and existence of God from the ideas of\nnecessary and contingent beings, of effect and cause, of order and\nintelligence, we again meet the same obstacle, and are still unable to\npass from the idea to the object.\n\nNo matter how much we cavil, we shall never get out of this circle,\nwe shall always return to the same point. The mind cannot think out\nof itself; what it knows, it knows by means of its ideas; if these\ndeceive, it has nothing left to set it right. All rectification, all\nproof must employ these ideas, and these, in their turn, require new\nproof and rectification.\n\n249. Many books of philosophy exaggerate the illusions of the senses,\nand the difficulty of assuring ourselves of the sensible reality, when\nthey solve this question: \"I perceive it to be so; but is it as I\nperceive?\" These same books immediately afterwards speak of the order\nof ideas with security equal to their mistrust in the sensible order.\nThis does not seem very logical, for phenomena relating to the senses,\nmay be examined by the light of reason, and it may be seen how far they\nagree with it: but what touch-stone have we for the phenomena of reason\nitself? If there be difficulty in the sensible, there is likewise in\nthe intellectual, and the more serious, since it affects the very basis\nof all cognitions, even those which relate to sensations.\n\nIf we doubt the existence of the external world which the senses\npresent to us, we may appeal to the connection of the sensations with\ncauses not in us; and so deduce by demonstration the relations of the\nappearances with the reality: but this requires the ideas of cause\nand effect; we must have some truth, some general principles, as for\nexample, that nothing can produce itself, and others similar, without\nwhich we cannot take one step.\n\n250. We do not believe any satisfactory reason can be given for the\nveracity of the criterion of evidence, although it is impossible not\nto yield to it. The connection, therefore, of evidence with reality,\nand consequently, the transition from the idea to the object, are\nprimitive facts of our nature, a necessary law of our understanding,\nthe foundation of all that it contains,--a foundation which in its turn\nrests, and can rest only on God, the Creator of our soul.\n\n251. We must observe the contradiction into which those philosophers\nfall who say: I cannot doubt what is subjective, what affects myself,\nwhat I feel within myself; but I have no right to go out of myself,\nand affirm that what I think is in reality as I think. Do you know\nthat you feel, that you think, that you have within you such or such\nan appearance? Can you prove it? Evidently you cannot. You yield to a\nfact, to an internal necessity which forces you to _believe_ that you\nthink, that you feel, or that such a thing appears to you; but then\nthere is equal necessity in the connection of the object with the idea,\nan equal necessity forces you to _believe_ that what _appears_ to you\nto be in such or such a condition is as it appears. Neither case admits\nof demonstration; in both there is an indeclinable necessity: where,\nthen, is philosophy, when it is attempted to establish so great a\ndifference between things which admit of none?\n\nFichte says: \"It is impossible to explain in a precise manner how a\nphilosopher can get beyond the _me_:\"[21] and we may with equal reason\nsay, that we cannot conceive how he has been able to raise a system\nupon the _me_. To what does he appeal? To a fact of consciousness, that\nis, to a necessity. And is not the assent to evidence, the certainty\nto which the reality apparently corresponds, also a necessity? On what\ndoes Fichte found his system of the _me_ and the _not-me_? We have\nonly to read his works to see that he only founds it on considerations\nwhich suppose a value in certain ideas, a truth in certain judgments.\nOtherwise it is impossible to speak or to think: and this even he\nhimself admits when, in commencing his investigations on the principle\nof our cognitions, he utters the words we have just quoted. He then\nconfesses that we cannot take one step without trusting all the laws\nof general logic, which are _not always demonstrated, but are supposed\ntacitly admitted_. And what are these laws, without objective truths?\nWhat are they without the value of ideas, without correspondence with\nobjects? Fichte says rightly, it is a circle; but he can no more get\nout of it than other philosophers.\n\n[21] _Wissenschaftslehre._ Erster Theil. \u00a7 3.\n\n252. To take from ideas their objective value, to reduce them to mere\nsubjective phenomena, to resist that internal necessity which obliges\nus to admit the correspondence of the soul to objects, is to destroy\nthe very consciousness of the soul. This must have been seen, and this\nwe think we can most evidently demonstrate.\n\n253. We have consciousness of ourselves. We now abstract what we\nfeel, what we are; but we know that we feel and that we are. This\nexperience is so clear, so vivid, that we cannot resist the truth\nof what it attests to us. But this _me_ is not only the _me_ of the\npresent instant, it is also the _me_ of yesterday, and of all prior\ntime of which we have consciousness. We are the same that we were\nyesterday, the being in which this succession is verified, to which\nthis variety of appearances is presented. The consciousness of the\n_me_ then includes the identity of a being at distinct times, in\nvarious situations, with different ideas, and diverse affections,--the\nidentity of a being which _endures_ and is the same throughout the\nchanges succeeding in it. If this duration of identity be broken,\nif I be not sure that I am the same _me_ that I was previously, the\nconsciousness of the _me_ is destroyed. There would exist a series\nof unconnected facts, isolated acts of consciousness, but not that\nintimate consciousness I now experience. This cannot be doubted; every\nman feels it in himself; it admits neither discussion nor proof in\nany one, it requires them of no one. The moment this consciousness of\nidentity fails, we are in our own eyes annihilated; whatever we may be\nin reality, for ourselves we are nothing. What is the consciousness\nof a being, formed from a series of acts of consciousness, without\nconnection or mutual relation? It is a being revealed successively to\nitself, yet not as itself, but as a new being, a being which is born\nand dies, and dies and is born before its eyes, without its knowing\nthat what is born is what died, or that what died is what was born:\nit is a light which burns and is extinguished, and again burns and is\nagain extinguished, without its knowing that it is the same light.\n\n254. This consciousness is completely destroyed by those who deny the\nconnection between the idea and object.\n\n_Demonstration._--In the instant A, I have no other subjective\npresence of my acts than the very act I am at that moment performing:\nI cannot therefore be certain that I have had any previously, if\nthey be not represented in the present idea; there is therefore a\nconnection between this idea and its object. Attending then simply\nto the phenomena of consciousness, to the mere consciousness of the\nsubject, we find that we do, by an irresistible necessity, attribute an\nobjective value to ideas, an objective truth to judgments.\n\n255. Without this objective truth, all certain recollection even of\ninternal phenomena, and by a legitimate consequence, all reasoning,\njudgment, and thought, are impossible.\n\nRecollection is of past acts. When we recollect them, they already are\nnot; for, if they were, we should not have recollection, but present\nconsciousness of them. Even when in the act of recollecting them we\nhave other similar acts, these are not the same, for something of past\ntime always enters into the idea of recollection. Therefore, we can\nhave no certainty of them, but by their connection with the present\nact, their correspondence with the idea presenting them to us.\n\n256. We have said that if, in internal phenomena, the certainty of\nthe objective truth fail, all reasoning is impossible. In fact, all\nreasoning supposes a _succession_ of acts; when one of them exists\nin the mind, the other does not exist; therefore, continued minute\nrecollections are required, lest the chain be broken; and thus, without\nthis chain, there is no reasoning; without recollection this chain\nis not; without objective truth, there is no certain recollection;\ntherefore, without objective truth there is no reasoning.\n\n257. All judgments also seem impossible. Judgments are of two classes:\nsome require demonstration, others do not. Those that require\ndemonstration would be impossible, for there can be no demonstration\nwithout reasoning, and reasoning in this case is impossible. As to\nthose that do not need demonstration, because they shine with immediate\nevidence; all of them, not relating to the present act of the soul, in\nthe very instant when the judgment is pronounced, would be impossible.\nTherefore, there could be no judgment but that of the present act,\nthat is, the consciousness of the present without relation to the\npreceding. But it is remarkable that even with respect to the acts of\nconsciousness, this judgment would be little less than impossible; for\nwhen we form a judgment upon an act of consciousness, this we do not\nby this act, but by a reflex act. This reflection requires succession,\nand succession cannot be known with certainty if there be no objective\ntruth.\n\nIt is even very doubtful if the judgments of immediate evidence\nwould be possible. They suppose, as we explained in the preceding\nchapter, relation of the partial conceptions into which the whole is\ndecomposed; and how can there be decomposition without succession? If\nthere is succession, there is recollection; if there is recollection,\nthere is no immediate presence of the thing recollected.\n\n258. Such consequences are astounding, but they are inevitable. If we\ndestroy objective truth, all rational thought disappears. Such thought\nincludes a certain continuity of acts corresponding to different\ninstants; if this continuity be broken, the human thought ceases to\nbe what it is, ceases to exist as _reason_. It is a series of acts\nwhich have no sort of connection, and which lead to nothing. In such a\ncase, all expression, all words fail; nothing has a fixed value; every\nthing is ingulfed in obscurity. Thus it is in the intellectual and\nmoral order as in the material; and man has not even the comfort of\npossessing himself; he vanishes from himself like an empty shadow.\n\n259. Sensations may also exist as an unconnected series, but there\nwill be no certain recollection of them, since the objective truth\nis wanting; past sensations exist only as past, and, consequently,\nas simple objects. All intellectual reflection upon them will be\nimpossible, for reflection is not sensation; sensation is an object of\nreflection, not reflection itself. Thus, the ignorant man has the same\nsensation as the philosopher, but not the same reflection upon it. A\nthousand times we have sensations without reflecting that we have them.\nSensible is very different from intellectual consciousness; the former\nis the simple presence of the sensation, or the sensation itself; the\nlatter is the act of the intellect occupied with the sensation.\n\n260. This distinction is also found in all purely intellectual acts:\nthe reflection upon the act is not the act itself. One is the object of\nthe other; they are not identical, and are often found separated. If,\nthen, there were no objective truth, reflection would be impossible.\n\n261. It is likewise difficult to comprehend how any act of the\nconsciousness of the _me_, even as present, can be possible. We have\nalready seen the _me_ disappear when the series of recollections is\nbroken, and without objective truth it is not even possible to conceive\nthe _me_ for one instant. The _me_ thinking knows the _me_ thought only\nas object. Whether it _perceive_ or _know_ it, to account to itself\nfor itself, it must reflect upon itself, and take itself for its own\nobject; and there being no objective truth, it is inconceivable how an\nobject can have any value.\n\nIt follows from this, that they who oppose objectiveness, attack a\nfundamental law of our mind, destroy thought, even consciousness, and\nevery thing subjective which could serve as its basis.\n\n262. In their arguments against objective certainty, its opponents are\naccustomed to depend upon the errors into which it leads us. The madman\nbelieves he sees objects, which do not exist; the lunatic believes\nfirmly in his disconnected thoughts; and why may not that which\ndeceives us in one instance, also deceive us in another, and all cases?\nCan that be a certain criterion which sometimes fails? Why not stop\nwith the purely subjective? The madman, the lunatic, are deceived in\nthe object, not in the subject; although what they think is not true,\nit is still very true and certain that they think it.\n\nThis is a specious objection; but it does not remove the difficulties\nunder which the system, in favor of which it is adduced, labors; and\nit may, on the other hand, be solved in so far as it tends to weaken\nobjective truth.\n\nThe madman, the lunatic, have also recollections of things that\nnever existed. These recollections do not relate solely to external,\nbut likewise to their internal acts. The madman who calls himself\nking, acts in accordance with his thought, with what he felt when\ncrowned, when dethroned; and yet, these intellectual phenomena never\nexisted. And, however this may be, he himself may have produced these\nrecollections. We hold, then, that the criterion with respect to memory\nis wrong in this case, and can be of avail in no case. Therefore, even,\nalthough we had not shown that without objective truth there is no\nrecollection even of the internal, the arguments of our adversaries\nwould have sufficed. This objection, if it prove any thing, confirms\nall that we have advanced in demonstrating that without objectiveness\nthere is no consciousness properly so called, and this even our\nopponents do not admit.\n\n263. Moreover, we at once see what weight an argument based on\ncraziness should have at the tribunal of reason. It all, at the most,\nonly proves the weakness of our nature, that in some unfortunate\nindividuals the established order of humanity is reversed; that the\nrule of truth, as it exists in so weak a creature, admits of some\nexceptions; but these exceptions are known, for their characters are\nmarked. The exception does not destroy, it only confirms the rule.(25)\n\n\n\n\nCHAPTER XXVI.\n\nCAN ALL COGNITIONS BE REDUCED TO THE PERCEPTION OF IDENTITY?\n\n\n264. Immediate evidence has for its objects those truths which the\nintellect sees with all clearness, and to which it assents without the\nintervention of any _medium_, as its name denotes. These truths are\nenunciated in propositions called _per se not\u00e6_, first principles, or\naxioms, in which it is sufficient to know the meaning of the terms\nto see that the predicate is contained in the idea of the subject.\nPropositions of this class are few in all sciences; the greater\npart of our cognitions are the fruit of reasoning which proceeds\nby mediate evidence. In geometry the number of truths that do not\nrequire demonstration, but only explanation, is very limited. The\nbody of geometrical science, with its present colossal dimensions,\nhas proceeded from reasoning: even in the most comprehensive works\nthe axioms occupy but a few pages; the rest is composed of theorems,\npropositions not of themselves evident, but requiring demonstration.\nThe same is true of all other sciences.\n\n265. Since in axioms the intellect perceives the identity of the\nsubject with the predicate, intuitively seeing that the idea of the\nlatter is contained in that of the former, there arises a very grave\nphilosophical question which may prove very difficult, and cause\nstrange controversies, if care be not taken to place it upon its true\nground. Is every human cognition reduced to the simple perception of\nidentity? and can its general formula be this: A is A, or: a thing is\nitself? Some philosophers of note maintain the affirmative; others\nthe contrary. We think there is a confusion of ideas not so much as\nto the question itself as to its state. Clear and exact ideas of what\njudgment is, and of the relation affirmed or denied by it, will greatly\nfacilitate the accurate solution of the question.\n\n266. There is in every judgment perception of identity or non-identity,\naccordingly as it is affirmative or negative. The verb _is_ does not\nexpress the union, but the identity of the predicate with the subject;\nand when accompanied with the negation _not_, it simply expresses\nnon-identity, abstracting union or separation. This is so true and\nso exact, that in things really united an affirmative judgment is\nimpossible, because they have no identity. We must, then, in such\ncases, if we would be enabled to make an affirmation, express the\npredicate in the concrete, that is, in some sense involving the idea\nof the subject itself in it; for the same property affirmed in the\nconcrete cannot be in the abstract, but must rather be denied. Thus\nwe may say, man is rational; but not, man is rationality: a body is\nextended; but not, a body is extension: paper is white; but not, paper\nis whiteness. Why is this? Is it that rationality is not in man,\nextension is not united to body, nor whiteness to paper? Certainly\nnot; but if rationality be in man, extension in body, and whiteness in\npaper, we have only not to perceive identity between the predicates and\nsubjects, to render affirmation impossible; on the contrary, despite\nthe union, we have negation: thus we may say, man is not rationality; a\nbody is not extension; paper is not whiteness.\n\nWe have said that, in order to save the expression of identity, we used\nthe concrete instead of the abstract term, and involved in the former\nthe idea of the subject. It cannot be said that paper is whiteness, but\nit may be said that paper is white; for this last proposition means\nthat paper is a white thing; that is, we make the general idea of a\n_thing_, or the idea of a modifiable subject, enter into the predicate\nwhile in the concrete; and this subject is identical with the paper\nmodified by whiteness.\n\n267. Thus it is easy to see, that the expression, _union of the\npredicate with the subject_, is, at the best, inexact. Every\naffirmative proposition expresses the identity of the predicate with\nthe subject. Use authorizes these modes of speaking, which still\nproduce some confusion when we endeavor perfectly to understand these\nmatters. And it must be observed, that ordinary language here, as often\nelsewhere, is admirably exact and appropriate. Nobody says, paper\nis whiteness, but, paper is white. It is only when we would greatly\nheighten the degree, to which a subject possesses a quality, that\nwe express it in the abstract, and then we join with it the pronoun\n_itself_. Thus, speaking hyperbolically, we say a thing is beauty\nitself, whiteness itself, goodness itself.\n\n268. Even what in mathematics is called equality, also means identity.\nThus in this class of judgments, besides what we have observed of\ngeneral in them all, to wit: the identity saved by expressing the\npredicate in the concrete, the very relation of equality denotes\nidentity. This needs explanation.\n\nWhoever says 6 + 3 = 9, expresses the same as he who says 6 + 3 are\nidentical with 9. Clearly in the affirmation of equality, no attention\nis paid to the form in which the quantities are expressed, but to the\nquantities themselves alone; otherwise we should be unable to affirm\nnot only identity, but also equality; for it is evident that 6 + 3,\nas to their form, neither written, spoken, nor thought, are identical\nwith, or equal to, 9. The equality is in the values expressed, and\nthese are not only equal but identical; 6 + 3 are the same as 9. The\nwhole is not distinguished from its united part; 9 is the whole, 6 + 3\nits united parts.\n\nThe different manner of conceiving 6 + 3 and 9 does not exclude the\nidentity. The difference is in the intellectual form, and occurs not\nonly here but also in the perceptions of the simplest things; there\nis nothing which we do not conceive under different aspects, and\nwhose conception we may not decompose in various ways; but we do not\ntherefore say that the thing ceases to be simple and identical with\nitself.\n\nWhat we have said of an arithmetical equation may be extended to\nalgebraical and geometrical equations. If we have an equation whereof\nthe first member is very simple, as Z, and the second very complicated,\nas the development of a series, we cannot say that the first expression\nis equal to the second; the equality is not in the expression but in\nthe thing expressed, in the value designated by the letters; in this\nsense it is true, in the former it is evidently false.\n\nTwo circumferences having the same radius are equal. Here we seem to\ntreat solely of equality, since there are two distinct objects, the\ntwo circumferences, which may be traced on paper or represented in the\nimagination; yet not even in this case is the distinction true, it is\nonly apparent, for here, as in algebraical and arithmetical equations,\nthere is distinction and even diversity in form with identity at\nbottom. The principal argument, on which the distinction is founded,\nmay be combatted by observing that the circumferences which may be\ntraced or represented, are only forms of the idea, not the idea itself.\nWhether traced or represented they have a determinate size and a\ncertain position on the planes seen or imagined; in the idea, and in\nthe proposition containing it, there is nothing of this; we abstract\nall size, all position, and speak in a general and absolute sense.\nTrue, the representations may be infinite either externally or in the\nimagination; but this, so far from proving them identical, shows their\ndiversity, since the idea is one and they are infinite; the idea is\nconstant, they are variable; the idea is independent of them, they\nare dependent on the idea, and have the character and denomination of\ncircumferences, inasmuch as they approach it by representing what it\ncontains.\n\nWhat, then, is expressed in the proposition: two circumferences, having\nthe same radius, are equal? The fundamental idea is, that the value\nof the circumference depends upon the radius, and the proposition\nhere enunciated is simply an application of this property to the\ncase of the equality of radii. The circumferences, then, conceived\nby us as distinct, are only examples which we inwardly consider in\norder to render the truth of the application apparent; but in what\nis purely intellectual, we find only the decomposition of the idea\nof circumference, or its relation to the radius applied to the case\nof equality. Then there are not two circumferences in the purely\nideal order, but one only, whose properties we know under different\nconceptions, and express in various ways.\n\nIf in all judgments there is affirmation of identity, or non-identity,\nand all our cognitions either begin or end in a judgment, it would seem\nthat they all ought to be reduced to a simple perception of identity.\nThe general formula of our cognitions will then be: _A is A_, or, _a\nthing is itself_. This result strikes one as an extravagant paradox,\nand is so, or not, according to the sense in which it is understood;\nbut if rightly explained, it may be admitted as a truth, and a very\nsimple one. From what has been said in the preceding paragraphs, the\nmeaning of this opinion may be discerned: but the importance of the\npresent matter requires still further explanation.\n\n\n\n\nCHAPTER XXVII.\n\nCONTINUATION OF THE SAME SUBJECT.\n\n\n269. It is even ridiculous to say that the cognitions of the sublimest\nphilosophers may be reduced to this equation: A is A. This, absolutely\nspeaking, is not only false, but contrary to common sense; but it is\nneither contrary to common sense nor false to say that all cognitions\nof mathematicians are perceptions of identity, which, presented under\ndifferent conceptions, undergoes infinite variations of form, and so\nfecundates the intellect and constitutes science. For the sake of\ngreater clearness we will take an example, and follow one idea through\nall its transformations.\n\n270. The equation circle = circle (1) is very true, but not very\nlucid, since it serves no purpose, because there is identity not only\nof ideas but likewise of conceptions and expression. To have a true\nprogress in science we must not only change the expression, but also\nvary in some way the conception under which the identical thing is\npresented. Thus, if we abbreviate the above equation in this form: C\n= circle (2), we make no progress, unless with respect to the purely\nmaterial expression. The only possible advantage of this is to assist\nthe memory, as instead of expressing the circle by a word, we express\nit by its initial letter, C. Why is this? Because the variety is in\nthe expression, not in the conception. If, instead of considering the\nidentity in all its simplicity in both members of the equation, we\ngive the value of the circle with reference to the circumference, we\nshall have C = circumference \u00d7 1/2 R (3), that is, the value of the\ncircle is equal to the circumference multiplied by one-half the radius.\nIn the equation (3) there is identity as in (1) and (2), because it\nis affirmed in it that the value expressed by C is the same as that\nexpressed by circumference \u00d7 1/2 R; just as in the other two it is\nexpressed that the value of the circle is the value of the circle. But\nis this equation different from the other two? It is very different.\nWhat is the difference? The first two simply express the identity\nconceived under the same point of view; the circle expressed in the\nsecond member excites no idea not already excited by the first; but in\nthe last, the second member expresses the same circle indeed, but in\nits relations with the circumference and radius; and, consequently,\nbesides containing a sort of analysis of the circle, it records the\nanalysis previously made of the idea of the circumference in relation\nto the idea of radius. The difference is not, then, solely in the\nmaterial expression, but in the variety of conceptions under which the\nsame thing is presented.\n\nCalling the value of the relation of the circumference with the\ndiameter N, and the circle C, the equation becomes: C = NR^2 (4). Here,\nalso, there is identity of value; but we discover a notable progress in\nthe expression of the second member, in which the value of the circle\nis given, freed from its relations with the value of the circumference,\nand dependent solely on a numerical value, N, and a right line, which\nis the radius. Without losing the identity, and only by a succession of\nperceptions of identity, we have advanced in science, and starting from\nso sterile a proposition as circle = circle, we have obtained another,\nby means of which we may at once determine the value of any circle from\nits radius.\n\nLeaving elemental geometry, and considering the circle as a curve\nreferred to two axes, with respect to which its points are determined,\nwe shall have Z = 2Bx-x^2(5); Z expressing the value of the ordinate;\nB the constant part of the axis of abscissas; and x the abscissa\ncorresponding to Z. We have here a still more notable progress of\nideas: in both members we now express the value, not of the circle,\nbut of lines, by which we may determine all points of the curve;\nand we easily conceive that this curve, which was contained in the\nfigure whose properties we determined in elemental geometry, may be\nconceived under such a form as belongs to a genus of curves, whereof it\nconstitutes a species by the particular relations of the quantities 2x\nand B; thus modifying the expression by adding a new quantity, combined\nin this or that manner, we may obtain a curve of another species. If,\ntherefore, we would determine the value of the surface contained\nin this circle, we may consider it, not solely with respect to the\nradius, but to the areas comprised between the various perpendiculars\nthe extremities of which determine points of the curve and are called\nordinates. It results from this, that the same value of the circle may\nbe determined under various conceptions, although this value is at all\ntimes identical; the transition from one conception to another is the\nsuccession of the perceptions of identity presented under different\nforms.\n\nLet us now consider the value of the circle dependent on the radius:\nthis will give us C = function x (6). This equation enables us to\nconceive the circle under the general idea of a function of its radius,\nor of x, and consequently authorizes us to subject it to all the\nlaws to which a function is subject, and leads us to the properties\nof their differentials, limits, and relations. By this equation we\nenter into infinitesimal calculus, the expressions of which present\nidentity under a form which records a series of conceptions of long\nand profound analysis. Thus, expressing the differential of the circle\nby dc, and its integral by S. dc, we shall have C = S. dc, (7), an\nequation in which are expressed the same values as in circle = circle,\nbut with this difference, that the equation (7) records immense\nanalytical labors: it results from a long succession of conceptions of\nintegral calculus, of differentials, and limits of the differentials\nof the functions, of the application of algebra to geometry, and of\na multitude of elementary geometrical notions, algebraical rules and\ncombinations, and of whatever else was needed to arrive at this result.\nTherefore, when we find the integral of the differential, and obtain\nby integration the value of the circle, it would clearly be most\nextravagant to affirm that the integral equation is nothing more than\nthe equation circle = circle; but it is not so to say that at bottom\nthere is identity, and that the diversity of expression to which we\nhave come, is the result of a succession of perceptions of the same\nidentity presented under different aspects. Supposing the conceptions,\nthrough which it has been necessary to pass, to be A, B, C, D, E, M,\nthe law of their scientific connection may be thus expressed: A = B, B\n= C, C = D, D = E, E = M; therefore A = M.\n\n271. What we have just explained cannot be well understood unless\nwe recall some characteristics of our intellect, in which is found\nthe reason of so great anomalies. Our intellect is so weak as to\nperceive things only successively: only after much study does it see\nwhat is contained in the clearest ideas. Hence a necessity, to which\ncorresponds with admirable harmony a faculty that satisfies it: the\nnecessity is of conceiving under various, and different, as well as\ndistinct, forms, even the simplest things: the faculty is that of\ndecomposing the conception into many parts, and multiplying in the\norder of ideas what in that of reality is only one. This faculty of\ndecomposition would be useless were not the intellect, in passing\nthrough the succession of conceptions, to find means of connecting and\nretaining them: otherwise it would continually lose the fruit of its\nlabors; it would slip from its hands as fast as it grasped it. Happily\nit has this means in signs either written, spoken, or thought; those\nmysterious expressions which at times not only designate an idea, but\nalso are the compendium of the labors of a whole life, and perhaps of\na long series of ages. When the sign is presented to us, we do not see\ncertainly and with full clearness all that it expresses, nor why the\nexpression is legitimate; but we know confusedly the meaning therein\ncontained; we know that in case of necessity, it is enough for us to\nfollow the thread of the perceptions through which we have passed,\nthus going back even to the simplest elements of science. In making\ncalculations, the most eminent mathematician does not clearly see\nthe meaning of the expressions he uses, except as they relate to the\nobject before him; but he is certain that they do not deceive him, that\nthe rules by which he is guided are sure; because he knows that at\nanother time he established them by incontestible demonstrations. The\nprogress of a science may be compared to a series of posts on which the\ndistances of a road are marked: he who marked the numbers on the posts\nuses them without necessity of recalling the operations which led him\nto mark the quantity before him; he is satisfied with knowing that the\noperations were well made, and that he wrote the result correctly.\n\n272. The proof of this necessity of decomposition, besides being fully\nestablished by the above example, is found in the elements of all\ninstruction, where, under a form of demonstration, it is necessary\nto explain propositions which express simply the definitions or\naxioms that have been before established. For example: we find in the\nelementary works on geometry this theorem: all the diameters of a\ncircle are equal; and we must, if we would have beginners understand\nit, give a demonstrative form to that which neither is nor can be any\nthing more than an explanation, and is almost a repetition of the idea\nof the circle. When we describe a circle, we fix a point around which\nwe revolve a line called the radius; since then the diameter is nothing\nmore than the sum of two radii continued in the same right line, the\nmere enunciation of the theorem would seem sufficient to show that it\nis evidently contained in the idea of the circle, and is as a sort of\nrepetition of the postulate, on which the construction of the curve is\nfounded: still it is not so, and it must be explained as if it were\na proof; we must show the diameter to be equal to two radii, these\nradii to be equal, and at times repeat that this is supposed in its\nconstruction: in a word, it is necessary to employ many conceptions to\nshow a truth, which ought to have been known by the simple intuition of\none alone, as is the case when the geometrical powers of the intellect\nhave acquired a certain strength and robustness.\n\n273. We may now appreciate at its just value, the opinion of Dugald\nStewart, who, in his _Elements of the Philosophy of the Human Mind_,\nsays: \"It may be fairly questioned, too, whether it can, with strict\ncorrectness, be said of the simple arithmetical equation, 2 plus 2\n= 4, that it may be represented by the formula A = A. The one is a\nproposition asserting the equivalence of two different expressions;\nto ascertain which equivalence may, in numberless cases, be an\nobject of the highest importance. The other is altogether unmeaning\nand nugatory, and cannot, by any possible supposition, admit of the\nslightest application of a practical nature. What opinion then shall we\nform of the proposition A = A, when considered as the representative\nof such a formula as the binomial theorem of Sir Isaac Newton?\nWhen applied to the equation 2 plus 2 = 4, (which in its extreme\nsimplicity and familiarity is apt to be regarded in the light of an\naxiom:) the paradox does not appear to be so manifestly extravagant;\nbut, in the other case, it seems quite impossible to annex to it any\nmeaning whatever.\"[22] This philosopher does not observe that the\npretended extravagance arises from his wrong interpretation of his\nadversaries' opinion. No one ever thought of denying the importance\nof the discoveries which prove different expressions equivalent: no\none doubts that Newton's formula of the binomial is a great advance\nupon the formula A = A: but the question consists not in this, but in\nseeing whether Newton's formula of the binomial is any thing more\nthan the expression of identical things; and whether even the merit of\nthe expression is or is not the fruit of a series of perceptions of\nidentity. Were the question presented under Dugald Stewart's point of\nview, it would be unworthy of discussion: for philosophy should not\ndispute upon things that are ridiculous as well as absurd.\n\n[22] Part II., Chap. II., Sect. 3, \u00a7 2, pages 436-7.\n\n\n\n\nCHAPTER XXVIII.\n\nCONTINUATION OF THE SAME SUBJECT.\n\n\n274. We will now explain how the doctrine of identity is applied in\ngeneral to all reasoning, whether upon mathematical objects or not:\nwith this view we will examine some of the dialectical forms in which\nthe art of reasoning is taught.\n\nEvery A is B; M is A: therefore M is B. In the major of this syllogism\nwe find the identity of every A with B; and in the minor, the identity\nof M with B. In each of these propositions there is affirmation, and,\nconsequently, perception of identity. Let us now see what takes place\nin the connection which constitutes the force of the argument.\n\nWhy do we say that M is B? Because M is A, and every A is B. M is\none of the As, expressed in the words _every A_; therefore, when we\nsay, M is A, we say only what we had before said by _every A_. What\ndifference, then, is there? There is this difference, that in the\nexpression _every A_, no attention is paid to one of A's contents, M,\nof which we had nevertheless affirmed that it was B, in affirming that\nevery A is B. If, in the expression _every A_, we have distinctly seen\nM, the syllogism would not have been necessary, because, in saying\nevery A is B, we had already understood that M is B.\n\nThis observation is so true and exact, that in treating of very\nclear relations we suppress the syllogism, and replace it with the\nenthymema, which is, it is true, an abbreviation of the syllogism;\nbut we must see in this abbreviation besides a saving of words, a\nsaving of conceptions, for the intellect sees one intuitively in the\nother, without necessity of decomposition. He is a man, therefore\nhe is rational; we omit the major, and do not even think of it, for\nwe intuitively see, in the idea of man, and its application to an\nindividual, the idea of rational without any gradation of ideas or\nsuccession of conceptions.\n\nLet us suppose that we have to demonstrate that the perimeter of a\npolygon inscribed in a circle is less than the circumference, and\nthat we make the following syllogism: The sum of all the right lines\ninscribed in their respective curves is less than the sum of those\ncurves; but the perimeter of the polygon is the sum of the right lines,\nand the circumference is the sum of the arcs or curves; therefore the\ninscribed perimeter is less than the circumference. We now ask, will\nany one who knows that the sum of the right lines is less than the sum\nof the curves, fail to see with equal facility that the perimeter is\nless than the circumscribed circumference, provided he understands the\nmeaning of the words? It is evident that he will not. What necessity,\nthen, of repeating the general principle? Is it to add any thing to the\nparticular conception? Certainly not; because nothing can be clearer\nthan the following propositions: the perimeter of the polygon is a\nsum of right lines; the circumference is a sum of arcs or curves;\nwhat the general principle does, is to call attention to a phase of\nthe particular conception, so that what otherwise could not be seen\nin it may be seen on reflection. The certainty of the conclusion does\nnot depend on the general principle; because, from thinking on the\nrelations of greater and less only with respect to the right lines of\nthe perimeter and the arcs, the sum of which forms the circumference,\nany one would have inferred the same thing.\n\nThis example also tends to prove that the enthymema is not a mere\nabbreviation of words; and it shows why we employ it in reasoning upon\nmatters familiar to the understanding. In any one of the conceptions\nwe see all that is necessary for the consequence; and, therefore,\none premise suffices, as in it the other is included rather than\nunderstood. A beginner may say: the arc is greater than the chord,\nbecause the curve is greater than the right line; but when familiarized\nwith geometrical ideas, he will simply say, the arc is greater than\nthe chord; he will see the idea of the curve in that of the arc,\nand the idea of the right line in that of the chord, without need\nof decomposition. If the arc is greater than its chord, this is not\nbecause every curve is greater than the corresponding right line. Did\nthe abstract idea of curve not exist, and were this particular arc of a\ncircle the only curve thought of; did the abstract idea of right line\nnot exist, and were this particular chord the only right line thought\nof, it would still, as at present, be true that the arc is greater than\nthe chord.\n\n275. When treating of the _necessary_ relations of things, the general\nprinciples, the middle terms, and all the auxiliaries to reasoning\nfurnished by logic, are only inventions of art to make us reflect upon\nthe conception of the thing, and see in it what otherwise we should\nnot see. Hence our judgments on necessary objects are in some sense\nanalytical; and Kant equivocates, when he says there are synthetic\njudgments not dependent on experience. Without experience we have only\nthe conception of the thing. We do not pretend that all propositions\nexpress such a relation between the subject and the predicate, that the\nconception of the former will always give that of the latter; but we do\nhold, that the reason of this insufficiency is the incompleteness of\nthe conception, either in itself, or in relation to our comprehension.\nBut if we suppose the conception complete in itself, and a due capacity\nin our intellect to understand whatever it contains, we shall find in\nthe conception all that can be the object of science.\n\n276. An example from mathematics will make this clearer. Large works on\ngeometry are filled with explanations, demonstrations, and applications\nof the properties of the triangle. The conceptions of right lines,\nand the angles formed by them, enter into the conception of the\ntriangle. We ask, can all the explanations and demonstrations of the\nproperties of triangles in general ever go beyond the ideas of right\nlines and angles? No. For the new elements introduced would be foreign\nto the triangle, and would consequently change its nature. Necessary\nrelations neither admit of more nor of less, neither additions nor\nsubtractions of any sort; what is, is, and nothing more. In passing\nfrom the triangle in general to its different species, such as\nequilateral, isosceles, right angled, scalene, it is to be observed\nthat the demonstration must rigorously attend to what is contained\nin the general conception, modified by the determining properties of\nthe species, that is, the equality of the three sides, of two, the\ninequality of all, the supposition of a right angle, and others.\n\n277. What we are now explaining is clearly seen in the application\nof algebra to geometry. A curve is expressed by a formula containing\nthe conception of the curve, or its essence. The geometrician, to\ndemonstrate the properties of the curve, does not need to go out of\nthis formula; it is a touch-stone in his hand, and he finds in it all\nthat he wants. He inscribes triangles, or other figures in the curve,\ndraws right lines from it to points without, but never goes out of the\nconception expressed in the formula; he decomposes it, and finds in it\nwhat before he had not discovered.\n\nIn this equation z^2 = (e^2/E^2)(2Ex-x^2), we find the expression of\nthe relations which constitute the ellipse; E expresses the greater\nsemi-axis, e the lesser, z the ordinates, and x the abscissas. With\nthis equation variously developed and transformed, the properties of\nthe curve are determined; it shows, with the help of constructions,\nthat the new property is contained in the conception, and to find it,\nwe have only to analyze it.\n\nIf we suppose an intelligence capable of conceiving the essence of the\ncurve, by an immediate intuition of the law governing the inflection\nof points, without the necessity of referring it to any line, whether\none axis instead of two suffices, or in any other manner not even\nimaginable by us; this intelligence will not need to follow all the\nevolutions which we have made in demonstrating the properties of the\ncurve; for it will perceive them to be clearly contained in the very\nconception of the curve. This supposition is not arbitrary; we see it\nrealized every day, though on a smaller scale. An ordinary geometrician\nconceives a curve as also does Pascal; but while Pascal at a glance\nsees the most recondite properties of the curve in this conception,\nan ordinary geometrician sees only after long study its most common\nproperties. Kant made no account of this doctrine, and therefore could\nnot solve the problem of pure synthetic judgments: had he examined the\nsubject more profoundly he would have seen that, strictly speaking,\nthere are no such judgments; and instead of wearing out his genius in\nattempting to solve an insolvable problem, he would have abstained from\nraising it.(26)\n\n\n\n\nCHAPTER XXIX.\n\nARE THERE TRUE SYNTHETIC JUDGMENTS A PRIORI IN THE SENSE OF KANT?\n\n\n278. The great importance attributed by the German philosopher to\nhis imaginary discovery, requires us to examine it at length. This\nimportance may be estimated from what he himself says: \"If any of the\nancients had only had the idea of proposing the present question, it\nwould have been a mighty barrier against all the systems of pure reason\ndown to our days, and would have saved many vain attempts which _were\nblindly made without knowing what was treated of_.\"[23] This passage\nis quite modest and naturally excites our curiosity to know what is\nthe problem which needed only to be proposed in order to avoid all the\naberrations of pure reason.\n\n[23] _Critik der reinen Vernunft._ Einleitung.\n\nHere are his words: \"All empirical judgments, as such, are synthetic.\nFor it would be absurd to ground an analytic judgment on experience,\nsince I am not obliged to go out of the conception itself in order to\nform the judgment, and therefore can have no need of the testimony of\nexperience. That a body is extended, is a proposition which stands firm\n_a priori_. It is no empirical judgment; for, prior to experience, I\nhave all the conditions of forming it in the conception of body, from\nwhich I deduce the predicate, extension, according to the principle of\ncontradiction, by which I at once become conscious of its necessity,\nwhich I could not learn from experience. But, on the other hand, I\ndo not include, in the primitive conception of body in general, the\npredicate, heaviness; yet this conception of body in general indicates,\nthrough experience of a part of it, an object of experience, to which\nI may add from experience other parts also belonging to it. I can\nattain to the conception of body beforehand, analytically, through\nits characteristics extension, impenetrability, form, etc., all of\nwhich are included in the primary conception of body. But I now\n_extend_ my cognition, and, as I recur to experience, from which I have\nobtained the conception of body in general, I find along with these\ncharacteristics the conception of heaviness. I therefore add this, as a\npredicate, to the conception of body. The possibility of this synthesis\ntherefore rests on experience; for both conceptions, although one does\nnot contain the other, yet belong as parts to a whole, that is to say,\nto experience, which is itself a union of synthetic, though contingent\nintuitions. But in the case of synthetic judgments _a priori_ we have\nnot this assistance. Here we have not the advantage of returning and\nsupporting ourselves on experience. If I must go out of the conception\nA in order to find another conception B, which is to be joined to it,\non what am I to rely? and by what means does the synthesis become\npossible?\"[24]\n\n[24] Ibid. pp. 9, 10.\n\n279. The reason of this synthesis is found in the faculty of our mind\nof forming total conceptions, in which the _relation_ of the partial\nconceptions composing it is discovered; and the legitimacy of the\nsame synthesis is founded on the principles on which the criterion of\nevidence is based.\n\nThe synthesis of the schoolmen consists in the union of conceptions,\nand does not refuse to admit as analytical the total conceptions, from\nthe decomposition of which results the knowledge of the relations of\nthe partial conceptions.\n\nIf Kant had stopped with the judgments of experience, there would be\nno objection to his doctrine. But extended to the purely intellectual\norder, it is either inadmissible, or at least expressed without much\nexactness.\n\n260. Kant says all mathematical judgments are analytic, and that this\ntruth which in his opinion \"is certainly incontestible and important\non account of its consequences, seems to have hitherto escaped the\nsagacity of the analysts of human reason, causing very contrary\nopinions.\" We think it is the sagacity of his Aristarchus, and not that\nof the analysts, that is at fault.\n\n\"One would certainly think at first sight that the proposition, 7\n+ 5 = 12, is a purely analytic proposition, which follows from the\nconception of a sum of seven and five, according to the principle of\ncontradiction. But if we examine it more closely, we find that the\nconception of the sum of seven and five contains nothing farther than\nthe union of both numbers in one, from which it cannot by any means be\ninferred what this other number is which contains them both.\"[25]\n\n[25] Kant, _ubi supra_, \u00a7 5.\n\nWere we to say that whoever hears seven plus five, does not always\nthink of twelve, because he does not see clearly enough that one\nconception is the same as the other, although it is under a different\nform, it would be true. But from this it does not follow that the\nconception is not purely analytic. The mere explanation of both\nsuffices to show their identity.\n\nThat this may be better understood, we will invert the equation thus:\n12 = 7 + 5. It is evident that if any one does not know that 7 + 5 =\n12, he will not know that 12 = 7 + 5. Now, in examining the conception\n12, we certainly see 7 + 5 contained in it. Therefore, the conception\nof 12 is identical with the conception of 7 + 5; and just as, because\nhe who hears 12, does not always think of 7 + 5, we cannot thence infer\nthat 12 does not contain 7 + 5; so, also, we cannot, because he who\nhears 7 + 5, does not always think of 12, thence infer that the first\nconception does not contain the second.\n\nThe cause of the equivocation is, that the two identical conceptions\nare presented to the intellect under different forms; and until we\nhave the form, and look to what is under it, we shall not discover the\nidentity. This is not, strictly speaking, _reasoning_ but _explanation_.\n\nWhat Kant adds concerning the necessity of recurring, in this case, to\nan intuition, with respect to one of the numbers, adding five to seven\non the fingers, is exceedingly futile. First, in whatever way he adds\nthe five, there will never be anything but the five that is added, and\nit will neither give more nor less than 7 + 5. Secondly, the successive\naddition on the _fingers_ is equivalent to saying 1 + 1 + 1 + 1 + 1 =\n5. This transforms the expression, 7 + 5 = 12, into this other, 7 + 1 +\n1 + 1 + 1 + 1 = 12; but the conception, 1 + 1 + 1 + 1 + 1, has the same\nrelation to 5, as 7 + 5 to 12; therefore, if 7 + 5 are not contained\nin 12, neither are 7 + 1 + 1 + 1 + 1 + 1 contained in it. It may be\nreplied that Kant does not speak of identity, but of intuitions. This\nintuition, however, is not the sensation, but the idea; and if the\nidea, it is only the conception explained. Thirdly, we know this method\nof intuition not to be even necessary for children. Fourthly, this\nmethod is impossible in the case of large numbers.\n\n281. Kant adds that this proposition, \"a right line is the shortest\ndistance between two points,\" is not purely analytic, because the\nidea of _shortest distance_ is not contained in the idea of _right\nline_. Waiving the demonstrations which some authors give, or pretend\nto give, of this proposition, we shall confine ourselves to Kant's\nreasons. He forgets that here the right line is not taken _alone_, but\n_compared_ with other lines. The idea of right line alone neither does\nnor can contain the ideas of _more_ or _less_; for these ideas suppose\na comparison. But from the moment the right line and the curve are\ncompared, with respect to _length_, the relation of superiority of the\ncurve over the right line is seen. The proposition is then the result\nof the comparison of two purely analytic conceptions with a third,\nwhich is _length_.\n\n282. If Kant's reasoning were good, even this judgment, \"the whole\nis greater than its part,\" would not be analytic; for the idea of\n_greater_ enters not into the conception of the _whole_ until the\n_whole_ is compared with its _part_. Thus, the judgment, four is\ngreater than three, would not be analytic, because the idea of four\nuntil compared with three does not include the conception of greater.\n\nThe axiom: \"things which are equal to the same thing are equal to each\nother,\" would not be analytic, because the conception, _equal to each\nother_, does not enter into the conception of _things which are equal\nto the same thing_, until we reflect that the equality of the middle\nterm implies the equality of the extremes.\n\nThe x, of which Kant speaks, would be found in almost all judgments,\nif we could not form total conceptions involving comparison of partial\nconceptions: in this case we should have no analytic judgments except\nsuch as are wholly identical, or directly contained in this formula, A\nis A.\n\n283. The comparison of two conceptions with a third, does not take from\nthe result the character of analytic judgment, as a predicate cannot be\nseen in the idea of the subject, without the aid of this comparison.\nThis comparison is often necessary, because we only confusedly think\nof what is contained in the conception which we already have; and\nsometimes it even happens that we do not think at all of it. One\noften says a thing and then contradicts himself, not observing that\nwhat he adds is opposed to what he had already said. We often ask, in\nconversation, do you not see that you suppose the contrary of what you\njust said; that the conditions you have just established imply the\ncontrary of what you now assert?\n\n284. A conception includes not only all that is expressly thought in\nit, but all that can be thought. If, on decomposing it, we find in it\nother things, it cannot be said that we add them, but that we find\nthem. It is not a synthesis, but an analysis. Otherwise we must admit\nno analytic conceptions, or only such as are purely identical. Except\nin this last case, of which the general formula is, A is A, there is\nalways in the predicate something not thought in the subject, if not\nin substance at least in form. The circle is a curve; this undoubtedly\nis one of the simplest analytical propositions imaginable; still the\npredicate expresses the general conception of curve, which may be\ncontained in the subject, in a confused manner, with relation to a\nparticular species of curve. Following a gradation in geometrical\npropositions, we may observe that there is nothing in one proposition\nnot in the preceding, except the greater or less difficulty of\ndecomposing the conception, so as to see in it what before we had not\nseen.\n\nIf we say, the circle is a conic section, evidently any one ignorant of\nthe terms, or who has not reflected on their true sense, will not think\nof the attribute in the subject. No addition is made to the conception\nof the circle; only a property not before known is discovered, and this\ndiscovery results from comparison with the cone. Is there any synthesis\nhere? No. There is only an analysis of the two conceptions, the circle\nand the cone, compared. As this error destroys the foundation of Kant's\ndoctrine on this point, we will develop it and place it on a more\nsolid foundation.\n\n285. Synthesis, properly so called, requires something to be added\nto the conception, which in nowise belongs to it, as the example\nbrought by Kant shows. The conception, extension, is contained in\nthe conception, body; but heaviness is an entirely foreign idea,\nwhich we can unite to the conception, body, only because experience\nauthorizes it. Only with this addition is there properly synthesis.\nThe union of ideas which results from the conception of the thing,\nalthough comparison may be necessary in order to fecundate them, does\nnot make a synthesis. The conceptions are not wholly absolute, they\ncontain relations, and the discovery of these relations does not give\na synthesis, but a more complete analysis. If it be said that in this\ncase there is something more than the primitive conception, we answer\nthat the same thing happens in all not purely identical. We may also\nadd that by the comparison a new total conception is formed resulting\nfrom the primitive conceptions; and the properties of the relations\nare then seen, not by synthesis, but by the analysis of the total\nconception.\n\nAccording to Kant, true synthesis requires the union of things so\ndifferent from one another, that the bond uniting them is a sort of\nmystery, an x, whose determination is a great philosophical problem. If\nthis x is found in the essential relation of the partial conceptions\nconstituting the total conception, the problem is resolved by a simple\nanalysis, or, to speak more exactly, it is shown that the problem did\nnot exist, because the x was a known quantity.\n\nWe know of no judgment more analytical than that in which we see the\nparts in the whole, since the whole is only the parts united. If we\nsay, one and one are two, or, two is equal to one plus one; it cannot\nbe denied that we have a total conception, two, in the decomposition\nof which, we find one plus one. If this be not an analytic conception,\nthat is to say, if the predicate be not here contained in the idea\nof the subject, it will be hard to tell what is. But even here there\nare different conceptions, one plus one; unite them, and they form\nthe total conception. The relation, although most simple, exists; and\nwhether it be more or less, simple or complicated, and, consequently,\nseen with more or less facility, does not alter the character of the\njudgments, or from synthetic convert them into analytic.\n\n286. We will complete this explanation with an example from elementary\ngeometry. \"The surface of a rhomboid is equal to the surface of a\nrectangle having the same base and altitude.\" First: in the idea of the\nrhomboid, we do not see the idea of its equality with the rectangle;\nand this we cannot see, because the relation does not exist when there\nis no other term to which it may relate. The idea of the parallelogram\ndoes not contain that of the rectangle, and consequently not that of\nequality. Second: the relation results from the comparison of the\nrhomboid with the rectangle; and, consequently, it must be found in a\ntotal conception containing them both. It cannot, therefore, be said\nthat we add any thing to the conception of the parallelogram which\ndoes not belong to it. On the contrary, we see this equality flow from\nthe conception of the rhomboid and that of the rectangle, as partial\nconceptions of the total conception, formed by the combination of them\nboth. The analysis of this total conception opens to us the relation we\nare now in quest of; for it must be observed that when the simple union\nof the conceptions compared does not suffice, we make use of another\nincluding them, and also something more; and from the new conception,\nduly analyzed, we deduce the relation of the parts compared.\n\n287. In the geometrical construction, that serves for the\ndemonstration of the above theorem, which we have used as an example,\nmay be seen what we have just explained with regard to total\nconceptions containing other conceptions besides those compared. If we\nplace the rectangle and the rhomboid upon the same base, we at once see\nthat there is something common to both, namely, the triangle formed by\nthe base, a part of one side of the rhomboid, and a part of one side of\nthe rectangle. Neither synthesis nor analysis is here required, because\nthere is perfect coincidence, and this in geometry is equivalent to\nperfect equality. The difficulty is in the two remaining parts, that\nis, in the trapezoids to which the parallelograms are reduced by the\nsubtraction of the common triangle. The mere sight of the figures\nteaches nothing concerning the equivalence of the two surfaces; we see\nonly that the two sides of the rhomboidal surface go on extending,\nbut including a less distance in proportion as the angle becomes more\noblique, under these two conditions: length of sides, and diminution of\ndistances between two limits, of which one is infinity, and the other\nthe rectangle. The relation of the equivalence of the surfaces may be\ndemonstrated by prolonging the parallel opposite the base, and thus\nforming a quadrilateral of which the trapezoids are parts; to discover\nthe equality of these trapezoids, it is only necessary to decompose\nthe quadrilateral, attending to the equality of two triangles, each\nrespectively formed by one of the trapezoids and a common triangle.\nIs any thing here added to the conception of each trapezoid? No. We\nonly compare them. They could not be compared directly, and therefore\nwe included them in a total conception, the mere analysis of which\nenabled us to discover the relation sought for. The conception does not\ngive this relation; it only shows it; for if the conception of the two\nfigures compared were more perfect, so that we might intuitively behold\nthe relation existing between the increment of the sides and the\ndecrement of their distance from each other, we should see that there\nis here a constant law, which supplies on one side what is lost on the\nother; and consequently we should discover, in the very conception\nof the rhomboid, the fundamental reason of the equality, that is,\nthe permanent value of the surface, notwithstanding the greater or\nless obliquity of the angles; thus obtaining what we deduced from the\nabove comparison, and generalize with reference to two constant lineal\nvalues, base and altitude. The same would happen with respect to the\nequivalence of all variable quantities differently expressed, could we\nreduce their conceptions to such clear and simple formulas as those of\napparent functions; for example, nx/mx, from which, whatever the value\nof the variable, there always results the same value of the expression,\nwhich is constant, to wit, n/m.\n\n288. Let not these investigations be imagined useless. In this, as\nin many other questions, it happens that most important truths are\nthe result of a philosophical problem which, in appearance, is merely\nspeculative. Thus, in the present case, we observe Kant explaining the\nprinciple of causality, in an inexact, and, as we understand him, in an\naltogether false sense; but, perhaps, the origin of his equivocation\nlies in his considering the principle of causality as synthetic,\nalthough _a priori_, whereas it must be regarded as analytic, as we\nshall show when treating of the idea of cause.\n\nIn consideration of the great importance of clear and distinct ideas\non the present subject, we will in a few words, sum up the doctrine we\nhave explained concerning mediate and immediate evidence.\n\nThere is immediate evidence when, in the conception of the subject, we\nsee its agreement or disagreement with the predicate, without requiring\nany other means than mere reflection on the meaning of the terms.\nJudgments of this class are with propriety called analytic, because we\nhave only to analyze the conception of the subject to find therein its\nagreement or disagreement with the predicate.\n\nThere is mediate evidence when, in the conception of the subject, we do\nnot immediately see its agreement or disagreement with the predicate,\nand therefore have to call in a middle term to make it manifest.\n\n290. Here arises the question whether judgments of mediate evidence\nare analytic. It is clear that if we mean by analytic only those in\nwhich we have solely to understand the meaning of the terms in order to\nsee the agreement or disagreement of the predicate, the judgments of\nmediate evidence cannot be called analytic; but if by analytic judgment\nwe mean a judgment in which it is only necessary to _decompose_ the\nconception of the subject in order to find therein its agreement or\ndisagreement with the predicate, we must say that the judgments of\nmediate evidence are analytic, and the means employed is only the\nformation of a total conception containing the partial conceptions, the\nrelation of which we seek to discover. In the union of these partial\nconceptions there is a synthesis, it is true; but there is none in the\ndiscovery of their relation, for this is done by analysis.\n\nA judgment is not the less analytic because formed by the union of\ndifferent conceptions; for then no judgment would be analytic. When we\nsay, man is rational, the two conceptions of _animal_ and _rational_\nenter into the conception of _man_, but do not take from it its\nanalytical character; for this, as its very name imports, consists\nin the analysis of a conception, being sufficient to show certain\npredicates in it, without reference to the manner of this conception's\nformation, whether two or more conceptions are united in it, or not.\n\n291. This clearly shows in what mediate evidence consists. The\npredicate is indeed contained in the idea of the subject; but, owing\nto the limitation of our intellect, either these ideas are incomplete,\nor we do not see them in all their extension, or else we do not well\ndistinguish what we in a confused manner perceive in them; and hence,\nto know the meaning of the terms does not enable us immediately to\nsee that the predicate is contained in the idea of the subject.\nMoreover, the objects, even such as are purely ideal, are presented\nto us separately; and hence, not knowing the sum of them all, we pass\nsuccessively from one to another, discovering their mutual relations in\nproportion as we approach them.\n\n292. It may, from what we have said, be inferred that all judgments\nin the purely ideal order are analytic, since every cognition of\nthis order is obtained by the intuition of whatever is more or less\ncomplicated in the conception, and there is no more synthesis than is\nnecessary to bring the objects together, by uniting their conceptions\nin one total conception, which serves for the discovery of the relation\nof the partial conceptions.\n\n293. The x, therefore, of which Kant speaks, and the removal of which\nis one of the most important problems of philosophy, is nothing more\nthan the faculty possessed by the soul to unite the conceptions of\ndifferent things in one total conception, and to discover in it their\nmutual relations. This faculty is no new discovery, for the schools\nhave all recognized it under one name or another. No one ever denied\nto the intellect the faculty of comparing; and comparison is the act\nwhereby the intellect places two or more objects before its sight so\nas to perceive their mutual relations. In this act the intellect forms\na total conception, of which the conceptions compared are a part. Thus\nwe have seen that in geometry to verify the mutual relation of certain\nfigures, we construct a new figure which includes them all, and is a\nsort of field whereon the comparison is made.\n\nThis exposition of analytic and synthetic judgments will suffice for\nthe present; as we proposed to treat of them here only in general, and\nas related to certainty; consequently we will not descend to their\nparticular application to various ideas, the analysis of which belongs\nto other parts of this work.\n\n\n\n\nCHAPTER XXX.\n\nVICO'S CRITERION.\n\n\n294. The doctrine of Vico on the criterion of truth is connected with\nthe matter of the preceding chapters on immediate and mediate evidence.\nThis philosopher thinks that the criterion consists in having made the\ntruth which is known; that our cognitions then only are completely\ncertain, and that they lose their certainty in proportion as the\nintellect loses its character of cause with respect to its objects.\nGod, the cause of all, knows every thing perfectly: creatures, whose\ncausality is very limited, are very limited in their cognitions; and if\nin any thing they may be likened to the infinite, it is in that ideal\nworld which they construct for themselves, and extend at pleasure,\nstopped by no impassable limits.\n\nLet the author speak for himself. \"The terms _verum_ and _factum_,\n_the true_ and _the made_, are used one for the other, in the Latin\nlanguage, or, as the schoolmen say, are convertible. _Intelligere_, to\nunderstand, is the same as to read with clearness and to know with\nevidence. They used _cogitare_ in the sense of the Italian _pensare e\nandar raccogliendo_; _ratio_ with them meant a collection of numerical\nelements, and also the gift by which man is distinguished from,\nand made superior to, the brute. They defined man to be an animal\nparticipating of reason; _animal rationis particeps_: and consequently\nnot absolutely possessed of it. As words are the signs of ideas, so\nalso are ideas the signs and representations of things. Thus, as to\nread, _legere_, is to unite the elements of writing, which form the\nwords; so to understand, _intelligere_, is to unite all the elements\nwhich constitute the perfect idea of anything. Hence we infer that\nthe doctrine of the ancient Italians concerning truth was as follows:\nTruth is the same as fact; and consequently God is the first truth,\nbecause he is the first maker, _factor_; the infinite truth, because\nhe made all things; the absolute truth, because he represents all the\nelements of things, both internal and external, for he contains them.\nTo know is to unite the elements of things: hence it follows that\nthought, _cogitatio_, is a property of the human mind; and intelligence\na property of the divine mind, because God contains all the internal\nand all the external elements of things, and therefore he unites them,\nand he it is that disposes them; whereas the human mind limited as\nit is, and separated from all that is not itself, may bring together\nextreme points, but cannot unite them; it may think of things, but\ncannot understand them; and this is why it is said to participate\nof reason, but not to possess it. Let us explain these ideas by a\ncomparison. Divine truth is a solid image of things, a sort of plastic\nfigure; human truth is an image on a plane, it has no depth, but is a\nsort of painting. Divine truth is true, because God knows in the same\nact by which he disposes and produces; human truth is in relation to\nthings which man in like manner disposes and creates. Science is the\ncognition of the mode in which the thing is made; a cognition in which\nthe mind makes its object, since it recomposes its elements. For God,\nwho understands every thing, the object is a solid; but it is a surface\nfor man who understands only the exterior. These points being settled,\nin order that we may more easily make them harmonize with our religion,\nlet us observe that the ancient philosophers of Italy identified\ntruth and fact, for they believed the world to be eternal. Thus the\npagan philosophers adored a God who always operated _ad extra_, a\npoint rejected by our theology. Wherefore in our religion, in which\nwe profess that the world was created in time, and out of nothing, it\nis necessary to distinguish, and identify created truth with what is\nmade, and uncreated truth with what is begotten, _genito_. Thus the\nSacred Scriptures, with an elegance truly divine, give the name of\n_the Word_ to the wisdom of God, which contains in itself the ideas\nof all things and the elements of these ideas. In the Word, truth is\nthe comprehension of all the elements of this universe, and it might\nproduce infinite worlds. From these elements, known and contained in\nthe divine omnipotence, is formed the Word real and absolute, known\nby the Father from all eternity and begotten by him also from all\neternity.\"[26]\n\n[26] _Ancient Wisdom of Italy_, L. 1, C. 1.\n\n295. From these principles Vico deduces some very transcendental\nconsequences, among others, the explanation of the reason why our\nsciences are divided into many branches, and that of the different\ngrades of certainty by which they are distinguished. Mathematics is\nthe most certain, because a kind of creation of the intellect, which,\nstarting with the unity of a point, constructs a world of forms and\nnumbers by prolonging lines, and multiplying unity even to infinity.\nThus it knows what it produces itself, and hence it is that the\ntheorems commonly held to be objects of pure contemplation depend\nupon action just as the problems do. Mechanics is a less certain\nscience than either geometry or arithemetic, because it considers\nmotions as realized by machines; and physics is even less certain yet,\nbecause it does not, like mechanics, consider the external motion of\ncircumferences, but the internal motion of their centres. There is\nstill less certainty in sciences of the moral order, because these\ndo not consider the motions of bodies arising from one certain and\ncommon origin, which is nature, but the motions of the soul, often most\nprofound, often also capricious.\n\n\"Human science,\" he says, \"owes its origin to a defect of the human\nmind; it is beyond all things in its extreme limitation, contains\nnothing of what it seeks to know, and is consequently unable to make\nthe truth to which it aspires. The most perfect sciences are those\nwhich have expiated the vice of their origin, and are assimilated, as a\ncreation, to divine science, that is, those in which the truth and the\nfact are mutually convertible.\n\n\"From what proceeds, we may infer that the criterion of truth, and the\nrule to recognize it, is _to have made it_: consequently, the clear\nand distinct idea of our mind which we have, is not a criterion of the\ntruth, nor is it even a criterion of our mind; because the soul does\nnot, by knowing itself, make itself; and not making itself, it knows\nnot in what way it knows itself. Since human science takes abstraction\nfor its basis, sciences are so much the more uncertain, as they more\nnearly approach corporal matter....\n\n\"In a word, the true and the good are convertible, if what is known as\ntrue derives its being from the mind which knows it; as human science\nimitates divine science, wherein God, by knowing the true, begets\nit _internally_ in eternity, and makes it _externally_ in time. The\ncommunication of goodness to the objects of his thought is to God the\ncriterion of the true: _vidit Deus quod essent bona_; to men it is _to\nhave made the truth which they know_.\"[27]\n\n[27] Ibidem, \u00a7 1.\n\n296. Vico's system undeniably shows him to have been a profound\nthinker, and to have carefully meditated the problems of intelligence.\nHis line dividing the certainty of sciences is exceedingly interesting.\nAt first sight, nothing is more specious than the difference marked\nbetween mathematical, natural, and moral sciences. Mathematics is\nabsolutely certain, because the work of the understanding, it is as\nthe understanding, which constructed them, sees them to be. On the\nother hand, the natural and moral sciences regard objects independent\nof reason, having by themselves an existence of their own; wherefore,\nthe understanding knows little of them, and even in this little it is\nthe more liable to err as it penetrates deeper into a sphere where it\ncannot construct. We call this system specious, because when examined,\nit is found to be destitute of all solid foundation. We recognize,\nhowever, a profound thought in its author; for one he must have had to\nconsider science under such a point of view.\n\n297. The understanding knows only what it makes. This proposition\nsums up Vico's whole system; and it must have some foundation, or\nhe cannot advance one step without begging his question. Why does\nthe understanding know only what it makes? Why can the problem of\nrepresentation have no possible solution out of causality? We think we\nhave shown another origin besides this in identity, also in ideality\nduly connected with causality.\n\n298. To understand is not to cause. There may be, and there really\nis, a productive intelligence; but the act of understanding and that\nof causing, in general, offer distinct ideas. Intelligence supposes\nan activity; otherwise that intimate life which distinguishes the\nintelligent being is inconceivable: but this activity does not produce\nthe objects known; it operates in an immanent manner on these objects,\npresupposed to be either mediately or immediately in union with the\nintellect.\n\n299. If the intellect be condemned to know nothing not made by itself,\nit is difficult to conceive how the act of understanding can commence.\nIf we place ourselves in the initial moment, we shall not know how to\nexplain the development of this activity; for, if it can only know\nwhat it has made, what is it to understand in the first moment before\nit has made any thing? In the system before us, the intellect has no\nobject but what it has itself produced; but to understand, without\nan object understood, is a contradiction, so that not having in its\ninitial moment yet produced any thing, there can be nothing understood;\nand, consequently, intelligence is inexplicable. We cannot suppose its\nactivity to be blindly exercised: nothing is done blindly when there\nis question of representation, and the productive activity essentially\nrelates to things represented as represented. So far as the problem\nof intelligence is concerned, it makes no difference that these are\nproduced externally, with an existence distinct from the intellectual\nrepresentation. As Vico himself explains, human reason knows what it\nconstructs in a purely ideal world; and God knows the Word which he\nbegets, although the Word is not without the divine essence, but is\nidentified with it.\n\n300. The Neapolitan philosopher, not satisfied with applying his\nsystem to human reason, makes it applicable to all intelligences, not\nexcepting the divine; although with a praiseworthy regard for religion,\nhe endeavors to reconcile his ideological doctrine with the dogmas of\nChristianity. Truly, the problems of intelligence cannot be completely\nsolved without greatly cumulating them. To trace the footsteps of human\nreason does not suffice to make us know the human understanding; we\nmust, moreover, propose the general problem of intelligence itself, now\nlimited, like our own, to faint glimmerings, now dilating itself in\na sea of light over the regions of infinity. The sublime words, with\nwhich St. John commences his Gospel, besides the august truth taught by\ndivine inspiration, involve transcendental doctrines of an importance\nhigher than can be found in the words of any man, even if considered\nunder a merely philosophical point of view.\n\nWhen Vico identifies truth with the made, he is aware that he must,\naccording to a dogma of our religion, distinguish between what is\ncreated and what is uncreated. What is created is made; what is\nuncreated, begotten. He admires the divine elegance of the Holy\nScriptures in calling the wisdom of God, in which the ideas of all\nthings are contained, and the elements of ideas themselves, his Word:\nbut when he would explain the conception of the Word, his expressions\nare very inexact; he would have us understand, so it would seem,\nthat the Word only results from the elements known and contained in\nthe divine omnipotence. \"In this Word,\" he says, \"the true is the\ncomprehension of all the elements of this universe; and it might form\ninfinite worlds: from these elements, known and contained in the divine\nomnipotence, is formed the Word real and absolute, known by the Father\nfrom all eternity, and by him begotten also from all eternity.\"[28]\n\n[28] Ancient Wisdom of Italy, L. 1, C. 1.\n\nIf the author means that the Word is conceived by the mere knowledge\nof what is contained in the divine omnipotence, his assertion is false;\nif he does not, his mode of speaking is inexact.\n\nSt. Thomas asks whether any relation to creature be contained in the\nname of the Word: \"_utrum in nomine Verbi importetur respectus ad\ncreaturam_;\" and he resolves the question with admirable laconism and\nsolidity. \"I reply that in the Word relation to creature is contained.\nFor God, by knowing himself, knows every creature. The Word, therefore,\nconceived in the mind, is representative of all actually understood\nby it. Wherefore there are in us different words according to the\ndifferent things we understand. But because God by one act understands\nboth himself and all things, his only Word is expressive not only of\nthe Father, but also of creatures. And as the science of God is, with\nrespect to himself, cognition, but with respect to creatures, cognition\nand cause; so the Word of God is expressive only of what is in God\nthe Father, but both expressive and productive of creatures; and this\nis why it is said in the Thirty-second Psalm: \"He said, and they were\nmade;\" because the productive reason of those things, which the Father\nmakes, is contained in the Word.\"[29]\n\n[29] Respondeo dicendum, quod in Verbo importatur respectus ad\ncreaturam. Deus enim cognoscendo se, cognoscit omnem creaturam. Verbum\nigitur in mente conceptum est representativum omnis ejus, quod actu\nintelligitur. Unde in nobis sunt diversa verba, secundum diversa, qu\u00e6\nintelligimus. Sed quia Deus uno actu et se, et omnia intelligit, unicum\nverbum ejus est expressivum, non solum Patris sed etiam creaturarum.\nEt sicut Dei scientia, Dei quidem est cognoscitiva tantum, creaturarum\nautem cognoscitiva et factiva; ita verbum Dei, ejus quod in Deo Patre\nest, est expressivum tantum, creaturarum vero est expressivum et\noperativum, et propter hoc dicitur in Psal. 32; Dixit, et facta sunt,\nquia importatur in Verbo ratio factiva eorum qu\u00e6 Deus facit. _Summa\nTheologi\u00e6_, P. 1^a, Q^a, 34^a, A 3^o.\n\nWe see by this passage, that, according to St. Thomas, the Word\nalso expresses creatures, and that it is conceived not only by the\ncognition of them, but, and this too, primarily, by the cognition of\nthe divine essence. Elsewhere, the Holy Doctor says: \"The Father, by\nunderstanding himself, the Son, and the Holy Ghost, and all other\nthings included in His science, conceives the Word, in such a manner\nthat the whole Trinity is expressed in the _Word_, and also all\ncreatures.\"[30]\n\n[30] Pater enim intelligendo se, et Filium, et Spiritum Sanctum, et\nomnia alia qu\u00e6 ejus scientia continentur, concipit Verbum, ut sic tota\nTrinitas Verbo dicatur, et etiam omnis creatura. P. 1^a, Q. 34^a, A.\n1^o, _ad._ 3^{un}.\n\n301. Another doctrine of St. Thomas is also opposed to this system of\nVico, according to whom, the intellect knows what it makes, and that\nonly, and because it makes it; and the made being the sole criterion\nof the true, the true and the made are convertible. Vico applies this\ndoctrine to the divine intelligence, only substituting _begotten_ for\n_made_; but this inverts the order of ideas, since, according to our\nmode of conceiving, God does not understand because he begets, but\nbegets because he understands: intelligence must be conceived before\nthe Word can be conceived. \"In whoever understands,\" says St. Thomas,\n\"_by the very fact of understanding_, something proceeds within him,\nwhich is the conception of the thing understood coming from the\nintellective power, and proceeding from its knowledge.\"[31]\n\n[31] Quicunque autem intelligit, ex _hoc ipso quod intelligit_,\nprocedit aliquid intra ipsum, quod est conceptio rei intellect\u00e6 ex\nvi intellectiva proveniens et ex ejus notitia procedens. Quam quidem\nconceptionem vox significat, et dicitur verbum cordis, significatum\nverbo vocis. P. 1^a, Q. 27^a, A. 1^o.\n\nThis doctrine of St. Thomas confirms the opinion, expressed above,\nconcerning the impossibility of explaining the intellectual act solely\nby production. To produce in the intellectual order, it is evidently\nnecessary to understand; and consequently in the initial moment of\nevery intelligence, the productive act cannot be performed without\nintuition of the object. St. Thomas speaks in this same sense of divine\nthings, as much as one can so speak; he does not found the divine\nintelligence on the generation of the Word, but rather the generation\nof the Word on the divine intelligence. God, according to St. Thomas,\nbegets the Word because he understands, but does not understand because\nhe begets. St. Thomas comprises in the Word the expression of every\nthing contained in God; for he presupposes the divine intelligence,\nby which he makes it possible to speak or utter the Word. This, then,\nis the order of conceptions; understanding, object understood, word\nproceeding from the act of understanding, whereby the intelligent being\nexpresses, or says to itself, the thing understood. These ideas applied\nto God, are: God the Father understanding; divine essence and all that\nit contains understood; Word or Son generated by this intellectual act,\nexpressive of all that is contained in the generative act.\n\n302. We have no disposition to blame Vico; we have only endeavored to\nmark the inexactness of his words, doing him, at the same time, the\njustice to believe that he understood things differently from what he\nexplained them, which, indeed, he has not succeeded in doing with due\nclearness. Let us now consider his system under less subtle points of\nview.\n\nIf the made be admitted as the only criterion of the true, the\nunderstanding is obviously excluded from communication with all that\nit has not itself produced. And not having made itself, it cannot know\nitself. \"The soul,\" says Vico, \"knowing itself does not make itself,\nand therefore knows not in what manner it knows.\" Thus abstracting\nthe problem of intelligibility proposed in our twelfth chapter, Vico\ndenies to our soul a criterion of itself, for the sole reason that it\nis not its own cause. Identity, therefore, far from being an origin of\nrepresentation, as was proved in our eleventh chapter, is incompatible\nwith it; nothing can know itself, because nothing has made itself.\n\nHence results a very grave error; for it may be inferred that not even\nGod can know himself, since he is not his own cause. It is not enough\nto say that he knows himself in the Word, since the Word is impossible\nif intelligence be not supposed.\n\n303. The whole world of reality, distinct from that of intellectual\nbeing, will forever remain unknown in Vico's system, which, for this\nreason, leads to the most rigid skepticism. What does he admit? The\ncognition by the mind of the mind's own work; and in this are comprised\nthe acts of consciousness and all the purely ideal objects which we\ncreate in it. This, also, is admitted by the skeptics, no one of whom\nwould deny that we have consciousness, and that there is an ideal world\nthe work of this consciousness, or at least attested by it.\n\nIf, then, we admit no criterion of truth but the made, we open the door\nto skepticism, and abandon the world of reality to fix ourselves in\nthat of appearance. Nevertheless, so strange are human opinions, Vico\nthought directly the contrary; he believed that only with his system\nwas it possible to refute skepticism. It is curious to hear him say\nwith perfect seriousness: \"The only means of destroying skepticism is\nto take this for the criterion of truth, that every one is certain of\nthe truth which he makes.\"\n\nBut what is the foundation of so odd an opinion? Let us listen to the\nphilosopher himself, who says, indeed, many good things, but does not\nshow how they may tend to the overthrow of skepticism: \"Skeptics are\nalways repeating that things _seem_ to them, but that they do not\nknow what they really _are_. They confess effects, and consequently\nconcede causes to them; but they assert that they do not know these\ncauses, because they do not know the genus or form according to which\nthings are made. Admit these propositions, and retort them thus: the\ncomprehension of causes which contains all the genera and all the\nforms under which effects are produced, and the appearances of which\nthe skeptic confessedly sees, although he denies that he knows their\nreal essence, is found in the first truth which comprises all, and\nin which all, even to the last, are contained. And since this truth\ncomprises all truths, it is infinite, it excludes none, and it has a\nsuperiority over every body, which is only an effect. This truth is\nconsequently something spiritual; in other words, it is God, the God\nof the Christian. By this we must measure human truth; for human truth\nis that truth, the elements of which we have co-ordinated within us,\nand which, by means of certain postulates, we may extend and follow to\ninfinity. By co-ordinating these truths we know and make them at one\nand the same time; and this is why, in this case, we have the genus and\nthe form according to which we make.\"[32]\n\n[32] _Ibid._ 3.\n\nWe discover nothing in this refutation of skepticism calculated to\ndestroy it. Even supposing all to admit the principle of causality,\nwhich all do not admit, what aid can he draw from this principle, when\nhe makes the work of that very understanding, which must make use of\nit, the only criterion? If causality be the only criterion of truth,\nthe understanding is isolated, and cannot, in the order of effects,\ntake one step beyond what it has itself produced; and, in the order of\ncauses, it cannot ascend higher than itself; for, were it so to ascend,\nit would know things not made by itself, would know its own cause. With\nthis supposition the skeptics must triumph; cognition is confined to\nthe internal world, to simple appearances; and when one would go out\nof these, he stumbles against the only criterion which opposes the\ncognition of all _not made_ by the understanding itself. We do then see\nreality, but are separated from it by an impassable abyss. The world in\nitself may be any thing we choose to suppose it; but with respect to\nus, it will be nothing. This law applies to every intelligence, so that\nvitality can only be known by the first cause.\n\nThese consequences, inadmissible as they are, if we would not throw\nourselves unreservedly into the tide of skepticism, are nevertheless\ninevitable in Vico's system. An original way truly of combatting\nskepticism, thus to throw open its widest gates!\n\n\n\n\nCHAPTER XXXI.\n\nCONTINUATION OF THE SAME SUBJECT.\n\n\n304. If the Neapolitan philosopher's criterion be anywhere admissible,\nit can only be in ideal truths; for as these are absolutely cut off\nfrom existence, we may well suppose them to be known even by an\nunderstanding which has not in reality produced them. So far as known\nby the understanding they involve no reality, and consequently no\ncondition that exacts any productive force not referable to a purely\nideal order. In this order the human reason seems really to produce. If\nwe, for example, take geometry, we shall readily perceive that, even\nin its profoundest parts and in its greatest complications, it is only\na kind of intellectual construction, wherein that only is to be found\nwhich reason has placed there.\n\nReason it is which by force of perseverance has succeeded in uniting\nelements and so disposing them as to attain that wonderful result, of\nwhich it may say with truth: _this is my work_.\n\nIf we carefully observe the development of the science of geometry, we\nshall perceive that the extended series of axioms, theorems, problems,\ndemonstrations and solutions, begins with a few postulates, and that\nit goes on with the aid of the same, or others discovered by reason\naccording to the demands of necessity or utility.\n\nWhat is a line? A series of points. The line, then, is an intellectual\nconstruction, and involves only the successive fluxions of a point.\nWhat is a triangle? An intellectual construction wherein the\nextremities of three lines are united. What is a circle? Also an\nintellectual construction; the space enclosed by a circumference\nformed by the extremity of a line revolved around a point. What are\nall other curves? Lines described by the movement of a point governed\nby a certain law of inflexion. What is a surface? Is not its idea\ngenerated by the motion of a line, just as that of a solid is generated\nby the motion of a surface? And what are all the objects of geometry\nbut lines, surfaces, and solids of various kinds, combined in various\nways? Universal arithmetic, whether arithmetic properly so called, or\nalgebra, is a creation of the understanding. Number is a collection\nof units, and it is the understanding that collects them. Two is only\none and one, and three only two and one; and thus with all numerical\nvalues. The ideas expressing these values consequently contain a\ncreation of our mind, are its work, and include nothing not placed\nthere by it.\n\nWe have already observed that algebra is a kind of language. Its\nrules are partly conventional, and its most complicated formulas may\nbe reduced to a conventional principle. Take one of the simplest: a^0\n= 1: but why is it? Because a^0 = a^{n-n}; why? Because there is a\nconventional usage to mark division by the remainder of the exponents;\nand consequently a^n/a^n, which is evidently equal to one, may be\nexpressed a^n/a^n = a^{n-n} = 1.\n\n305. These observations seem to prove Vico's system to be really true,\nso far as pure mathematics, that is, science of the purely ideal order,\nis concerned. Possibly also the same may be said of it in relation to\nother science, as for example, metaphysics; but we shall not follow it\nfarther, since it is not easy to find a ground free from conflicting\nopinions. Moreover, having shown how far Vico's system is admissible in\nmathematics, we have thereby given a solution to difficulties to which\nit is subject in its other branches.\n\n306. That in a purely ideal order the understanding constructs is\nundeniable, and the schools agree in this. There is no doubt that\nreason supposes, combines, compares, deduces; operations which are\ninconceivable without some kind of intellectual construction. The\nunderstanding in this case knows what it makes, because its work is\npresent to it: when it combines it knows that it combines; when it\ncompares or deduces, it knows that it compares or deduces; when it\nbuilds upon certain suppositions, which it has itself established, it\nknows in what they consist, since it rests upon them.\n\n307. The understanding knows what it makes; but this is not all that it\nknows; for it has truths which neither are nor can be its works, since\nthey are the basis of all its works, as, for example, the principle of\ncontradiction. Can the impossibility of a thing being and not being at\nthe same time be said to be the work of our reason? Assuredly not.\nReason itself is impossible if this principle be not supposed; the\nunderstanding finds it in itself as an absolutely necessary law, as a\ncondition _sine qua non_ of all its acts. Here, then, Vico's criterion\nfails: \"the understanding knows only the truth it makes:\" and yet the\nunderstanding knows but does not make the truth of the principle of\ncontradiction.\n\n308. Facts of consciousness are known by reason, although they are not\nits production. These facts are not only present to consciousness, but\nare also objects of the combinations of reason: here, then, Vico's\ncriterion again fails.\n\n309. Although in those things that are a purely intellectual work,\nthe understanding knows what it makes, it does not make whatever it\nchooses; for then we should have to say that science is perfectly\narbitrary: instead of the geometrical results we now have, we might\nhave others as numerous as the individuals who deal in lines, surfaces,\nand solids. This shows reason to be subject to certain laws, its\nconstructions to be connected with conditions which it cannot abstract.\nOne of these conditions is the principle of contradiction, which\nwould, were it to fail, annihilate all knowledge. True, by a series of\nintellectual constructions one may ascertain the size of a sphere; but\ncan two understandings obtain two different values of it? They cannot,\nfor that would be an absurdity: they may choose different ways, or\nexpress their demonstrations and conclusions in different terms; but\nthe value is the same: if there be any discrepancy, it is because one\nor the other has fallen into an error.\n\n310. If we thoroughly examine this matter, we shall perceive that the\nintellectual construction, of which Vico speaks, is a fact generally\nadmitted. There are in this philosopher's system two new things, the\none good, the other bad; the good, is to have indicated one reason of\nthe certainty of mathematics; the bad, is to have exaggerated the\nvalue of his criterion.\n\nWe have said that his system expressed a fact generally recognized,\nbut exaggerated by him. The understanding undoubtedly creates, in some\nsense, ideal sciences; but in what sense? Solely by taking postulates,\nand combining its data in various ways. Here ends its creative power,\nfor in these postulates and combinations it discovers truths not placed\nthere by itself.\n\nWhat is the triangle in the purely ideal order? A creation of the\nunderstanding, which disposes the lines in a triangular form, and,\npreserving this form, modifies it in a thousand ways. Thus far there is\nonly one postulate and different combinations of it: but the properties\nof the triangle flow by absolute necessity from the conditions of the\npostulate: the understanding, however, does not make these properties,\nit discovers them. The example of the triangle is applicable to all\ngeometry. The understanding takes a postulate; this is its free work,\nbut it must not come in conflict with the principle of contradiction.\nFrom this postulate flow absolutely necessary consequences, independent\nof intellectual action, and involving an absolute truth known by the\nunderstanding itself. Consequently it is false to say of them that it\nmakes them. Suppose a man so to place a body, that, left to itself,\nit will fall to the ground: is it the man who gives it the force to\nfall? Certainly not, but nature. The man only supplies the condition\nnecessary for the force of gravity to produce its effect: when once\nthe condition is performed, the fall is inevitable. Here, then, is\na simile which shows clearly and exactly what happens in the purely\nideal order. The understanding performs the conditions; from them flow\nother truths, _not made_, but known, by the understanding. This truth\nis absolute, is as the force of gravity in the order of ideas. Hence\nwe see what is admissible, and what inadmissible in Vico's system.\nThe power of combination, a generally recognized fact, is admissible;\nthe exaggeration of this fact extended to all truths, when it only\ncomprises postulates in their various combinations, is inadmissible.\n\nThe rules of algebra are conventional inasmuch as they relate to\nthe _expression_, for this might evidently have been different.\nSupposing, however, the expression, the development of the rules, is\nnot conventional, but necessary. In the expression a^n/a^n the number\nof times the quantity has entered as factor might clearly have been\nexpressed in infinite ways; but supposing the present to have been\nadopted, the rule is not conventional, but absolutely necessary; since\nwhatever the expression, it is always certain that the division of\na quantity by itself, with distinct exponents, gives for result the\ndiminution of the number of times it has entered as factor: this is\ndenoted by the remainder of the exponents; and consequently if the\nnumber of times be equal in the dividend and the divisor, the result\nwill be = 0. Thus we see that even in algebra, what the understanding\nhas to do, is to perform the conditions, and express them as seems to\nit best: but here its free work ends, for necessary truths result from\nthese conditions; and these it does not make, but only knows.\n\n311. Vico's merit in this point consists in having expressed a very\nclear idea of the cause of the greater certainty of the purely ideal\nsciences. In these the understanding itself performs the conditions\nupon which it has to build its edifice; it chooses the ground, forms\nthe plan, and raises the construction conformably to it. In the real\norder this ground is already designated, just as are the plan of the\nedifice and the materials for its construction. In both cases it is\nsubject to the general laws of reason, but with this difference, that\nin the purely ideal order, it has to regard these laws and nothing\nelse; but in the real order, it cannot abstract the objects considered\nin themselves, and is condemned to submit to all the inconveniences\nthey are of a nature to cause. We will explain these ideas by an\nexample. If we would determine the relation of the sides of a triangle\nunder certain conditions, we have only to suppose the conditions and\nattend to them. The ideal triangle is in our understanding a perfectly\nexact, and also a fixed, thing. If we suppose it to be an isosceles\ntriangle with the relation of the sides to the base as seven to five,\nthis ratio is absolute, immutable, so long as the supposition remains\nunchanged. In all our operations upon these data, we are liable to\nmistakes of calculation, but no error can arise from inexactness of\ndata. The understanding knows, indeed, for what it knows is its own\nwork. If the triangle be not purely ideal, but realized upon paper, or\non the ground, the understanding vacillates because those conditions,\nwhich, in the purely ideal order, it fixes with all exactness, cannot\nbe transferred in like manner to the real order; and even were they\ntransferred, the understanding would have no means of appreciating\nthem. Therefore, Vico says, with great truth, that our cognitions lose\nin certainty in the same proportion as they are removed from the ideal\norder and swallowed up in the reality of things.\n\n312. Dugald Stewart probably had in view this doctrine of Vico when he\nexplained the cause of the greater certainty of mathematical sciences.\nIt does not, he says, depend upon axioms, but upon definitions; that\nis, he adopts, with a slight modification, the system of the Neapolitan\nphilosopher, that the mathematical are the most certain, because they\nare an intellectual construction founded upon certain conditions placed\nby the understanding and expressed by the definition.\n\nThis difference between the purely ideal and the real order did not\nescape the scholastics. They were accustomed to say that there was\nno science of contingent and particular, but only of necessary and\nuniversal things. In the place of _contingent_ substitute _reality_,\nsince all finite reality is contingent; and instead of _universal_ put\n_ideal_, since the purely ideal is all universal; and you will have\nthe same doctrine enunciated in distinct words. It is not easy to show\nexactly how far modern philosophers have availed themselves of the\nscholastic doctrine, in so far as the distinction between pure and\nempirical cognitions is concerned; but it is certain that some very\nclear passages upon these questions are to be found in the works of\nthe scholastics. It would not be strange if some moderns, particularly\nGermans, whose laboriousness is proverbial, especially in matters of\nerudition, had read them.(27)\n\n\n\n\nCHAPTER XXXII.\n\nTHE CRITERION OF COMMON SENSE.\n\n\n313. _Common sense_ is an exceedingly vague expression. It should,\nlike all expressions which contain many and different ideas, be\nconsidered under two aspects: that of its etymological, and that of\nits real value. These two values are not always the same; they are\nsometimes greatly discrepant; but even in their discrepancy, they\nusually preserve intimate relations. We must not, in order duly to\nappreciate the meaning of such expressions, confine ourselves to their\nphilosophical, and contemn their vulgar meaning. In the latter there is\noften a profound philosophy; for, in such cases, the vulgar sense is\na kind of precious sediment left by the flow of reason upon the word\nduring many ages. It thus happens that in measure, as the vulgar sense\nis understood and analyzed, the philosophical question is determined,\nand the most intricate questions solved with the greatest facility.\n\n314. It is remarkable, that besides the corporal senses there should be\nanother, called _common sense_. _Sense_: This word excludes reflection,\nall reasoning, all combination; nothing of this kind enters into the\nmeaning of the word _to sense_. When we sense, the mind is rather\npassive than active; it does nothing of itself; it does not give, it\nreceives; it suffers, but does not perform, an action. This analysis\nleads us to a very important result, and this is, the separation from\ncommon sense of all that upon which the mind exercises its activity;\nand the determination of one character of this criterion, which is,\nwith respect to common sense; the understanding has nothing to do but\nsubmit itself to a law _perceived_, to an instinctive and unavoidable\nnecessity.\n\n315. _Common_: This word excludes all individuality, and shows the\nobject of common sense to be general to all men.\n\nThe simple facts of consciousness are facts of sense, but not of\ncommon sense; the mind feels them when it abstracts objectiveness\nand generality; what it experiences within itself is an experience\nexclusively its own, and one which has no connection with others.\n\nThe word _common_ shows the objects of this criterion to be common\nto all men, and consequently referable to the objective order, since\nthe purely subjective, as such, is limited to the individual, and in\nno wise affects what is general. So exact is this observation, that\nin ordinary language no internal phenomenon, however extravagant, is\never said to be opposed to common sense, provided it be expressed\nsimply with abstraction from its relation to the object. If a man says:\nI experience such or such a sensation, I seem to see such or such a\nthing, common sense is not against him; but if he says, such or such\na thing is in such a manner, and the assertion is extravagant, it is\nagainst him, for this is contrary to common sense.\n\n316. I believe the expression _common sense_ to denote a law of our\nmind, apparently differing according to the different cases to which\nit applies, but in reality and apart from its modifications, only\none, always the same, consisting in a natural inclination of our mind\nto give its assent to some truths not attested by consciousness nor\ndemonstrated by reason, necessary to all men in order to satisfy the\nwants of sensitive, intellectual, and moral life.\n\nIf the fact be agreed on, the name is of little moment: whether _common\nsense_ be or be not the most adequate to signify it, is a philological,\nnot a philosophical, question. What we have to do, is to inquire if\nthis inclination of which we have spoken, really exists, under what\nforms it is presented, to what cases it is applicable, and how far, and\nto what degree it may be considered a criterion of truth.\n\nEvidently this inclination cannot, in the complication of the acts\nand faculties of our soul, and in the multitude and diversity of the\nobjects offered to it, always be presented with the same character;\nit must undergo various modifications capable of causing it to be\nconsidered as a distinct fact, although in reality still the same,\ntransformed in a suitable manner. The best means of avoiding a\nconfusion of ideas, will be to designate the various cases in which the\nexercise of this inclination occurs.\n\n317. We at once detect it in the case of truths immediately evident.\nThe understanding neither does nor can prove them, and yet it must\nassent to them, or perish like a flame that has nothing to feed\nupon. The possession of one or more of these primitive truths is an\nindispensable condition to intellectual life; without them intelligence\nis an absurdity. Here, then, we find all that is comprised in the\ndefinition of common sense: the impossibility of proof; an intellectual\nnecessity, which must be satisfied by assent; and an irresistible and\nuniversal inclination to give this assent.\n\nIs there any objection to calling this inclination common sense? For\nmyself, I shall not dispute upon words; I mark the fact, and this is\nall I need do in philosophy. I grant that the inclination to assent is\nnot, in treating of immediate evidence, usually called common sense,\nand this not without a reason. In order that the word sense may be\nproperly applied to it, the understanding ought to feel rather than\nknow: but in immediate evidence it knows rather than feels. However\nthis may be, I repeat that the name is of no account; yet, it would not\nbe difficult to find this criterion of truth called by grave authors\n_common sense_. What I wish is to establish this law of our nature\ninclining us to give our assent to certain truths, independently of\nconsciousness and ratiocination.\n\n318. Not immediate evidence alone has this irresistible inclination in\nits favor; mediate evidence also has it. Our understanding necessarily\nassents, not only to first principles, but also to all propositions\nclearly connected with them.\n\nThe natural inclination to assent is not limited to the subjective\nvalue of ideas; it also extends to their objective value. We have\nalready seen that this objectiveness is not directly demonstrable _a\npriori_, and yet we stand in need of it. If our understanding is not\nto be limited to a purely ideal and subjective world, we must know not\nonly that things _seem_ to us, as they do with mediate or immediate\nevidence, but also that they really _are_ such as they seem to be. It\nis then necessary to assent to the objectiveness of ideas, and we find\nwithin ourselves an irresistible and universal inclination to such an\nassent.\n\n319. What we have said of immediate and mediate evidence relatively\nto the objective value of ideas, is true, not only in the purely\nintellectual, but also in the moral order. The soul, endowed as it is\nwith free will, needs rules for its direction: if first intellectual\nprinciples are necessary in order to know, moral principles are not\nless so in order to will and work. What truth and error are to the\nunderstanding, good and evil are to the will. Besides the life of\nthe understanding, there is a life of the will; the one, without\nprinciples on which to rest, is annihilated; the other, as a moral\nbeing, perishes, or becomes an inconceivable absurdity, if it have no\nrule, the observation or violation of which constitutes its perfection\nor imperfection. Here is another necessity for the assent to certain\nmoral truths, and another reason of this irresistible and universal\ninclination to assent.\n\nI would here remark, that as it is not enough in the intellectual order\nto know, but it is also necessary to act, and one of the principles of\naction is perception by the senses; so moral truths are not only known\nbut felt. When they are offered to the mind the understanding assents\nto them as unshaken, and the heart embraces them with enthusiasm and\nlove.\n\n320. Sensations considered as purely subjective do not meet the wants\nof sensitive life. We must be sure that our sensations correspond to an\nexternal world, real and true, not phenomenal. Men do not ordinarily\npossess either the capacity or the time requisite to investigate the\nphilosophical questions of the existence of bodies, and to decide for\nor against Berkeley and his followers. What is necessary is perfect\ncertainty that bodies do exist, that sensations have an external\nobject in reality. All men have this certainty when they assent with\nan irresistible force to the objectiveness of ideas, that is, to the\nexistence of bodies.\n\n321. Faith in human authority furnishes us with another case of this\nwonderful instinct. Both the individual and society require faith:\nwithout it society and family would be impossible; the individual would\nbe condemned to isolation, and, therefore, to death. The speech of man,\nthe human race itself, would disappear were it not for faith. This\nbelief has distinct grades according to different circumstances, but it\nalways exists; man is inclined, by a natural instinct, to believe his\nfellow man. When many men speak, and none raise their voices against\nthem, the force of this inclination increases in the same proportion as\nthe number of witness, until it becomes irresistible. Who doubts the\nexistence of Rome? And yet, the greater part of us only know it upon\nthe authority of other men.\n\nWhat foundation has faith in human authority? Most men are ignorant\nof the philosophical reasons which may be assigned; but their faith\nis not therefore less lively than that of philosophers. But why is\nthis so? Because there is a necessity, and at its side an instinct\nto be satisfied. Man must believe in man, and he believes. And here\nnote well, that the greater the necessity, the greater the faith. The\nvery ignorant and imbecile believe all that is told them; they make\nother men their guide, and blindly follow them. The tender child,\nknowing nothing, abandons itself to the absolute belief of the greatest\nmarvels: the word of those around is to it an invaluable criterion of\ntruth.\n\n322. Besides the cases of first intellectual and moral principles, the\nobjectiveness of ideas and sensations, the weight of human authority,\nman must give his instantaneous assent to certain truths, which,\nalthough he might, had he the time, demonstrate, he cannot now,\nbecause so suddenly are they presented to him, that they exact an\nimmediate formation of judgment, and, sometimes, also action. In all\nthese cases, there is a natural inclination impelling us to assent.\n\nHence it is that we instinctively judge it impossible, or little\nless than impossible, to cause a determinate effect, by a fortuitous\ncombination; as, for example, to form a page of Virgil by a chance\nmixture of types, or to hit the bull's eye of a target without\ntaking aim, and other similar things. In this there is assuredly\na philosophical reason, but one not known to common people. There\nis evidence of this reason in the theory of probabilities: it is a\ndistinct application of the principle of causality, and of the natural\nopposition of our understanding to supposing an effect without a cause,\nand order where there is no ordering intelligence.\n\n323. Arguments of analogy, are in human life necessary in infinite\ncases. How do we know that the sun will rise to-morrow? By the laws of\nnature. How do we know that these will continue in force? Evidently, we\nmust finally recur to analogy. The sun will rise to-morrow, because it\nhas risen to-day; it rose yesterday, and it has never failed to rise.\nHow do we know that spring will again bring flowers, and autumn fruits?\nBecause it has so happened in former years. Men ordinarily do not know\nthe reasons which might be given for founding the argument from analogy\non the constancy of the laws of nature, and on the relation between\ncertain physical causes and determinate effects; but their assent is\nrequired and given.\n\n324. In all the cases cited, excepting, perhaps, that of immediate\nevidence, the inclination to assent may be, and really is, called\n_common sense_. The reason of this exception is, that in this case,\nalthough there is no demonstration, the predicate is nevertheless most\nclearly seen contained in the idea of the subject; but in the other\ncases there is neither demonstration nor this vision. Man assents by a\nnatural impulse; and if any thing is objected to his belief, he does\nnot call attention to his conception, as in immediate evidence, but is\ncompletely disconcerted, and knows not what to answer; he then applies\nto the objection, not the name of error, nor of absurdity, but that of\nextravagance, of something contrary to common sense.\n\nSuppose, for example, a little grain of sand to be mixed with a great\nheap, and some one to come and say: I will put my hand into the heap,\nand instantly draw out the one grain hidden there. What will you object\nto such a one? What will the beholders reply? Nothing; or, looking at\neach other in perfect surprise, they will exclaim: \"What extravagance!\nHe has no common sense!\" Or suppose some one to say, that all we see\nis nothing, that there is no external world, that we have no body, or\nthat all told us of the existence of a city called London is untrue.\nWhoever hears such madness, knows not what to answer; but he repels it\nby a natural impulse, and the mind feels that this is nonsense without\nstopping to examine.\n\n325. We shall now inquire whether common sense be a certain criterion\nof truth, whether it be so in all, or in what cases, and what\ncharacters it must have in order to be an infallible criterion.\n\nMan cannot lay aside his nature: when it speaks, reason will not\nallow it to be ignored. A natural inclination, simply because it is\nnatural, is in the eyes of philosophy something highly respectable: it\nis the province of reason and free will not to allow it to go astray.\nWhat is natural to man is not always so perfectly fixed as it is in\nbrutes, where instinct is blind as it must be, where there is neither\nreason nor free will. The exercise of man's natural inclinations is\nsubordinate to his reason and free will, and, consequently, when these\nare called instincts, the word has a very different meaning from what\nit has when applied to brutes. What happens in the moral order is also\nverified in the intellectual. We have not only our heart to watch, but\nalso our understanding; both are subject to the law of perfectibility;\nthe objects which they offer to us are good and evil, truth and error.\nNature herself shows us which one we ought to choose, but does not\nforce our choice; life and death are before us, we may select the one\nwe please.\n\n326. There is in man, independently of the action of free will,\na quality which oftentimes has the effect of turning his natural\ninclinations from their object; it is weakness. Hence, it is nothing\nextraordinary for these inclinations to be so distorted as to lead to\nerror instead of truth, and this renders it necessary to determine what\ncharacters _common sense_ should have, in order to be an absolutely\ninfallible criterion.\n\n327. We will point out the conditions, such as we conceive them to be,\nof true and never-erring common sense.\n\n_First Condition._--That the inclination be every way irresistible, so\nthat one cannot, even by the aid of reflection, resist or avoid it.\n\n_Second Condition._--That every truth of common sense be absolutely\ncertain to the whole human race. This condition follows from the first.\n\n_Third Condition._--That every truth of common sense stand the test of\nreason.\n\n_Fourth Condition._--That every truth of common sense have for\nits object the satisfaction of some great necessity of sensitive,\nintellectual, or moral life.\n\n328. When possessed of all these characters, the criterion of common\nsense is absolutely infallible, and may defy skeptics to assign a case\nwherein it has failed. The higher the degree in which the conditions\nare satisfied, the more certain will the criterion be. We will explain\nthis by a few examples.\n\nThere is no doubt that ordinary men make their sensations so far\nobjective as to transfer what passes within themselves to the exterior,\nwithout distinguishing between the subjective and the objective.\nThus, when they consider colors to be in things themselves, they do\nnot take the green, for example, to be the sensation of the green,\nbut a thing certain, a quality, or whatever else it may be called,\ninherent in the object. But in reality this certainly is not so. The\ncause of the sensation is in the external object; such a disposition\nof facts also as to produce through the medium of light the impression\ncalled _green_. Common sense here deceives; for philosophical analysis\nconvicts it of error. But here common sense has not the requisite\nconditions. In the first place, it ought to stand the test of reason;\nso soon as we reflect upon the case, we discover an illusion as fair as\ninnocent. Moreover, it is not irresistible, for our assent is withheld\nthe instant we are convinced of the illusion. Neither is the assent\nuniversal, for not all philosophers have it. Nor is it indispensable\nto the satisfaction of some great necessity of life. It therefore has\nno one of the conditions just laid down. What we have said of sight is\napplicable to the other senses. What is the value of the testimony of\ncommon sense inasmuch as it leads us to make sensations objective? We\nwill answer this question.\n\nA certainty that sensations correspond to external objects is necessary\nto the wants of life. Upon this all men without exception are agreed.\nReflection cannot despoil us of our natural inclination; and although\nreason, when most it cavils, may shake the foundations of this belief,\nit never succeeds in convicting it of error. Even they who give the\nmost weight to such cavils, cannot prove that bodies do not exist: they\ncan only say that we do not know that they exist.\n\nThe natural inclination then possesses upon this point all the\ncharacteristics necessary to elevate it to the rank of an infallible\ncriterion: it is irresistible, universal, satisfies a great necessity\nof life, and stands the test of reason.\n\nAs to qualities, the direct objects of sensation, it is not necessary\nfor us that they exist in bodies themselves; it is enough that these\nbodies have something which produces in us, in some way or other, a\ncorresponding impression. It is of little moment whether a green, or\norange color be, or be not, a quality of objects, so long as they have\nsome quality which produces in us the sensation of green, or orange\ncolor, as the case may be. The ordinary wants of life are not at all\naffected by this question; and man's relations with the sensible world\nwould not be disturbed by the generalization of philosophical analysis.\nThere is, perhaps, a kind of disenchantment of nature, since, despoiled\nof sensations, it is not nearly so beautiful; but the enchantment\nstill continues with most men; and philosophy itself, except in brief\nmoments of reflection, is subject to it; and even in these moments it\nexperiences an enchantment of a different kind, as it considers how\nmuch of the beauty attributed to objects, belong to man in his own\nright, and that the simple exercise of a sensible being's harmonious\nfaculties suffices to make the whole universe glow with splendor and\nglory.(28)\n\n\n\n\nCHAPTER XXXIII.\n\nERROR OF LAMENNAIS ON COMMON CONSENT.\n\n\n329. The instinctive faith in human authority, of which we have\njust treated, is a fact attested by experience, and one which no\nphilosopher has presumed to call in doubt. This faith, duly directed\nby reason, constitutes one criterion of truth. The errors to which\nit may sometimes lead are inherent in human weakness, and are amply\ncompensated for by the advantages derived from it by society and\nindividuals.\n\nA celebrated writer undertook to include all criteria in that of human\nauthority, resolutely affirming \"common consent, _sensus communis_,\nto be to us the only seal of truth.\"[33] His system, as strange as\nerroneous, in which words as unlike as _sensus_ and _consensus_ are\nconfounded, is defended with that eloquent exaggeration characteristic\nof its eminent author; but profound philosophy does not always\naccompany eloquence. The sad fate of this genius, as brilliant as\nerring, shows the results of such a doctrine; it opens an abyss which\nswallows up all truth, and the author himself was the first to fall\ninto it. To appeal to the authority of others in all things, and\nfor all things, is to despoil the individual of every criterion,\nto annihilate them all, not excepting the very one he attempts to\nestablish. It is inconceivable how such a system could have found favor\nwith so gifted an intellect. We feel, when reading the eloquent pages\nof its development, an undefinable pain to see such brilliant passages\nsquandered on the repetition of all the common-places of skepticism,\nending in a most glaring paradox, and the least philosophical system\nimaginable.\n\n[33] Lamennais, _Essai sur l'Indifference en Mati\u00e8re de Religion_. T.\n2, C. 13.\n\nLamennais calls common sense the only criterion; nevertheless, we have\nonly to glance at the others to be convinced that this new criterion is\nsterile, and could not produce them.\n\n330. The testimony of consciousness, in the first place, cannot rest in\nany sense upon the authority of others. Formed as it is by a series of\nacts intimately present to our own mind, and, as without it, it is not\npossible for us even to conceive individual thought, it must evidently\nexist prior to the application of any criterion, since no criterion is\npossible to him who does not think.\n\nUnder a scientific aspect nothing can be weaker than his pretended\nrefutation of Descartes' principle. \"When, trying to rise from his\nmethodical doubt, Descartes establishes this proposition, _I think,\ntherefore I am_, he passes an immense abyss, and lays in the clouds\nthe corner-stone of the edifice he is about to raise; for, strictly\nspeaking, we cannot say _I think_, we cannot say _I am_, we cannot say\n_therefore_, or affirm anything as a consequence.\"[34]\n\n[34] Ibid.\n\nDescartes' principle merited a more careful examination from whoever\nwould invent a system. To oppose to it that we cannot say _therefore_,\nis to repeat the worn-out argument of the schools; and to affirm that\nwe cannot say _I think_, is to contradict a fact of consciousness not\ndenied even by skeptics. In place of this, we will explain at due\nlength what is, or at least, what ought to be, the sense of Descartes'\nprinciple.\n\nIf, according to Lamennais, we cannot say _I think_, still less can we\nsay that others think; and as his system recognizes one only criterion,\ncommon consent, which absolutely needs the thought of others, it\nfollows that Lamennais has laid his corner-stone higher in the clouds\nthan he who founded philosophy upon a fact of consciousness.\n\n331. A criterion, especially when it pretends to be the only one, ought\nto have these two conditions: to apply to all cases, and not to suppose\nanother. Now the criterion of common consent is precisely that which is\nfarthest from possessing these conditions: prior to it is the testimony\nof consciousness; prior also to it is the testimony of the senses, for\nwe cannot know the consent of others if sight or hearing do not make us\ncertain of it.\n\n332. In many cases this criterion is impossible; in many others it is\nexceedingly difficult if not wholly impossible. To what point is common\nconsent needed? If the word _common_ refers to the whole human race,\nhow are the suffrages of all mankind to be recognized? If the consent\nneed not be unanimous, to what point does the contradiction, or the\nsimple non-assent of some, destroy the legitimacy of the criterion?\n\n333. Lamennais' error consists in taking the effect for the cause, and\nthe cause for the effect. We detect certain truths, upon which all men\nare agreed, and we say: the guaranty that each one is right is the\nconsent of all. If we analyze this well, we shall perceive that the\nreason of each individual's certainty is not the consent of others; but\non the contrary the reason why all agree is that each one for himself\nfeels obliged to give his assent. In this universal voting of the\nhuman race, each one gives his own vote, impelled in a certain sense\nby nature herself; and as all experience the same impulse, all vote\nalike. Lamennais says every one votes in the same way, because all vote\nso; but he does not observe that then the voting could never begin\nnor end. This comparison is not an accidental satire, but a strictly\nphilosophical argument, to which there can be no reply; it suffices to\nshow the system of Lamennais to be unfounded and contradictory; just\nas, on the other hand, it indicates the origin of the equivocation, the\ntaking the effect for the cause.\n\n334. Lamennais, in order to prove his criterion to be the only one,\nappeals to the testimony of consciousness. In our opinion this\ntestimony establishes directly the contrary. Who ever waited for the\nauthority of others to be certain of the existence of bodies? Do we not\nsee even brutes, by force of a natural impulse, making, in their own\nway, their sensations objective? Had we not in giving our assent to the\nwords of men some other criterion than common consent, we could never\nbelieve any one, for the simple reason that it would be impossible to\nbe certain of what others say or think without beginning by believing\nsome one. Does the child refer to the authority of others before giving\nfaith to what its mother recounts? Does it not rather obey the natural\ninstinct communicated to it by the beneficent hand of the Creator? It\ndoes not believe because all believe; but all children believe because\neach one of them believes: their individual belief does not spring from\na general belief, but rather the general belief is formed from the\nassemblage of individual beliefs; it is not natural because universal,\nbut universal because natural.\n\n335. Lamennais' chief argument consists in this: that in certain cases\nin order to make sure of the truth relatively to the other criteria,\nwe appeal to that of common consent, and that folly itself is only the\ndeviation from this consent. If you tell a man that his eyes deceive\nhim as to an object which he sees, he instinctively turns to other\nmen, and asks them if they do not see it in the same way. If all agree\nthat he is wrong, and he is satisfied they are in earnest, he will\nexperience a momentary vacillation of his faith in the testimony of\nsight; he will approach the object, will take a different position,\nor adopt whatever other means may seem to him best suited to make\nsure that he is right. If he still sees the object in the same way,\nand the same persons and others who arrive persist in assuring him\nthat the thing is not as he sees it, he will distrust the testimony\nof sight, and believe himself subject to some infirmity affecting his\nsight. To this is the argument of Lamennais reduced. What results from\nit? Nothing to support the system of common consent. True, the other\ncriteria are, in exceptional circumstances, liable to error; in certain\ncases when a doubt arises an appeal is taken to the testimony of\nothers: but why? Simply, in order to make sure that one has not labored\nunder one of those derangements to which human misery is subject. We\nknow that what is natural is general; and he who doubts inquires of\nothers, that he may ascertain if he has by some accident been out\nof his ordinary natural state. Who sees not the unreasonableness of\nraising an exceptional means to the rank of sole and general criterion?\nWho sees not the extravagance of asserting that we are assured of the\ntestimony of the senses by the authority of other men, solely because,\nin extreme cases fearing some derangement of our organs, we ask others\nif something appears to them as it does to us?\n\n336. Greater exaggeration we cannot have than that of Lamennais,\nwhen he affirms \"that the exact sciences are also founded on common\nconsent; that in this they enjoy no privilege, and that the very term\n_exact_, is one of those empty titles under which man seeks to conceal\nhis weakness; that geometry itself only exists by virtue of a tacit\nconvention, a convention which may be thus expressed: _we are obliged\nto hold such principles to be certain, and we pronounce every one\na rebel to common sense, that is, to the authority of the number,\nwho shall demand a demonstration of them_.\" This is an intolerable\nexaggeration. The arguments which he adduces in his notes to prove\nthe intrinsic uncertainty of mathematics are exceedingly feeble;\nand some of them might make us suspect the author of the _Essai sur\nl'Indifference_ to be a less profound philosopher than eloquent writer.\n\nI am not ignorant of what has been advanced against the certainty\nof the exact sciences, nor of the difficulties they present when\ncalled before the tribunal of metaphysics. In the first volume of\n_Protestantism compared with Catholicity_, I consecrated a chapter to\nwhat I call _instinct of faith_; and this instinct, I there maintained,\nalso exercises its influence upon the exact sciences. These I do not\nplace above moral sciences; I esteem these latter the more; but I must\navoid an exaggeration that would destroy them all.\n\n\n\n\nCHAPTER XXXIV.\n\nSUMMARY AND CONCLUSION.\n\n\n337. In concluding this book, I wish to give a summary of my views on\ncertainty, wherein I shall show the connection between the doctrines\nexposed in the different chapters.\n\nWhen philosophy meets a necessary fact its duty is to accept it.\nSuch a fact is certainty. To dispute its existence, is to dispute\nthe splendor of the sun at mid-day. Mankind are certain of many\nthings; philosophers, skeptics not excluded, are equally so. Absolute\nskepticism is impossible.\n\nSetting aside the question of certainty, philosophy is free from\nextravagance, and is established in the domain of reason; it can there\nexamine how we acquire certainty, and upon what it is based.\n\nThe human race is endowed with certainty as a quality annexed to life,\na spontaneous result of the development of the soul's faculties.\nCertainty is natural; consequently it precedes all philosophy, and is\nindependent of the opinions of men. For the same reason the question\nof certainty, although important to the knowledge of the laws to which\nour mind is subject, is, and always will be, unproductive of practical\nresults. It is a dividing line fixed by reason lest at any time\nsomething should descend from the realm of abstraction prejudicial to\nsociety or individuals. Thus from its first investigations, philosophy\nforms a kind of alliance with good sense; they mutually promise never\nto be hostile to each other.\n\nWhen we examine the foundations of certainty a question arises upon the\nfirst principle of human cognitions: does it exist, and what is it?\n\nThis question may have a double meaning. It may either mean a primitive\ntruth containing all others, as the seed does plants and fruits; or\nsimply a resting-point. The former gives rise to the question of\ntranscendental science; the latter is the cause of the disputes in\nthe schools on the preference of different truths in relation to the\ndignity of first principle.\n\nIf truth exists, there must be means of knowing it, hence the question\nof the value of criteria.\n\nThere is in the order of being one truth, the origin of all truths,\nGod, who is also in the absolute intellectual order the origin of all\ntruths. In the human intellectual order there is no one truth, the\norigin of all others; neither is there in the real, nor in the ideal\norder. The philosophy of the _me_ can be of no account in establishing\ntranscendental science. The doctrine of absolute identity is an\nabsurdity; besides, it explains nothing.\n\nThe problem of representation is here proposed. The representation may\nbe of identity, causality, or ideality. The last is founded on the\npreceding, but is distinct from it.\n\nBesides the problem of representation we examined that of immediate\nintelligibility, a difficult problem, but one of the greatest\nimportance to a perfect knowledge of the world of intelligences.\n\nThe disputes on the value of different principles, as to which has the\nright to be called fundamental, originate in a confusion of ideas.\nWe attempt to compare things of very diverse orders, whereas this\nis impossible. Descartes' principle is the enunciation of a simple\nfact of consciousness; that of contradiction, an objective truth, the\nindispensable condition of every cognition: that of the Cartesians is\nthe expression of a law of our mind. The three, each in its own way and\nsphere, are necessary; no one of them is totally independent of the\nothers; the ruin of any one destroys our intelligence.\n\nWe have various criteria; but they may all be reduced to three:\nconsciousness, or internal sense, evidence, and intellectual instinct,\nor common sense. Consciousness embraces all facts intimately present\nto our soul as purely subjective; evidence extends to all objective\ntruths, upon which our reason is exercised; intellectual instinct is\nthe natural inclination to assent in cases which lie without the domain\nof consciousness and evidence.\n\nThe intellectual instinct obliges us to give an objective value to\nideas; in this case it mingles with the truths of evidence, and is, in\nordinary language, confounded with evidence.\n\nWhen the intellectual instinct operates upon non-evident objects and\ninclines us to assent, it is called _common sense_.\n\nConsciousness and the intellectual instinct constitute the other\ncriteria.\n\nThe criterion of evidence includes two things: the appearance of ideas,\nwhich belongs to consciousness; the objective value, existing or\npossible, which belongs to the intellectual instinct.\n\nThe testimony of the senses also has two parts: sensation as purely\nsubjective, and this pertains to consciousness; and the belief in the\nobjectiveness of sensations, and this pertains to the intellectual\ninstinct.\n\nThe testimony of human authority is composed of that of the senses,\nwhich place us in relation with our fellow-men, and that of the\nintellectual instinct, which induces us to believe them.\n\nNot everything is susceptible of proof; but every criterion stands the\ntest of reason. The criterion of consciousness is a primitive fact of\nour nature; in that of evidence we discover the indispensable condition\nof the existence of reason itself; in that of the intellectual instinct\nby which we make our ideas objective, is found a law of our nature\nlikewise indispensable to the very existence of reason; in that of\ncommon sense, properly so called, is the instinctive assent to truths,\nwhich, when examined, are seen to be perfectly reasonable; in that of\nthe senses, and in that of human authority, we discover the same thing\nas in the other cases of common sense, which is a means of satisfying\nthe necessities of sensation, intellectual, and moral life.\n\nThe criteria do not conflict with, but mutually aid and confirm each\nother. Neither is reason at war with nature, nor nature with reason;\nboth are necessary to us; both direct us with certainty, although they\nare both liable to err, since they belong to a limited and very feeble\nbeing.\n\n338. The philosophy which considers man only under a single aspect\nis incomplete, and in danger of becoming false. So far as certainty\nis concerned, we must bear in mind this last observation: to become\nexcessively exclusive is to place one's self on the brink of error.\nWe may analyze if we will the sources of truth; but we must not lose\nsight of their connection when examining them separately. To begin by\nconceiving a system, and then making everything conform to its demands,\nis to place truth in the bed of Procrustes. Unity is a great good;\nbut we must be satisfied with the measure imposed upon us by nature.\nWe must seek truth by human means, and in proportion to our capacity.\nThe faculties of our soul are subject to certain laws, which we cannot\nabstract.\n\nOne of the most constant laws of our being is the necessity of a\nsimultaneous exercise of our faculties, not only in order to become\ncertain of truth, but even to discover it. Man joins the greatest\nmultiplicity with simplicity: his soul is one, is endowed with various\nfaculties, and united to a body of such variety and complication as\nto be called with much reason a little world. His faculties are in\nintimate and mutual relation; they exert a continuous influence upon\neach other. To isolate them is to mutilate, and sometimes to extinguish\nthem. This remark is important, for it indicates the radical vice of\nall exclusive philosophy.\n\nIf a man have no sensations, his understanding has no materials, nor\nhas it that stimulus, without which it remains dormant. When God united\nour soul and body, it was that one might aid the other; wherefore he\nestablished that admirable correspondence between the impressions of\nthe body and the affections of the soul, which, therefore, needs the\nbody as a medium, as an instrument, whether the action of the body\nupon it be supposed to be a true action, or only a simple occasion of\ncausality of a higher order.\n\nIf a man, having no sensations, were to think, he would only think as a\npure spirit; he would not be in relation with the external world, nor\nwould he be a man in the sense in which we use this word. In such a\ncase the body is superfluous, and there is no reason why it should be\nunited to the soul.\n\nIf we admit sensations, and abstract reason, man is converted into a\nbrute. He feels, but does not think: he experiences impressions, but\ndoes not combine them, for he is incapable of reflecting. Every thing\nsucceeds in him as a series of necessary, isolated phenomena, which\nindicate nothing, lead to nothing, and are nothing but affections\nof a particular being who does not comprehend them, nor render to\nhimself an account of them. It is even difficult to say of what kind\nare his relations with the external world. Arguing from appearances\nand analogy, it is probable that brutes also make their sensations\nobjective; but ordinarily, their objectiveness differs from ours. Let\nus take sleep for example. If brutes sleep, and they probably do sleep,\nas certain appearances seem to indicate, it would not be strange should\nthey not distinguish as we do between waking and sleeping.\n\nThis supposes some reflection upon acts, some comparison between the\norder and constancy of some, and the disorder and inconstancy of\nothers; a reflection which man makes even in infancy, and continues\nto make all his life without adverting to it. When we awake from a\ndeep sleep, we sometimes remain for several moments in doubt if we are\nasleep or awake: this doubt alone supposes a comparative reflection\nof the two states. What do we do in order to resolve this doubt? We\nexamine the place where we are; and the fact that we are abed, in the\nsilence and darkness of night, indicates that the previous vision had\nno connection with our situation, and therefore that we were asleep.\nWithout this reflection, the sensations of sleeping and waking would be\nconnected, and all confounded in one and the same class.\n\nThe instinct conceded to brutes, but denied to men, shows that reason\nwas given to us in order to appreciate sensations.\n\nThere are, then, in man no criteria of truth absolutely isolated. They\nare all in relation with each other, they mutually affirm and complete\neach other; for we must note that those truths, of which all men are\ncertain, do in some sense rest upon all the criteria.\n\nSensations instinctively lead us to believe in the existence of an\nexternal world; and if this belief be submitted to the examination of\nreason, it confirms the same truth, resting upon the general ideas of\ncause and effect. The pure understanding knows certain principles, and\nassents to them as to necessary truths. The senses, if these principles\nbe submitted to their experience, confirm them as much as their own\nperfection, or that of the instruments which they use, permit. \"All the\nradii of a circle are equal.\" This is a necessary truth. The senses\nperceive no perfect circle, but they see that the more perfect the\ninstrument is with which they construct it, so much more nearly equal\nare the radii. \"There is no change without a cause to produce it.\" The\nsenses cannot prove the proposition in all its universality, for they\nare by nature limited to a determinate number of particular cases; but,\nso far as their experience goes, they discover the order of such a\ndependence in the succession of phenomena.\n\nThe senses mutually aid each other. The sensation of one sense is\ncompared with those of the others, when there arises a doubt as to its\ncorrespondence with its object. We seem to hear the whistling of the\nwind; but our hearing has more than once deceived us: to make sure of\nthe truth we look at trees or other objects. We see a figure, but\nthere is not light sufficient to distinguish it from a shadow, we\napproach and touch it.\n\nThe intellectual and moral faculties also exercise a salutary influence\nupon each other. Ideas rectify sentiments, and sentiments ideas.\nThe value of the ideas of one order is verified by those of another\norder; and the same with sentiments. Pity for one suffering punishment\ninspires the pardon of all criminals; the indignation inspired at\nseeing the victims of crime, induces to the application of punishment;\nboth sentiments involve something that is good; but the one would\nengender impunity, the other cruelty; it is to temper them that the\nideas of justice exist. But this justice in its turn might pronounce\nexcessively absolute sentences; justice is one, and the circumstances\nof peoples very different. Justice only considers the culpability, and\nconsequently pronounces such sentences. A sentence may not be proper;\nfor here come in other moral ideas of a distinct order, the amendment\nof the guilty joined with reparation made to the injured party; ideas\nalso of public convenience which are not repugnant to sound morals, and\nwhich may direct their application.\n\nComplete truth, like perfect good, exists only with harmony. This is a\nnecessary law, and to it man is subject. Since we do not intuitively\nsee the infinite truth in which all truths are one, and all good is\none; and as we are in relation with a world of finite, and consequently\nmultiple beings, we need different powers to place us in contact, so\nto speak, with this variety of truths and finite goods; but as they,\nin their turn, spring from _one_ same principle, and are directed to\n_one_ same end, they are submitted to harmony, which is the unity of\nmultiplicity.\n\n339. With these doctrines we believe philosophy without skepticism\nto be possible. Examination is not excluded; on the contrary, it is\nextended and completed. This method has another advantage; it does not\nmake philosophy extravagant, and philosophers exceptional. Philosophy\ncannot be so generalized as to become popular; human nature is opposed\nto this; but there is not on the other hand any necessity of condemning\nit to a misanthropic isolation by force of extravagant professions.\nIn such a case philosophy degenerates into philosophism. Exposition\nof facts, conscientious examination, clear language; such we conceive\nsound philosophy to be. This does not require it to cease to be\nprofound, unless by profoundness be meant darkness. The rays of the sun\nlight up the remotest depths of space.\n\n340. I am aware that some philosophers of our age think otherwise, that\nthey deem it necessary, when they examine the fundamental questions of\nphilosophy, to shake the foundations of the world; and yet I have never\nbeen able to persuade myself that it was necessary to destroy in order\nto examine, or that in order to become philosophers we ought to become\nmadmen. We may render the unreasonableness and extravagance of these\nmasters of humanity sensible by an allegory, although the simplicity of\nmy language may somewhat mortify their philosophical profoundness. The\nreader needs some solace and rest, now that he has followed me through\nsuch abstruse treatises, which all the power of the writer does not\nsuffice to illustrate, and still less to render attractive.\n\nA noble, rich, and numerous family preserves in magnificent archives\nthe records of its nobility, alliances, and possessions. Some of these\ndocuments are hardly legible, either on account of the handwriting,\ntheir great antiquity, or the wear and tear of years. There is also\na suspicion that many of these documents are apocryphal; although it\nis certain that many must be authentic, since the nobility and other\nrights of the family, so universally recognized, must be founded on\nsome of them, and it is known that no other exists. Such is the state\nof things. Some curious person enters the archives, and casting a\nglance upon the shelves, recesses, and drawers, says: \"This is all\nconfusion; to distinguish what is authentic from the apocryphal, and\nput all in good order, we must light a fire at the four corners of the\narchives, and then examine the ashes.\"\n\nWhat shall we think of such a proceeding? This curious person is\nthe philosopher who, to distinguish the true and the false in our\ncognitions, begins by denying all truth, all certainty, all reason.\n\nWe may be told that there is no question of denying, but of doubting;\nbut whoever doubts all truth, destroys it; whoever doubts all certainty\ndenies it; whoever doubts all reason annihilates it. Prudence and\ncommon sense in small things are based upon the same principles as\nwisdom in great things. Let us go on with our allegory, and see what\ncommon sense would indicate ought to be done in this case.\n\nTo take an inventory of whatever now exists, without forgetting any\nthing, however contemptible it may appear; to make such temporary\nclassifications as are deemed most proper to facilitate the\nexamination, reserving the final classification to the close; to note\ncarefully dates, characters, references, and thus to distinguish\npriority and posteriority; to see if there may be found some primitive\ndocuments, referring to others anterior, which certify the origin\nof the family; to establish clear rules for the distinguishing that\nwhich is primitive from what is only secondary; and not to insist\non referring all documents to one alone, exacting a unity which,\nperhaps, they have not; for it may have happened that there were\nseveral primitive and mutually independent documents. It would even be\nadvisable in distinguishing the authentic from the apocryphal not to\nburn any thing, for the apocryphal sometimes aids in the interpretation\nof what is authentic, and it may be desirable to ascertain who were the\nfalsifiers, and what their motives. Moreover, who knows but what he\njudges a document to be apocryphal, which seems to him so to be solely\nbecause he does not understand it? Care, then, is to be taken to make\na due separation, and if the apocryphal is of no use in establishing\ntitles, or in defending them, it may serve for the history of the\narchives, which is no trifling reason for distinguishing the apocryphal\nfrom the authentic.\n\nThe human mind does not examine itself until well developed; then, at\nthe first glance, it sees in itself a connection of sensations, ideas,\njudgments, and affections of a thousand kinds, the whole interwoven in\nan inextricable manner. To increase the complication, it is not alone,\nbut in intimate relation with its like, in mutual communication of\nsensations, ideas, and sentiments; and all in their turn in contact\nwith, and under the influence of, dissimilar beings of amazing variety,\nthe union of which forms the universe. Shall it begin by throwing it\nall down? Shall it reduce all to ashes, and hope to rise like the\nphenix from the pyre? Shall it arbitrarily invent a fact, a principle,\nand say: \"I must have a resting-point, I will take this, and upon it I\nwill found science!\" Shall we, before examining, before analyzing, say:\n\"all this is one; there is nothing if there be not absolute unity; in\nit I place myself, and all that I do not see from my point of view I\nreject?\" No! what we have to do, is first to ascertain what is in our\nmind, and then to examine, classify it, and give to it its true value;\nnot commence by mad and impotent efforts against nature, but to lend an\nattentive ear to her inspirations.\n\nThere is no philosophy without a philosopher; no reason without a\nrational being; the existence of the subject is then a necessary\nsupposition. No reason is possible if the contradiction of being and\nnot-being be possible; all reason, then, supposes the principle of\ncontradiction to be true. When we examine reason it is reason that\nexamines; it needs rules, light; all examination, then, supposes this\nlight, the evidence and the legitimacy of its criterion. Man does\nnot make himself, he finds himself already made; it is not he who\nimposes the conditions of his being; he finds them already imposed.\nThese conditions are the laws of his being, and why contend against\nthem? \"Besides factitious prejudices,\" says Schelling, \"man has others\n_primordial_, placed in him not by education, but by _nature herself_,\nwhich in _all_ men hold the place of principles of cognition, and are a\n_shoal_ to the free-thinker.\" For my own part I do not seek to be more\nthan _all_ men; if I cannot be a philosopher without ceasing to be a\nman, I renounce philosophy and adhere to humanity.\n\n\n\n\nBOOK SECOND.\n\nON SENSATION.\n\n\n\n\nCHAPTER I.\n\nSENSATION IN ITSELF.\n\n\n1. Sensation considered in itself is simply an internal affection; but\nit is almost always accompanied by a judgment. This judgment may be\nmore or less explicit and more or less noticed by the subject of the\nsensation.\n\nSuppose I see two architectural ornaments at a proper distance, and I\ndiscover no difference between them. In this sensation there are two\nthings to be considered.\n\nI. The internal affection which we call _seeing_. On this point all\ndoubt is impossible. Whether I am asleep or awake, raving or in my\nsober senses, whether the ornaments are alike or unlike, whether,\nin fine, they exist or not, there still exists in my soul the\nrepresentation which I call _seeing the ornaments_.\n\nII. I also at the same time form a judgment that, besides the internal\naffection which I experience, the ornaments exist, that they are in\nrelief, and that they are before my eyes. In this judgment I may be\ndeceived; for I may be asleep or in a delirium; it may be that the\nornaments are behind me, and that I only see their reflection in a\nmirror; it may be that what I see is only a paper placed in such a\nmanner behind a glass, as to make upon the retina of my eyes the same\nimpression as the ornaments would if they were really present; or,\nfinally, it may all be the work of a skilful painter who has given\nthis illusory appearance to his canvas.\n\nFrom this we see that, admitting the existence of the internal fact of\nsensation, it is possible:\n\nI. That there is no external object.\n\nII. That the objects exists, but not in the position supposed.\n\nIII. That the object is not the architectural ornaments.\n\nIV. That both are plane surfaces; or, that one is in relief, and the\nother a plane.\n\nThis brings us to the evident conclusion that mere sensation has no\nnecessary relation to an external object; for it not only can, but it\nnot unfrequently does, exist without any such object.\n\nThis correspondence of the internal to the external belongs to the\njudgment which accompanies sensation, not to sensation itself.\n\nIf brutes refer their sensations to objects, as they probably do,\ninstinct must supply in them the want of judgment, as in the child who\nhas not acquired the use of the intellectual faculties.\n\nSensation, therefore, in itself considered, affirms nothing. It is a\nmere affection of our being, an effect produced in our soul, and does\nnot determine whether there is any action of an external object upon\nour senses, nor whether the object is what it seems to be.\n\n2. Let us imagine an animal reduced to the one sense of touch, and\nthat not developed as in us, but confined to a few rude impressions\nlike those of heat and cold, warmth and dryness; and let us compare\nit with human sensibility. What an immense distance between the two!\nSensibility in such an animal borders on insensibility, whilst in man\nit approaches intelligence, the representations of his senses are so\nvaried and so extended as to produce within him a whole world, and\nthey might produce infinite others. Man is at the highest round of\nthe ladder, so far as our observation goes, but who can tell how much\nhigher it may be possible to go?\n\n3. However developed and perfected we suppose sensibility, it falls far\nshort of intelligence, from which it must ever remain separated, as\nfrom a faculty of a different order. Though we suppose the sensitive\nfaculties capable of indefinite perfectibility, they can never reach\nthe sphere of intelligence, properly so called. This perfectibility\nwould lie in a different order, eternally distinct from that of\nintellectual beings. If we suppose a color infinitely perfected, it\nwill never become a sound, a sound a taste, a taste a sound, nor a\nsound a color; because perfectibility is confined to its own order.\nTherefore, however it may be perfected, sensibility can never become\nintelligence.\n\nThis observation will serve to guard against one of the most fatal\nerrors of our age, which consists in regarding the universe as the\nresult of a mysterious force, which, developing itself by a continual\nmovement, at once spontaneous and necessary, goes on giving birth\nto beings and elevating species by a perpetual transformation. Thus\nthe greater perfection of the vegetable organization would produce\nthe animal faculties; these being perfected would become sensitive,\nand in measure as they progressed in the order of sensation they\nwould approach the realm of intelligence, and would finally attain\nit. There is not a little analogy between this system and that which\nmakes thought a transformed sensation; it effaces the dividing line\nbetween intelligent and non-intelligent beings; the sensations of an\noyster may, according to it, be so perfected as to be converted into\nan intelligence superior to that of Bossuet or of Leibnitz; and the\ndevelopment of the faculties of the man-statue would be an emblem of\nthe development of the universe.\n\n4. It may have been already remarked that we are now speaking of the\nsensitive faculty in itself considered, abstracting from its relations\nto external objects; and that we therefore comprehend in the word\n_sensation_, all affections of the senses, whether actually produced,\nrecollected, or imagined; that is, all affections in all degrees from\nthe first direct consciousness of them, or when they are presented to\nthe being which experiences them, until they reach the limit where\nintelligence, strictly so called, commences.\n\nIt is impossible here to draw the dividing line between the sensible\nand the intelligible; this requires profound and extensive studies upon\nsensations compared with ideas, which does not belong to this place:\nbut it will be well to have pointed out the existence of this line, in\norder to avoid confusion in a most subtle matter, in which every error\nis attended with the most serious consequences.\n\n5. In what does sensation consist? What is its internal nature? We\nonly know that it is a modification of our being, and that we cannot\nexplain it. No words suffice to convey an idea of a sensation to one\nwho has never experienced it. The man born blind may listen to all that\nphilosophers have said and written on light and colors, but can never\nimagine what light and colors are.\n\nExperience is the only teacher here; and thus, if we suppose a man's\nsenses to be changed so that green appears to him purple, and purple\ngreen, notwithstanding his constant communication with other men, he\nwill never be freed from his error, and he will never suspect that\nduring his whole life he has made use of the words green and purple in\na different sense from other men.\n\n6. Analogy and nature incline us to believe that brutes are not mere\nmachines, but that they also have sensations. The vast scale over which\nirrational beings are distributed, shows that the faculty of feeling\nis spread over the universe in different degrees, and with a wonderful\nprofusion.\n\nOur experience is confined to the globe in which we live; but are the\nlimits of sensitive life the same as those of our experience? Even\non this globe our observation is confined to what the imperfection\nof our senses, and the instruments which we use, permit; but how far\nis the chain of life prolonged? Where is its term? Is there not some\nparticipation of this mysterious faculty in those beings which we hold\nto be inanimate? Is the universe, as Leibnitz pretends, composed of a\ncollection of monads endowed with a certain perception? This is indeed\nan unfounded hypothesis; but since our means of observation are so\nlimited, we should be cautious how we assign boundaries to the realm of\nlife.\n\n7. We ordinarily speak of the faculty of sensation as of something\nbelonging to a very inferior order; so it is, in fact, if compared\nwith intellectual faculties; but this does not prevent it, in itself\nconsidered, from being a wonderful phenomenon, of a nature to astonish\nand confound all who meditate upon it.\n\nSensation! With this word alone we pass an immense gap in the scale\nof beings. What is the non-sensible compared with the sensible? The\ninsensible is, but experiences not that it is; there is nothing in it\nbut itself: the sensible experiences that it is; and there is in it\nsomething besides itself, all that it feels, all that is represented\nin it. The insensible, although surrounded with beings, is in complete\nisolation,--in solitude; the sensible, although alone, may be in a\nworld of infinitely varied representations.\n\n8. The idea of the _me_ is in some sense applicable to every sensitive\nbeing; for sensation is inconceivable without a _permanent_ being,\nwhich experiences what is _transitory_; that is, without a being which\nis _one_ in the midst of _multiplicity_. Every sensible being, were\nit capable of reflection, might, in its own way, say _I_; for it is\ntrue of all of them that it is _one same_ being that experiences the\n_variety_ of sensations. Without this bond, this unity, there is no\n_one_ sensible being, but a _succession_ of sensations as unconnected\nphenomena of the whole.\n\n9. There is no sensation without direct consciousness; for, as this\nis nothing but the very presence of the phenomenon to the being\nexperiencing it, it would be contradictory to say that it feels without\nconsciousness. A sensation experienced, is a sensation present; a\nsensation not present, that is, not experienced, is inconceivable, is\nan absurdity.[35]\n\n[35] See Bk. II., Ch. XXIII., \u00a7 226.\n\n10. Every sensation involves presence, or direct consciousness, but\nnot representation. I think this distinction important. The sensations\nof smell, taste, and hearing, are not representative; they remain in\nthemselves, and in their object. The being experiencing them might\nbelieve himself enclosed in himself, in an absolute solitude, with no\nrelation to other beings; but touch, and, above all, sight, are by\ntheir nature representative; they involve relation to objects; and they\nimply relation to other beings, not as to mere _causes_ of the internal\naffection, but as the _originals_ represented in the sensation.\n\nThe class of sensible beings endowed with the faculty of representation\nseems to be of an order very superior to the others; these beings not\nonly have consciousness, but also a mysterious power whereby they see\nwithin themselves an entire world.\n\n11. What is the most perfect degree of sensitive life? What the most\nimperfect? These questions we cannot answer, for we cannot judge of\nthese things otherwise than by experience and analogy. But viewing the\nimmensity of the scale, experience shows us we may infer that nature is\nfar richer than we imagine. Let us not disturb its profound secrets,\nbut be content to suspect that they exist.\n\n\n\n\nCHAPTER II.\n\nMATTER IS INCAPABLE OF SENSATION.\n\n\n12. The phenomenon of sensibility reveals to us the existence of an\norder of beings distinct from matter. However perfect we may suppose\nmaterial organization, it cannot rise to sensation; matter is wholly\nincapable of sensation; and the absurd system of materialism can\nneither explain the phenomena of intelligence, nor even of sensation.\n\nIt is of little consequence to us that we do not know the intrinsical\nnature of sensitive being, or of matter; it is enough to know their\nessential properties, in order to infer with certainty that they belong\nto distinct orders. It is not true that the principal idea of the\nessence of things is necessary, in order to demonstrate their absolute\ncontradiction; thousands of times we consider two geometrical figures\nwhose essential property we do not know; yet not, therefore, do we fail\nto see that they are different, and that one cannot possibly be the\nother.\n\nMatter, whatever opinion may be entertained of its essential property,\nis necessarily a composite being; matter without parts, is not matter.\nA composite being, although called _one_, inasmuch as its parts are\nunited together, and conspire to the same end, is always a collection\nof many beings; for the parts though united are still distinct If\nsensation could be predicated of a composite being, the sensitive\nwould not be a single being, but a collection of beings; but sensation\nessentially belongs to a being which is _one_, and if divided is\ndestroyed; therefore, no composite being, however well organized, is\ncapable of sensation.\n\nIf we observe what takes place in us, and reason from analogy, to other\nsensitive beings, we shall discover amid the variety of sensations a\nsingle being which perceives them; it is one and the same being that\nhears, sees, touches, smells, and tastes; that remembers sensations\nafter they have disappeared; that seeks them when agreeable, and avoids\nthem when unpleasant, enjoys the former and suffers in the latter.\nAll this enters into the idea of sensitive being; if brutes had not\nthis _common_ subject of all sensations; were they not _one_ in the\nmidst of multiplicity, _identical_ in diversity, and _permanent_ under\nsuccession, they would not be sensitive beings, such as we conceive\nthem to be; they would have no sensation, properly so called; for there\nis no sensation, in the sense in which we here understand it, without a\nbeing affected by it, a being which perceives it.\n\nIf we imagine a flow and ebb of sensations without any connection,\nwithout a constant being to experience them, the result will not be a\nsensitive being, but a collection of phenomena, each one of which by\nitself alone offers the same difficulty as all united, the necessity of\na being to experience it.\n\n13. Let us take a being composed of two parts, A and B, and see if\nit can acquire, for instance, the sensation of sound. If both parts\nperceive, either both perceive the whole sound, or each a portion of\nit. If both perceive it entire, one of them is superfluous, for we are\nonly seeking to explain the realization of the phenomenon, which would\nthus be verified in one alone. If each part hear the sound, not entire,\nbut only a portion of it, we shall have a divided sound; and what is\nthe division of a sound?\n\nBut even such an imaginary division does not serve to explain the\nphenomenon; for the part of the sound perceived by A will not be\nperceived by B; never, therefore, will there result a complete\nsensation.\n\nShall we suppose A and B to be in relation, and to mutually communicate\ntheir corresponding parts? But then A perceives all its own part and\nalso what B communicates to it: of what use, then, is B, if A perceives\nthe whole? Why not place the whole primitive sensation in A? We here\nsee that such a communication is an absurd hypothesis, since it\nwould make a successive and mutual communication of the parts, and a\nperception by each of its own part, and also of that transmitted to it\nby the others, indispensable to the formation of an entire sensation.\nThus we should have not one sensation only, but as many as there are\nparts; not one sensitive being only, but as many such beings as there\nare parts.\n\nThis hypothesis of communication of the parts paves the way for our\nsystem, since it recognizes the necessity of unity to constitute\nsensation. Why do the parts mutually communicate what they have\nrespectively perceived? Because an entire sensation could not otherwise\nbe formed, and so each part must receive what it has not of itself. The\nobject of this is, that each one may perceive the whole; the sensation,\ntherefore, must be wholly in only one subject; therefore, at the very\ntime that unity is denied, it is acknowledged to be necessary.\n\n14. These parts, A and B, either are simple or they are not; if they\nare simple, why persist in advocating materialism, when we must finally\nreturn to simple beings? It is a manifest contradiction to say that\nsensation is an effect of organization, and yet place it in a simple\nbeing, for the simple cannot be organized; there is no organization\nwhere there are no parts organized. If we admit the simple being,\nand place the sensation in it, the organization will then be, if\nyou choose, a medium, a conduit, an indispensable condition to the\nrealization of the phenomenon; then not it, but the simple being will\nbe the subject. If these parts are not simple, they are composed of\nothers; and of these we may argue the same as of the former; for we\nmust come to simple beings, or else proceed to infinity. If we admit\nsuch a process, the sensible being will not be one, but infinite;\nthe difficulties encountered with only two parts, A and B, will be\nmultiplied even to infinity, and so the sensible being will be not one\nbut infinite, and every sensation infinite.\n\n15. Here we find a very serious difficulty. If matter be incapable of\nperceiving, the soul of brutes is not material; if immaterial, it is a\nspirit, which cannot be admitted.\n\nLet us determine well the meaning of the words, and this difficulty\nwill vanish. An immaterial being is not the same as a spirit; every\nspirit is immaterial, but not every thing immaterial is a spirit.\n_Immaterial_ denotes negation of matter; spirit implies more than this;\nfor we understand by it a simple being endowed with understanding and\nfree-will. The soul of brutes is then immaterial, but not a spirit.\n\nSome one may say, that what is not body is spirit, that between\nthese two classes of beings there is no medium. But why? Whence such\ncertainty? If it be said that there is no medium between the material\nand the immaterial, this is true; for there is, in truth, no medium\nbetween yes and no; every thing either is or is not; but there enters\ninto the idea of spirit much more than the simple negation of matter;\nthere is the idea of an active, intelligent, and free principle.\n\n16. It may then be asked: wherein consists the nature of the soul of\nbrutes? And we ask, wherein consists the nature of the greater part of\nthe things which we perceive? Do we know this nature in itself or in\nits acts? Do we see our own soul intuitively? Or do we, perchance, know\nit by the acts of which we are conscious? If so, we know in like manner\nthe sensitive soul by its acts, that is, by perception of the senses;\nwe know that it is not matter, for matter is incapable of sensation;\nand the reasons which show us that our soul is a simple being, an\nactive principle endowed with understanding and free-will enable us to\nsay that the soul of brutes is a simple being endowed with the faculty\nof feeling, and with instincts and appetites of the sensible order.\n\nWe know not what this active principle in itself considered is, but\nits acts show it to be a force superior to bodies, one of the many\nactivities which are the life of nature. We encounter this living\nforce in a portion of matter admirably organized; the end of this\norganization is the harmonious exercise of the faculties of that living\nbeing which we call animal. Not to know what this force in itself is,\ndoes not prevent us from affirming its existence, for phenomena reveal\nit to us in an indisputable manner.\n\n17. What, then, will be the fate of these souls, or living forces,\nif the organization which gives them life be destroyed? Will they be\nreduced to non-existence, since, not being composed of parts, they\ncannot be decomposed? Will they continue to exist until their turn\nshall come to preside over a new organization? It will be well to\nseparate these various questions, and examine them apart.\n\nIf the soul of brutes be not composed of parts, it cannot perish by\ndisorganization; what has no organizable parts is not organized, and\nwhat is not organized cannot be disorganized. Hence we infer that the\nsoul of brutes cannot perish by corruption, properly so called; for no\nbeing not composed of matter can. We see not what difficulty can arise\nfrom this view; but the question is only resolved in its negative part,\nfor thus far we know only that the soul of brutes cannot die, or be\ncorrupted by decomposition; we must know what is done with it. Is it\nannihilated? Does it continue to exist? And if so, in what way? These\nare different questions.\n\nFirst of all we must observe, that we have here only conjectures, and\nthese rather as to the possibility than as to the reality. Philosophy\nmay indeed enable us to see what may be, but not what is, for we can\nknow the reality only by experience, which in the present case we\ncannot have. When sound philosophy, examining this point, is asked what\nis, its best reply is, that it knows not; if it is asked what may be,\nit enters into an argumentation founded on general principles, and more\nespecially upon analogy.\n\n18. It is usually said that nothing is annihilated; but this needs some\nexplanation. What is the meaning of _annihilation_? To cease to be, so\nthat nothing, which before was, remains. If a body be disorganized, it\nceases to be as an organized body; but the matter remains, and there is\nno annihilation. Is it true that nothing is annihilated? Some say we\nmust distinguish between substances and accidents; for, as these latter\nare a kind of incomplete beings, there is no reason why they should not\ncease to exist, and nothing of them remain; but in this disappearance\nthere is no annihilation, strictly so called; thus we see things\ncontinually transformed, and undergoing a succession of accidents which\ncease to exist whenever the thing ceases to be modified by them. As to\nsubstances, there would indeed be true annihilation should they cease\nto exist, but this they do not, because no substance is annihilated.\nThus some think; we know not how true this system may be, for we know\nnot upon what solid foundation it rests. If a substance be destined to\nan end, why may it not be annihilated when this end no longer exists? A\ncreated being incessantly needs the conservatory action of the Creator,\nfor which reason conservation is said to be a continued creation; when,\nthen, the end to which the created substance was destined ceases, why\nmay it not be annihilated? We see nothing in its being annihilated\nrepugnant to the wisdom or goodness of God. The artificer abandons\na tool no longer serviceable; this, in God, would be equivalent to\nthe withdrawal of his conservatory act, and in the creature, to the\nreduction to non-existence. If it be not repugnant to the wisdom and\ngoodness of God for an organized being to be disorganized, or cease to\nexist as an organized being, why may he not allow a substance which has\naccomplished the object for which it was created to cease to exist?\nFrom this we infer that it would not be against sound philosophy to\nmaintain that the souls of brutes are reduced to non-existence.\n\n19. But supposing there is no question of annihilation, is there any\nreason against their continuing to exist? If there be, we know not what\nit is.\n\nWe know not of what use they would be; but we may conjecture that\nabsorbed anew into the bosom of nature they would not be useless.\nNeither do we know the use of many other beings, and yet we cannot\ntherefore deny their existence, or doubt their utility. Who says that\nthe vital principle residing in brutes can have no object if the\norganization which it animates be destroyed? Does the destruction\nof a plant involve, perchance, the extinction of all the vital\nprinciples residing in it? Do these principles, by not operating\nupon the organized being just destroyed, therefore cease to be of any\nuse in the wonderful laboratory of nature? Who will say that a vital\nprinciple cannot be useful if it does not act upon an object within\nour observation? Who will assert that vital principles do not in\nthe recesses of nature act in many and different ways, and that the\neffects of their activity are not presented very differently according\nto circumstances, yet always in conformity to laws established by\ninfinite wisdom? Do not the magnificent profusion of radical materials,\nthe gems without number which we everywhere discover, the immense\namount of matter susceptible of transformation and assimilation by the\nliving being, the mysteries of generation in the animal and vegetable\nkingdoms, all indicate to us that there are scattered over the universe\nan infinite number of vital principles, which exercise their activity\nin very different ways, and over a scale of astonishing extent? Who\nshall assure us that the same vital principle may not present very\ndiverse phenomena, according to the conditions which determine its\naction? Does not the same principle reside in the acorn, as in the\ngnarled old oak that for ages has defied the fury of the tempest?\nDid experience not show it to be so, who would ever have suspected\nthe vital principle of a shapeless and filthy caterpillar to be the\nsame as that of a beautiful butterfly? It is not then contrary either\nto reason or to experience to suppose the soul of brutes, the vital\nprinciple residing in them, to continue after the organization of the\nbody is destroyed, and, absorbed anew in the treasures of nature, to\nbe there preserved, not as a useless thing, but in the exercise of its\nfaculties in different ways, according to the conditions to which it is\nsubjected.(29)\n\n\n\n\nCHAPTER III.\n\nSLEEP AND WAKING.\n\n\n20. The fact of sensation is connected with many others, and from this\nconnection results a great part of our knowledge. It has been said in\na tone of great confidence, that it was not possible to demonstrate by\nsensations the existence of bodies; for as sensations are something\npurely internal, they cannot enable us to infer the existence of any\nthing external, and there is no reason for not regarding all our\nsensations as a collection of individual phenomena, inclosed in our\nsoul. At first view it seems impossible to solve the difficulty;\nnevertheless, if we examine it thoroughly, we shall see that too great\nimportance has been attached to it.\n\n21. The first objection ordinarily made to the testimony of the senses,\nis the difficulty of distinguishing with certainty between the state of\nsleep and that of waking. We receive when asleep impressions similar to\nthose we receive when awake: how shall we know that the illusion is not\nperpetual? Lamennais, with characteristic exaggeration, says: \"He who\nshall show that all life is not a sleep, an indefinable chimera, will\ndo more than all philosophers have thus far been able to do.\"\n\nThere are here, no doubt, grave difficulties; but we cannot persuade\nourselves that they are insolvable. First of all we shall examine if\nsleep and waking be different, not only in the eyes of common sense,\nbut also in those of reason. Lamennais pretends that only at the\ntribunal of common consent can a satisfactory and definitive sentence\nbe obtained: we are convinced that very close reasoning can arrive at\nthe same result to which consciousness, common sense, common consent,\nor, in other words, the testimony of our own being and that of our\nfellow mortals, conjointly conduce.\n\n22. Man finds in himself a perfectly satisfactory certainty of the\ndifference between sleep and waking: we need no testimony of others to\nknow that we are awake.\n\nThe difference between these states must not be solely sought in the\nclearness and vividness of sensations, and the certainty which they\ngenerate. Undoubtedly images are sometimes presented to us in sleep\nwith as much clearness as if we were awake, and our certainty for the\ninstant is complete. Who has not in sleep experienced great joy, or\nterrible anguish? Sometimes, but very rarely, we have, when we awake,\nthe reminiscence of having in the very act of sleep doubted if we\nwere asleep; but this seldom happens, and it is in general true, that\neven our dreams are not accompanied by this twilight of reflex reason\nwhich warns us of our state and of the illusion that we are under.\nOrdinarily, while we dream, we have no thought that we are asleep,\nand we embrace a friend with the same effusion of tenderness, or weep\ndisconsolately over his tomb, with the same affections as we should\nwere all real.\n\n23. The difference is not in momentary uncertainty, for we usually\nhave, on the contrary, complete certainty. Whence, then, is this? How\ndoes reason explain it? How does philosophy come to the support of\nconsciousness and common sense? This is the matter we now purpose to\nexamine.\n\nIf we abstract sensations having or not having relation to external\nobjects, and also the sufficiency of their testimony in any particular\ncase, and consider them solely as phenomena of our soul, we shall find\ntwo orders of facts completely distinguished by marked characters,\nsleep and waking. In our soul these two orders are totally distinct;\neven in the system of the idealist this distinction must be recognized.\n\nIf we reflect upon what we have experienced since first we had\nconsciousness of what passes within us, we shall observe in our being,\ntwo classes of phenomena. Periodically and constantly we experience two\nseries of sensations; some more or less clear, more or less vivid, are\nconfined simply to their object, without the concurrence of many of\nour faculties, and above all, without reflection upon them; others are\nalways clear, always vivid, accompanied by acts of all our faculties,\nour reflection upon them, and their difference from those that went\nbefore, is entirely subject to our free will in all that is relative;\nwe vary and modify them in a thousand different ways, or suppress and\nreproduce them.\n\nI see the paper upon which I write; I reflect upon this sight; I\nabandon and resume it at pleasure; and if I choose, I connect this\nsensation with others, with a thousand thoughts or different caprices.\nWhat takes place in this act, always has happened to me, and always\nwill, whenever that same series of phenomena is produced in me while\nawake. But if I dream that I write, although it happen not, as it\nordinarily does, that I cannot hold my pen exactly right, nor see\nclearly, but only confusedly, I neither feel the simultaneous exercise\nof all my faculties, nor reflect upon my present state; I do not have\nthat full consciousness of what I am doing, that clear and strong light\nwhich is scattered over all my waking actions and their objects. When\nawake I think upon what I have done, what I am doing, what I shall\ndo; I recollect my dreams and call them illusions, pronounce them\nunconnected and extravagant appearances, and compare them with the\norder and connection of phenomena offered to me while awake. Nothing\nof this kind takes place in dreams; I may, perhaps, have a clear,\nlively sensation but it is independent of my will, it is an isolated\nimpression, the use of only one faculty without the aid of the others,\nwithout fixed and constant comparisons, such as I make when awake; and\nabove all, this phenomenon quickly vanishes, and I either fall into a\nstate of unconsciousness of my being, or enter another state in which\nthe same series of phenomena as before is reproduced; they are clear,\nlucid, connected; they stand the test of reason, which compares them\nwith each other, and with anterior phenomena. Apart, then, from all\nidea of the external world, and even of all being outside of ourselves,\nwe are certain of the distinction between the two orders of phenomena,\nthose of sleep and those of waking.\n\nTherefore, they who attack the certainty of our cognitions because of\nthe difficulty of distinguishing between these states, make use of a\nvery weak argument, and rely upon a fact entirely false. So far am I\nfrom believing it impossible to distinguish philosophically between\nsleep and waking, that I deem the difference between these two states\none of the clearest and most certain facts of our nature.\n\nHaving established this truth, and supposing no one to doubt that the\nsensations experienced in sleep are not produced by external objects,\nand that, consequently, they cannot be a means of acquiring truth, I\npass to another more difficult and important question.\n\n\n\n\nCHAPTER IV.\n\nRELATION OF SENSATIONS TO AN EXTERNAL WORLD.\n\n\n24. Have our sensations any relation to external objects, or are they\nmerely phenomena of our nature? Can we infer the existence of an\nexternal world from the existence of that internal world resulting from\nthe union of the scenes presented by sensations?\n\nThis question is theoretical, not practical, and depends solely on the\nforce of reasoning, not on the voice of nature,--a voice stronger than\nall argument, and irresistible. To whatever result the philosophical\nexamination of the relations of the ideal and the real worlds may lead,\nwe must submit to that necessity of our nature which makes us believe\nin the existence of such relations. The great majority of mankind\nnever have thought, and probably never will think of making such an\nexamination; and yet they have no shadow of doubt that there exists a\nreal world, distinct from us, but in incessant communication with us.\nNature precedes philosophy.\n\nWe have no wish to show reason to be unable to vindicate the legitimacy\nof the inference whereby the real is deduced from the ideal, the\nexistence of the external world from that of the internal; we would\nonly point out a landmark to philosophy, which, if it does not\nillustrate it, may at least inspire it with sobriety in investigating,\nand with mistrust in its results. Indeed we cannot but see that\nthat science must be erroneous which is opposed to a necessity, and\ncontradicts an evident fact: it merits not to be called philosophy,\nif it struggles with a law to which all humanity, not even excepting\nthe philosopher who presumes to protest against it, is inevitably\nsubject. All that can be said against this law, may be as specious\nas you please, but it will only be a vain cavil, a cavil which, if\nunanswerable by our weak understanding, nature herself will resist\nuntil we shall in another life see the depths of these secrets, and how\nthose links are joined whose points of contact reason cannot detect,\nalthough nature feels their irresistible union at every moment of her\nexistence.\n\n25. That sensations are something more than mere phenomena of our soul,\nthat they are effects of a cause distinct from ourselves, is seen by\ncomparing them with each other. We refer some to an external object;\nothers we do not: these two orders of phenomena present very different\ncharacters.\n\nI now have within me the representation of the country where I was\nborn and spent my earliest years. I see clearly a vast plain with\nits fields and prairies, its little hills, now forming only isolated\nhillocks, now stretching in various directions, sinking to the level of\nthe plain, or gradually rising until incorporated with the mountains,\nthe lofty chain of which surrounds all the plain, and makes it a great\namphitheatre, with no outlet except on the south, and here and there\na chasm, seemingly torn in the mighty wall reared by nature. All this\nis very perfectly represented within me, although more than a hundred\nleagues distant, and this whenever, and as long as I choose. The same\nspectacle may, perhaps, be offered to me without the concurrence of my\nwill, but I am always free to distract myself from it; I may drop the\ncurtain upon this scene, or raise it anew at my pleasure.\n\nWhat happens in this case is confirmed by many others; and thus I\ninternally experience a series of phenomena representative of external\nobjects, but am under no necessity to submit to them, for I can\nabandon or resume them by simple acts of my free will.\n\nBut, at the same time, I feel within myself another class of phenomena\nwhich are not dependent upon my will, and which I cannot abandon and\nresume at pleasure; they are subject to certain conditions which I\ncannot dispense with under pain of not attaining my purpose.\n\nI now experience that a painting is represented to me; or, in ordinary\nlanguage, I see a painting before me. Let us suppose this to be\na purely internal phenomenon, and observe the conditions of its\nexistence, abstracting, however, all external reality, that of my own\nbody included, and that, also, of the organs whereby the sensation is,\nor seems to be, transmitted to me.\n\nNow I experience the sensation; now I do not. What has intervened? The\nsensation of a motion that has produced another sensation of sight,\nand has destroyed the first; or, passing from ideal to real language,\nI have placed my hand between my eyes and the object. But why can I\nnot during the last, reproduce the first sensation? We see clearly\nthat if external objects do exist, and my sensations are produced by\nthem, my sensations must be subject to the conditions which they impose\nupon them; but if they are only internal phenomena, there is no way of\nexplaining them. This is only the more incomprehensible as we do not\nfind in the sensations, which we consider as mere phenomena with no\nimmediate relation to an external object, a close dependence of some\nupon others, but rather, on the contrary, great discordance.\n\n26. Purely internal phenomena, those which we regard as truly such,\nare, so far as their existence and their modifications are concerned,\ngreatly dependent upon the will. I produce in my imagination, whenever\nI please, a scene representing the Column of the Place Vend\u00f4me at\nParis, and I suppress it at my pleasure. The same occurs with respect\nto all other objects which I recollect to have seen; their presence\nwithin me depends upon my will. It is true that sometimes objects which\nwe do not wish are represented to us, and that some effort is necessary\nto make them disappear. If we see a dying person, his countenance\npale and damp with sweat, his wandering eyes, his clenched hands, his\ndistorted mouth and painful breathing, interrupted with piteous groans,\nremain long after stamped upon our imagination: this sad spectacle will\noften recur to us in spite of ourselves; but it is very certain that\nif we go into some complicated calculation, or engage in the solution\nof some difficult problem, we shall succeed in making it disappear. We\nsee by this, that even in exceptional cases, so long as we are of sane\nmind, our will always exerts a great influence over purely internal\nphenomena.\n\nIt is otherwise with those which have immediate relation to external\nobjects. We cannot, when in presence of the dying person, avoid\nseeing and hearing him. If these sensations be only a purely internal\nphenomenon, this phenomenon is of a very different order from that of\nthe other. The one is wholly independent of our will, not so the other.\n\nPurely internal phenomena have a very different mutual relation from\nthat of external phenomena. The will exerts a great influence upon the\nformer, but not upon the latter. The former also are offered either by\na mere act of the will, or by themselves, in isolation, and need no\nconnection with other preceding phenomena. I write at Madrid, and all\nat once I find myself on the banks of the Thames, with its countless\nfleet of ships and steamers. But this did not require me to pass\nthrough the series of phenomena which represent what are called France\nand Spain. I can represent the Thames to myself immediately, after a\nthousand sensations, neither connected among themselves, nor with it;\nbut if I would produce in myself the phenomenon called _seeing_, I must\npass through the whole series of phenomena consequent upon a voyage;\nand this not in any way I may fancy, but so as to feel really and truly\nall the accompanying pleasures and inconveniences; I must make a true\nresolution to depart, and arrive punctually at such an hour, at the\nrisk of missing the sensation called, _seeing the stage_, and another,\nwhich I call, seeing myself started; in fine, all the disagreeable\nsensations arising from such a mischance.\n\nWhen I would represent this series of internal phenomena, or, in common\nlanguage, adventures of travel, only internally, I dispose all at my\npleasure; I stop, or travel faster; I take steps of a hundred leagues,\nand pass immediately from one point to another, and I experience\nnone of those inconveniences which render the reality fatiguing. I\nam in a world where I am master. I command, and the coach is ready,\nthe driver on his box, the postilion in his saddle; and I fly as\nborne on the wings of the wind. Beautiful landscapes, barren lands,\ngigantic mountains, and plains whose boundaries join the heavens,\nall pass before my eyes with wonderful rapidity. Tired of the land,\nI embark upon the lofty deep; I see the angry waves, and hear, amid\ntheir roaring and dashing against the ship, the voice of the captain\ngiving his orders. I see the sailors work the ship; I speak with the\npassengers, and roam through the cabins; and yet perceive no offensive\nsmell, and neither feel the qualms of sea-sickness, nor observe them in\nothers.\n\n27. If purely internal sensations, especially when they proceed from\nexternal sensations, be indeed mutually connected, their connection is\nnot such that it may not be modified in a thousand ways. When we think\nof the Obelisk of the Place de la Concorde, its fountains and statues,\nare very naturally presented to us; so, also, are the Palace of the\nTuileries, and that of the Chamber of Deputies, the Madeleine, and the\nChamps-Elys\u00e9es; but we can, by an act of the will, change the scene;\nand if we choose we may transfer the Obelisk to the Place du Carrousel,\nand admire the effect it produces there, until, satisfied with the\noperation, we restore it to its granite base, or think no more of it.\n\nBut with sight, or the external phenomenon, we should in vain strive to\nperform such man\u0153uvres; everything keeps its place, or, at least, seems\nto; and the sensations are bound together with bands of iron. One comes\nafter the other, and we cannot pass by any. The mere observation, then,\nof what passes within us reveals the existence of two wholly distinct\norders of phenomena: in the one, everything, or almost everything,\ndepends upon our will; in the other, nothing. In the one, the phenomena\nhave certain mutual relations, very variable, however, and to a great\nextent subject to our fancy; in the other, they are dependent upon each\nother, and are produced only under certain conditions. We cannot see,\nif we do not open the blinds so as to allow the light to enter. Here\nthe phenomena of blinds and sight are necessarily connected; but they\nare not always so; for we may open them at night, and yet not see; and\nthen we require another auxiliary phenomenon, which is, artificial\nlight. We cannot, if we would, change this law of dependence.\n\n28. What does all this show? Does it not show that the phenomena not\ndependent upon our will, but subject both as to their existence and\naccidents to laws which we cannot change, are produced by beings\ndistinct from ourselves? They are not ourselves, for we often exist\nwithout them; they are not caused by our will, for they often occur\nwithout its concurrence, often also against it; they are not produced\none by the other in the purely internal order, for it very frequently\nhappens that a phenomenon which has a thousand times followed another\nsuddenly ceases, however often the former be reproduced. This leads us\nto examine an hypothesis which will greatly confirm the doctrine we\nhave laid down.\n\n\n\n\nCHAPTER V.\n\nAN IDEALIST HYPOTHESIS.\n\n\n29. The system of the Idealists cannot stand without supposing the\nconnection and dependence which we refer to external objects, to exist\nonly within us, and the causality which we attribute to external\nobjects, to belong solely to our own acts.\n\nI pull a rope in my chamber, and a bell never fails to ring; or in\nidealist language, the sensation formed from that union of sensations\ninto which enters what we call the _rope and pulling it_, produces\nor involves that other, which we call _ringing a bell_. Either from\nhabit or some hidden law, that relation of two phenomena will exist,\nthe never interrupted succession of which causes the illusion in us,\nwhereby we transfer to the real order, what is purely imaginary. This\nis the most irrational explanation possible, and a few observations\nwill show it to be futile.\n\nToday, we pull the rope, and strangely enough, no bell rings: but why\nnot? The causing phenomenon exists; for undoubtedly there passes within\nus the act called pulling the rope, and yet we pull and pull again, and\nthe bell does not ring. Who has changed the succession of phenomena?\nWhy does not the phenomenon which a little while ago produced another,\nnot produce it now? Nothing new has happened within us, we experience\nthe first phenomenon just as clearly and vividly as before; why, then,\nis not the second presented? Why is it that formerly we experienced\nthe second whenever we wished, by only exciting the first, and now we\ncannot? We make the act of our will just as efficaciously as before;\nwho, then, has rendered our will impotent?\n\nHence we infer: first, that the second phenomenon does not depend\nupon the first, considered only as a purely internal fact, for this\nnow exists precisely as it did before, and yet produces not the same\nphenomenon; secondly, that it does not depend upon the act of our will;\nfor this is now as firm and strong as before, and yet produces nothing.\nWe cannot, however, doubt that there is some connection between the two\nphenomena, for we have innumerable times seen one follow the other, and\nthis cannot be explained by mere chance. Since then, one does not cause\nthe other in the internal order, they must have some dependence in the\nexternal order; in other words, still keeping in view the case under\nexamination, although the cause which produced the first phenomenon\ncontinues to exist, its connection with that which produced the other\nphenomenon must be interrupted; and so it was, in fact; for when we\npulled the rope no sound followed, for the simple reason that the bell\nhad been removed. This is comprehensible, if there be causes external\nto what we call sensations; but if there be only simple internal\nphenomena, no rational explanation can be given.\n\n30. And here it is to be observed, that when we would explain the\nfailure of succession of those phenomena which always have been\nunited, we may recur to many very different ones, such as are internal\nphenomena, which, as such, have neither relation nor resemblance, and\ncan only have some connection as corresponding to external objects. We\nmay, when seeking the reason why the bell did not ring, in order to\nexplain the cause of the change in the regular order of appearances,\nthink of various causes, which we now consider as mere appearances or\ninternal phenomena; we may have the following sensations: the rope\nbroken, or caught, the bell broken, or removed, or without a tongue.\nWe may attribute the failure of sound to any one of these sensations:\nbut nothing can possibly be more irrational than to attribute it to\nthem, if we regard them as mere internal facts; for as sensations, they\nnowhere appear. We cannot discourse rationally if we do not make an\nexternal object correspond to each of these sensations, of itself alone\nsufficing to interrupt the connection between pulling the rope and the\nvibration of the air which produces the sound.\n\n31. Hence we conclude: First, that our sensations considered as purely\ninternal phenomena, are divided into two very different classes; some\ndepend upon our will, others do not; some have no mutual connection, or\nare variable in their relations, at the pleasure of him who experiences\nthem; others have a certain connection which we can neither change\nnor destroy. Secondly, we conclude that the existence as well as the\nmodifications of this last class, proceeds from causes not ourselves,\nindependent of our will, and outside of us. That instinct, therefore,\nwhich impels us to refer these sensations to external objects, is\nconfirmed by reason: therefore the testimony of the senses, in so\nfar as it assures us of the reality of objects, is admissible at the\ntribunal of philosophy.\n\nThis demonstrates, in a certain manner, the existence of bodies; for we\nfind, in philosophically examining the conception of body, something in\nit distinct from our own being, the presence of which causes us such\nand such sensations. We know not the intimate essence of bodies; but\neven if we did know it, it would not aid our present purpose, for we\nare not treating of the idea which a philosopher would in such a case\nform, but of that formed by the generality of men.\n\n\n\n\nCHAPTER VI.\n\nIS THE EXTERNAL AND IMMEDIATE CAUSE OF SENSATIONS A FREE CAUSE?\n\n\n32. A difficulty, at first sight serious, but in reality futile, may be\nbrought against the existence of bodies. Who knows, it may be asked,\nbut what some cause, not at all resembling the idea which we form of\nbodies, produces in us all the phenomena that we experience? God may,\nif he pleases, cause one or many sensations in us; and who shall assure\nus that he does not? Who shall assure us that other beings may not do\nthe same, and so all our imaginations of a corporeal world be a pure\nillusion?\n\n33. The first and simplest solution that can be given is, that God,\nbeing infinitely true, can neither deceive us himself, nor allow other\ncreatures to deceive us constantly and in a way that we cannot resist.\nBut this solution although well founded, just, and reasonable, labors\nunder the inconvenience of establishing the physical by recurring to\nthe moral order; and so it would never satisfy those who desire to see\nthe truth of the testimony of the senses demonstrated by arguments\ndrawn from the nature of things. Such arguments we think we can supply.\n\n34. Our sensations do not proceed _immediately_ from a free cause; the\nbeing that produces them, as well as that which experiences them, is\nsubject to fixed and necessary laws. To be convinced of this, we have\nonly to reflect that we cannot, if placed in certain conditions, fail\nto experience a determinate sensation, and that if these conditions be\nwanting, we cannot experience it. And this proves that we, as well as\nthe being which causes the impression in us, are subject to a necessary\norder. Were it not thus, we could not produce the sensation even by\nthe means of certain conditions; for as its cause would be subject\nto no law, but only to its own free will, it might a thousand times\nhappen, that our will would not agree with its will, and so the desired\nimpression would not be produced.\n\nAfter experiencing a sensation of touch in which it seems that an\nopaque body covers our eyes, we do not see, and we cannot with all our\nefforts produce, the sensation called _seeing_; on the other hand, if\nat a corresponding hour and place this sensation of contact ceases to\nexist, we cannot possibly fail to experience the sensation of seeing\ndifferent objects. Here, therefore, we are subject to a necessity;\nthe being, also, that causes the sensations in us, is subject to a\nlike necessity; for if we perform the condition once or a thousand\ntimes of closing our eyes, once or a thousand times the sensation will\ndisappear; or if we open them once or a thousand times in a light\nplace, so many times also the sensation will be produced; the same, if\nwe retain everything in the same state, and varied at our pleasure,\nif we change our situation or the objects around us. There does,\ntherefore, exist without us, subject to necessary laws, a collection of\nbeings which produce our sensations.\n\n35. It is remarkable not only that the influence they exert upon us\ndoes not flow from election or spontaneity in them, but that they are\nnot even presented as endowed with an activity of their own. A painting\nhung upon the wall produces in us the same sensation as often as we\nlook at it; and, saving the deterioration of time, it will continue\nfor ever to produce the same sensation.\n\nIt is, moreover, evident that these beings are subject to our action,\nfor we can, by acting upon them differently, make them produce\ndifferent impressions. We touch a ball, and the continuation of the\nsensation of a hard, polished, spherical body, assures us that it is\none and the same being that produces it for a certain length of time;\nand yet, in this interval, we may receive many and various sensations\nfrom the same object, by presenting it to the light in different ways.\n\n36. The subjection of these beings to necessary laws is not necessarily\nwith respect to sensations, but is rather a mutual connection of their\nown. The connection of impressions which we receive from them is an\neffect of the dependence of some of them upon others; so that, in\norder to produce a determinate impression, we often employ an object\nwhich is, in itself considered, of no direct use, but which brings\nanother into action, and so leads to what we desire. To raise a curtain\nhas no connection with a magnificent landscape; and yet, oftentimes,\nwe do nothing else when we wish to obtain a pleasant prospect. The\nrelation in question is not then of sensations, but of their objects;\nthe connection of these is what induces us to make use of one of them\nin order to obtain another. There is, therefore, outside of us a\ncollection of beings subject to fixed laws, as well with respect to\nour sensations as to themselves mutually; therefore the external world\nexists, and the internal world, which represents it to us, is not a\npure illusion.\n\n\n\n\nCHAPTER VII.\n\nANALYSIS OF THE OBJECTIVENESS OF SENSATIONS.\n\n\n37. Is the external world such as we believe it to be? Are the beings,\ncalled _bodies_, which cause our sensations in reality what we believe\nthem? May we not, even after having demonstrated the existence of these\nbeings, and their necessary subjection to constant laws, still doubt\nwhether we have demonstrated the existence of bodies? Does it suffice\nfor this to have proved the existence of external beings in relation\namong themselves and with us by means of laws fixed and independent of\nthem as of ourselves?\n\n38. Thoroughly to understand this question, it will be well to simplify\nit, and confine it to a single object.\n\nI hold in my hand and see an orange. I am certain, from what has just\nbeen demonstrated, that an external object exists in relation with\nother beings, and with myself, by necessary laws; I am also certain\nthat I may receive different impressions from it; I see its color,\nsize, and shape, perceive its odor, try its taste; feel in my hand its\nsize, weight, and form, its concavities and convexities, and also hear\na little noise when I press it with my hand.\n\nThe idea of body is composite, and such is that of the orange; for it\nis that of something external, extended, colored, odorous, and savory.\nWhenever all these circumstances exist together, whenever I receive\nfrom an object these same impressions, I say that I see an orange.\n\n39. Let us now examine how far the object corresponds to the sensations\nit causes in us.\n\nWhat do we mean when we say a thing is savory? Simply, that it produces\nan agreeable impression upon our palate; and the same is true of\nsmell. Therefore, the two words, odorous and savory, express only\nthe _causality_ of these sensations resident in the external object.\nWe may say the same of color, for, although we commonly transfer the\nsensation to the object, and openly contradict the philosophical theory\nof light and color, this contradiction is less real than apparent; for\nthe judgment well examined is found to consist only in referring the\nimpression to determinate objects; so that when we for the first time\nhear professors of physics tell us that colors are not in the object,\nwe easily accustom ourselves to reconcile the philosophical theory with\nthe impression of the sense; especially since this theory does not\nrender it less true that this or that impression comes to us from this\nor that object, or its different parts.\n\n40. Here, it is not difficult to explain the phenomena of sensation\nor their correspondence with external objects; for the correspondence\nis saved if these objects be really the cause (or occasion) of the\nsensations. The question of extension is more difficult; for this is\nas the basis of all other sensible properties; and abstracting its\nconstituting or not constituting the essence of bodies, it is certain\nthat we know no body without extension.\n\n41. The following observation will render palpable the difference\nbetween extension and other sensible qualities. He who has never\nthought of the relation of external objects to his sensations is\nindescribably confused; he in some sense transfers color, odor, taste,\nand even sound, to objects themselves, and considers confusedly these\nthings to be qualities inherent in them. Thus the child and the\nuneducated man believe the color green to be really in the foliage,\nodor in the rose, sound in the bell, taste in the fruit. But this\nis readily seen to be a confused judgment, of which they render no\nperfectly clear account to themselves; a judgment which may be changed\nor even destroyed without changing or destroying the relations of our\nsensations with their objects. Even at a very tender age we easily\naccustom ourselves to refer color to light, and even not to fix it\ndefinitively, but to regard it as an impression produced upon our\nsense by the action of that mysterious agent. It costs us no more to\nconsider smell as a sensation produced by the action of the effluvia\nof bodies upon the organ of smell; we also cease to consider sound as\nsomething inherent in the sonorous body, and come to see in it only the\nimpression caused upon the sense by the vibration of the air, excited\nin its turn by the vibration of the sonorous body.\n\nThese philosophical considerations may, at first sight, seem to be\nin contradiction to our judgment, but they do not change to us the\nexternal world; they cause no inversion of our ideas of it; they only\nmake us fix our attention upon some relations which we had imperfectly\ndefined, and do not allow us to attribute to objects what in reality\ndoes not belong to them. They make us limit the testimony of the senses\nto their appropriate sphere, and in some manner rectify our judgments;\nbut the world continues the same that it was before, excepting that we\nhave discovered in the marvels of nature a closer relation with our own\nbeing, and have perceived that our organization and our soul play a\nmore important part in them than we had imagined.\n\n42. If we destroy extension, take this quality from external objects,\nand regard it as only a mere sensation, of which we only know that\nthere is an external object which causes it, the corporeal world at\nonce disappears. The whole system of the universe will be reduced to\na collection of beings which cause us different impressions; without\nthe idea of extension we can neither form any idea of body, nor know\nif all that we have thought of the world be aught else than a pure\nillusion. I can easily resign my infantile belief that the color I see\nin my hand is in it, or the noise made when I clap my hands is in them;\nbut I cannot, do what I will, lay aside the idea of extension; I cannot\nimagine the distance from my wrist to the extremity of my fingers to\nbe only a pure illusion, that there only exists a being which causes\nit without my knowing whether in reality this distance exists. I can\neasily separate from the fruit which I find savory the quality of\nsavor; and I may, if I examine it philosophically, admit, without\nany inconvenience, that it has nothing resembling taste, but that it\nis only composed so to affect my palate as to produce an agreeable\nsensation. But I cannot take from the fruit its extension; in no wise\ncan I regard it as something indivisible; I cannot possibly regard\nthe distance from one of its points to another as a mere sensation.\nMy efforts to consider the savory object as in itself indivisible are\nall in vain; and if, for a single instant, I seem to have overcome the\ninstinct of nature, every thing is overturned. By the same right that\nI make the fruit something indivisible, I may make the whole universe\nso; but an indivisible universe is to me no universe; my intellect is\nconfounded, and all around me is annihilated. I am in worse than chaos;\nfor chaos is at least something, although the elements are in horrible\nconfusion and frightful darkness; but now I am worse off, for the\ncorporeal world, such as I have conceived it to be, returns to nothing.\n\n\n\n\nCHAPTER VIII.\n\nSENSATION OF EXTENSION.\n\n\n43. Two of our senses perceive extension; sight and touch. Sound,\ntaste, and smell accompany extension, but are something different\nfrom it. The sight perceives nothing not extended; extension is every\nway inseparable from this sensation. We may be so enchanted by the\nsweet harmony of many instruments as to forget the extension of the\ninstruments, the air, and our organs; but we cannot, in contemplating\na painting even in the midst of our most ardent enthusiasm, make its\nextension vanish. If we withdraw from the _Transfiguration_ of Raphael\nits extension, the marvel disappears; for even considered as a simple\nphenomenon of our soul, continuity and distance enter of necessity into\nits very essence.\n\nThe same is true of touch, although less generally so. Hardness\nand softness, roughness and smoothness, squareness and roundness,\nall involve extension; but it cannot be denied that there are some\nimpressions of touch, in which it is less clearly involved. The acute\npain of a puncture, and others felt without any known external cause,\nare not so clearly referred to extension, but seem to have something\nof that simplicity which distinguishes the impressions of the other\nsenses. However this may be, it is certain that the perception of\nextension belongs in a special manner to sight and touch.\n\n44. In order to form a clear idea of extension in its relations to\nsensation, we will analyze it at some length.\n\nAnd first of all, it is to be remarked, that extension involves\nmultiplicity. An extended being is of necessity a collection of\nbeings, more or less closely united by a bond which makes them all\nconstitute one whole, but does not prevent them from continuing many. A\nsplendid painting, wherein the unity of the artist's thought dominates,\ndoes not cease to be composed of many parts; the _moral_ chain which\nunites, does not identify them; it only connects, co-ordinates them,\nand makes them conspire to one end. The firm adhesion of the molecules\nforming the diamond does not prevent these molecules from being\ndistinct: the material chain unites, but does not identify them.\n\nThere is then no extension without multiplicity: where there is\nextension, there is, rigorously speaking, not one only being, but many\nbeings.\n\n45. Multiplicity does not constitute extension, for it may exist\nwithout extension. Neither the multiplicity of sounds, of tastes, nor\nof odors, constitutes extension. We conceive in the material, as in\nthe moral and intellectual orders, multiplicity of beings of different\norders, and yet this multiplicity involves no idea of extension.\nEven if we confine ourselves to the purely mathematical order, we\nfind multiplicity without extension, in arithmetical and algebraic\nquantities. Therefore multiplicity, although necessary, does not alone\nsuffice to constitute extension.\n\nIf we reflect upon the species of multiplicity required to constitute\nextension, we shall observe that it must be accompanied by continuity.\nSensations of touch as well as of sight involve continuity; for it is\nimpossible for us to see or to touch, without receiving the impression\nof objects continuous, immediately adjoining each other, co-existing\nin their duration, and at the same time presented as continuous one\nwith another in space. Without this continuity, multiplicity does not\nconstitute extension. If, for example, we take four or more points on\nthe paper on which we now write, and by an abstraction consider them as\nindivisible, this multiplicity will not constitute extension: we must\nunite them by lines at least imaginary; and if continuity be wanting to\nthe body in which we suppose them situated, we shall find it necessary\nto recur to the continuity of space; that is, to regard this space as a\ncollection of points whose continuation connects the first points. No\npossible efforts can enable us to consider a collection of indivisible\npoints, neither continuous nor united by lines, as extension; this\ncollection will be to us as that of beings having no connection with\nextension. It is worthy of observation, that if we assign them a\ndeterminate position in space, this we do only by connecting them with\nother points, by means of imaginary lines: for we cannot otherwise\nconceive either distances or position in space. If we attempt to\nabstract all this, we either fall into intellectual nothingness, we\nannihilate all idea of the object, or we pass to another order of\nbeings having no relation either to extension or space. We quit matter\nand sensations, and mount to the realm of spirits.\n\n46. Multiplicity and continuity are therefore necessary to constitute\nextension; and we believe that these two conditions suffice; for where\nthey exist, extension exists, and with them alone, we form the idea of\nextension. The object of geometry is extension; and only multiplicity\nand continuity constitute it. Lines, surfaces, solids, such as are the\nobject of geometry, are only this continuity considered in its greatest\nabstraction. Empty space suffices, or rather is requisite for geometry;\nsince, it does not, in making its applications to bodies, find all the\nexactness of continuity in the abstract.\n\n47. If multiplicity and continuity constitute extension in space,\nit really exists in the objects which cause our sensations. Basing\nourselves upon the relation of phenomena among themselves and to their\ncauses, we have shown that external objects correspond to sensations:\nthus it is that this relation also exists with respect to multiplicity\nand continuity; these two properties are therefore found in nature.\nThe impressions that we receive by sight and touch, are, although\nwe confine ourselves to a single object, multiple, and consequently\ncorrespond to many objects: they are continuous, and consequently\ncorrespond to continuous objects.\n\nWe will explain this reasoning. Looking at a painting, I receive an\nimpression coming from many different points; and this impression,\nit must be observed, comes uninterruptedly from the whole surface\npresented. If, as we have shown, the sight of one external point\nsufficed to convince me of its existence, that of many will make me\nsure of the existence of many; and the continuity of the impression\nwill also make me certain of the continuity of the impressing points.\n\nIf I touch the object seen, my touch will confirm that testimony\nof sight, in what corresponds to it, that is, the multiplicity and\ncontinuity, I experience the same continued succession of sensations;\nand this shows me the existence and continuity of the objects causing\nthem.\n\n48. In a few words, extension supposes the co-existence of many\nobjects, in such a way, however, that they are one by continuation of\nothers: of both, sensation makes us certain: therefore the testimony of\nthe senses suffices to make us certain that there are external objects,\nand that they may produce various impressions. These ideas contain\nevery thing included in the idea of body: therefore the testimony of\nthe senses makes us certain of the existence of bodies.\n\n\n\n\nCHAPTER IX.\n\nOBJECTIVENESS OF THE SENSATION OF EXTENSION.\n\n\n49. Having proved the testimony of the senses sufficient to assure us\nof the existence of bodies, we now come to examine how far the ideas it\nmakes us form are correct. It is not enough to know that we may be sure\nof the existence of extension; we must inquire if it in reality be such\nas the senses represent it; and what we say of extension is applicable\nto the other properties of bodies.\n\nIn our opinion, the only sensation that we transfer, and cannot help\ntransferring, to the external, is that of extension; all others relate\nto objects only as effects to causes, not as copies to originals.\nSound, taste, and smell represent nothing resembling the objects\ncausing them, but extension does; we attribute extension to objects,\nand without it we cannot conceive them. Sound outside of me is not\nsound, but only a simple vibration of the air, produced by the\nvibration of a body. Taste outside of me is not taste, but only a\nbody applied to an organ of which it causes a mechanical or chemical\nmodification. The same is true of smell. Even in light and colors,\noutside of me, there is only a fluid which falls upon a surface,\nand either directly or reflexly comes, or may come, to my eyes. But\nextension outside of me, independently of all relation with the senses,\nis true extension, is something whose existence and nature stand in\nno need of my senses. When I perceive, or imagine that I perceive it,\nthere is in it, and in my impressions, something besides the relation\nof an effect to its cause; there is the representation, the internal\nimage of what exists externally.\n\n50. In order that the truth of what we have just advanced may be\nperfectly understood, and strongly felt, we would offer the reader a\npicture whence determinate sensations may be successively eliminated,\nand made to mark the degree of elimination which it is possible to\nreach, but not pass.\n\nLet us suppose all animals at once to lose the sense of taste, or all\nbodies to be by nature destitute of the property of causing by their\ncontact with an organ the sensation called taste. The external world,\nnevertheless, continues to exist as before; the same bodies that caused\nin us the sensations now lost, continue to exist, and may be applied\nto the very organ they before affected, and cause in it sensations of\ntouch, as of soft or hard, warm or cold. Either savory bodies, or the\norgans of animals, have undergone some change, which has interrupted\ntheir previous relations; a cause which before produced an effect\nis now seen to be impotent to produce it. This may be owing to a\nmodification of the bodies without changing their nature, so far as we\nknow it; and it is also possible that they have not been changed, but\nthat this difference arises solely from an alteration of the organs.\nBut in any case, the disappearance of this sensation has not made\nanything resembling it disappear from the universe; if the change has\nbeen only in the organs, external bodies remain untouched; and if it\nhas taken place in bodies, it has made them lose a _causing_ property\nof the sensation, but not a property _represented_ by the sensation.\n\nWe have taken all taste from food, and the universe exists as before;\nlet us now take away all odors, by changing odoriferous bodies, or the\norgan of smell. The same follows as in the case of taste. Odoriferous\nbodies will continue to exist, and even transmit to our organ the\neffluvia that before produced the sensation of smell; and the only\nnovelty will be the non-existence of that sensation. Either the\ndisposition to receive the necessary impression will be wanting in our\norgans, or a causality will have disappeared from the universe, but not\na thing represented by the sensation. Gardens will not be despoiled of\ntheir beauty, nor the fields of their luxuriant verdure; the tree will\nstill display its leafy bower, and the fair fruit hang from its boughs,\nand be shaken by the wind.\n\nLet us proceed in our destructive march, and now suddenly make all\nanimals deaf. The musician becomes the actor of a silent pantomime; the\nbell-rope is pulled, and only the mute metal is struck; conversation\nis reduced to oral gestures, and the howlings of brutes are only the\nopening and closing of their mouths. But the air vibrates as before;\nits columns strike as before the drum of the ear; nothing has been\nchanged; nothing has failed in the universe but one sensation. The\nlightning ploughs the skies, rivers follow their majestic course,\ntorrents dash onwards with the same rapidity, and the proud cascade\nstill leaps from its lofty rocks, and displays its changing hues and\nfoaming waves.\n\nBut let us now commit the greatest cruelty; let us make all living\ncreatures blind. The sun still pours out his immense torrents of the\nfluid we call light; it is reflected from surfaces, and is refracted\nfrom the bodies it meets, and passes to the retinas of eyes that\nformerly saw, but are now converted into insensible membranes, placed\nbehind a crystal; but every thing called color and sensation of light\nhas disappeared. Yet the universe exists as before, and the celestial\nbodies still follow their immense orbits.\n\nAs it is most difficult for us to abstract the sensation of\nlight and colors from objects; or, in other words, as we have a\ncertain propensity to imagine that there really exist without us\nimpressions which are only in us, and to consider the sensation as a\nrepresentation of the exterior; so it costs us most to conceive all\nliving creatures to be blind, and nothing to remain of what sensations\nof this kind represented to us, not even a fluid which reflects from\ncertain surfaces, and passes through some bodies, not otherwise than\nas an invisible fluid. Wherefore, in condescension to the difficulty\nwhich some experience in ceasing to externally realize what exists only\nwithin them, we will frame our supposition differently; for it will\nthen be all that the demonstration requires, and we may eliminate from\nobjects whatever relates to any sensation excepting that of extension.\n\nWe will not then make all animals blind, nor practise the cruelty\nof Ulysses in the cave of Polyphemus, but spare in our inversion of\nthe world that destructive instinct. It matters little that men and\nanimals are not blind, provided they cannot see. We will then leave\nthose organs untouched, but we will in return, take all light from\nthe universe; quench like faint torches the sun and stars and all the\ncelestial bodies, extinguish their feeblest scintillations upon the\nearth, the tall tapers which illumine the rich man's dwelling, and the\nfire kindled in the peasant's cot, the spark struck from the flint, and\nthe pale phosphorescences emitted from the graves of the dead. Every\nthing is involved in obscurity, and it is as if that darkness which\nrested upon the face of the abyss before the Creator said: _let there\nbe light_, were restored.\n\nWe must bear in mind that we have not, by plunging the world into such\nfrightful obscurity, changed any one of its laws. The gigantic orbs\ndescribe as before with astonishing rapidity and admirable precision\ntheir immense orbits. Hence we infer that although we destroy smell,\ntaste, sound, light, and colors, the world still exists, and we may\nwithout difficulty so conceive it to be. We may even destroy the\nsensation of touch, for it is easy to suppose that we perceive no\nimpression by this sense. We may substitute some sensations, whose\ncauses lie in bodies like those of heat and cold, hardness and\nsoftness, for others, without therefore believing the universe no\nlonger to exist.\n\n51. Let us now make another abstraction, and see what will happen.\nLet us destroy extension. The world resists not this trial; the stars\nvanish, and the earth disappears beneath our feet, distances no longer\nexist, and motion is an absurdity: our own body fades away and the\nwhole universe is tumbled into nothingness, or if it continues somehow\nto exist, it is totally different from what we now imagine it to be.\n\nAnd so indeed it is. If we abstract extension, if we do not externally\nrealize that sensation, or idea, or whatever else it may be, which we\nhave of it, if we do not consider it as the representation of what\nexists without us, every thing is overthrown: we know not what to think\neither of our sensations, or their relation to the objects causing\nthem; things all go roundabout, and one basis of our cognitions fails:\nin vain we stretch out our arms to lay hold of some fixed point; and we\nask in our trouble, if all that we perceive be only a pure illusion, if\nBerkeley's extravagances be true.\n\n52. It is worthy of remark that, even if we make extension objective\nby transferring it to the external, it is not altogether correct to\nsay that it is represented by the sensation. It is better to say that\nit is a receptacle of certain sensations, a condition necessary to\nthe functions of some of the senses, but not their object. Extension\nabstracted from the sensations of sight and touch, is, as we have\nalready said, reduced to multiplicity and continuity. The knowledge\nof it comes to us from the senses, but it is different from what the\nsenses represent it to us. When we take color and light from the\nsensations, received through the sense of sight, we certainly still\nretain the idea of a thing extended, but not of a visible thing, nor\nof an object represented by the sensation. In like manner, if we\ndespoil the sensations received through the sense of touch, of those\nqualities which affect this sense, the object that caused them is not\nannihilated, neither is it represented by the impressions it transmits\nto us.\n\n53. These remarks show that we do not transfer our sensations to the\nexterior, that they are a medium whereby our soul is informed, but not\nimages wherein it contemplates its objects. All sensations indicate an\nexternal cause; but some, like those of sight and touch, in an especial\nmanner denote multiplicity and continuity, or extension.\n\nHence we also infer that the external world is not a pure illusion, but\nthat it really exists with its great masses, its various motions, its\nunlimited geometry: but much of its beauty lies rather within ourselves\nthan in it. The Creator of it has in an especial manner, shown his\ninfinite wisdom and omnipotent hand in sensible beings, and above all\nin intelligences. What would the universe be were there no one to feel\nand to understand? The beauty, the harmony, the marvels of nature\nconsist in the close relation, the continuous communication of objects\nand sensible beings. The rarest painting, were there no one to perceive\nand admire its beauty, would be only a collection of lineaments, a\nhieroglyphic of unintelligible characters; but so soon as it is seen by\na feeling and knowing being, it is animated, is what it ought to be;\nand in this wonderful communication the object gains in beauty all that\nit imparts of pleasure.\n\nSuppose a collection of instruments disposed by the proper mechanism\nto execute with admirable precision the highest conceptions of Bellini\nor Mozart: to what is it all reduced if there be no sensitive being?\nTo vibrations in the air governed by some law, to mere movements of\na fluid, subject to geometrical necessity. Introduce a man, and the\ngeometry is changed into celestial harmony, then there is music,\nenchantment.\n\nThe symmetry of the walks of a garden, the elegance of its shrubbery,\nthe color and beauty of its flowers, the fragrance of its odors, are,\nwithout a sensitive being, only geometrical figures, surfaces disposed\naccording to some law, volumes of such or such a kind, columns of\nfluids springing from them and disappearing in space. Introduce man,\nand the geometrical figures are adorned with a thousand beauties, the\nflowers covered with gay colors, and the columns of fluids changed into\nexquisite perfumes.\n\n\n\n\nCHAPTER X.\n\nFORCE OF TOUCH TO MAKE SENSATIONS OBJECTIVE.\n\n\n54. It has been said that touch is the surest, and perhaps the only\nwitness of the existence of bodies; for without it, all sensations\nwould be nothing more than simple modifications of our being, to which\nwe could attribute no external object. But this I do not believe to\nbe true. We receive by touch an impression, just as we do by the\nother senses; this impression is in all cases an affection of our\nbeing, and not something external. When, from the continuance of these\nimpressions, their order, and their independence of our will, we judge\nthem to proceed from objects without us, our judgment is true not only\nof impressions of the sense of touch, but also of those of the other\nsenses.\n\n55. One of the reasons whereon it has been attempted to base the\nsuperiority of touch to attest the existence of bodies, is that it\ngives us the idea or sensation of extension; for if we suppose a man\nto be deprived of all his senses but that of touch, and to pass his\nhand over the surface of a body, he will experience that continuity of\nthe sensation which involves extension. This observation of those who\nmaintain the supremacy of touch does not prove what they propose. If\nwe pass our sight over various objects, or the different parts of one\nobject, we shall experience the sensation of continuity just as clearly\nas by touch. We cannot conceive why the sensation of extension must be\nany clearer when the hand is passed along a balustrade than when it is\nseen by the eyes.\n\n56. The advocates of this opinion assert that we acquire by the touch\nof our body a double sensation, which we do not by the other senses.\nIf we pass our hand over our forehead, we feel with both our hand and\nour forehead, and so verify a continuity of sensations, all originating\nand terminating in ourselves. Thus we are conscious that both the\nsensations of our hand and our forehead belong to us.\n\nBut this reason, by some deemed conclusive, is nevertheless exceedingly\nfutile; it labors under the sophism called by dialecticians _begging\nof the question_, for it supposes what was to be proved. The man\ndestitute of all senses but that of touch will, indeed, experience the\ntwo sensations and their continuity; but what can he infer from them?\nDoes he even know that he has either hand or forehead? Suppose him not\nto know, how is he to acquire this knowledge? Both sensations belong\nto him, and of this he is internally conscious; but whence they came,\nhe knows not. Does the coincidence of the two sensations, perchance,\nprove something in favor of the existence of his forehead and hand,\nobjects of which we suppose him to have no idea? If this coincidence\nproved what is pretended, with still greater reason would it prove the\ncombination of some senses with others to elevate us to the knowledge\nof the existence of bodies, and consequently that this knowledge is not\nproduced exclusively by touch. Whenever I have the sensation of the\nmotion of placing my hand before my eyes, I find that I lose sight of\nthe objects before me, and in their room is presented another always\nthe same, my hand. If, from this coincidence, I infer the existence of\nexternal objects, the supremacy of touch is destroyed, for sight, also,\nacts a part in the formation of such a judgment. I also observe that\nwhen I have the sensation of clapping my hands together, I experience\nthe sensation of hearing the noise of their contact; if, therefore,\ncoincidence is of any account, hearing as well as touch comes in. What\nI say concerning the clapping of my hands, is applicable to what I\nexperience when I pass a hand over any part of my body, for instance my\narm, so as to produce some noise. In this case there are two sensations\ncoincident and continuous.\n\nIt will, perhaps, be replied, that these examples refer to different\nsenses, and produce sensations of different kinds. This, however, is of\nno consequence; for, if the being that perceives, infers the existence\nof objects from the coincidence of various sensations, the supremacy of\ntouch is destroyed, which is what we undertook to demonstrate.\n\n57. The sensation of the hand is not that of the forehead, for the\none is warmer or colder, harder or softer than the other, and so the\nsensation caused by the hand upon the forehead will not be the same\nas that produced upon the hand by the forehead. It is to be observed,\nthat the less difference we suppose between the two sensations, the\nless lively will be the perception of their duality, and consequently\nthe less marked the coincidence on which the judgment is founded. Thus\nby rigorously analyzing this matter we discover that the diversity of\nsensations contributes in an especial manner to form judgments of the\nexistence of objects, and therefore the combination of two senses will\nmore conduce to this end than two sensations of one sense. Far, then,\nfrom its being necessary to consider touch as alone or superior upon\nthis point, it is only to be held as auxiliary to the other senses.\n\nIn truth, it is almost beyond doubt that the sense of touch also\nrequires the aid of the other senses, and that the judgments resulting\nfrom it are similar to those coming from the other senses. It is\nprobable that only after repeated trials do we refer the sensation of\ntouch to the object that causes it, or even to the part affected. The\nman who has had his arm amputated, feels pain as if he still preserved\nit; and this is because a repetition of acts has formed the habit\nof referring the cerebral impression to the point where the nerves\ntransmitting it terminate. There is, therefore, no necessary relation\nbetween the sense of touch and the object; and this sense is, like the\nothers, liable to illusions. Therefore, it is not exact to say that\nthe idea of body springs up under our hand, if this be understood as\nexcluding touch; for the same is true of the other senses, particularly\nof sight.\n\n\n\n\nCHAPTER XI.\n\nINFERIORITY OF TOUCH COMPARED WITH OTHER SENSES.\n\n\n58. That superiority, or rather that exclusive privilege, conceded by\nCondillac and other philosophers to touch, not only has no foundation,\nas we have just seen, but seems to be in contradiction to the very\nnature of this sense. In short, it assigns the first place to the\ncoarsest, the most material of all the senses.\n\nIt cannot be known what ideas a man reduced to the one sense of touch\nwould form of things; but it seems to me that far from entering into\nclear and vivid communication with the external world, and finding a\nsufficient foundation whereon to base his cognitions, he would grope\nin the profoundest ignorance, and labor under the most transcendental\nerrors.\n\n59. If we compare touch with sight, or even with hearing and smell, we\nshall at once perceive a very important difference to its disadvantage.\nTouch transmits to us only impressions of objects immediately joining\nour body; whereas, the other three, and especially sight, place us in\ncommunication with far distant objects. The fixed stars are separated\nfrom us by a distance such as almost to pass our imagination, and yet\nwe see them. Neither smell nor hearing, it is true, go so far; but the\nformer fails not to warn us of the existence of a garden at many paces\nfrom us; and the latter gives us notice of a battle fought at many\nleagues distance, of the electric spark which has cloven the clouds\non the confines of the horizon, or of the tempest roaring over the\nimmensity of ocean.\n\n60. The limitation of touch to what is immediate to it involves a\nscarcity of the ideas originating in it alone, and of necessity places\nit in a lower grade than the other three senses, particularly sight.\nLet us in order to form clear ideas upon this point compare the range\nof sight with that of touch relatively to some object, for example, a\nbuilding. By means of sight we in a few instants obtain an idea of its\nfront, and other external parts; and in a short time become acquainted\nwith its internal divisions, with the arrangement even of its ornaments\nand furniture. Can we accomplish all this by touch? Even if we suppose\nthe most delicate sense of touch, and the most tenacious memory of the\nimpressions communicated, long hours would be necessary to pass the\nhand over the front of the building, and form some idea of it. How will\nit be when we come to the whole exterior of the building? the whole\ninterior? We see that it would be necessary to renounce such a task,\nthat the elaborate workmanship of a cornice, a pedestal, a peristyle,\nthe magnificence of a tower, a cupola, the boldness of an arch, a\nvault, which the eye seizes in an instant, would require the poor being\npossessed of touch alone to go often on all fours, climb over dangerous\nscaffoldings, and expose himself to the danger of falling from fearful\nheights; and yet he would never be able to acquire the millionth part\nof what the eyes so easily and so quickly perceive.\n\nApply these observations to a city, to vast countries, to the universe,\nand see what immense superiority sight has over touch.\n\n61. We do not indeed find so vast a superiority when we compare touch\nwith the other senses; nevertheless, it does exist in a very high\ndegree.\n\nThe first difference is the ability to act from a distance. Certainly,\ntouch also may in some manner perceive the presence or absence of the\nsun, by means of the impressions of heat and cold; and in like manner\nthe presence or absence, and the more or less close proximity of some\nbodies, etc.; but not only are these impressions far from having the\nsame variety and rapidity as those of hearing, but they would not\neven give us any idea of distance, if we had not already perceived it\notherwise than by touch.\n\nHeat and cold, dryness and moistness, are what the impressions which\nsome bodies, though distant, may make upon touch are reduced to; and\nthese impressions are clearly of a nature to be exposed to many serious\nerrors.\n\n62. If we suppose a man, having only the sense of touch, to know the\npresence or absence of the sun above the horizon, his only rule being\nthe temperature of the atmosphere, which depends upon a thousand\ncauses having no connection with the orb of day, it will happen that\nthe natural or artificial change of it will lead him into error. The\ndampness which we perceive around a lake is a sign of the nearness\nof the water; but do we not a thousand times experience the feeling\nof dampness from causes operating on the atmosphere, altogether\nindependent of the waters of a lake?\n\nIt is certain that the concentration of all sensitive forces upon one\nsense, the absence of all distraction, and continual attention to only\none kind of sensations, might raise the delicacy of touch to a degree\nof perfection which we probably do not know; just as the habit of\nconnecting ideas with respect to only one order of sensations, and of\nforming judgments concerning them, produces a precision, exactness,\nand variety, far superior to all that we can imagine. But however far\nwe might extend our conjectures upon this head, it is certain that\nthere is a limit in the nature of the organ and of its relations to\nbodies. This organ must be limited to contiguous objects, in order to\nreceive well determined impressions; and with respect to those that\nare distant, and can act upon it, they can do this by causing on it an\nimpression such as the nature of both permits, heat or cold, dryness or\ndampness, and if you will, a certain pressure either greater or less.\nSo far as a great many other objects are concerned, we cannot imagine\nany action. However much the circle of this class of sensations be\nenlarged, it must ever be very limited. Moreover, we must observe, that\nthe perfectibility of touch by means of its isolation does not belong\nto it exclusively, but extends likewise to the other senses; for it is\nfounded on the laws of organization, and the generation of our ideas.\n\n63. To comprehend the superiority of hearing to touch in this matter,\nwe have only to consider the relation of distances, the variety\nof objects, the rapidity of the succession of sensations, the\nsimultaneousness so much greater in hearing than in touch, and their\nrelations to speech.\n\nI. Relation of distances. On this point, hearing is clearly superior to\ntouch, for the latter generally requires contact, the former does not,\nbut for the due appreciation of its object even requires a distance\nsuited to the class of the sound. Of how many distant objects does\nhearing inform us of which touch can tell us nothing? The gallop of the\nhorse threatening to trample us under foot, the roaring of the torrent\nwhich may carry us away in its course, the thunder rumbling from afar,\nand announcing the tempest, the roar of cannon, telling that a battle\nhas begun, the rattle of carriages in the streets, drums and bells,\nand clamor of voices which indicate the explosion of popular fury, the\nnoisy music that proclaims the joy caused by happy news, the concert\ndedicated to the pleasures of the saloon, the song that brings back\nmelancholy recollections, sentiments also of hope and love, the groan\nthat warns us of suffering, the plaint that afflicts us with the idea\nof misery; all this hearing tells us, but touch can tell us nothing of\nany of these.\n\nII. Variety of objects. Those distant objects which we know by touch,\nare of necessity little varied; and for the same reason the ideas\nresulting from it will be liable to a deplorable confusion and to great\nuncertainty. Hearing, on the contrary, informs us of infinite and\nexceedingly different objects, and that, too, with perfect precision\nand exactness.\n\nIII. Rapidity of the succession of impressions. It is evident that\nhearing has here an incalculable superiority over touch. When touch\nperceives by juxtaposition, it is under the necessity of successively\ngoing over the objects and even their different parts if it would\nreceive varied impressions; and this, however small their number,\nrequires much time. If the objects do not act by juxtaposition, but by\nsome medium, the succession will require much more time, and there will\nbe much less variety. Compare this slowness to the rapidity with which\nhearing perceives a whole series of sounds in musical combinations,\nthe infinite inflexions of the voice, the countless number of\ndistinct articulations, the infinity of noises of all kinds which we\nuninterruptedly perceive and classify, and refer to their corresponding\nobjects.\n\nIV. The simultaneousness of sensations so vast in hearing, is extremely\nlimited in touch; for in the latter it can only be in relation to a few\nobjects; but in the other it extends to many very different objects.\n\nV. But what most triumphantly indicates the superiority of hearing\nto touch, is the facility it affords us of placing ourselves\nin communication, by means of speech, with the mind of our\nfellow-mortals,--a facility, resulting from the rapidity of succession\nalready remarked. Undoubtedly, this communication of mind with mind,\nmay be established by touch, if we express our words by characters\nsufficiently raised to be distinguished: but what an immense difference\nbetween these impressions and those of hearing? Even if we suppose\nhabit and a concentration of all the sensitive forces to have produced\nsuch a facility in passing the fingers over lines, as far to surpass\nall that we see in the most dexterous players of musical instruments,\nwhat comparison can there be instituted between this velocity and\nthat of hearing? How much time would be requisite only to go over\ntablets whereon is written a discourse which we hear in a few minutes?\nMoreover, all men have means of hearing, they need only make use of\ntheir organs. But in order to converse by touch, it is necessary to\nprepare tablets, which can only serve for one object, and cannot be at\nthe same time used by two persons; whereas by means of hearing, one man\nalone may in brief time communicate an infinity of ideas to thousands\nof listeners.\n\n\n\n\nCHAPTER XII.\n\nCAN SIGHT ALONE GIVE US THE IDEA OF A SURFACE?\n\n\n64. I have, I believe, made the inferiority of touch to sight and\nhearing palpable, and have, consequently, shown the extravagance of\nendeavoring to make it the basis of all cognitions, to found upon it\nthe certainty of the judgments to which our other senses lead us, and\nto make it a supreme judge to decide in the last appeal upon the doubts\nthat may arise.\n\nI hold it to be manifestly untrue that we cannot make the transition\nfrom the internal to the external world, or from the existence of\nsensations to that of the objects causing them, otherwise than by means\nof touch; for not only have I combated the principal, or rather the\nsolitary reason upon which it is pretended to found this privilege,\nbut I have also demonstrated the mode of making this transition\nwith respect to all the senses, reasoning from the very nature and\nconnection of internal phenomena.\n\nI have likewise said and proved that the sensation of extension is the\nonly one that is representative, and that in all others there was only\na relation of causality, that is, a connection of some sensation or an\ninternal phenomenon with an external object, without our transferring\nto this any thing resembling what we experienced in that.\n\n65. There are two senses which inform us with certainty of extension,\nsight and touch. We shall not now inquire if that be a true _sensation_\nwhich we have of extension, or if it be an _idea_ of a very different\norder, resulting from the sensation. I propose hereafter to examine\nthis point, but shall now confine myself to comparing sight with touch\nonly as tending to give us the sensation of extension, or, if you will,\nto furnish us with what is necessary to form an idea of it.\n\nWe cannot but see that extension lies within the domain of touch, and\nthat, too, whether it be considered only as a surface, or also as a\nsolid. The same faculty cannot be denied to sight, so far as surfaces\nare concerned; for it is impossible to see if at least a plane be not\npresented to the eye. A point without extension cannot be painted\nupon the retina, but the instant an object is painted, it has painted\nparts. We can by no effort of our imagination, conceive colors without\nextension; for what is color without a surface over which it may extend?\n\n66. So hostile was Condillac to the sense of sight that he was\nunwilling to allow it even the faculty of perceiving extension in\nsurfaces; but as he is of all philosophers the one who has most\ncontributed to the propagation and establishment of this opinion, we\nwill examine his doctrine and its fundamental reasons. We have only\nto read the chapters in which he explains it, to see that he was\nnot himself very confident of its truth, but that he felt himself\ncontradicted by both experience and reason.\n\nIn his _Trait\u00e9 des Sensations_,[36] where he examines the ideas\nof a man limited to the sense of sight, he says that colors are\ndistinguished by the sight because they seem to form a surface of which\nthe eyes occupy a part, and then asks: \"Will our statue, judging itself\nto be at one time many colors, perceive itself as a sort of colored\nsurface?\" We must bear in mind that, according to Condillac, the statue\nconfined to one sense will believe itself the sensation, that is, it\nwill think that it is the odor, the sound, or the taste, according\nas the sense of smell, hearing, or taste, is the sense in exercise;\nfor which reason, if a surface enter into the sensation of sight, the\nstatue ought to believe itself a colored surface. I shall not examine\nthe correctness of these observations, but shall confine myself to the\nmain point, which is the relation of sight to a surface.\n\n[36] P. 1. C. xi.\n\n67. According to Condillac, the statue will never believe itself a\ncolored surface, that is, although it may perceive the color, it will\nnot perceive the surface. Let the philosopher himself speak, for\nhis own words will suffice to condemn his opinion, and to show the\nuncertainty with which he advanced it, or else the obscurity under\nwhich it labors: \"The idea of extension supposes the perception of many\nthings, _some distinct from others_. _This perception we cannot deny\nto the statue_, for it feels that it is repeated outside of itself as\nmany times as there are colors modifying it. When it is the red, it\nfeels itself _outside_ of the green; when the green, it feels itself\n_outside_ of the red, and so with other colors.\" Some may imagine\nthat, conformably to these principles, Condillac goes on to establish\nthat sight gives us the idea of extension, since it makes us perceive\nthings, some _outside_ of others, in which, according to him, the idea\nof extension exactly consists. But he does not; far from following\nthe true road, he miserably loses his way; he not only violates the\nprinciple he has just laid down, but notably changes the state of the\nquestion. He continues: \"But in order to have a distinct and precise\nidea of magnitude, it is necessary to see how the things perceived,\nsome outside of others, are connected, how they mutually terminate,\nand how they are all enclosed in the limits which bound them.\" This, I\nrepeat, is to change the state of the question; we are not now treating\nof a distinct and precise idea, but simply of an idea. How far the idea\nof extension given by sight is perfect, is another question; although\nit is manifest that if sight can give us an idea of extension, it will\ncome by continual exercise to render this idea more perfect.\n\n68. The statue, in Condillac's opinion, could not perceive itself to\nbe circumscribed by any limit, because it could know nothing beyond\nitself; but did he not just now tell us that the statue would believe\nitself different colors; that some of these were outside of others;\nand that when it would be one, it would perceive itself outside of the\nothers? Does this not imply not only one but many limits?\n\nThis difficulty did not altogether escape Condillac; for after having\nasked if the _me_ of the statue, when modified by a blue surface,\nbordered with white, would not believe itself a limited blue color,\nhe says: \"At first sight we were inclined to believe that it would;\nbut the contrary opinion is much more probable.\" But why? \"The statue\ncannot perceive itself extended by this surface, save inasmuch as\neach part modifies it in the same way; each part should produce\nthe sensation of blue color; but if it is alike modified by a foot\nof this surface and by an inch, it cannot perceive itself, in this\nmodification, to be one magnitude rather than another. Therefore it\ndoes not perceive itself as magnitude; therefore the sensation of\ncolor does not involve the idea of extension.\" It is easy to see that\nCondillac either supposes what is in debate, or else says nothing to\nthe point. According to him, the statue is alike modified by a foot\nof colored surface and by an inch. If by this he means that the two\nmodifications are identical under all aspects, he supposes the very\nthing he ought to have proved; for this is precisely the point in\ndispute, whether surfaces differing in magnitude do, or do not, produce\ndifferent sensations. If he means, as his words seem to indicate, that\nthe sensation as color, and solely as color, is the same in a foot of\ncolored surface as in an inch, he utters, indeed, an incontestable\ntruth, but one not at all to his purpose. Undoubtedly, the sensation\nof blue, as blue, is the same in different magnitudes, and no one ever\nthought of denying it. But this is not the question: it is whether, the\ncolor remaining one and the same, the sensation of sight is modified\ndifferently, according to the variety of magnitude of the colored\nsurface. Condillac denies it, but in an uncertain and hesitating way.\nWe believe his negation to be so groundless that the direct contrary\nmay be proved.\n\n69. I would ask Condillac if he can have color without surface; if an\nobject without extension can be painted upon the retina; if we can even\nconceive a color without extension. No one of these is possible, sight\nis therefore necessarily accompanied by extension.\n\n70. Condillac places the idea of extension in some things being\npresented to us outside of others. This, as he him self confesses, is\nverified in the sensation of color; therefore the sight of what is\ncolored must produce the idea of extension. Condillac's subterfuge\nhere is an exceedingly weak one. He pretends that it is necessary, in\norder to have the idea of extension, to have that of its limits. But\nfirst of all, we have shown from his own doctrine that these limits\nare perceived by the senses; besides it is a very strange pretension\nto attribute to sight the faculty of giving us the idea of unlimited\nextension, and to deny to it that of producing the idea of limitation;\nas if there did not by the very fact of our seeing what is extended,\nrise within us the idea of limitation, if from no other cause, from\nthe very limitation of our organ; or as if an unlimited were not more\ninconceivable than a limited sensation.\n\nBut suppose the limits not be perceived by the senses, does unlimited\nextension therefore cease to be extension? Is it not rather extension\nof the highest order? Does the idea of space without end, because\nunlimited, cease to be an idea of extension?\n\n71. Two colored circles, one an inch, and the other a yard in diameter,\nare placed before our eyes; will the effect produced upon the retina\nbe the same in both, abstraction made from all sensation of touch?\nEvidently not; experience shows the contrary, and the reason is founded\non the laws of the reflection of light, and on mathematical principles.\nIf the impressions are different, the difference will be perceived;\ntherefore the difference of magnitude can be appreciated.\n\nWe will now suppose some one in spite of reason and experience to\npersist in maintaining that the sensation of the two circles will be\nthe same in order to make the extravagance, even the ridiculousness\nof this opinion palpable. Let us imagine the two circles to be of a\nred color, and terminated by a blue line; and now placing the less\nupon the greater circle so as to bring their centres together, we ask,\nwill not the eye cast upon the figure see the less within the greater\ncircle? Will not the blue line that terminates the circle of an inch in\ndiameter be sure to be contained within the blue line that terminates\nthe other circle of a yard in diameter? But what else is the perception\nof extension than the perception of some parts beyond others? Is it\nnot to perceive the difference of magnitude, to perceive some greater\nthan others, and containing them? Evidently it is. The sight therefore\nperceives magnitude; therefore it perceives extension.\n\n72. We may still further confirm this truth. Experience teaches, and\ndid it not exist, reason would still teach that there must be a limit\nto the field of sight, according to our distance from the object. Thus,\nwhen we fix our sight upon a wall of great extent we do not see it all,\nbut only a part. Now suppose an object of given magnitude to be within\nthe range of sight, but not so great as to cover the surface embraced\nby the eye. According to Condillac's system, there can be no difference\nin the perception, provided the color be the same; whence, it will\nfollow, that the sensation will be just the same, whether the object\noccupy the whole, or only an exceedingly minute part, of the visual\nfield. It will likewise follow, that, if this visual field be, for\nexample, a great white curtain a hundred yards square, and the object a\npiece of blue cloth a yard square, the sensation will be just the same\nwhether the blue cloth be one inch or ninety yards square.\n\n73. These arguments, which must have occurred at least confusedly\nto Condillac, made him hesitate in his expressions, and even use\ncontradictory language. We may have already observed this in\nthe passages cited, but we shall see it yet more clearly in the\nfollowing:--\"We have no term to express with exactness the sentiment\nthat the statue modified by many colors at one time has of itself; but\nin fine, it knows that it exists in many ways, and perceives itself in\na certain mode _as a colored point beyond which_ are others, in which\nit turns to find itself; and under this point of view, it may be said,\nthat it _perceives itself extended_.\" He had before said, that color\ndid not seem extended to the statue, until, sight being instructed by\ntouch, the eye became accustomed to refer the one simple sensation to\nall the points of the surface: and in the very next line, as we have\njust seen, he asserts the contrary; the statue now perceives itself\nto be extended, and the ideologist discovers no way of avoiding the\ncontradiction, but to warn us that the sentiment of extension will\nbe vague because it wants limits. This is a contradiction which we\nhave already made evident. But whence this want of limits? If various\nfigures of different colors, green, red, etc., be supposed to be upon\na visual field of a hundred yards square of white surface, the sight\nwill, as is evident, perceive the limits of these figures; where, then,\ndid Condillac discover that illimitation of which he talks?\n\n74. Although it is very true that even if the sensation of color were\nto involve that of extension, it would not therefore follow that it\nwould produce it in us, because we do not take from sensations all the\nideas they contain, but those only which we know. This does not at all\naffect the present question. We do not treat of what we can take from\nthe sensation, but of what is in it. If Condillac maintains that we may\ntake the idea of extension from the sensation of touch, by what right\ndoes he deny the same faculty with respect to sight, supposing the idea\nof extension to be contained in both sensations?\n\nIf I mistake not, this is a tacit confession of the falseness of his\nopinion. The idea of extension is in the sensation of sight, but we\ncannot take it thence. Why not? Because it is vague. But then what\nis to prevent exercise, involving comparison and reflection, from\nrendering it distinct? The difficulty consists in acquiring it in one\nway or another; to perfect it is the work of time.\n\nUndoubtedly the first sensations of sight will not have that exactness\nwhich they have after much exercise; but the same is true of the sense\nof touch. This sense is perfected like the others; it like them needs\nto be educated, so to speak; and those born blind, who, by force of\nconcentration and labor, come to possess it to an astonishing degree of\ndelicacy, offer us a manifest proof of this truth.\n\n\n\n\nCHAPTER XIII.\n\nCHESELDEN'S BLIND MAN.\n\n\n75. Cheselden's blind man, of whom Condillac spoke, in confirmation\nof his opinions, presents no phenomenon upon which they can rest.\nThis blind person was a youth of thirteen or fourteen years of age,\nupon whom Cheselden, a distinguished London surgeon, performed the\noperation of removing cataracts, first from one eye, then from the\nother. He could before the operation tell day and night, and in a very\nstrong light distinguish, white, black, and red. This is an important\ncircumstance, and merits attention. The phenomena the most remarkable,\nand having the most relation to the question now before us, were the\nfollowing:\n\nI. When he began to see, he believed that objects touched the external\nsurface of his eye. This would seem to show that sight alone cannot\nenable us to judge of distances; but, after close examination,\nwe shall clearly see that the argument is not conclusive. No one\nwill pretend that sight, in the first moment of its exercise, can\ncommunicate equally clear and distinct ideas to us, as when experience\nhas accustomed us to compare its different impressions. This is the\nsame with touch as with sight. A blind person, from his frequent\ncustom of guiding himself, in many of his movements by sensations of\ntouch alone, comes to know the position and distances of objects with\nwonderful precision. If we suppose a man deprived of the sense of\ntouch suddenly to acquire it, neither will he at first judge with the\nsame certainty the objects of this sense as after having exercised\nit. Experience teaches that the sense of touch is capable of a high\ndegree of perfection. We see it in blind persons at its highest point;\nand probably the lowest point of its perfection, in the first moments\nof its exercise, would greatly resemble that of sight at the instant\nof being freed from the cataracts; objects would be presented to it\nlikewise in confusion; and the subject experiencing them could not\nwell appreciate their differences until practice had taught him how to\ndistinguish and classify.\n\nWith respect to distance, it is to be observed, that this blind person\nof Cheselden, so far from having the habit of appreciating it, had\nfalse ideas upon it. As he was not totally blind, the light, which he\nperceived through the cataracts, was sufficient to even enable him to\ndistinguish between white, black, and red, which seemed to him to touch\nhis eye. We may form some idea of this by observing what happens to\nus if we close our eyes in a very strong light. Hence he ought, when\nhe gained his sight, to have imagined that the new sight was the same\nas the old, and, consequently, that nothing had happened but a simple\nchange of object. A person totally blind would have better shown the\npower of sight to appreciate distances; for he would have had no habit\neither favorable or unfavorable to their knowledge.\n\nII. It cost him much trouble to conceive that there were other objects\nbeyond those he saw; he could not distinguish limits; every thing\nseemed to him immense. Although he knew by experience that his chamber\nwas smaller than the whole house, he could not conceive how he could\nsee this.\n\nFrom these facts Condillac draws a confirmation of his system. We are\nastonished that he should pretend to found an entire philosophy upon\nsuch data. We submit the following considerations to the reader:\n\n76. The subject is here a youth of thirteen or fourteen years, and\nconsequently without any habit of observation. He would naturally\nexpress very confusedly the impressions he received in so new and\nstrange a situation.\n\nThe organ of sight must, when exercised for the first time, be\nexceedingly weak, and consequently perform its sensitive functions\nonly in a very imperfect way. We ourselves repeatedly experience that\nwe cannot, if we suddenly pass from darkness to light, especially if\nit be a very strong light, distinguish objects, but we see every thing\nin great confusion; what then would happen to a poor child, when at\nthe age of thirteen years, he for the first time opens his eyes to the\nlight?\n\nAccording to Cheselden's own account, objects were presented to him in\nsuch confusion that he could not distinguish them, no matter what their\nsize or shape. This confirms what we have just said, that the partial,\nif not the sole cause of the confusion, was that the organ did not\nproduce impressions well, because if these had been properly produced,\nhe would have been able to distinguish the limits of the different\ncolors; for, in simple sensation, to see is to distinguish.\n\nWe are also told that he could not recognize by sight the objects\nwhich he knew by touch. But this only proves that not having been\nable to compare the two orders of sensations, he could not know what\ncorresponded in one to the impressions of the other. By touch he would\nhave known a spherical body; but as he was still ignorant of the\nimpression which a globe makes on the eye, it is clear that if any one\nshould show him a ball which he had handled a thousand times, he would\nnot even have suspected that the object seen was the same which he had\ntouched. This leads me to another observation which I consider very\nimportant.\n\n77. The child on whom these experiments were made was obliged to\nexpress his sensations in the visual order, in a language which he did\nnot understand. For any one who is deprived of one of the senses must\nbe absolutely ignorant of all the ideas which have their origin in\nthat sensation. Hence it follows that he knows nothing of the language\nrelating to that sense, and the ideas which he joins to the words\nare entirely different from what those who possess that sense mean\nto express. The blind man will speak of colors and the impressions\nproduced by sight, because he hears others speak of these things; but\nfor him the word to see does not mean to see, light is not light, nor\ncolor color, as we understand them, but they express different ideas\nwhich he has formed according to the circumstances, in conformity with\nthe explanations he has heard. What importance then should we attach to\nwhat a child may say who, besides the thoughtlessness natural to his\nage, is placed in a situation new to him, and required to express his\nideas in a language which he does not know? He is asked, for example,\nif he can distinguish a greater object from another which is smaller,\nwithout considering that the words greater and smaller as he understood\nthem, inasmuch as they expressed abstract ideas, or were referred to\nthe sensations of touch, were altogether new to him when applied to\nobjects seen, since he had no means of knowing what was meant when\nreferred to a sensation which he experienced for the first time. If\nwithin a circle, a number of smaller circles of a different color were\ndescribed, he would see the smaller circles within the circumference of\nthe greater; but if asked if one appeared greater than the rest, or if\nhe could distinguish the limits which, separated the smaller circles\nfrom each other, he could not but give very absurd answers, which the\nobservers might perhaps take as the expression of curious phenomena.\nThey speak to him of figures, lines, extremities, size, position, and\ndistances in relation to sight, and as he is ignorant of this language,\nyet knows not that he is ignorant of it, he must necessarily talk in a\nvery strange manner. A more attentive and profound observer would have\nperceived the same misunderstanding as when a deaf man disputes without\nhearing what was said.\n\nThese remarks are further confirmed by the contradiction in the account\nof Cheselden. The oculist tells us that the child could not distinguish\nthe objects, even those which differed most in form and size: but that\nhe found those most agreeable which were the most regular. He must\nthen have distinguished them; for otherwise, the sensation could not\nhave been more or less pleasing. And here in choosing an alternative\nin this contradiction, we must hold that he distinguished the objects,\nsince there is a strong argument in its favor. When two objects,\nthe one regular, the other irregular, were presented to him, and he\nwas questioned as to their resemblance and difference, he must have\nanswered so absurdly as to create the suspicion that he could not\ndistinguish them. The reason of this is, that besides the confusion of\nsensations, to which he was always more or less subject, he was also\nignorant of the language, and although he distinguished the objects\nplainly, still he could not understand what he was asked, nor express\nwhat he felt. But when examined as to the nature of the impression\nand whether it was pleasing or otherwise, he found himself on a field\ncommon to all sensations, the ideas of pleasure and displeasure were\nnot new to him, and he could say without confusion, this pleases me;\nthat is displeasing to me.\n\nTo sum up what I have said, I believe that the phenomena of Cheselden's\nblind man, only prove that sight, like all the other senses, needs a\ncertain education, that its first impressions are necessarily confused,\nthat the organ acquires the proper strength and precision only after\nlong practice, and finally, that the judgments formed in consequence,\nmust be very incorrect until comparison, joined with reflection, has\ntaught how to rectify inaccuracies.[37]\n\n[37] See Book 1, \u00a7 56.\n\n\n\n\nCHAPTER XIV.\n\nCAN SIGHT GIVE US THE IDEA OF A SOLID?\n\n\n78. It has been asserted that sight can not give us the idea of size or\nof a solid, but that this can be obtained only by the help of touch. I\nbelieve the contrary may be proved with convincing certainty.\n\nWhat is a solid? It is the union of three dimensions. If sight can\ngive us the idea of surfaces which consist of two, why not also of\nsolids which consist of three dimensions? This one reflection is enough\nto show that it has been denied without reason; but I shall not stop\nwith this, but shall prove, by the most rigorous observation, and the\nanalysis of its phenomena, that sight can give us the idea of a solid.\n\n79. I willingly agree, that if we suppose a man deprived of all the\nother senses, to have his eyes immovably fixed on an immovable object,\nhe would never be able to distinguish between what is solid and what\nis merely perspective in the object; or, in other words, that all the\nobjects permanently painted on the retina will appear to be projected\non a plane. The reason of this is founded on the very laws of the\norgan of this sense, and of the transmission of its impressions to the\nbrain.\n\nThe soul refers the sensation to the extremity of the visual ray;\nand since in the present instance it has been unable to make any\ncomparisons, it can have no motive for placing these extremities at\nunequal distances, which constitutes the third dimension.\n\nIn order to understand this better, let us suppose the object to be\na cube placed so that three of its sides are seen. It is evident\nthat although the three surfaces are equal, they will not appear so\nto the eye, because their respective positions do not permit them to\nsend their rays equally to it. But as the soul has not had occasion\nto compare this sensation with any other, it can not calculate the\ndifference produced by the different positions and distances, but must\nrefer all the points to the same plane, regarding the sides of the cube\nas unequal; though, in reality, they are not so.\n\nSight, in this case, presents the whole object on a perspective plane;\nand as it could have no means of calculating the distance of the object\nfrom the eye, it would probably believe it joined to the eye, or,\nmore strictly speaking, the sensation would represent only a simple\nphenomenon, the relations and cause of which we could not explain.\n\n80. It is likewise probable, that if, while the eye remained fixed, we\ncould open and shut the lids, we might form the idea that the object\nseen was outside of us; so that by this motion alone, we should obtain\na point of comparison, by the succession of the alternate disappearance\nand reproduction of the sensation of the object by the interposition\nor non-interposition of an obstacle. Then the idea of a greater or\nless distance would arise, and as this would be in the direction\nperpendicular to the plane of the object, we should already have the\nidea of a solid.\n\nFortunately, nature has been more beneficent to us, and we are not\nobliged to limit ourselves to a supposition which thus curtails our\nmeans of acquiring ideas. Still it will not be useless to have examined\nthe phenomenon on this supposition; for, from this examination, we\nshall gain light to understand what I propose to demonstrate.\n\n81. In order that sight may originate the idea of a solid, it requires\nmotion. This motion is an indispensable condition, though it may be\neither in the object or in the eye itself.\n\nLet us suppose an immovable eye, and see how by the motion of the\nobjects, the sensation of sight may present or produce the idea of\na solid. The only difficulty is to show how it can add to the two\ndimensions which constitute the plane, the third which forms the solid.\n\nLet a fixed eye be directed to a point where there is a right\nrectangular parallelopipedon B, so placed that its two bases are wholly\nconcealed, and let the right line drawn from the centre of the eye to\nthe edge of the parallelopipedon divide the plane angle into two equal\nparts. Let us also suppose the sides of the parallelopipedon to be of\ndifferent colors,--white, green, red, and black. In this case, the\neye sees the two planes as one, and the edge appears as a right line\nseparating the two parts of the same plane which differ only in color.\nIt is impossible for it to conceive the inclination of the two planes,\nbecause as it refers the object to the extremity of the visual ray, and\nhas not been able to compare the varieties which result from difference\nof position and distance, and from the manner in which the object\nreceives the light, it can only distinguish the different parts of the\nsame plane.\n\nIt is well known that perspective can perfectly imitate a solid. For,\nif instead of the solid B, we suppose two planes exactly representing\nthe two sides seen, the sensation will be the same, the illusion\ncomplete. Therefore, there are two distinct ways of producing the\nsame sensation; and consequently, unless there has been a previous\ncomparison, there is no means of distinguishing them apart; but the\nidea which would naturally result would be the most simple; that is,\nthe idea of a plane.\n\n82. If we suppose the parallelopipedon B to revolve on a vertical axis,\nit will present the four planes successively to the eye, and they will\nappear greater or less according to their inclination to the visual\nray, the surface of the plane reaching its maximum when perpendicular\nto the ray, and its minimum when parallel to it.\n\nThe succession and variety of the sensations will immediately produce\nthe idea of motion; for the same planes of the parallelopipedon are\nseen in different positions. The uniform manner in which these planes\nsucceed one another, will also suggest the idea that the green which\nappears a few moments after the black, is the same which was seen a few\nmoments before; and so of the other colors. Also, as one is constantly\nhiding behind the other, this naturally gives rise to the idea of\nextension in the direction, or continuation of the visual ray; and this\nis sufficient to produce the idea of size or of a solid. When we see a\nplane we have the two dimensions which constitute a surface; to form\nthe idea of a solid, we need only the idea of one dimension more; this\ncan not be found in the same plane, but is produced by the motion of\nthe parallelopipedon.\n\n83. This motion which we have supposed to be around a vertical axis, we\nmay equally suppose to take place around a horizontal axis. We shall\nthen see in succession the two opposite sides, and the bases of the\nparallelopipedon with different appearances, according to their various\npositions; or, in other words, according to the angle formed by the\nplanes and the visual ray. These appearances will help more and more\nto form the idea of the third dimension, which is not to be found in\nthe primitive plane, and consequently to supply what was wanted to\nconstitute the idea of a solid.\n\n84. Just as we have supposed the eye fixed and the object movable, we\nmay suppose the eye in motion and the object immovable. The result\nis the same; for, it is evident that if the eye should move around\nthe parallelopipedon, now vertically, and now horizontally, it\nwould experience the same sensations as when it was quiet, and the\nparallelopipedon moved. Thus, although we suppose the subject wholly\ndeprived of the sense of touch, so as to be unable to perceive its own\nmotion, it can still form the idea of solid by the impressions of sight\nalone. True, it could distinguish which moved, the eye or the object,\nbut this does not interfere with the formation of the idea composed of\nthe three dimensions.\n\n\n\n\nCHAPTER XV.\n\nSIGHT AND MOTION.\n\n\n85. I said that the observer could not distinguish between his own\nmotion and that of the object; sight alone can not give us a true idea\nof motion. Thus in a boat, although we are certain that we are moving,\nthe motion seems to us to be in the objects along the shore. Also if\nthe motion of the object and that of the observer are simultaneous,\nin the same direction, and with the same velocity, all appearance of\nmotion is lost. But if there are two objects, one of which moves in the\nsame direction as ourselves, and the other in the opposite direction,\nwe perceive only the latter. Thus in a canal boat, the horse which\nwalks on the bank in the same direction which the boat follows, seems\nto move without advancing. Of the two motions of the horse, we perceive\nonly the vertical, the horizontal escapes us.\n\nThe reason of this is clear, we can judge the object only by our\nimpressions. When the impression varies, we have the idea of motion;\nbut not otherwise. When the object or the eye is in motion, there is\na succession of impressions on the retina, from which the idea of\nmotion arises. But if the motion of the eye accompanies the motion of\nthe object, one cancels the other, the impression on the retina is\nconstant, and the object does not seem to move.\n\n86. In the same manner if the motion of the object and that of the\neye are simultaneous, but of unequal velocity, we perceive only the\ndifference; that is to say, if the motion of the eye be represented by\n3 and that of the object by 5, the motion of the object will appear as\n2, or the difference between 5 and 3. If our motion is more rapid than\nthe motion of the object, although in the same direction, the object\nwill appear to move in the opposite direction, as when we sail down a\nriver faster than the current, the water seems to flow backwards. An\nimmovable object at the same time seems to move in a direction opposite\nto our own with greater velocity than the current; for, here also, of\nthe two motions we perceive only the difference. The motion of the\nboat, which is equal to 5, seems transferred to the fixed object, which\nappears to move in the opposite direction with the velocity represented\nby 5; and if we suppose the velocity of the current to be equal to 3,\nit will have the appearance of moving backwards with a velocity of 5-3,\nor 2.\n\n87. From these considerations it would seem to follow that although\nsight is sufficient to give us the idea of motion, it is not\nsufficient to enable us to distinguish our own motion from that of the\nobject, but for this we have need of touch. But this is not so; for by\nsight alone, we can distinguish the motion of the eye from that of the\nobject, and if in some cases this is impossible, the same is true of\ntouch.\n\nWe must observe that in the above examples touch is of much less use\nthan sight in order to preserve us from illusions. How by the aid of\ntouch alone could we perceive the motion of a boat gliding smoothly\ndown a river? Sometimes by the help of sight we observe this motion,\nespecially if we regard the objects along the bank which we pass; but\ntouch is essentially limited to what affects the body immediately, and\ntherefore cannot discover motion when the body is not affected by it.\n\nIt is also well to observe that we do not refer the motion perceived by\ntouch to the objects around us until after we have acquired this habit\nby means of repeated comparisons. When for the first time the hand is\npassed over an object, we are unable to tell whether the hand moves\nover the body, or the body under the hand.\n\nThe reason of this is that the sensation of motion is essentially\na successive sensation, and this succession exists equally whether\nthe hand moves or the object. Let us suppose the hand to pass along\nan object of a varied surface, we shall experience the variety of\nsensations corresponding to the surface; suppose now that the hand\nremains motionless, and the object passes under it with the same\nvelocity, pressure, and friction, the sensations will be the same as\nbefore. Every one must have observed that when leaning on a slippery\nobject, it is often difficult to tell whether it is the object which\nmoves, or ourselves. Therefore touch also confirms what we have\nadvanced, that the distinction between the motion of the member and\nthat of the object does not arise from simple sensation.\n\n88. In this respect, therefore, touch does not help sight; let us see\nif sight alone can enable us to distinguish between the motion of the\neye and that of the object. We have already observed that a single\nsensation with respect to one object only is insufficient, but there\nis no difficulty in proving that this result may be obtained by the\ncomparison of different sensations.\n\nLet us suppose the eye at a point A, looking at an object B; the object\nwill appear at the extremity of the range of the sight as if projected\non a plane. To be more definite we will imagine the object B to be\na column in the middle of a large hall, and the point A a corner of\nthe same hall. The column will appear to the eye to be a part of the\nopposite wall. If the eye changes its position, the column will appear\nin another part of the wall; so that if the eye should pass around the\ncolumn, it would appear successively on every part of the wall. The\nsame succession of phenomena would be observed if the eye should remain\nfixed and the column should move around it; for it is evident that if\nthe observer is placed in the centre of the room, and the column moves\naround him, the column will appear on all the parts of the opposite\nwall. From this we infer that only one sensation of sight, with only\none object, is not enough to determine whether the eye moves or the\nobject.\n\nBut if instead of one object we suppose several moving simultaneously,\nit is easy to see how the distinction of motions arises. Let us suppose\nthat at the same time that the eye sees the column, it also sees\nother objects, such as chandeliers, statues, or other columns, placed\nbetween the eye and the opposite wall. If the eye moves every time the\ncolumn changes its position on the opposite wall, the other columns,\nthe chandeliers, statues, everything in the room seems to change its\nposition; whereas, if the column moves and the eye remains fixed,\nthe column alone changes its position, while everything else remains\nmotionless. Therefore sight alone gives us two distinct orders of\nphenomena of motion:\n\nI. The first, in which all the objects change their position.\n\nII. The second, in which one object only changes its position.\n\nThese two orders of phenomena cannot remain unperceived; for by the\nhelp of reflection excited and enlightened by the repetition of the\nphenomena, we must come to the conclusion that when there is an entire\nand constant change of all the objects, it is not they that move, but\nthe eye; and that when only one or a part of the objects change their\nposition, the rest remaining fixed, it is not the eye that moves, but\nthe objects which change their position. When everything around us\nchanges we infer that it is the eye that moves; when one or two change\ntheir position we conclude that they move and not the eye. This is not\nmerely a supposition, it is the reality. The ideas derived from touch\nare essentially limited, and it is therefore impossible that they\nshould proceed from distant objects which cannot be touched.\n\n89. I believe I have demonstrated that the pretended superiority of\ntouch is without foundation, and that the opinion which makes this\nthe basis of our knowledge of external objects, the touch-stone of\nthe certainty of the sensations transmitted by the other senses, is\nan error. Without it we can acquire the certainty of the existence\nof bodies; without it we can form the idea of surfaces and solids;\nwithout it we discover motion, and distinguish the motion of the object\nfrom that of the organ which receives the impression. The theory of\nsensation here explained, and the results which are deduced from the\nrelations of the dependence or independence of the phenomena among\nthemselves, and with our will, may all be applied to the sight as well\nas to the touch.\n\n90. Summing up all we have said, we have the following results:\n\nI. We distinguish sleep from waking, even abstracting the objectiveness\nof the sensations.\n\nII. We distinguish two orders of phenomena of sensation;--the one\ninternal, the other external, here also abstracting their objectiveness.\n\nIII. The senses give us certainty of the existence of bodies.\n\nIV. Sensations have no type in the external object of what they\nrepresent, except _extension_ and motion.\n\nV. Touch is not the basis or touch-stone of certainty.\n\nVI. All that we know by means of the senses may be reduced to this;\nthat there are external beings, that is to say, beings placed outside\nof ourselves, which are extended, subject to necessary laws, and which\nproduce in us the effects which we call sensations.\n\n\n\n\nCHAPTER XVI.\n\nPOSSIBILITY OF OTHER SENSES.\n\n\n91. Lamennais writes: \"Who can say that a sixth sense would not disturb\nthe harmony of the others by a contrary impression? On what foundation\ncould he deny it? If we suppose other senses different from those which\nnature gave us, might not our sensations and our ideas be different?\nPerhaps a slight modification in our organs would be sufficient to ruin\nour whole science. Perhaps there are beings so organized that their\nsensations are wholly opposed to ours, and what is true for us is false\nfor them, and reciprocally. For, if we examine the matter closely, what\nnecessary connection is there between our sensations and the reality?\nAnd if there were such a connection, how could the senses make it known\nto us?\"[38]\n\n[38] Essai sur l'Indifference, Tome II., Part III., Ch. I.\n\nThe questions which these words raise are of the highest importance and\nmerit a serious examination.\n\n92. Is there any intrinsical impossibility of an organization different\nfrom ours, and an order of sensations different from those which we\nexperience? It seems not; and if this impossibility exists, it is\nunknown to man.\n\nWhatever opinion we adopt as to the manner in which external objects\nact upon the soul by means of the organs of the body, there is no\nnecessary relation, nor even analogy, between the object and the effect\nwhich it produces in us.\n\nA body receives upon its surface rays of the fluid which we call\n_light_, these rays are reflected upon the retina, which is another\nsurface in communication with the brain. So far all is well, and\neasily understood. There is a fluid which moves, goes from one surface\nto another, and may cause this or that purely physical effect on the\ncerebral matter; but what connection is there between this and the\nimpression of a distinct order which we call _seeing_, an impression\nwhich is neither the fluid nor the motion, but an affection of which\nthe living and thinking being, the _me_ is intimately conscious?\n\nIf, instead of the luminous fluid and its mechanism, we suppose\nanother, as, for example, the air which vibrates upon the tympanum,\nwhat _essential_ reason is there why this should not produce a\nsensation similar to that of sight? It must be confessed that it is\nimpossible to assign an _essential_ reason. To one who has no idea of\nour present organization, both phenomena are equally incomprehensible.\n\n93. What has been said of sight and hearing may be applied to the other\nsenses. In all there is a bodily organ affected by a body; we see the\nsurfaces placed one before or under the other, we see motions of one\nkind or another; but how can we pass over the immense distance which\nseparates these physical phenomena from the phenomenon of sensation?\nFor my part, I see no way to do it; this point is a barrier to the\nhuman intellect; all appearances indicate that there is no connection\nbetween these two orders of phenomena except what the will of the\nCreator has _freely_ established; if there is any necessary connection,\nthis necessity is a secret to man. Examine the textures which receive\nthe impression of the objects, the material substance which composes\nthe nervous system which is the organ of sensations, and say what\nrelation you can find between the physical phenomena of this matter and\nthe wonderful harmony of sensible phenomena.\n\n94. Still greater will be the difficulty if you consider that, although\nprotected from any injury, the organs cease to produce sensations from\nthe moment they are deprived of communication with the substance of\nthe brain. The phenomena of light are produced in the cavity of the\nskull amid the most profound darkness; and all the wonderful magic\nof sensations by which the magnificent spectacle of the universe\nis presented to our mind, which plunges the soul into raptures at\nthe sound of music, and which produces such varied and delightful\nsensations of taste and odors, all arises in the brain, a whitish,\nrude, and unformed substance, from the appearance of which no one could\nimagine it destined to such noble functions.\n\n95. Why is it that when the nerve A, in communication with the brain is\naffected, we experience the sensation which we call _seeing_, or if the\nnerve B is affected, the sensation which we call _hearing_, and so of\nthe other senses? There may be a reason, but, at least, we do not know\nit; and it is probably no other than the free will of the Creator.\n\nHere, it is true, philosophy confesses its weakness, but, at the same\ntime, it shows its power; for it sees the immense distance which\nseparates these phenomena, between which there can be no point of\ncommunication but what is established by the Almighty. When there are\nsecond causes, it is the merit of philosophy to discover them; but when\nthere are none, its merit is in rising to the first cause. A confession\nof its ignorance is sometimes a more sublime act of reason than the\nimpotent effort of an unbounded pride. If the perception of profound\ntruths exalts the intellect, is not the intellect exalted in perceiving\nits own ignorance, which is sometimes a profound truth?\n\n96. The existence of another sense is, then, possible; at least, we see\nno impossibility of it. If the deaf man who has no idea of sound, and\nthe blind man who knows not what color is, would be foolish to deny\nthe possibility of those sensations of which they are deprived, can\nwe, with any more show of reason, assert the impossibility of an order\nof sensations different from what we possess? If we examine the system\nof sensations by the light of reason, we can discover no essential\ndependence between the sensations and their respective organs, nor\nbetween the organs and the objects and circumstances by which they are\naffected. Why does the impression of the light upon my eyes cause in me\na particular sensation, which cannot result from the same impression\non a different part of my body? Why may not the brain receive the same\nimpression in various forms? Why must this fluid which we call _light_,\nand no other, produce the impression? Why may not this same sensation\nof _seeing_ proceed equally from other affections of the brain? A\nviolent blow on the head produces the sensation of many luminous\npoints, whence the common expression of \"seeing stars by daylight.\"\nWe must confess that philosophy knows nothing of these secrets, that\nas yet it has not been able to penetrate them, and it can give no\nanswer to these questions. It sees an order of facts, but no necessary\nconnection between them, or rather, judging from its ideas of mind and\nbody, every thing induces it to believe that these phenomena in our\nlife depend solely on the will of our Creator.\n\n97. If an entirely new order of sensations is possible, there may be\nbeings with six or seven senses. The imagination cannot conceive their\nnature; but reason sees in them no impossibility.\n\n\n\n\nCHAPTER XVII.\n\nEXISTENCE OF NEW SENSES.\n\n\n98. Is it certain that we have only five ways of sensation? I have\nsome doubts on this point. In order to present them with the greatest\nclearness, and solve the questions which they raise, it is well to\nsettle the meaning of the terms.\n\nWhat is sensation? In the ordinary acceptation of the word, it is the\nperception of the impression transmitted to us by one of the organs of\nthe five senses. Thus understood it is clearly limited to the action\nof the organs, but if considered as expressing a certain class of\nanimal phenomena, it is the experiencing of any affection produced by\nan impression of the organism. Even in common use the word sensation\nin its broadest signification is not restricted to the impressions\nof the five senses, and although we make a great difference between\n_sentiment_ and _sensation_; still we are often forced to confound\nthem, and to use the word _sensation_ to express things which have\nnothing whatever to do with the five senses. Thus we say: \"The news\nmade a great sensation;\" \"I cannot resist the force of such strong\nsensations,\" etc., in which cases it is evident that there is no\nreference to seeing, hearing, smelling, tasting, or touching, but to a\ndifferent order of affections of the soul.\n\n99. I said we were forced to use the word in the broader meaning;\nit is the truth which forces us. For, to the eyes of philosophy,\nthe phenomenon of sensation consists in the production in the soul\nof a particular affection determined by an impression on an organ;\nand of whatever order this affection may be, and whatever organ may\nbe affected, the animal phenomenon is substantially the same. The\ndifference is in the class of affections and of the organ which is\ntheir medium, the essence of the phenomenon does not change. And if by\nsensations we understand such distinct orders of affections as those of\nsight and of touch, why may we not include other impressions caused by\nany other organ, whatever that organ may be?\n\n100. Whatever use we may make of the word sensation, it is certain that\nwe experience many affections caused by organic impressions, besides\nthose of the five senses. What are passions but affections of the soul,\nspringing from organic impressions? Does not the mere presence of an\nobject often excite love, anger, pity, joy, grief, and many other\nsentiments of the soul?\n\nYou may say there is an essential difference between the impressions of\nthe senses and those of the passions, that the former are independent\nof all previous idea and reflection, which the latter more or less\npresuppose. Thus, when an object is present to our open eyes, we\ncannot but see it and always in the same manner; and yet this object\nwill excite in us at one time one passion, at another time another, and\nsometimes none; and almost always with great difference in the degree\nof its intensity. Moreover it is not only the mere presence of the\nobject which causes an affection, but certain conditions are necessary,\nfor example; the remembrance of a benefit or of an injury, etc., from\nwhich it is easy to see that there is an essential difference between\nthe two classes of impressions.\n\n101. If we reflect well upon this objection we shall find that though\nit is specious and under many aspects true, it contradicts nothing\nwhich I have asserted. I did not deny that the new impressions were\nsubject to very different conditions from those that govern the five\nsenses; but on the contrary I have all along supposed a difference\nnot only in the class of impressions and the diversity of the organ,\nbut also in the manner in which the organ is affected, and the\ncircumstances in which the sensation is produced in the soul. I only\ncontended that the animal phenomenon was substantially the same, that\nwe find in it the three things which constitute its nature; a corporeal\nobject; an organ affected by this object; and an impression produced in\nthe soul. Because this impression cannot exist without the aid of this\nor that idea, this or that recollection, it does not follow that the\nphenomenon does not exist, or that it is not the same; it is merely to\nimpose a new condition, and nothing more.\n\n102. But there is no necessity of admitting that some previous idea\nor reflection is requisite in order that the sight of the object may\nproduce certain impressions in the soul;--daily experience proves\nthe contrary. How is it that the presence of an object charms in an\ninstant a tender and perhaps innocent heart? Whence then arises that\nsudden fascination which is preceded by no idea, accompanied by no\naffection, and is scarce voluntary? Not from the thought of gross\nenjoyments; for perhaps he of whom I speak knows not their existence\nuntil he experiences this emotion; he feels for the first time in his\nbreast a trouble unknown before. We must therefore recur to an organic\naffection similar to that which we find in the other senses. Certain\nconditions of age and temperament may be requisite, one object may have\nbeen necessary, among a thousand, in particular circumstances, of which\nthe soul can give no account to itself though affected by them; yet it\nis still true that there is an external object, an affection of the\norganism, and an impression in the soul, all connected together by a\nmysterious, but undeniable bond.\n\nIt is easy to discover a series of strong impressions in the phenomena\nrelating to reproduction; but although they presuppose the action of\nsome one of the five senses, they nevertheless belong to a different\norder. No physiological studies are necessary to prove that these\naffections depend on the organization, and that they are greatly\ninfluenced by age, health, temperament, food, climate, and the seasons.\n\n103. There is a difference between sentiments and sensations which,\nthough it does not change the fact physiologically and psychologically\nconsidered, still greatly modifies it in its intellectual and moral\nrelations. The passions are commonly excited by an animate and sensible\nobject, whence it would seem that there is more communication between\nmind and mind, between soul and soul, than there is between one body\nand another. The sad and mournful appearance not only of a man, but\neven of an animal, immediately excites in our breast the sentiment of\ncompassion, because it expresses the suffering of a living being. This\nonly proves that nature has mysterious ways by which it transmits to us\nthe knowledge of hidden things; but this transmission is made by the\nmedium of a body which affects in some way our organic constitution.\nThere is here, if you please, a more admirable, more penetrating,\nand more spiritual a magic than that of the senses alone; but the\ndifference is in the degree, not in the nature of the phenomena.\n\nIt is certain that living beings, and those of the same species in\nparticular, are in a constant communication which mutually excites\ntheir affections, and that these affections frequently suppose a\nmysterious correspondence with unknown agencies. Physical nature\nis full of fluids whose qualities are daily becoming known through\nscientific observation. The phenomena of electricity and galvanism have\nrevealed secrets of which we had no suspicion before. Who can tell\nby what means the functions of this vast and complicated system of\nanimal life, spread over the universe, are performed? It is probable\nthat there are profound secrets in the correspondence and relation of\norganisms and in the way in which they influence one another yet to\nbe discovered; perhaps they will remain forever veiled to the eyes of\nmortality.\n\n104. Is it true that sensible beings can alone excite the passions?\nor have not inanimate causes repeatedly affected our organs? Why are\nwe sometimes joyful and sometimes sad, at some times peaceful and at\nothers irritable, when we have had no communication with any living\nbeing? It is clear that this depends on the affections of our organism,\nand has no relation to the state of other sensible beings.\n\n105. Therefore, besides the impressions caused by the five senses,\nthere are others which proceed from purely corporeal and inanimate\nobjects. Besides the phenomena of ordinary sensations, there are others\nwhich differ from them only in the kind of impression and the organ\naffected; and there is no more difference between these sensations\nand the former than there is between the impressions of one and those\nof another of the five senses. Therefore it is not correct to say that\nthere are only five kinds of sensation.\n\n\n\n\nCHAPTER XVIII.\n\nSOLUTION OF LAMENNAIS' OBJECTION.\n\n\n106. From the preceding observations we shall now deduce an important\nconsequence,--the solution of the difficulty presented by Lamennais.\nThe existence of new senses would involve new sensations, it is true;\nbut they would not disturb the harmony of those we already have. We\nhave shown that bodies affect our organs in a different manner, and\nproduce impressions different from those of the five senses; but this\ndoes not disturb the agreement of our sensations, nor change our ideas.\nConsequently, the supposition of Lamennais would not involve the\ndisorder which he suspects.\n\n107. Sensations in themselves are mere affections of the soul, and have\nno external object which corresponds to them except the existence and\nextension of bodies. Therefore a new order of sensations would only be\na new order of affections, which would in nowise alter our ideas.\n\nFrom what we have hitherto said, it is easy to see that the supposition\nof Lamennais is already realized; for there are sensations different\nfrom those of the five senses; therefore this supposition does not\ncontradict the nature and order of our ideas, nor the certainty of our\nknowledge.\n\nA musical instrument beautifully fashioned has charms for the ear, the\neye, and the touch, none of these impressions destroys the other; if we\nsuppose it placed in new relations with our organs, so as to produce in\nthe soul new impressions, why is it impossible that they should accord?\nDoes the melody of its sound cease because our soul experiences new\naffections whose nature has no connection with it? Certainly not. Why\nthen fear the overthrow of our knowledge by the introduction of a new\norder of sensations? Why give such importance to a supposition, the\neffects of which we can very well calculate, and which, if we examine\nthe phenomena of our present sensations, we find already realized?\n\n108. It is true that we know of no other means of placing ourselves\nin contact with external objects than the five senses; but it is\nequally true, that this contact existing, the impressions in the soul\ncorrespond mysteriously to the external objects; so that, while we\nobserve the sensations by which the communication is established, it is\nstill impossible for us to explain them.\n\nLet us examine the magical effects of music. They are of two orders;\nthe purely auditive, and the intellectual or moral. The first stop\nat the ear, the second pass to the brain and to the heart; and one\nmay be admirably organized for the former, yet unable to appreciate\nthe latter. Two persons listen to a sonata, both hear the _material_\nmusic, but the intellectual and moral effects are not the same on both.\nBoth perceive the least defect in the time or in the instrument, both\nadmire the art of the composer, both are charmed; but while the heart\nof one is unmoved, the brain and the heart of the other are bounding\nwith delight, the power of his fancy is multiplied, thoughts and images\ncrowd upon his mind, as though he had caught inspiration from the\nmagic notes of the music. His heart is transported with tenderness,\nmelancholy, hatred, love, anger, generosity, and courage. He is\nunder a magical influence which, moves him in spite of himself; the\nvibrations of a chord have raised in his heart a mysterious tempest\nwhich the might of reason can hardly quiet.\n\n109. From this we must conclude, that besides the ordinary relations\nbetween objects and the organs of the senses, there are other relations\nstill more intimate and more delicate between these objects and our\norganic system, and that these latter are as certain as the former.\nIn them there is greater variety of individuals, and the conditions\nnecessary to produce determinate results are less known, but there\ncan be no doubt of their existence, and this in the eyes of sound\nphilosophy is sufficient to dissipate those absurd suppositions which\nwould pretend to undermine the edifice of our knowledge.\n\n110. Thus, then, the objection is answered, which says: \"If we had\nanother sense, what would it tell us?\" Nothing which would destroy the\ncertainty of our knowledge, or the nature and order of our ideas. The\nonly new result would be _one more_ added to the many ways in which\nobjects now affect us. The same thing would happen to us as to a man\nwho after being deprived of the sense of smell, should suddenly regain\nit: he would have one sensation more; the same thing would happen to\nus as to a man who experiences a new sentiment which he had not known\nbefore: he has one affection more. New impressions have their own rank,\nneither interfering with, nor changing those which previously existed.\n\n\n\n\nBOOK THIRD.\n\nEXTENSION AND SPACE.\n\n\n\n\nCHAPTER I.\n\nEXTENSION INSEPARABLE FROM THE IDEA OF BODY.\n\n\n1. Having seen that among the objects of our sensations, extension\nalone has any external existence for us as any thing more than a\nprinciple of causality, let us now try to understand what extension is.\n\nThe idea of extension seems to be inseparable from that of body; at\nleast, I am unable to conceive a body without extension. Take away\nextension, and the parts disappear, and with them all that has relation\nwith our senses; there is no longer an object, or, if the object\nremains, it is something altogether different from what is contained\nin the idea of body. Imagine an apple, for instance, from which you\nsuddenly take away extension. What will remain of it?\n\nI am not now going to examine whether Descartes is right when he says,\nthat the essence of body consists in extension; all that I here assert\nis that a body cannot be conceived without extension. I do not affirm\nthe identity of two things, but only the inseparability of two ideas in\nour mind. It is not an opinion, but a fact asserted by consciousness,\nwhich is now under discussion.\n\nAbstracting extension, I can conceive, it is true, a substance, or, to\nspeak more generally, a being; but, then, there is no idea of body,\nunless we confound this idea with, that of substance or of being, in\ngeneral.\n\n2. All our notions of bodies are obtained through the senses, but\nwithout extension no sensation is possible; for without it there can\nbe no color, no sound, no touch, no smell, and no taste; therefore,\nwithout extension there remains only something of which we have no\nidea, a vague notion which cannot enable us to distinguish one object\nfrom another, a pure abstraction, and nothing more.\n\n3. To solve the difficulties which attend the separation of the two\nideas of extension and of body, it is necessary to determine the\nessence of body. When we can distinguish the essence of a body from its\nextension, the difficulty will be overcome, but not until then.\n\n4. In order to understand the reason of this inseparability, it\nis necessary to remember what was said before, that extension is\nthe basis of all other sensations; it is the _substratum_ which is\nconfounded with none, depends on none of them in particular, yet is an\nindispensable condition of them all.\n\nI look at an apple, and examine the mutual relations of the sensations\nwhich it produces.\n\nIt is evident that though I abstract the smell, I do not thereby\ndestroy any of the other sensations which it causes. Though it lose its\nodor, it is still extended, colored, it has a taste, and may produce\na sound. I may also, in like manner, abstract its taste, its color,\nand all that relates to the sight, but I have still an object which is\ntangible, and consequently extended, figured, and possessed of all its\nother properties which affect the touch.\n\nIf instead of abstracting what relates to the sight, I abstract what\nbelongs immediately to the touch, I may do this without destroying the\nother sensations; for I can still see the apple, its extension, form,\nand color.\n\nI may even go farther, and strip the apple of all its sensible\nqualities, of its taste, smell, color, hardness, and whatever the\nsenses can perceive, still there remains extension, not indeed\nsensible, but conceivable. Extension exists abstracted from its\nvisibility, since it exists for the blind man: abstracted from its\ntangibility, since it exists for the sight; abstracted from odor,\ntaste, and sound, since it exists for those who are deprived of these\nsensations, so long as they have sight or touch.\n\n5. Here a difficulty arises. There seems to be a mistake in what\nwe have said of the existence of extension abstracted from other\nsensations; for, although in making this abstraction we conceive\nourselves to be deprived of these sensations, still we retain the\n_imagination_ of them; thus, when I strip the apple of all light and\ncolor, it is still extended; but that is because I still imagine a\ncolor, or, if I make a strong effort to destroy the color, it appears\nto me like a black object, on a ground of greater or less darkness,\ndistinct from the apple. Does not this prove that there is an illusion\nin such abstractions, and that there is no complete abstraction, since\nthe reality which we abstract is succeeded by the imagination of the\nsame qualities, or of others which supply their place, so as to make\nthe extension perceptible?\n\nThis objection is specious, and it would be difficult to give a\nsatisfactory answer if the existence of men deprived of sight did not\ninstantly dissipate it. No such imagination is possible in the case\nof a blind man, for him there is no color, no shade, no light, no\ndarkness, nor anything which relates to sight, and still he conceives\nextension.\n\n6. But at least, some one will answer, it must be confessed that the\nidea of extension is necessarily dependent on the sensations of touch;\nblind men also possess this sense, and by it they acquire the idea of\nextension. Therefore the idea of extension is inseparable from the\nsensations of touch. This argument is no better than the other; for,\nalthough we may acquire the idea of extension by the sense of touch,\nand this sense is all that is required to produce it, it is not true\nthat this idea can only be acquired by touch. I have already proved\nthat sight is sufficient of itself alone to produce the idea of the\nthree dimensions which constitute a solid or extension in its full\ncomplement. But here I do not need the idea of a solid, that of a\nsurface is sufficient; the extension of a surface is inseparable from\nsight. There is no sight without color, or light of some kind or other,\nand this cannot even be imagined without a surface.\n\nI have another argument. Geometricians, doubtless, conceive extension,\nand yet they abstract all its relations to sight or touch; therefore,\nthere is no necessary connection between them.\n\nIn any object submitted to the sight, what quality relating to the\ntouch is necessary in order to produce the idea of extension? If we\nexamine it closely, we shall find that there is none. Let us take a\nliquid; is its fluidity the necessary quality? No; for when congealed\nextension remains. Is it heat or cold? No; for without destroying\nits extension we may change its temperature as much as we please,\nno alteration is perceptible. Whatever quality relative to touch we\nmay take, we shall find that it may be varied, modified, or entirely\ndestroyed, without visibly affecting the extension.\n\nIt often happens that we have a clear and definite idea of the\nextension of an object without knowing any thing of its qualities in\nrelation to touch. I see an object at a distance, I distinguish its\ncolor and its form, but I know not of what material it is, whether\nit is of marble, or wood, or wax, nor whether this material is hard\nor soft, moist or dry, warm or cold. I do not even know if it is\ntangible, as in the case of figures formed by vapors which are\nimperceptible to the touch.\n\n7. Without extension there can be neither sight, nor touch, nor any\nother sensation. As to taste, it is clear that it requires touch, and\ncannot exist without it. Our assertion is less clear with regard to\nsound and smell; for, although we cannot separate these sensations from\nthe idea of extension as they always involve this idea in one way or\nanother, we do not know how it would be with a man who was deprived of\nall the other senses, and retained only those of smelling and hearing.\nBut without speculating on this hypothesis, it is enough to know:\n\nI. That nothing which is not extended can act upon our organs, unless\nby means wholly unknown to us, and which would give no idea of what we\nunderstand by body.\n\nII. That even supposing the sensations of smelling and hearing to be\npossible without the idea of extension, they would in that case be only\nsimple phenomena of our being, and would not place us in communication\nwith the external world, as we now perceive it; because, if we should\nnot know that they proceeded from another cause, we could have no more\nconsciousness of them than that which we have of the _me_; and if\nwe should know it, this cause would be represented to us only as an\nagent influencing us, and not by any means as a being having any thing\nsimilar to what we understand by body.\n\nIII. That in such a case we should have no idea of our own\norganization, nor of the universe; for it is clear that every thing\nbeing reduced to mere internal phenomena, and their relation to the\nagents producing them, and the idea of extension wanting, neither the\nuniverse nor our own body would be to us what they now are. What would\nthe universe,--what would our body be without extension?\n\nIV. That for the present we limit ourselves to the demonstration of\nthe dependence which in the present system, of things, all sensations\nhave in relation to extension; and this demonstration holds good, even\nthough we suppose the man who possesses only the sense of smelling or\nthat of hearing not to form any idea of extension, and not to need it\nin order to experience its sensations.\n\nV. That even on this supposition, the proposition before established,\nthat the idea of extension is independent of the other sensations,\nstill remains unassailed.\n\nVI. That the truth which we are principally endeavoring to demonstrate,\nthat for us the idea of extension is inseparable from that of body,\nalso stands firm.\n\n8. This inseparability is so certain, that theologians explaining the\naugust mystery of the Eucharist, distinguish in the extension of bodies\nthe relations of the parts to each other, and their relation to place,\n_in ordine ad se, et in ordine ad locum_; and they say that the sacred\nbody of our Lord Jesus Christ is in this august Sacrament, by extension\n_in ordine ad se_, though not by extension _in ordine ad locum_. This\nproves that the theologians saw that it is not possible for man to\nlose all idea of extension, without at the same time losing all idea\nof body; and thus they invented this ingenious distinction, of which I\nshall speak at greater length in another place.\n\n\n\n\nCHAPTER II.\n\nEXTENSION NOT PERCEPTIBLE AS THE DIRECT AND IMMEDIATE OBJECT OF\nSENSATIONS.\n\n\n9. Extension has the remarkable peculiarity of being perceived by\ndifferent senses. As regards sight and touch this is evident; it is\nalso true as far as concerns the other senses. We perceive taste in\ndifferent parts of the palate, and we refer sound and smell to distinct\npoints in space, and this involves the idea of extension.\n\nBut what is more strange is, that although extension is the\nindispensable basis of all sensations and therefore perceived by all\nthe senses, it is, in itself, and separated from every other quality,\nimperceptible to them all. The eye perceives only light, and the ear\nsound, the palate taste, the smell odor, and the object of touch is\nthat which is warm or cold, moist or dry, solid or liquid, etc. None\nof these objects is extension, none _in particular_ is necessary for\nthe perception of extension; for we constantly find it separated from\neach of these qualities, and yet it is still perceptible. No one _in\nparticular_ is necessary for the perceptibility of extension, but some\none is indispensable; for, unless accompanied by some one of them, it\nis imperceptible to the senses.\n\nHence, extension is a necessary condition of our sensations, but is\nnot itself perceived by the senses. Still it is not therefore unknown,\nand this brings me to some other reflections which take us out of the\nphenomenal into the transcendental order, and give rise to very serious\nand difficult questions, which have hitherto been insolvable, and it is\nto be feared must ever remain so.\n\n10. We have seen that extension in itself is not the direct object of\nsensation. What, then, is it? What is its nature?\n\nThere are two things which may be considered in the idea of extension:\nthat which it is in us, and that which it represents to us; or, in\nother words, its relation to the subject, and its relation to the\nobject. The first being subject to immediate observation, inasmuch as\nit exists within us, is difficult but not impossible to explain. The\nsecond is more difficult, and almost impossible to explain, because it\nis a very abstract and transcendental idea, and also requires a series\nof arguments, the thread of which may be broken without the one who\nreasons perceiving it.\n\n11. Extension in us is not a sensation, but an idea. Sometimes we\nimagine it under a sensible form, confounding it with a determinate\nobject; at other times we picture it to ourselves as a vague\nobscurity in which bodies are placed; but these are only fictions of\nthe imagination. A man born blind can have none of these internal\nrepresentations, and yet he forms a very good conception of extension.\nWe ourselves in thinking of extension abstract all these forms under\nwhich we imagine it.\n\nTwo different sensations, those of sight and touch, produce the same\nidea of extension. This is conclusive proof that extension is rather\nintelligible than sensible.\n\nWhatever may be the relation of extension to sensation, we cannot\ndeny that it is an idea if we reflect that it is the foundation of\nthe whole science of geometry. Thus, although we form various images\nof extension, they are only the particular forms with which the mind\nclothes the idea, if we may use the expression, according to the\ncircumstances of the case. That which is fundamental and essential in\nthe idea, is of a different and higher order, and has nothing in common\nwith the applications which the mind makes in order to explain and\napply it. This idea includes dimensions, but not determined or applied;\nthey are mere conceptions which represent nothing in particular.\n\n12. The idea of extension is a primitive fact of our mind. It is not\nproduced by sensations, but precedes them, if not in time, at least\nin the order of being. There is no ground for asserting that the idea\nof extension exists in the mind prior to the first impression of the\nsenses, but unless extension serves as their basis these impressions\nare inconceivable. Whether this idea is innate or developed, or\nproduced in the mind by the impressions, there can be no doubt that it\nis distinct from them, necessary to them, and independent of any one of\nthem in particular.\n\nIt may be that when these impressions are first received extension\nmay not be known as a separate idea; but it is certain that it\nis afterwards separated and stripped of the corporeal form, and\nspiritualized, and that this phenomenon may be occasioned but not\ncaused by the sensation.\n\nIn sight, abstracting extension, there is color, but we cannot discover\nin it any thing from which we can produce so fruitful an idea as\nthat of extension. Even at first we see that the color itself is not\nperceptible without extension, and so far from extension being produced\nby color, it is on the contrary an indispensable condition without\nwhich color cannot be perceived.\n\nColors as the objects of sensation are only individual phenomena,\nwhich have no connection with one another nor with the general idea of\nextension. What has been said of them will equally apply to all the\nimpressions of touch.\n\n\n\n\nCHAPTER III.\n\nSCIENTIFIC FRUITFULNESS OF THE IDEA OF EXTENSION.\n\n\n13. In order to understand the superiority of the idea of extension\nover mere sensations; or rather, in order to understand that there is\na true idea of extension considered in itself, and that there is no\nsuch idea of the direct and immediate objects of sensation, I wish to\ncall attention to the fact that among all the objects of the senses,\n_extension alone gives origin to a science_.\n\nThis is a very important fact;--to explain it as it deserves, I shall\nestablish the following propositions:\n\n\nFIRST PROPOSITION.\n\nExtension is the basis of geometry.\n\n\nSECOND PROPOSITION.\n\nNot only is extension the basis of geometry, but all that we know\nof the nature of bodies may be reduced to the manifestations,\napplications, and modifications of extension, with the addition of the\nideas of number and time.\n\n\nTHIRD PROPOSITION.\n\nWhatever we know of sensations that deserves the name of science is\nincluded in the modifications of extension.\n\n\nFOURTH PROPOSITION.\n\nWe can form no fixed idea of corporeal objects, nor make any\nobservation on the sensible world, unless we are guided by the rule of\nextension.\n\nThese four propositions are nothing more than the enunciation\nof certain facts, the mere exposition of which is a sufficient\ndemonstration.\n\n14. Extension is the basis of geometry. This is evident, since geometry\ntreats only of dimensions, and the idea of dimension is essential to\nextension.\n\nWhen geometry treats of figures, it is still extension which it is\ntreating of; for figures are only extension with certain limitations.\nThe quadrilateral contains two triangles. To distinguish them, it is\nonly necessary to draw their limit, which is the diagonal. The idea of\nfigure is merely the idea of limited extension, and the figure is of\nthis or that kind according to the nature of its limits. Consequently,\nthe idea of figure is nothing new superadded to extension; but merely\nits application.\n\nMoreover, limit or termination is not a positive idea; it is a pure\nnegation. If I have extension and wish to form all the figures\npossible, I need not conceive any thing new, but only abstract what I\nhave already; I do not add, but take away. Thus in the quadrilateral\nI obtain the conception of the triangle by abstracting one of the two\nequal parts into which it is divided by the diagonal. In the same\nmanner I deduce the quadrilateral from a pentagon by abstracting the\ntriangle formed by a line drawn from one of its angles to either of the\nopposite angles. These observations apply to all geometrical figures.\n\nThe idea of extension is like an immense ground on which we have only\nto _draw limits_ in order to obtain whatever we want.\n\nIt does not follow from this that the understanding cannot proceed\nby addition or the synthetic method; for, just as the subtraction\nof one of the parts of the quadrilateral formed a triangle, so\nalso the addition of two triangles with an equal side will produce\na quadrilateral. And in the same way points produce lines, lines\nsurfaces, and surfaces solids. In all these cases the idea of figure\nis that of limited extension, since the quantities which constitute it\nare merely extension with certain limitations.\n\n15. An observation here presents itself to my mind, which I think must\nthrow great light upon the question which we are now discussing. If we\ncompare the two methods by which the idea of figure is obtained; the\nsynthetic, or that of composition or addition, and the analytic, or\nthat of subtraction or limitation, we shall find that the second is\nmore natural than the other; because that which the analytic method\nproduces is permanent in the figure and essential to it, whilst the\nsynthetic only seems to constitute it, and as soon as it is thus\nconstituted the marks of its formation are obliterated.\n\nAn example will make this clearer. In order to conceive a rectangle\nI have only to limit indefinite space by four lines in a rectangular\nposition; that is, to _affirm_ a part, and _deny_ the rest. The lines\nare nothing in themselves, and represent only the limit beyond which\nthe space included in the rectangle cannot pass. To abstract this\nlimitation or denial of all that is not contained in the surface of the\nrectangle, would be to destroy the rectangle. Therefore, the denial\nin which this method consists is always permanent, the manner of the\nproduction of the idea is inseparable from the idea itself.\n\nBut if, on the other hand, I proceed to form the rectangle by addition\nor by joining the hypotheneuse of two right-angle triangles, the\nideas of the two component parts are not necessary to the idea of\nthe rectangle after its formation. I can conceive the rectangle even\nabstracting the diagonal.\n\nThus, then, it is demonstrated that the idea of extension is the only\nbasis of geometry, and that this idea is an immense field on which,\nby means of limitation or abstraction, we can obtain all the figures\nwhich form the object of geometry. Figures are only extension limited,\na positive extension accompanied by a negation, and consequently\nwhatever is positive in geometry is extension.\n\n16. We cannot doubt that, whatever we know of the nature of bodies, may\nbe reduced to certain modifications or properties of extension, if we\nobserve that the entire object of the natural sciences is the knowledge\nof the motion or of the different relations of things in space, which\nis nothing more than the knowledge of the different kinds of extension.\n\nStatics is occupied in determining the laws of the equilibrium of\nbodies, but in what way? Does it penetrate into the nature of the\ncauses? No; it only determines the conditions to which the phenomenon\nis subject, and the only ideas which enter into these conditions are\nthe _direction of the force_, that is to say, a _line_ in space, and\nthe velocity, which is the relation of space to time.\n\nThe idea of time is the only idea which is here joined with that of\nextension. In another place I shall prove that time, separated from\nthings, is nothing, and consequently, although this idea is here joined\nto that of extension, it does not interfere with the truth of what I\nhave established. In statics, all that relates to other sensations is\ncounted as nothing; in order to solve the problems of the composition\nand decomposition of forces, we abstract all color, smell, and other\nsensible qualities of bodies in motion. What has been said of statics\napplies equally to dynamics, hydrostatics, hydraulics, astronomy, and\nto all sciences which regard motion.\n\n17. Here an objection may be made. That with the ideas of time and\nspace, we seem to combine another which is distinct from them, and\nnecessary, in order to complete the idea of motion, and this is the\nidea of a body moved. It is not time, nor is it space, for space is\nnot moved, therefore it is distinct from them.\n\nTo this I reply, first, that I am speaking of extension, and not of\nspace alone, which it is important to remember, for what I shall\nafterwards say; and secondly, that science regards the thing moved as a\npoint, and this is sufficient for all its purposes. Thus in the systems\nof forces there is a point of application for each of the component\nforces, and another for the resultant. This point is not regarded as\nhaving any properties, but is in relation to motion what the centre\nis in relation to a circle. Every thing is related to it, yet it is\nnothing in itself, except inasmuch as it occupies a definite position\nin space. It may change according to the quantity and direction of\nthe forces, it may run over or describe a line in space with greater\nor less velocity, and the line may be of this or that class, and\naccompanied by various conditions. If a body be impelled by two forces,\nB and C, acting upon a point A, science considers in the body only the\npoint through which the resultant of the forces B and C passes, and\nabstracts all the other points of the body which, being joined to the\npoint A, move with it.\n\n18. When I say that the natural sciences go no farther than the\nconsideration of extension, I only mean to exclude the other\nsensations, but not ideas; for it is clear that the ideas of time and\nnumber are combined with the idea of extension. This is so true in\nmechanics, in this sense at least, that all its theorems and problems\nare reduced to geometrical expressions, and even the idea of time is\nexpressed by lines.\n\nIn every force there are three things to be considered: the direction,\npoint of application, and intensity. The direction is represented by a\nline, and the point of application by a point in space. The intensity\nis represented only in the effect which it can produce, and this\nis expressed by a line, the length of which expresses the intensity\nof the force. The effect of the intensity which is represented by a\nline includes the time also; for the measure of a motion cannot be\ndetermined until we know its velocity, which is merely the relation\nof space to time. Therefore, although the idea of time is combined\nwith that of extension, the result is expressed by lines, that is, by\nextension.\n\n19. There is another circumstance still which shows the fruitfulness\nof the idea of extension. It is that in the expression of the laws of\nnature, it reaches cases which are beyond the idea of number. If we\nsuppose two equal rectangular forces, AB and AC, acting on the point A,\nthe resultant will be AR. Now, if we consider AR to be the hypotheneuse\nof a right-angled triangle, AR^2 = AB^2 + AC^2, extracting the square\nroot AR = \u221a(AB^2 + AC^2). If we suppose each of the component forces\nequal to 1, AR = \u221a(1^2 + 1^2) = \u221a2, a value which can neither be\nexpressed in whole numbers nor in fractions, but which is represented\nby the hypotheneuse.\n\n20. In the physical sciences, such words as force, cause, agent, etc.,\nare frequently used, but the ideas which these terms express are a part\nof science only inasmuch as they are represented by effects. This is\nnot because true philosophy confounds the cause with the effect, but\nas physical science regards only the phenomenon in all that relates to\nthe cause, it limits itself to the abstract idea of causality, which\npresents nothing determinate, and consequently is not the object of its\nscientific labors. The system of universal attraction has immortalized\nthe name of Newton, and he begins by confessing his ignorance of the\ncause of the effect which he explains. When we go beyond the phenomena\nand the calculations to which they give rise, we enter the field of\nmetaphysics.\n\n21. The natural sciences consider certain qualities of bodies which\nhave no relation to extension, as, for example, heat and light, and\nthis might seem to be a refutation of what we have said of extension.\nStill this objection disappears when we examine in what manner science\ntakes note of these qualities, and instead of overthrowing our thesis,\nthe result will strengthen, extend, and explain it.\n\nHeat is not measured by the sensation which it produces in us. If we\nenter a room where the temperature is very high, we experience a strong\nsensation of heat, which gradually grows weaker, while the temperature\nremains the same. If we reach our hand to a friend we experience a\nsensation of heat or cold, in proportion as his hand is warmer or\ncolder than our own.\n\nHeat and cold are measured, not in themselves, nor in relation to our\nsensations, but in the effect which they produce. These effects are\nincluded in the modification of extension; for the thermometer marks\nthe temperature by a greater or less elevation of the mercury in a\n_line_. Its degrees are expressed by parts of a line, on which they are\nmarked.\n\nI know that what is measured is distinct from extension; but, its\nmeasurement is only possible by relation to extension, and by attending\nto effects which are modifications of extension. Thus, the temperature\nat which water boils is 212\u00b0, and this is discovered by the motion of\nthe water, and has relation to extension. So, also, the rarefaction\nand condensation of bodies are modifications of extension, since these\nstates consist in the occupation of greater or less space, or in the\nincrease or diminution of their dimensions.\n\n22. All that science teaches us of light and colors relates to the\ndifferent directions and combinations of the rays of light. Our\nobservation goes no farther than sensation. We know that we can combine\nthe rays in different manners, and direct them, so as to modify our\nsensation, but this is nothing more than the scientific knowledge of\nextension in the medium which we make use of, and of the sensation\nexperienced in consequence. All beyond this is entirely unknown.\n\n23. We may say the same of all other sensations, that of touch\nincluded. What is that quality of bodies which we call hardness? the\nresistance which we encounter when we touch them? But abstracting\nsensation, which only produces the consciousness of itself, what do we\nfind? Impenetrability. And what do we understand by impenetrability?\nThe impossibility of two bodies occupying the same space at the\nsame time. Here, then, we meet with extension. If, by hardness, we\nmean the cohesion of molecules, in what does cohesion consist? In\nthe juxtaposition of parts in such manner that they cannot, without\ndifficulty, be separated. But, to be separated, is to be made to occupy\na place different from that which was before occupied. Here, too, we\nfind the idea of extension.\n\nOf sound we know nothing scientifically, except as relates to extension\nand motion. The musical scale is expressed by a series of fractional\nnumbers representing the vibrations of the air.\n\n24. These examples demonstrate the third of the above propositions,\nthat whatever we know of sensations that deserves the name of science,\nis included in the modifications of extension.\n\n25. It is the same with the fourth proposition, that without the idea\nof extension, we can have no fixed idea of any thing corporeal, no\nfixed rule in relation to phenomena, but are like blind men. If, for\nan instant, we abstract the idea of extension, it is impossible for us\nto take a step in advance. The examples already adduced in order to\ndemonstrate the second proposition, render further explanation here\nunnecessary.\n\n26. Although extension is essentially composed of parts, there is in it\nsomething fixed, unalterable, and, in some manner, simple. There may be\nmore or less extension, but not different kinds. One right line may be\nlonger or shorter than another, but its length is not of a different\nspecies. One surface may be larger than another, a solid of a certain\nkind greater than another of the same kind, but not in a different\nmanner.\n\nWhen I say that in the idea of extension objectively considered there\nis a _certain sort_ of simplicity, I do not mean that there is any\nthing _entirely_ simple; for I have just said that its _object_ is\n_essentially_ composite. Neither do I abstract its essential elements,\nwhich are the three dimensions, nor any idea which it involves, as its\nlimitability, or capacity to be limited in various ways. All I wish to\nshow is that in all the different figures these fundamental notions are\nsufficient, that they are never modified, but always present the same\nthing to the mind.\n\nLet us compare a right line with a curve. A right line is a direction\nwhich is always constant; the curve a direction which is always\nvaried. A direction always varied is a collection of _right directions\ninfinitely small_. Therefore, the circumference of a circle is\nconsidered as a polygon of an infinite number of sides. The curve is\ntherefore formed by the variety of directions reduced to infinitesimal\nvalues. This theory which explains the difference of the right line and\nthe curve, is evidently applicable to surfaces and solids.\n\nLet us compare a quadrilateral with a pentagon; all that the second has\nwhich the first has not is one side more in perimeter, and in area the\nspace contained in the triangle formed by a line drawn from one of its\nangles to either of the opposite angles. The lines are of the same\nkind, the surfaces differ only in the ways in which they terminate. But\ntermination is the same as limitation. Therefore, all that is essential\nto the idea of extension, that is, direction and limitability, remain\nalways the same and unchangeable.\n\nThis intrinsical constancy is indispensable to science. That which\nis mutable, may be the object of perception, but not of scientific\nperception.\n\n\n\n\nCHAPTER IV.\n\nREALITY OF EXTENSION.\n\n\n27. We now come to more difficult questions. Is extension any thing in\nitself, abstracted from the idea of it? If any thing, what is it? Is it\nidentified with bodies, or is it confounded with space?\n\nI have proved[39] that extension exists outside of ourselves, that it\nis not an illusion of the senses; and this solves the first question,\nwhether extension is any thing.\n\n[39] Book II. Ch. ix.\n\nWhatever may be its nature or our ignorance on this point, there is in\nreality something which corresponds to our idea of extension. Whoever\ndenies this truth must be content to deny every thing except the\nconsciousness of himself, if indeed he does not experience doubts even\nof this too. Whatever idealists may assert, there is not, nor ever was\na man who in his sound judgment seriously doubted the existence of an\nexternal world. This conviction is for man a necessity against which it\nis vain to contend.\n\nThis external world is for us inseparable from that which is\nrepresented by the idea of extension. It either does not exist, or\nelse it is extended. If we could be persuaded that it is not extended,\nit would not be difficult to convince us that it does not exist. For\nmy part, I find it just as difficult to imagine the world without\nextension as without existence, and if I could be made to believe its\nextension an illusion, I should easily believe its existence also an\nillusion.\n\n28. It is to be observed that although we confess our ignorance of the\ninternal nature of extension, it is still necessary to admit that we\nknow something of it; its dimensions, namely, and what serves as the\nbasis of geometry. The difficulty is not in knowing what extension\nis geometrically considered, but what it is in reality. We know the\ngeometrical essence, but what we want to ascertain is, whether this\nessence realized is something which is confounded with some other real\nthing, or is only a quality which we know without knowing the being to\nwhich it belongs. Without this distinction we should deny the basis of\ngeometry; for, it is evident that if we should not know the essence of\nextension in the aforesaid manner, we could not be sure that we are not\nbuilding in the air when we raise upon the idea of extension the whole\nscience of geometry.\n\n29. Thus then under this aspect, we are certain that extension exists\noutside of us, and that there are true dimensions. This idea is a\nnecessary consequence of the idea of the external world, as we said\nbefore. The dimensions in the external world must be subject to the\nsame principles as those which we conceive, or the very idea which we\nhave formed of the external world is reversed. I do not mean by this\nthat a real circle may be a geometrical circle, but only that what is\ntrue of the second must be true of the first also, in proportion as\nit is constructed with greater or less exactness. Beyond what can be\nformed by the most perfect and exact instruments, I can conceive,\nwithout passing from the order of reality, a circle or any other\nfigure, as near as I please to the geometrical idea. The sharpest\ninstrument can never mark an indivisible point, nor draw a line without\nbreadth; but this surface, on which the point is marked, on the line\ndrawn, being infinitely divisible, I can conceive a case in which the\nreality will come infinitely near to the geometrical idea.\n\n30. Astronomy and all the physical sciences rest on the supposition\nthat real extension is subject to the same principles as ideal\nextension; and that experience comes closer to theory in proportion\nas the conditions of the second are more exactly fulfilled in the\nfirst. The art of constructing mathematical instruments, which has been\nbrought in our day to a surprising perfection, regards the ideal as the\ntype of the real order; and progress in the latter is the approximation\nto the models of the former.\n\nTheory directs the operations of practice, and these in their turn\nconfirm by the result the foresight of theory. Therefore, extension\nexists not only in the ideal order, but also in the real; and it\nis something, independently of our ideas; and geometry, that vast\nrepresentation of a world of lines and figures, has a real object in\nnature.\n\nHow far the real corresponds with the ideal, we shall examine in the\nnext chapter.\n\n\n\n\nCHAPTER V.\n\nGEOMETRICAL EXACTNESS REALIZED IN NATURE.\n\n\n31. The disagreement which we discover between the phenomena and the\ngeometrical theory makes us apt to think that reality is rough and\ncoarse, and that purity and exactness are found only in our ideas.\nThis is a mistaken opinion caused by want of reflection. The reality\nis as geometrical as our ideas; the phenomenon realizes the idea in\nall its purity and vigor. Be not startled by this seeming paradox; for\nit will soon appear to you a very true, reasonable, and well-grounded\nproposition.\n\nWe shall first prove that the ideas which are the elements of geometry\nhave their objects in the real world, and that these objects are\nsubject to precisely the same conditions as the ideas. This proved, it\nclearly follows that geometry in all its strictness exists as well in\nthe real as in the ideal order.\n\n32. Let us begin with a point. In the ideal order, a point is an\ninvisible thing, it is the limit of a line and its generating element,\nand it occupies a determinate position in space. It is the limit of a\nline; for when we take away its length, we have a point remaining which\nwe are forced to regard as the limit of the line unless we destroy it\nentirely so as to have nothing left. The more the line is shortened\nthe nearer it approaches to a point, yet can never be identified with\nit until its length is wholly suppressed. The point is the generating\nelement of the line; for we form the idea of lineal dimension by\nconsidering a point in motion. The occupation of a determinate position\nin space is another indispensable condition of the idea of a point, if\nwe wish to use it in geometrical figures. The centre of a circle is a\npoint in itself indivisible, it fills no space; but in order that it be\nof any use as centre, we must be able to refer all the radii to it, and\nthis is impossible unless it occupy a determinate position equidistant\nfrom all points of the circumference. As a general rule, geometry acts\nupon dimensions, and these dimensions require points in which they\ncommence, points through which they pass, and points in which they\nend, and by which distances, inclinations, and all that relates to\nthe position of lines and planes, are measured. Nothing of all this\ncan be conceived unless the point, although not extended, occupies a\ndeterminate position in space.\n\n33. Does there exist in nature anything which corresponds to the\ngeometrical point, and unites all its conditions with as great\nexactness as science in its purest idealism can desire? I believe there\ndoes.\n\nPhilosophers have adopted different opinions as to the divisibility\nof matter. Some maintain that there are unextended points in which\nthe division ends, and that all composite bodies are formed of these.\nOthers assert that it is not possible to arrive at simple elements,\nbut the division may continue _ad infinitum_ continually approaching\nthe limit of composition, but never reaching it. The first of these\nopinions is equivalent to the admission of geometrical points realized\nin nature; the second, though apparently less favorable to this\nrealization, must come to it at last.\n\nUnextended molecules are the realization of the geometrical point, in\nall its exactness. They are the limit of dimension, because division\nends with them. They are the generative elements of dimension,\nbecause they form extension. They occupy a determinate position in\nspace, because bodies with all their conditions and determinations\nin space are formed of them. Therefore, from this opinion, held by\neminent philosophers like Leibnitz and Boscowich, it follows that the\ngeometrical point exists in nature in all the purity and exactness of\nthe scientific order.\n\nThe opinion which denies the existence of unextended points, admits, as\nit necessarily must admit, infinite divisibility. Extension has parts,\nand therefore is divisible; these parts, in their turn, are either\nextended or not extended; if unextended, the supposition fails, and\nthe opinion of unextended points is admitted; if extended, they are\ndivisible, and we must either come at last to unextended points, or\ncontinue the division _ad infinitum_.\n\nI remarked above that, although less favorable to the real existence of\ngeometrical points, this opinion as well as the other does acknowledge\ntheir realization. The parts into which the composite is divided are\nnot created by the division, but exist before the division, and without\nthem the division would be impossible. They do not exist because they\nmay be divided, but they may be divided because they exist. This\nopinion therefore, does not expressly admit the existence of unextended\npoints, but it admits the possibility of eternally coming nearer to\nthem, and this not only in the ideal, but also in the real order;\nbecause the divisibility is not affirmed of the ideas, but of the\nmatter itself.\n\nAlthough our experience of division is limited, divisibility itself\nis unlimited. A being endowed with greater powers than we possess,\nmight carry the division further than we are able to do. Our ability\nto divide is limited, but God, by his infinite power, can push the\ndivision _ad infinitum_, and His infinite intelligence sees in an\ninstant all the parts into which the composite may be divided.\n\nOmitting the difficulties which attend an opinion which seems to\nsuppose the existence of what it denies, I will ask if geometry can\nrequire more rigorous exactness than is found in the points to which\ninfinite power can come, if we suppose it to exercise its eternal\naction in dividing the composite; or, in other words, can there be\nany more strictly geometrical points than those seen by an infinite\nintelligence in an infinitely divisible being? This not only satisfies\nour imagination and our ideas of exactness, but goes even beyond.\nExperience teaches us that to _imagine_ an unextended point is not\nimpossible; and to _think_ it in the purely intellectual order, is only\nto conceive the possibility of this infinite divisibility, and to be\nsuddenly placed at the last limit,--a limit which must still be far\ndistant from that to which, not abstraction, but the sight of infinite\nintelligence can reach.\n\nIf the geometrical point exists, the geometrical line also exists; for\nit is only a series of unextended points; or, if we are unwilling to\nacknowledge these, a series of extremes to which division infinitely\ncontinued at last arrives. A series of geometrical lines forms a\nsurface; and a union of surfaces forms a solid, the ideal order\nagreeing with reality in its formation as in its nature.\n\n34. This theory of the realization of geometry extends equally to all\nthe natural sciences. It is an error to say, for example, that the\nreality does not correspond to the theories of mechanics. It should\nrather be said that it is not the reality that is at fault, but the\nmeans of experimenting; the blame should not be imputed to the reality,\nbut rather to the limitation of our experience.\n\nThe centre of gravity in a body, is the point where all the forces\nof gravitation in the body unite. Mechanics supposes this point to\nbe indivisible, and in accordance with this supposition, establishes\nand demonstrates its theorems, and solves its problems. Here stops\nthe mechanician, and the machinist begins, who can never discover the\nstrict centre of gravity supposed in the theory. Experience disagrees\nwith the principles, and we ought to correct the former by adhering to\nthat which is determined by the latter. Is this because the centre of\ngravity does not exist in nature with all the exactness which science\nsupposes? No; the centre exists, but the means of finding it are\nwanting. Nature goes as far as science; neither remains behind; but our\nmeans of experience are unable to keep up with them.\n\nThe mechanician determines the indivisible point in which the centre\nof gravity is situated, supposing the surface without thickness,\nlines without breadth, and the length divided at a determinate point\nof space, which has no extension. Nature entirely fulfills these\nconditions. The point exists, and the reality should not be blamed\nfor the limitation of our experience. The point exists in either of\nthe hypotheses mentioned above. The first, which favors unextended\npoints, admits the existence of the centre of gravity in all its\nscientific purity. The other is not so decided, but it says to us: \"Do\nyou see this molecule, this little globe of infinitesimal diameter,\nthe smallness of which the imagination cannot represent? Make it still\nsmaller, by dividing it for all eternity, in decreasing geometrical\nprogression, and you will always be coming nearer the centre of gravity\nwithout ever reaching it. Nature will never fail; the limit will ever\nretire from you; but you will know you are approaching it. Within this\nmolecule is what you seek. Continue to advance, you will never reach\nit,--but what you want is there.\" In this case I do not see that the\nreality falls short of scientific exactness; no mechanical theory\nimagined or conceived can go farther.\n\n35. These reflections place beyond all doubt that geometry with all\nits exactness, and theories in all their rigor, exist in nature. If we\ncould follow it in our experience, we should find the real conformed\nto the ideal order, and we should discover that when experience is\nopposed to theory, it is not the latter which is wrong, but the\nlimitation of our means makes us lay aside the conditions imposed by\nthe theory. The machinist who constructs a system of indented wheels\nfinds himself obliged to correct the rules of theory, on account of\nfriction, and other circumstances, proceeding from the material which\nhe employs. If he could see with a glance the bosom of nature, he would\ndiscover in the friction itself a new system of infinitesimal gearing\nwhich would confirm with wonderful exactness those very rules which a\nrude experience represents to him as opposed to reality.\n\n36. If the universe is admirable in its masses of gigantic immensity,\nit is not less so in its smallest parts. We are placed between two\ninfinities. Man in his weakness, unable to reach either one or the\nother, must content himself with feeling them, hoping that a new\nexistence in another world will clear up the secrets which are now\nveiled in impenetrable darkness.\n\n\n\n\nCHAPTER VI.\n\nREMARKS ON EXTENSION.\n\n\n37. If extension is something as we have proved; what is it?\n\nWe find extension in bodies and also in space because in both we\nfind that which constitutes its essence, which is dimension. Is the\nextension of bodies the same as the extension of space?\n\nI see and hold in my hand a pen: it is certainly extended. It moves,\nand its extension moves with it. The space in which its motion is\nexecuted remains immovable. At the instant A the extension of the pen\noccupies the point A\u2032; at the moment B the same extension of the pen\noccupies the part B\u2032 of space which is distinct from the part A\u2032;\ntherefore neither the part A\u2032 of space nor the part B\u2032 is identified\nwith the extension of the body.\n\nThis seems to have all the force of a demonstration; but to make\nit more clear and more general, I will put it into the form of a\nsyllogism. Things which are separated or may be separated are distinct;\nbut the extension of bodies may be separated from any part of space;\ntherefore the extension of bodies and the extension of space are\ndistinct. I said that this reasoning seems to have all the force of a\ndemonstration, but it is nevertheless subject to serious difficulties.\nThese difficulties cannot be understood without a profound analysis of\nthe idea of space, and therefore I shall reserve my opinion until this\nhas been treated of in the following chapters.\n\n38. Is the extension of a body the body itself? I cannot conceive a\nbody without extension, but this does not prove that extension is the\nsame thing as the body. My soul has acquired a knowledge of the body\nby means of the senses. These senses have _awakened_ in me the idea of\nextension; but they have told me nothing of the intrinsic nature of the\nbody perceived.\n\nIn those beings which we call bodies we find the power of producing in\nus impressions very distinct from that of extension. From two bodies of\nequal extension we receive very different impressions, therefore there\nis in them something besides extension. If extension was their only\nquality, this being equal, the effect would be the same; but experience\nteaches us that it is not so.\n\nMoreover we conceive extension in pure space where there is no\nbody. The idea of body implies the idea of mobility, while space is\nimmovable. It implies the power of producing impressions; the extension\nof space has not of itself this power.\n\nTherefore the simple idea of extension does not include even in our\ncognitions the whole idea of a body. We do not know in what the essence\nof body consists; but we know that in the idea which we have of it\nthere is something more than extension.\n\n39. When it is said that a body is inconceivable without extension\nit is not meant that extension is the constitutive notion of the\nessence of body. This essence is unknown to us, and therefore we\ncannot know what does or does not belong to it. The true meaning of\nthis inseparability of the two ideas of extension and body is this:\nAs we have no knowledge _a priori_ of bodies, but whatever we know\nof them, their existence included, we derive through the senses, all\nthat we think or imagine concerning them must presuppose that which is\nthe basis of our sensations. This basis, as we have already seen, is\nextension; without it there is no sensation, and consequently without\nit a body ceases to exist for us, or is reduced to a being which we\ncannot distinguish from others.\n\nI will explain my ideas. If I strip bodies of extension and leave\nthem only the nature of a being which causes the impressions which I\nreceive; this being is the same, so far as I am concerned, as a spirit\nwhich should produce the same impressions. I see this paper, and it\ncauses in me the impression of a white surface. There is no doubt that\nGod could produce in my mind the same sensation without the existence\nof any body. Then supposing that I knew that no external extended\nobject corresponded to my sensation, which was caused by a being acting\nupon me, it is evident that there would be two distinct things in my\nmind. First, the phenomenon of sensation, which under all hypotheses\nis the same; and secondly, the idea of the being which produced it,\nwhich is only the idea of a being distinct from myself, acting upon me,\nwhich in relation to the external world, would involve two ideas; those\nof distinction and causality.\n\nI now take from the paper extension, and what remains? The same as\nbefore. 1. An internal phenomenon, made known by consciousness. 2. The\nidea of a being the cause of this phenomenon.\n\nI do not know whether this must always be a body; but I know that\nthe idea of a body, as I understand it, includes something more than\nthis. I know that being is not in relation to myself distinguishable\nfrom other beings, and that if there is any thing in its nature to\ndistinguish it from them, it is something unknown to me.[40]\n\n[40] See Ch. I.\n\n40. This is the sense in which I say that we cannot separate the idea\nof extension from the body. But from this it must not be inferred that\nthe things themselves are identified; perhaps, even, a more profound\nknowledge of matter would show us that instead of being identical, they\nare entirely distinct. We have seen that it is so with their ideas, and\nthis is a sign that it is so in reality.\n\n41. We have few ideas as clear as that of extension geometrically\nconsidered; every attempt to explain it is useless; we know it more\nperfectly by mere intuition than whole volumes could make it known to\nus. It is so clear an idea, that on it is founded a whole science,\nthe most extensive and evident which we possess, that of geometry.\nTherefore there is reason to believe that we know the true essence of\nextension, since we know its _necessary_ properties, and even base\na whole science on this knowledge. Yet we do not discover in this\nidea, either impenetrability or any of the properties of bodies; but\nrather on the contrary, we find a capacity indifferent to them all. We\nconceive extension penetrable as easily as impenetrable, empty or full,\nwhite or green, with properties by which it can be placed in relation\nwith our organs, as easily as without them. We can conceive extension\nin a body acting on another body, or in pure space; in the sun which\nenlightens and warms the world, or in the vague dimensions of an empty\nimmensity.\n\n\n\n\nCHAPTER VII.\n\nSPACE.--NOTHING.\n\n\n42. It may have been remarked in the preceding chapters that the\nidea of extension is always united with that of space, and when we\nendeavor to determine the _real_ nature of the former, we encounter the\nquestions which relate to the latter. It is not possible to explain\none, while the other remains in obscurity. It is for this reason that\nI have concluded to examine carefully the questions concerning space\nunder its ideal as well as under its real aspect; since only in this\nmanner is it possible to determine clearly the nature of extension.\n\n43. Space is one of those profound mysteries which the natural order\npresents to man's weak understanding. The deeper he examines it the\nmore obscure he finds it; the mind is buried in the darkness which\nwe imagine to exist beyond the bounds of the finite, in the abyss of\nimmensity. We know not if what we behold is an illusion or a reality.\nFor a moment we seem to have found the truth, and then we discover that\nwe have stretched our arms to embrace a shadow. We form arguments\nwhich in any other matter would be conclusive, but are not so here,\nbecause they are in direct contradiction to others equally conclusive.\nWe seem to have reached the limit which the Creator has put to our\ninvestigations; and in endeavoring to pass beyond it, our strength\nfails, for we find ourselves out of the element which is natural to our\nlife.\n\nWhen certain philosophers pass rapidly over the questions relating to\nspace, and flatter themselves with explaining them in a few words,\nwe can assure them that either they have not meditated much upon\nthe difficulty which these questions involve, or else they have not\nunderstood them. It was not so that Descartes, Malebranche, Newton, or\nLeibnitz proceeded.\n\nTo descend this bottomless abyss is not to lose time in useless\ndiscussion; even though we should not find what we seek, we obtain\na most precious result, for we reach the limits assigned to our\nintellect. It is well to know what may be known and what cannot; for\nfrom this knowledge philosophy draws high and valuable considerations.\nMoreover, though we have small hope of success, we cannot pass over\nwithout examining an idea that is so closely connected with all our\nknowledge of corporeal objects, that is to say, extension. There must\nbe a motive of investigation since all philosophers have investigated\nit, and who can say that after long ages of efforts the truth is not\nperhaps reserved as the reward of constancy?\n\n44. What then is space? Is it something real or only an idea? If an\nidea is there any object in the external world which corresponds to it?\nIs it a pure illusion? And is the word space without meaning?\n\nIf we do not know what space is, let us at least fix the meaning of the\nword, and thus determine in some measure the state of the question. By\nspace we understand the extension in which we imagine bodies to be\nplaced, or the capacity to contain them to which we attribute none of\ntheir qualities except extension.\n\nLet us suppose a glass to be hermetically sealed, and the interior to\nremain empty by the annihilation of what it contained; this cavity\nor capacity which in our way of understanding it may be occupied by\na body is a part of space. Let us imagine the world to be an immense\nreceptacle in which all bodies are contained; let us suddenly make\nit empty and we have a cavity equal in space to the universe. If we\nimagine beyond the limits of the world a capacity to contain other\nbodies, we have an unlimited or imaginary space.\n\nSpace appears to us at first sight, if not infinite, at least\nindefinite. For in whatever part we conceive a body to be placed, we\nalso conceive the possibility of its moving, describing any class of\nlines, or taking any kind of direction and departing indefinitely from\nits first position. Therefore we imagine no limit to this capacity, to\nthese dimensions. Therefore space appears to us as indefinite.\n\n45. Is space a pure nothing? Some philosophers maintain that abstracted\nfrom the surface of bodies, and considered as a mere interval, it is\na pure nothing. At the same time they admit that it is only owing to\nspace that two bodies are really distant from each other, and add that\nif we suppose the whole world, with the exception of one body only, to\nbe reduced to nothing, this body could move and change its place. I am\nconfident that this opinion involves irreconcilable contradictions. To\nsay _extension-nothing_ is a contradiction in terms, and the opinion of\nthese philosophers is reduced to this expression.\n\n46. If every thing in a room be reduced to nothing, it seems impossible\nfor the walls to remain distant from each other; for the idea of\ndistance implies a medium between the two objects; and nothing, being\nnothing, cannot be the medium required. If the interval is nothing,\nthere is no distance. To attribute properties to nothing, is to destroy\nall ideas,--to affirm that a thing may be and not be at the same\ntime,--and consequently to overthrow the foundation of human knowledge.\n\n47. To say that if the contents were annihilated, a negative space\nwould remain, is only to play with words without touching the\ndifficulty to be solved. This negative space is either something or\nnothing; if it is something, the opinion we are opposing is false; if\nit is nothing, the difficulty remains the same.\n\n48. But, it may be said, although nothing remains between the surfaces,\nthey still retain the capacity of containing something. To this I\nreply, that this capacity is not in the surfaces themselves, but in\ntheir distance from each other; for if it were in the surfaces, they\nwould still preserve it, no matter how they may be placed, which is\nabsurd. We have not therefore advanced a single step. We must explain\nwhat this capacity, or this distance, is; and this is still untouched.\n\n49. Perhaps it may be said that annihilating all that is contained\nbetween the surfaces, does not destroy the volume which they form, and\nthe idea of this volume implies the idea of capacity. But I reply, that\nthe idea of volume involves that of distance, and there is no distance\nif this distance is a pure nothing.\n\n50. In our efforts to surmount these difficulties, another seemingly\nspecious solution offers, but if we examine it we shall find it as weak\nas the others.\n\nDistance, it might be said, is a mere negation of contact, but negation\nis a pure nothing; therefore this nothing is what we seek. I say\nthis solution is as weak as the others; for, if distance is only the\nnegation of contact, all distances must be equal, because negation\ncannot be greater or less. The negation of contact is the same whether\nthe surfaces are a million leagues or only the millionth part of an\ninch distant from each other. This negation, therefore, explains\nnothing, and the difficulty still remains.\n\n51. Not only is the idea of distance not explained by the idea of\ncontact, but on the contrary, the idea of contact can only be explained\nby the idea of distance. Contiguity is explained by immediate union\nof two surfaces; we say that they touch each other because there is\nnothing between them, or there is no distance. The idea of contact does\nnot involve the qualities which relate to the senses, nor the action\nwhich one body may exercise upon another which touches it, as impulse\nor compression. Contiguity is a negative, and purely geometrical,\nidea, and implies only the negation of distance. Contiguity cannot be\ngreater or less; it is all that it can be when there is a true negation\nof distance. Two objects may be more or less distant, but they cannot\ntouch more or less, with respect to the same parts. There may be\ncontact of more points, but not more contact of the same points.\n\n52. If we attribute distance and capacity to space, the argument in\nfavor of its reality becomes still stronger. Let us suppose an empty\nsphere two feet in diameter. Within there is only space; if space is\nnothing there is nothing in it.\n\nIs motion possible in this empty sphere? It does not seem that there\ncan be any doubt of this. There is a movable body, an extension\ngreater than the extension of the body, and a distance to be passed\nover. We may add to this, that if motion were not possible, it would\nnot be possible to make the sphere empty, or after making it empty,\nto fill it. Neither emptying nor filling the sphere can be done\nwithout motion of bodies in the interior of the sphere, and motion of\na body in another body is only possible in space, because bodies are\nimpenetrable, and also because, when the sphere is filled after it is\nempty, the body which enters does not meet another body; and when the\nsphere is made empty, the body which passes out, moves over the space\nwhich it abandons, and in which nothing remains after it has passed out.\n\nTherefore, supposing the sphere empty, there may be motion in it. But\nif the space contained in the sphere is a pure nothing, the motion also\nis nothing, and consequently does not exist. Motion can neither exist\nnor be perceived without a distance passed over. If, therefore, the\ndistance is nothing, there is no motion. If we say that the body has\npassed over half of the diameter, or one foot, what does this mean? If\nthe space is nothing, it can mean nothing. I see no reply which can be\nmade to these arguments, which are all based on the axiom, that nothing\nhas no properties.\n\n53. However great may be the difficulties opposed to the reality of\nspace, they are not so great as those which are brought against the\nopinion, which, while granting extension to space, still regards it\nas a pure nothing. The former, as we shall soon see, are produced by\ncertain inaccuracies in our way of conceiving things, rather than by\narguments founded on the nature of things; whilst those objections\nwhich we have brought against the opinion denying the reality of space,\nare founded on the ideas which are the basis of all our knowledge,\nand on this evident proposition: nothing has no properties. If this\nproposition is not admitted as an established axiom, the principle of\ncontradiction falls, and all human knowledge is destroyed. For, it\nwould be a plain contradiction, if nothing could have any properties\nor parts; if any thing could be affirmed of nothing, or could be moved\nin nothing; if a science like geometry could be founded upon nothing;\nor if all the calculations which are made on nature are referred to\nnothing.\n\n\n\n\nCHAPTER VIII.\n\nDESCARTES AND LEIBNITZ ON SPACE.\n\n\n54. If space is something, what is it? Here is the difficulty. To\noverthrow the opinion of our adversaries was easy, but to maintain our\nposition is more difficult.\n\nCan we say that space is only the extension of bodies; that conceived\nin the abstract it gives us the idea of what we call pure space; and\nthat the different points and positions are mere modifications of\nextension?\n\nIt is easy to see that if space is the extension of bodies, where\nthere is no body there can be no space, and consequently vacuum is\nimpossible. This consequence is unavoidable.\n\nThis has been the opinion of celebrated philosophers like Descartes\nand Leibnitz; but I cannot understand why they both gave the universe\nan indefinite extension. It is true that by this means they avoid the\ndifficulty of the space which we imagine beyond the limits of the\nuniverse; since, if the universe is not limited, there can be nothing\nbeyond its limits, and therefore, whatever we can imagine, must be\nwithin the universe. But our object is not to avoid difficulties, but\nto solve them; and it argues nothing for the soundness of our opinion\nthat it escapes difficulties.\n\n55. According to Descartes, the essence of body is in extension, and\nas we necessarily conceive extension in space, it follows that space,\nbody, and extension, are three essentially identical things. Vacuum,\nas it is generally conceived, that is, an extension without a body, is\nthen a contradiction; for it is a body, because it is extension, and it\nis not a body, because we suppose that there is no body.\n\nDescartes accepts all the consequences of this doctrine. He does not\nadmit the supposition that if God should annihilate all the matter\ncontained in a vessel, this vessel could still retain its form.\n\n\"We shall observe,\" he says, \"in opposition to this serious error,\nthat there is no necessary connection between the vessel and the body\nwhich fills it; but such is the invincible necessity of the relation\nbetween the concave figure of the vessel and the extension contained\nin this concavity, that it is not more difficult to imagine a mountain\nwithout a valley, than to conceive this concavity without the extension\ncontained in it, or this extension without a thing extended. Nothing,\nas we have often said, cannot be extended. Therefore, if any one should\nask, what would happen if God should destroy the matter contained in a\nvessel, without replacing it, we must say that the sides of the vessel\nwould come so closely together as to touch each other. Two bodies must\ntouch each other, when there is nothing between them. It would be a\ncontradiction to assert that these two bodies were separated; that is\nto say, that there was a distance between them, if this distance were\nnothing, or did not exist. Distance is a property of extension, and\ncannot exist without extension.\"[41]\n\n[41] Descartes, _Principes de la Philosophie_. P. 2, \u00a7 18.\n\n56. If Descartes had gone no farther than to maintain that space,\nbecause it contains real distances, cannot be a mere nothing, his\nreasoning would seem conclusive. But when he adds that space is body,\nbecause space is extension, and extension constitutes the essence of\nbody, he asserts what he does not prove.\n\nBecause we cannot imagine or conceive a body without extension, it only\nfollows that extension is a property of bodies without which we cannot\nconceive them,--not that it is their essence. To be able to say this,\nit would be necessary for us to have the idea of body as we have that\nof extension, in order that we might see if they are identical. But all\nthat we know of bodies is derived through the senses; we are not able\nto penetrate into their more intimate nature.\n\nWhence arises the inseparability of the ideas of body and extension?\nIt arises from the idea which we have of bodies being a confused\nidea, since we conceive it to be a substance in certain relations to\nourselves, and causing in us the impressions which we call sensations.\nBut since the basis of sensations is extension, as we have demonstrated\nin a former chapter, this is the only medium by which we are placed in\nrelation with bodies. When we suppress this basis, by abstracting it,\nwe retain nothing of body beyond a general idea of being or substance\nwithout any thing to characterize it, or to distinguish it from others.\nWe find all this in the order of our ideas, but we cannot infer from\nthis that bodies have no other reality than extension.\n\n57. The same reasoning destroys the opinion of indefinite or infinite\nextension. Descartes, explaining his doctrine on the idea of extension,\nsays: \"We shall also know that this world, or the extended matter which\ncomposes the universe, is without limits; for, no matter how far off we\nplace these limits, we can imagine spaces indefinitely extended beyond\nthem; and we not only imagine these spaces, but we conceive them as\nreally existing such as we imagine them, and containing an indefinitely\nextended body, as the idea of extension which we conceive in every\nspace is the true idea which we ought to form of a body.\"[42]\n\n[42] Descartes, Ibid., \u00a7 II, p. 21.\n\nIn this passage, besides the error in relation to the essence of\nbodies, there is a gratuitous transition from a purely ideal or rather,\nimaginary order, to the real order. It is certain that wherever I may\nimagine the limits of the universe, if I consider them as an immense\narch surrounding it, I still imagine new immensities of space beyond\nthis arch; but to conclude that the reality is as I imagine it, does\nnot seem conformed to the rules of good logic. If it is as clear as\nDescartes supposes, if it is not only an imagination, but a conception\nfounded on clear and distinct ideas, how happens it that so many\nphilosophers see in all this only a play of the imagination?\n\n58. Leibnitz thinks that space is \"a relation, an order, not only\nbetween things existing, but also between possible things as if they\nexisted.\"[43] He also believes vacuum impossible, but not for the\nreason which Descartes gives. These are his words:\n\n[43] Leibnitz, _Nouveaux Essais_. L. II., C. XIII., \u00a7 17.\n\n\"_Philalethes._--Those who take matter and extension for the same\nthing, pretend that the sides of a hollow empty body would touch each\nother. But the space which is between the two bodies is enough to\nprevent their mutual contact.\n\n\"_Theophilus._--I am of your opinion; for, although I do not admit a\nvacuum, I distinguish matter from extension, and concede that although\nthere were a vacuum in a sphere, the opposite poles would not on that\naccount unite. But I do not believe this is a case which the divine\nperfection would permit.\"[44]\n\n[44] Leibnitz, Ibid., \u00a7 21.\n\n59. Leibnitz seems to me to commit what logicians call _petitio\nprincipii_, or, \"begging the question.\" He says that in the case\nsupposed, the sides would not touch each other, because the space\nbetween them would prevent it; but this is what he had to prove,--the\nreal existence of this space. This reality is what Descartes denies.\n\n60. If we compare the opinions of Descartes and Leibnitz, we shall see\nthat both agree in denying to space a reality distinct from bodies, but\nbasing their denial on very different reasons. Descartes places the\nessence of body in extension; where there is extension there is body;\nwhere there is space there is extension; consequently, there neither\nis nor can be a vacuum. Leibnitz does not believe an empty capacity\nintrinsically absurd, and that he does not admit it is solely because,\nin his conception, it is repugnant to the divine perfection. The two\nillustrious philosophers started from very different principles, but\narrived at the same conclusion. Descartes rests upon metaphysical\nreasons, founded on the essence of things. Leibnitz bases his opinion\non the absolute essence of things only in its relations with the\ndivine perfection. Empty capacity is a contradiction in the opinion of\nLeibnitz, only inasmuch as it is opposed to optimism.\n\n61. It is very remarkable that three so distinguished philosophers\nas Aristotle, Descartes, and Leibnitz, should agree in denying the\nexistence of this capacity which is called space, considered as a being\ndistinct from bodies, and with the possibility of existing by itself.\nThe difference of their opinions only proves that at the bottom of\nthe question there is a difficulty more serious than some ideologists\nbelieve, who explain the idea of space and its generation with the same\nease as though they were treating of the simplest matters.\n\n\n\n\nCHAPTER IX.\n\nOPINION OF THOSE WHO ATTRIBUTE TO SPACE A NATURE DISTINCT FROM BODIES.\n\n\n62. The preceding considerations seem to me to establish beyond any\nquestion, that space and nothing are contradictory terms. If space is\na capacity with dimensions that can be really measured, it has real\nproperties, and therefore is distinct from a pure nothing. We have the\nidea of space, on it is based a certain and evident science, that of\ngeometry; this idea is also necessary for the conception of motion. A\npure nothing cannot be the object which corresponds to this idea.\n\nIs space something distinct from the extension of bodies? It is\nobjected to the opinion which maintains this, that space must be either\nbody or spirit, and if not body it must be spirit, which is absurd,\nsince that which is essentially composed of parts, as space is, cannot\nbe a spirit, which is a simple being.\n\nThere are strong arguments against the opinion which attributes to\nspace a nature distinct from bodies, but I do not attach much weight to\nthe above objection; for it is only necessary to deny the disjunctive\nproposition and the whole argument falls to the ground. How can it be\nproved that there is no medium between body and spirit? We know the\nessence of neither body nor spirit, and shall we arrogate to ourselves\nthe right to assert that there is nothing in the universe which is not\ncomprised under one of two extremes, the nature of which we know not.\n\n63. It may be replied, that there is no medium between the simple and\nthe composite, any more than between yes and no; and therefore there\nis no medium between body which is composite, and spirit which is\nsimple. I concede that there is no medium between the simple and the\ncomposite, and that whatever exists is one or the other; but I deny\nthat whatever is composite is body, and whatever is simple is spirit.\n\nThese two propositions: every composite is a body, and: every body is\ncomposite, are not identical. There may, therefore, be composites that\nare not bodies. Composition, or the possession of parts, is a property\nof bodies, but does not constitute their essence, or, at least, we do\nnot know that it does. If it were so, we should be obliged to embrace\nthe opinion of Descartes, that extension constitutes the essence of\nbodies. How do we know that there may not be things which have parts,\nand yet are not bodies?\n\n64. Even the state of the question makes us suppose space to be a\nsubstance, that is, a being subsisting by itself without requiring\nanother being in which to exist. The difficulty once overcome on this\nsupposition, it is solved in its most essential and inaccessible point,\nand therefore in all others. If we suppose space to be distinct from\nbodies, and at the same time a true reality, we must consider it as a\nsubstance, as it exists in itself without any other being in which it\ninheres.\n\n65. I said that a simple being is not necessarily a spirit. To explain\nthis, I need only observe, that to say every spirit is simple, is not\nthe same as to say every simple being is a spirit. Simplicity is a\nnecessary attribute of a spirit, but does not constitute its essence.\nThe idea of simplicity expresses only the negation of parts, and the\nessence of spirit cannot consist in a negation.\n\n66. The argument of those who object to this opinion which attributes\nto space a nature distinct from bodies, making it an extended\nsubstance, that it must also be infinite, is equally inconclusive.\nFor even on this hypothesis, there is no reason why a limit may not be\nassigned to space. What is there beyond this limit? Nothing. We may, it\nis true, conceive a vague extension, but imagination is not reality. We\nalso imagine an epoch prior to the Creation; if, then, imagination were\nan argument in favor of the infinity of the world, it would also be an\nargument for its eternity.\n\nThe arguments with which I have fought against the opinion that space\nis a pure nothing, are not founded on our imaginations, but on the\nimpossibility of nothing being extended, or having any properties. This\nis the principal argument which I have used against those who, while\nthey hold space to be a pure nothing, maintain the possibility of the\nconception or existence of the properties which they attribute to space.\n\n\n\n\nCHAPTER X.\n\nOPINION OF THOSE WHO HOLD SPACE TO BE THE IMMENSITY OF GOD.\n\n\n67. Overwhelmed by these difficulties, and unable to reconcile the\nreality which space offers us with nothing, or to conceive in any thing\ncreated the immobility, infinity, and perpetuity which we imagine in\nspace, some philosophers have put forth the opinion that space is the\nimmensity of God. At first sight this seems an extravagant absurdity,\nbut if we wish fairly to prove the falsity of this opinion, we must\ndo justice not only to the right intention of those who have defended\nit, and the sound explanations which they brought to their assistance,\nbut also to the reasons which forced them to this extremity, and\nwhich, though certainly not weighty or solid, are far from being so\ncontemptible as one may imagine.\n\n68. The argument in favor of this opinion may be put in the following\nform. Space is something. Before God created the world space existed.\nIt is not possible to conceive bodies as existing without space in\nwhich they are extended. Before they exist, we conceive this capacity\nin which they may be placed, as already existing. Therefore, space is\neternal. There is no motion without space; and in the first instant of\nthe creation bodies could move and be moved. Though we suppose only\none body in the world, it could be moved; and this motion could be\ninfinitely continued. Therefore space is infinite. Annihilate now this\nbody also, and the extension in which it moved will remain; in it new\nbodies, new worlds may be created. Therefore space is indestructible.\nBut an eternal, infinite, and indestructible being cannot be created.\nTherefore, space is uncreated. Therefore it is God himself. But it\nmust be God inasmuch as we conceive him in relation to extension; and,\ntherefore, space is the immensity of God. Immensity is the attribute\nby which God is in every part; it is an attribute which relates to\nextension. Space is, therefore, the immensity of God. Only by adopting\nthis theory can we reasonably admit that space is eternal, infinite,\nand indestructible.\n\n69. The objection to this opinion is that it destroys the simplicity of\nGod. If space is a property of God, it is God; for, whatever is in God,\nis God. Therefore, as space is essentially extended, God too must be\nextended.\n\nClarke saw the force of this argument; he was made to feel it by the\narguments of his adversary, Leibnitz; but he answers it very weakly.\nHe says that space has parts, but they are not separable. But, however\nthis may be, it is certain that space has parts. True, in the idea\nof space we distinguish parts without separating them; but we really\nconceive them in it, and we cannot conceive space without them.\nBesides, if we should admit this theory, what would become of the\nproofs of the immateriality of the soul? If the infinite wisdom is\nextended, why may not the human soul with much more reason be so?\n\nCarried away by his favorite idea, Clarke went so far as to write\nwhat we should not have expected from such a man, that: \"In questions\nof this nature, when we speak of parts, we mean parts that are\n_separable_, composite, and disunited like those of matter, which for\nthis reason is always a compound and never a simple substance. Matter\nis not one substance, but a composition of substances. This is why, _in\nmy opinion, matter is incapable of thinking_. This incapacity does not\nproceed from extension, but from the parts being distinct substances,\ndisunited, and independent of each other.\"[45] This explanation tends\nto destroy the simplicity of thinking beings; for by simplicity has\nalways been understood the absolute wanting of all parts and not the\nabsence of this or that kind of parts. Inseparability does not destroy\nthe existence of parts; it merely asserts the force of cohesion.\n\n[45] Fragment of a Letter.--(I do not know what letter the author here\nrefers to, but the same opinion in almost the same words may be found\nin Clarke's fourth and fifth letters to Leibnitz, _Tr._)\n\n70. It is also to be feared that this doctrine opens the door to\npantheism. It was even objected to Clarke that it made God the soul of\nthe world, and although he defended himself from this charge, there\nstill remains an objection which was not proposed to him, and which\nis a very serious one. If we say that God is space, or that space is\na property of God, what hinders our saying that God is the world, or\nthat the world is a property of God? The world is extended; but so is\nspace. If God and space are not contradictory ideas in the same being,\nwhy are God and the universe contradictory? Clarke says that bodies are\ncomposed of different substances, that they are not one substance; but\nit is certain that all we know of bodies is that they are extended, and\nthat they cause certain impressions in us. Since, then, extension is\nnot repugnant to God, and much less so the causality of impressions,\nthere can be no reason against saying that what Clarke calls distinct\nsubstances, are only the parts, or, if he prefers it, the properties\nof the infinite substance. Newton went so far as to say that space\nwas the sensorium of God, and even Clarke maintained against Leibnitz\nthat Newton's expression might bear a sound interpretation, as it was\nintended only as a comparison. But Leibnitz insists so strongly on this\ncharge that it is plain that he had very great objections to this word.\n\n71. Whatever tends to confound God with nature, or to place him\nin constant communication with it, otherwise than by pure acts of\nintellect and will, places us on a very slippery declivity, where we\ncan hardly help being precipitated to the bottom, and at this bottom is\npantheism, which is but a phasis of atheism.(30)\n\n\n\n\nCHAPTER XI.\n\nFENELON'S OPINION.\n\n\n72. Clarke's opinion is very similar to that of Fenelon, who in his\n_Treatise on the existence and attributes of God_, explains immensity\nin a very surprising manner. He says: \"After considering the eternity\nand immutability of God, which are the same thing, I ought to examine\nhis immensity. Since he is by himself, he is sovereignly, and since he\nis sovereignly, he has all being in himself. Since he has all being\nin himself, he has without doubt extension; extension is a manner of\nbeing, of which I have an idea. I have already seen that my ideas upon\nthe essence of things, are real degrees of being, which actually exist\nin God, and are possible out of him, because he can produce them.\nTherefore, extension is in him; he can produce it outside of himself,\nonly because it is contained in the fulness of his being.\"\n\nTo a certain extent the words of Fenelon may be explained in a sense\nwhich most theologians would not reject. They distinguish two classes\nof perfections; those which involve no imperfection; such as wisdom,\nholiness, and justice; and those which involve imperfection, as,\nfor example, all which belong to bodies, extension, form, etc. The\nformer, which are also called perfections _simpliciter_, are in God\n_formaliter_; that is to say, just as they are, because their nature\ninvolves no kind of imperfection, and, therefore, in God, they do not\ndiminish nor tarnish his infinite perfection. Those of the second\nclass, which are called perfections _secundum quid_, are in God not\n_formaliter_; for the imperfection which they involve is repugnant to\nhis infinite perfection, but _virtualiter_ or _eminenter_; that is to\nsay, that all the perfection, all the being which they contain is in\nGod, who is infinite perfection, infinite being; and God can produce\nthem exteriorly by his creative omnipotence. But inasmuch as they\npre-exist in an infinite being, they are freed from all limitation and\nimperfection, and identified with the infinite essence, and have a mode\nof being far superior to what they are in reality. This is expressed by\nthe term _eminenter_.\n\nAmong these perfections _secundum quid_, extension has always been\nnumbered.\n\n73. If the illustrious Archbishop of Cambrai had held to this sense, we\nshould have nothing to say in relation to his doctrine, but the words\nwhich follow seem to show that he inclined to the opinion of those who\nmaintain that space is the immensity of God.\n\n\"Whence, then,\" he adds, \"is it that I do not call him extended and\ncorporeal? It is because there is an extreme difference, as I have\nalready remarked, between attributing to God all that is positive in\nextension, and attributing to him extension with a limit or negation.\n_He that places extension without limits changes extension into\nimmensity_; he who places extension with limits, makes a corporeal\nnature.\" From these words it might be believed that Fenelon did not\ndistinguish the two modes of being of extension as theologians do; but\nhe gives to God all that is positive in extension, though he gives\nit to him without limit. From this it would seem to follow that God\nis really extended, although his extension is infinite. With all the\nrespect due to the illustrious shade of one of the greatest ornaments\nof the Catholic Church, and one of the greatest men of modern times, I\nmust say that such an opinion does not seem to me to be sustainable. A\nGod really extended though with an infinite extension is not God. That\nwhich is extended is essentially composite; God is essentially simple.\nTherefore, God and extension are contradictory.\n\n74. But let us hear the illustrious prelate continue the explanation\nand defence of his opinion. He says: \"From the moment that you place\nno limit to extension, you take from it figure, divisibility, motion,\nand impenetrability;--figure, because this is only a mode of limiting\nby surfaces;--divisibility, because, as we have seen, that which\nis infinite cannot be diminished, therefore, it cannot be divided,\nand consequently, it is not _composite_ and divisible;--motion,\nbecause, if you suppose a whole, which has no parts nor limits,\nit cannot move beyond its place, because there can be no place\nbeyond the true infinite; neither can it change the arrangement and\nsituation of _its parts_, because it has _no parts_ of which it is\ncomposed;--impenetrability, in fine, because impenetrability can only\nbe conceived by conceiving two limited bodies, one of which is not the\nother, and cannot occupy the same space as the other. There are no two\nsuch bodies in infinite and indivisible extension; therefore there is\nno impenetrability in this extension. These principles established,\nit follows that all that is positive in extension is in God, although\nGod has no figure, is not movable, divisible, or impenetrable, and\nconsequently is not palpable, nor measurable.\"\n\nFrom this passage it is very evident that Fenelon was far from\nimagining a composite God, a God with parts. He expressly denies it\nmore than once in these few lines. Not less was to be looked for from\nhis deep penetration and the purity of his doctrines; but, although\nthis saves the rectitude of his intention, it does not satisfy\nphilosophical exactness. For my part, I honestly confess that if\nextension is to be taken in its true sense, I cannot conceive how\ntaking away its limits destroys its parts. On the contrary, I should\nrather say that an infinite extension would have infinite parts. If it\nis infinite it will have no figure; because figure involves a limit;\nbut if it be true extension, it is a sort of immense field on which all\nimaginable figures may be traced. It will have no essential figure of\nits own, but it will be the recipient of all figures, the inexhaustible\nsea from which they all arise. That which is traced in it, will be in\nit; the points which terminate the figures must be in it. Is not this\nto have parts, composition? Infinite extension could have no figure,\nnot because it has no parts, or is simple, but because it has infinite\nparts, because its composition is infinite.\n\nI agree that an infinite extension would not be divisible, if by\ndividing, is meant separating; because in that immense fulness\neverything would be in its position with infinite firmness. So also\nwe imagine space, the place of all motion, with its parts immovable,\nthe field of all separation, with its parts inseparable; but we are\ntreating of division, not of separation. If there is true extension, it\nis divisible; we conceive space with its parts inseparable, but still\ndivisible; for we measure them, count them, and it is by relation to\nthem that we form an idea of the size, distance, and motion of bodies.\n\n74. Such clear and conclusive reflections could not fail to present\nthemselves to the mind of the illustrious philosopher; but he seems\nto have preferred inconsequence or obscurity of language to the fatal\ncorollaries of his first proposition. He said plainly and without any\nrestriction, that all that is positive in extension, except the limit,\nis in God. He had asserted that extension with limits is corporeal, and\nthat to change extension into immensity it was only necessary to take\naway its limits. He consequently attributed to God a true, although\ninfinite, extension, and then wishing to explain and strengthen\nhis doctrine he tells us that this extension has no parts. What is\nextension without parts? Who can conceive it? Does not extension\nnecessarily imply an order of things of which some are outside of\nothers. It has been always so understood. To speak of an extension\nwithout parts is to speak of an extension improperly so called. When\nspeaking of such extension it is not enough to say it has no limits,\nit should be added that it is of an entirely different nature, that\nthe word extension is used in another sense. Fenelon seemed to know\nthis, when, notwithstanding the obscurity of his former expressions,\nelevated on the wings of his religion and his genius, he says: \"God is\nin no place, as in no time; for his absolute and infinite being _has\nno relation to place or time_, which are but limits and restrictions\nof being. To ask if he is beyond the universe, if he exceeds its\nextremities in length, breadth, and depth, is as absurd a question as\nto ask if he was before the world, and if he will still be when the\nworld is no more. As there is neither past nor future in God, so there\nis neither hither nor thither. As his absolute permanence excludes all\nmeasure of succession, so also his immensity excludes all measure of\nextension. He has not been, he will not be, but _he is_. In the same\nmanner, to speak properly, he is not here, he is not there, he is not\nbeyond such a limit, but he is, absolutely. All expressions which\nplace him in relation to any term, or fix him in a certain place, are\nimproper and unbecoming. Where then is he? He is. He is in such a\nmanner that we must not ask where. That which only half is, or with\nlimits, is a certain thing in such a way that it is nothing else. But\nGod is not any particular and restricted thing. He is all; he is being;\nor better and more simply, _he is_. For the fewer words we use, the\nmore we say. _He is._ Beware of adding any thing to this.\"\n\n76. While reading these magnificent words, I am carried away by the\nelevation and grandeur of his ideas of God and of his immensity, and\nI forget the objections to the first proposition, which, if not false\nor inexact, is not, to say the least, expressed with all the clearness\nthat could be desired. Still, I do not hesitate to maintain that his\nopinion coincides with Clarke's; although the illustrious writer,\nChristian, and poet, seem to merit a pardon for the philosopher.\n\n\n\n\nCHAPTER XII.\n\nWHAT SPACE CONSISTS IN.\n\n\n77. Descartes' opinion wholly confounds space and bodies, making the\nessence of bodies consist in extension, and asserting that wherever\nthere is space, there is body. This opinion we have seen to be void of\nall reasonable foundation. Perhaps he would come nearer the truth who\nshould say, that in reality space is nothing more than the extension\nof bodies, without reference to the question whether extension does or\ndoes not constitute the essence of bodies, and denying its infinity.\n\n78. Let us examine this last opinion. Analyzing the origin of the idea\nof space, we find that it is merely the idea of extension taken in\nthe abstract. If I hold before my eyes an orange, I may, by means of\nabstractions, arrive at the idea of a pure extension, equal to that\nof the orange. In order to do this, I begin by abstracting its color,\ntaste, smell, and all its qualities which affect the senses. I then\nhave left only an extended being, and if I take from it its mobility,\nit is reduced to a part of space equal to the size of the orange.\n\nIt is plain that the same abstraction is possible in relation to the\nuniverse, and the result will be the idea of all the space which the\nuniverse occupies.\n\n79. Here I shall answer an objection which might be made to this\nexplanation of the idea of space, and thereby take advantage of\nthis opportunity to throw some light upon the origin of the idea of\ninfinite, or imaginary space.\n\nThe difficulty is this. If we form the idea of space by the mere\nabstraction of the qualities which accompany extension, we can only\nconceive a space equal to the size of the body from which we have\nabstracted all its sensible qualities. The abstraction made upon an\norange can only give a space equal to the size of the orange, and that\nmade upon the universe can only give a space equal to what we conceive\nin the universe. Consequently, we can never, by this means, obtain the\nidea of a space without limits which always presents itself to our mind\nwhen we think of space considered in itself.\n\nThe solution of this difficulty is in the truth that abstraction\nrises from the particular to the general. From the idea of gold, by\nabstracting those properties which constitute gold, and attending\nonly to those which it possesses as metal, I arrive at the much more\ngeneral idea of _metal_, which belongs not only to gold, but to all\nother metals. By this abstraction I pass the limit which separates\ngold from other metals, and form an idea which extends to all, neither\nspecifying, nor excluding any. If from the idea of metal I abstract all\nthat constitutes metal, and attend only to what constitutes _mineral_,\nI pass another limit, and arrive at a still more general idea. Thus\npassing successively the idea of inorganic, of body, and of substance,\nuntil I come to the idea of being, I thus form the most general idea\npossible, and which includes every thing.[46]\n\n[46] I take no notice in this place of the different manner in which\nthe idea of being is applicable to God and to creatures.\n\nThus passing over the limits which distinguish and, as it were,\nseparate objects, abstraction rises to the most general. If we apply\nthis doctrine to the abstractions made upon bodies, we shall discover\nthe reason of the illimitability of the idea of space.\n\nWhen after the abstractions made upon the orange, I have left only the\nidea of _its_ extension, the abstraction has not reached the highest\npoint possible; for my conception is not that of extension in itself,\nbut only of the extension of the orange; I conceive _its_ extension,\nnot _extension_ itself. But if I abstract all that makes this extension\nthe extension of the orange, and attend only to extension in itself,\nthen the idea of figure disappears, the extension expands indefinitely,\nit is impossible for me to assign any term to it, for any limit would\nmake it a determinate, a particular extension, not extension in itself.\nThen the frontiers of the universe, so to speak, disappear; for\nhowever great the universe may be, it is limited, and can give only a\nparticular extension, not extension itself. This is the manner in which\nthe idea of imaginary space seems to be formed.\n\n80. An observation of the phenomena of the imagination will confirm\nwhat we have explained by the mere order of intelligence. When I\n_imagine_ the extension of an orange, I imagine it with a limit, with\nthis or that color, and with these or those qualities; since it is\nnot possible for me to imagine a figure without lines which terminate\nit. This limit in the imagination is distinct both from the extension\nwhich it encloses, and from the extension which it excludes. If it\nwere not so distinguished, we could not imagine it as limit, and it\nwould not answer its object, which is to enable us to distinguish that\nwhich it encloses. Therefore, the abstraction is not complete. In the\nimagination there is always something determinate, which is the limit\nor the lines which constitute the limit. Destroy these limits, and the\nimagination expands, until it becomes lost in a sort of dark, unbounded\nabyss, such as we imagine beyond the universe.\n\nA very simple example will make this explanation clearer. Our\nimagination may be compared to a black board on which a figure is\nmarked with chalk. When we see the white line on the board which forms\nthe figure, we see the figure also; but if we rub out the line, there\nremains only the uniform figure of the board. If we suppose the lines\nwhich terminate the black board to be indefinitely withdrawn, we shall\nlook in vain for a figure; we see only a black surface indefinitely\nextended. There is a sufficient parity between this and the manner in\nwhich the imagination pictures to itself an endless space.\n\n81. The idea of an abstract extension which is limited, is a\ncontradiction. Limit takes from extension generality; and generality\ndestroys the limit. There can, therefore, be no abstract idea of\nlimited extension; but when we form an idea of extension in the\nabstract, we conceive it as unlimited, and the imagination attempting\nto follow the understanding, pictures to itself an indefinite space.\n\n82. Summing up this doctrine, and deducing its inevitable consequences,\nwe may say:\n\nI. That space is nothing else than the extension of bodies.\n\nII. That the idea of space is the idea of extension.\n\nIII. That the different parts conceived in space are the ideas of\nparticular extensions, from which we have not taken their limits.\n\nIV. That the idea of infinite space is the idea of extension in\ngeneral, abstracted from all limit.\n\nV. That indefinite space arises necessarily from the imagination,\nwhich destroys the limit in attempting to follow the generalizing march\nof the understanding.\n\nVI. That where there is no body there is no space.\n\nVII. That what is called distance is only the interposition of a body.\n\nVIII. That if every intermediate body be taken away, distance ceases;\nthere is then contiguity, and, consequently, absolute contact.\n\nIX. That if there were only two bodies in existence, it would be\nmetaphysically impossible for them to be distant from each other.\n\nX. That all vacuum, of whatever kind, or however obtained, is\nabsolutely impossible.\n\n83. These are the consequences which follow from the principle\nexplained in this chapter.\n\nIf the reader ask me what I think of them and of the principle on which\nthey are based, I frankly confess that, although the principle seems\ntrue and the conclusions legitimate, still the strangeness of some of\nthem, and yet more so with regard to others which I shall point out as\nwe come to them, makes me suspect that there is some error concealed in\nthe principle, or else the reasoning which deduces these consequences\ncontains some defect which is not easy to discover. I do not put\nforth a settled opinion, so much as a series of conjectures, with the\narguments in their favor. The reader may see by this what sense I\nattach to the word _demonstration_, when in the sequel he sees it often\nemployed in treating of the deduction of certain consequences which\nare exceedingly strange, although, in my opinion, deserving a careful\nattention. I say this not only to explain what is passing in my own\nmind, but also to warn the reader against too great confidence on these\npoints, whatever may be the opinion which he adopts. Before commencing\nthese investigations on space, I remarked that the arguments on both\nsides seemed equally conclusive; which shows that the human reason\nhas reached its bounds, and makes us suspect that this investigation\nis beyond the sphere to which the mind is restricted by a primary\ncondition of its nature.\n\nHowever this may be, let us continue to conjecture; and although we\ncannot pass beyond certain limits, let us exercise the understanding\nby examining them in their full extent. Thus, if we were placed on\na very elevated ground with deep precipices on all sides, we should\ntake pleasure in walking around the circumference, and gazing upon the\nimmense depth under our feet.\n\nI shall now proceed to deduce other results, and to solve as far as\npossible the difficulties which arise, making some applications, the\nimmense importance of which produces uncertainty and causes fear.\n\n\n\n\nCHAPTER XIII.\n\nNEW DIFFICULTIES.\n\n\n84. If space is the extension of bodies, it follows that extension has\nno recipient, that is to say, no place in which it can be situated.\nThis seems to be in direct contradiction to our most common ideas; for\nwhen we conceive any thing to be extended, we conceive the necessity of\na place equal to it in which it can be contained and situated.\n\nThis difficulty, which seems so serious at first, immediately vanishes\nif we deny that every extended thing needs a place in which it may be\nsituated. What is this place? It is an extension in which the thing\nmay be contained. Does this extension also require another extension\nin which it may be placed, or does it not? If it does, then the same\nquestion may be asked of this new place in which the other place is\ncontained, and so on _ad infinitum_. This is evidently impossible, and\ntherefore we must admit that it is false that all extension requires\nanother extension in which it may be placed. Just as the extension of\nspace does not require another extension, so the extension of bodies\ndoes not require space. There is no disparity between the two cases.\nTherefore the necessity of a place for every extension is merely\nimaginary, and is opposed to reason. Extension, therefore, may exist in\nitself, and there is no reason why the extension of bodies may not also\nexist in this manner.\n\n85. What in this case would be the meaning of changing place? It would\nsimply mean that bodies change their respective position. This is the\nexplanation of motion.\n\nSuppose three bodies, A, B, and C, to be situated in space. Their\nrespective distances are the bodies which are interposed between them.\nThe change which a new position causes, is motion.\n\n86. Therefore, if there were only one body there could be no motion.\nFor motion is necessarily the passing over a distance, and, there is no\ndistance when there is only one body.\n\nThis seems at first absurd, because it is opposed to our way of\nthinking and imagining; but if we carefully examine this way of\nthinking and imagining, we shall see that the phenomena of our mind are\nin accordance with this theory.\n\nMotion has no meaning for us, we do not feel or perceive it, when we\ncannot refer it to the position of different bodies among themselves.\nIf we sail down a river, shut up in the cabin of the vessel which bears\nus on, we really move, though we have no perception of this motion.\nWe know that we move when watching the objects on the shore, we see\nthat they are continually changing. Even then, the motion seems to be\nin the objects around us, not in ourselves, and the phenomena would\nbe absolutely the same with respect to us, if, instead of the objects\nbeing at rest, and the vessel in motion, the vessel should be at rest\nand the objects in motion, supposing the motion of the objects to be\nproperly combined.[47]\n\n[47] See Book II., Chap. xv.\n\nTherefore, take away the agitation, which is all that informs us of\nour own motion, and we are unable to distinguish whether the motion is\nin us or in the objects; and we are naturally more inclined to refer\nthe motion to them than to ourselves. When the vessel that carries us\nleaves the port, we know very well that it is not the port which moves,\nand yet the illusion is complete, the port seems to retire from us.\n\nHence motion for us is only the change of the respective position of\nbodies. If we had not experienced this change, we should have no idea\nof motion. Thus no one denies that the phenomena of diurnal motion are\nthe same, whether the heavens revolve around us from east to west, or\nthe earth turns on its axis from west to east.\n\nTherefore, the motion of only one body is a pure illusion; and there is\nno proof of the argument founded on it which is brought to oppose our\ndoctrine of space.\n\nHence, also, the whole universe considered as only one body, is\nimmovable, motion takes place only in its interior.\n\n87. But one of the strangest results of this theory is the _a\npriori_ demonstration that the universe can only be terminated in a\ncertain manner, to the exclusion of a multitude of figures which are\nessentially repugnant to it.\n\nAccording to the doctrine which we have put forth, if we suppose only\none body to exist, it cannot have any part of its surface so disposed\nthat the shortest line from any one point to another shall pass outside\nof the body. For, as we suppose only one body, _outside_ of it is pure\nnothing; and can, therefore, contain no distances which can be measured\nby lines. This excludes a multitude of irregular figures, and thus we\nfind geometrical regularity growing out of a metaphysical idea.\n\nHence if only one body were in existence, it would be impossible for\nit to have any angles entering into it. For, its figure requires that\nthe point A, the vertex of the angle, should be at the distance A D\nfrom the point D, the vertex of another angle. This distance cannot\nexist, for there is no distance where there is no body. Therefore,\nthe distance would exist and not exist at the same time, which is\ncontradictory. It would also be an absurdity, because the capacities\nmarked by the angles would not be filled.\n\nThe observation of nature confirms the former result, inasmuch as its\ntendency is always to terminate every thing with curved lines and\nsurfaces. The orbits of the stars are curves, and the stars themselves\nterminate in curve surfaces. The great irregularities which are\nobserved in their surfaces might seem to destroy this conclusion,\nbut it must be remembered the limit of the figure is not in these\nirregularities, but in the atmosphere which surrounds them, and which,\nbeing a fluid, can have no irregularities of surface.\n\n88. Another consequence, as strange as the former, is, that we are\nobliged to admit the existence of a perfect geometrical surface, and\nthis _a priori_.\n\nIf, where there is no body, distance is metaphysically impossible,\nthis must be just as true in small as in great things, and even in\ninfinitesimals. This is also a reason of the impossibility of vacuum.\nIt is evident that a surface is not perfect when some of its points go\nfarther out than others, so that the less they go out from the surface\nthe more perfect it becomes. As there are no such points in the last\nsurface of the universe, this surface is the realization of geometrical\nperfection.\n\nWe have demonstrated that it is impossible for the surface to have any\nangles entering into it; it is equally impossible for it to have any,\neven the least, prominence. The difference is only in greater or less,\nwhich does not affect the metaphysical impossibility. It is, therefore,\ndemonstrated that in the ultimate surface of the universe there is no\nirregularity, but that its surface is geometrically perfect.\n\n\n\n\nCHAPTER XIV.\n\nANOTHER IMPORTANT CONSEQUENCE.\n\n\n89. I now proceed to deduce the last consequence of the principle\nexplained above. It is of the greatest importance, and seems to deserve\nthe careful attention of all those who unite their metaphysical and\nphysical studies.\n\nThe existence of universal gravitation may be demonstrated _a priori_.\n\nUniversal gravitation is a law of nature by which some bodies are\ndirected to others. [We abstract here the manner.] This direction is\nmetaphysically necessary, if we suppose that there is no distance\nwhere there is no body. For, if this be so, two bodies cannot exist\nseparated. The law of contiguity is a metaphysical necessity, and\ntherefore the incessant approaching of some bodies to others is a\ncontinual obedience to this necessity.\n\nThe velocity with which they approach must be in the ratio of the\nvelocity with which the medium departs. The limit of the velocity of\nthis motion is the relation of space with an indivisible instant, such\nas we might suppose if God should suddenly annihilate the intervening\nbody.\n\nAs the solid masses which revolve above our heads would in this case\nbe submerged in a fluid, supposing this fluid to be of such nature as\neasily to change its place, it follows that the stars must be subject\nto the law of approximation, because the medium which separates them is\ncontinually retiring in various directions. If we suppose this fluid to\nbe immovable, the metaphysical necessity of this approximation ceases.\n\n90. This theory seems to lead to the explanation of the mechanism of\nthe universe, by simple geometrical laws, and destroys what some have\ncalled occult properties, and others forces.\n\nAlthough it is easy to explain by metaphysical and geometrical ideas,\nthe fact of gravitation, or the mere tendency of bodies mutually to\napproach, it is still very difficult to determine by this order of\nideas the conditions which govern gravitation.\n\n91. If the motion of approximation depended only on the intervening\nbody, inequality of these bodies would produce unequal motions. It is\nimpossible to calculate the degree of this inequality in bodies which\nare not subject to our observation.\n\n92. Besides this difficulty there is another still greater, which is,\nthat bodies which move in a medium have no fixed direction, but vary\ntheir motions with the variations of the medium.\n\nIf the gravitation of the body A towards the body B, depends only on\nthe motion of the retiring medium, the gravitation will not be in the\nright line AB, but will follow the undulations described by the medium.\nThis is contrary to experience.\n\n93. From these considerations, it follows that even though the\ngravitation naturally arises from the position of the bodies, still\nthis necessity would not produce the order which exists, if its results\nwere not subject to certain laws. And, therefore, the phenomena of\nnature, although founded on a necessity, would still, admitting the\nexistence and position of bodies, be contingent in all that relates to\nthe application of this necessity.\n\n94. Going still deeper into this matter, we find that the tendency to\napproximation, although necessary, is not sufficient either to produce\nmotion or to preserve it.\n\nWhenever one body moves, it is always necessary that another should\nfollow it, in order to preserve the contiguity; but, there being no\nvacuum, there is no reason why any body should move, and consequently,\nno cause of motion.\n\nTherefore, geometrical ideas are not sufficient to explain the origin\nof motion, but we must look for its cause elsewhere. Contiguity being\na metaphysical necessity, if the body A moves in any direction, the\ncontiguous bodies B and C must also move; but if the contiguity already\nexisted, there is no reason why the body A should begin to move, nor,\nconsequently, why the bodies B and C should follow its motion.\n\nAt any instant whatever, if we suppose motion, we must suppose\ncontiguity; for the state of the question supposes this condition\nalways present, as being metaphysically necessary. There is then\nno reason why the motion should at any time be prolonged; for the\nbodies being at every instant contiguous there is no reason for its\ncontinuation. The motion of the body A draws with it the body B; B\ndraws C, and so on. Now, if the motion of the body B has no other\norigin than its contiguity to A, the motion of C has no other origin\nthan its contiguity to B. The cause of the motion is only not to\ninterrupt the contiguity; this contiguity always existing as is\nabsolutely necessary, there is no reason why the motion should begin,\nor after it has begun, why it should continue.\n\n95. The laws of nature cannot then be explained by geometrical and\nmetaphysical ideas, although we suppose approximation to be an\nintrinsical necessity of bodies. Under any supposition it is necessary\nto seek out of matter a superior cause which impresses, regulates, and\ncontinues motion.\n\n\n\n\nCHAPTER XV.\n\nILLUSION OF FIXED POINTS IN SPACE.\n\n\n96. Since space is only the extension of bodies, and there is no\nspace where there are no bodies, it follows that the extension which\nwe conceive distinct from bodies, with fixed points and dimensions,\nimmovable in itself, and the receptacle of all that is movable, is a\npure illusion, and there is nothing in reality corresponding to it.\n\nIn order to explain this doctrine and at the same time to solve certain\nobjections which may be made, it will not be out of place to analyze\nthe idea which we form of fixedness in relation to space. Because\nthere are certain immovable points in the world in relation to which\nwe conceive directions, we form the idea that these points are fixed,\nand in relation to them and because of them we imagine fixedness,\nimmobility, as one of the properties which distinguish this ideal\nreceptacle which we call space. The four cardinal points, East, West,\nNorth, and South, have had a great influence in producing this idea.\nStill it is easy to show that there is no such thing and that it is a\npure illusion.\n\n97. We shall first destroy the fixedness of East and West. Supposing\nthe earth to have a diurnal motion of rotation on its axis, as\nastronomers now hold, the points of East and West, so far from being\nfixed, are continually changing their position. Thus, supposing an\nobserver at the point A of the earth, East to him will be the point B,\nand West the point C. If the earth revolves on its axis, the East and\nWest of the observer will be successively at the points M, N, P, Q,\netc. of the heavenly arch. Although we suppose this arch fixed, East\nand West have no fixed meaning.\n\nIf we deny the rotation of the earth, the appearances will be the same\nas though this rotation existed; and the most that we can say is that\nthis fixedness is an appearance. Besides, if we suppose the earth to be\nat rest, and the heavens to move round it, it is still more impossible\nto determine the fixed points of East and West; for, in this case, the\npoints in the heavens to which we refer them are in continual motion.\n\nWe repeat that all this is a mere appearance. If a man who knows not\nthat the earth is spherical, but imagines it to be a plane surface,\nwalks from West to East, he will believe that these two points are\nimmovable, although they are continually changing. He would still\nimagine that he was going farther from the place where he started,\nalthough, after passing over the whole circumference of the earth, he\nwould find himself where he was at first.\n\n98. North and South seem to present greater difficulty, by reason of\ntheir fixedness in relation to us; still it is easy to show that this\nis not absolute, but only apparent. Let N and S represent the north\nand south poles. If we imagine the earth and the heavens to turn at\nthe same time from south to north, it is evident that the fixedness\nof the points N and S would not exist, and yet the observer A would\nbelieve that every thing was immovable, because the appearances would\nbe absolutely the same.\n\nTo an observer travelling from the equator toward either pole, the pole\nwould rise over the horizon, while to another who remains in the same\nplace, the pole would be at rest.\n\nEven in relation to the same position on the earth the altitude of the\npole changes, by the variation of the angle formed by the plane of the\necliptic with the plane of the equator, which variation is according\nto some calculations 8\u2033 in a century, according to others 0\u2033.521 in a\nyear, or 52\u2032.1\u2033 in a century.\n\n99. It follows from these reflections that the position of bodies\nis not absolute, but relative; that one body might exist alone, but\nthen it would have no position, as this is entirely a relative idea,\nand there is no relation in this case, because there is no point of\ncomparison; and that absolutely speaking there is no such thing as\n_above_ or _below_; for although we imagine these to be fixed points,\nthis imagination is only a comparison which we make between two points:\nbelow being that point toward which we gravitate, and above the\nopposite. Thus in the antipodes above is what we call below, and below\nwhat we call above.\n\n100. Direction is impossible without points to which it can be\nreferred. Therefore, without the existence of bodies, directions are\npurely ideal, and if only one body existed, it could have no directions\nout of its own extension.\n\n101. Here arises a difficulty apparently serious, but in reality of\nlittle weight. If only one body existed, could God give it motion? To\ndeny it seems to limit the omnipotence of God; and to concede it is to\ndestroy all that has been said against space distinct from bodies.\n\nThis objection derives its seeming importance from a confusion of\nideas, which is caused by not understanding the true state of the\nquestion. Is this motion _intrinsically impossible_, or is it not? If\nit is impossible, there is no reason why we should be afraid to say\nthat God cannot produce it: for omnipotence does not extend to things\nwhich are contradictory. If the possibility of this motion is admitted,\nthen we must return to the questions on the nature of space, and\nexamine whether the reasons on which this impossibility is founded are,\nor are not, valid.\n\nThe questions relating to omnipotence are out of place here, and this\ndifficulty can be solved without them. If the impossibility of the\nmotion is demonstrated, it is no limitation of the omnipotence of\nGod to say that he cannot produce it, no more than it is when we say\nthat he cannot make a triangle a circle. If the impossibility is not\ndemonstrated, then the question of omnipotence does not come in at all.\n\n102. Neither does the argument founded on the existence of vacuum\ndestroy the doctrine which we have established. Natural philosophers\ngenerally admit vacuum, and suppose it necessary for the explanation of\nmotion, condensation, rarefaction, and other phenomena of nature. But\nto this I reply as follows:\n\nI. The opinions of Descartes and Leibnitz are of weight in what relates\nto nature, whether experimental or transcendental, and neither of them\nadmitted a vacuum.\n\nII. No observation can prove its existence, because disseminated vacuum\nwould occupy such small spaces that no instrument could reach them, and\nalso because observation can only be made on those objects which affect\nour senses, and we know not but what there may be bodies which, on\naccount of their excessive tenuity, are not perceptible by the senses.\n\nIII. We can determine nothing certain concerning the internal\nmodifications of matter in motion, condensation, and rarefaction, until\nwe know the elements of which it is composed.\n\nIV. It is not strange that we are unable to comprehend the phenomena\nwhich seem incompatible with the denial of matter: for we can neither\nunderstand infinite divisibility, nor how extension can be composed of\nunextended points.\n\nV. The existence of vacuum is a metaphysical question which does not\nbelong to the regions of experience, and is not affected by the system\nof the sciences of observation.\n\n103. By making the idea of space consist in abstract or generalized\nextension we reconcile all that is necessary, absolute, and infinite\nin it with its objective reality. This reality is the extension of\nbodies, while necessity and infinity are not found in the bodies\nthemselves, but in the abstract idea. Objects themselves are confined\nto the sphere of reality, and are, therefore, limited and contingent.\nThe objectiveness of the abstract idea includes both the existent and\nthe possible, and has, therefore, no limits, and is not subject to any\ncontingency.\n\n\n\n\nCHAPTER XVI.\n\nOBSERVATIONS ON KANT'S OPINION.\n\n\n104. We have already shown that extension considered in us, is\nsomething more than a mere sensation, that it is a true idea, the basis\nof some sensations, and at the same time a pure idea. As far as it\nrelates to sensations, it is the foundation of our sensitive faculties;\nand in so far as it is an idea, it is the root of geometry. This is an\nimportant distinction, and we shall find it useful to enable us rightly\nto appreciate the value of Kant's opinion of space.\n\n105. All our sensations are, either more or less, connected with\nextension; although if we consider sensation _a priori_ by itself,\nand independently of all habit, it would seem as though only the\nsensations of sight and touch were necessarily connected with an\nextended object. It does not seem to me that the loss of these two\nsenses would necessarily involve the privation of the impressions of\nhearing or smelling, or, perhaps, even of taste; for although it is\ntrue that the sensations of touch, such as hardness or softness, etc.,\nare always united with the sensations of the palate; it is equally\ncertain that those sensations are wholly distinct from the sensation\nof taste, and we have no reason for asserting that they cannot be\nseparated from it.\n\n106. Extension, considered in us or in its intuition, may be regarded\nas a necessary condition of our sensitive faculties. Kant saw this,\nbut he exaggerated it when he denied the objective reality of space,\nasserting that space is only a subjective condition _a priori_ without\nwhich we cannot receive impressions, the form of phenomena, that is, of\nappearances, but nothing in reality. I have already said that space,\nas distinguished from bodies, is nothing, but the object of the idea\nof space is the extension of bodies; or, rather, this extension is\nthe foundation from which we deduce the general idea of space, and is\ncontained in this idea.\n\n107. To say, as Kant does, that space is the form under which the\nphenomena are presented to us, and that it is a necessary subjective\ncondition of their perception, is equivalent to saying that the\nphenomena which are presented as extended, require that the mind should\nbe capable of perceiving extension. This is very true, but it throws\nno light on the nature of the idea of space, either in itself or in\nits object. \"Space,\" says Kant, \"is no empirical conception which is\nderived from external experience. For in order that certain sensations\nmay be referred to something out of me, that is, to something in\nanother part of space than that in which I am, and in order that I may\nconceive them as outside of and near one another, and, consequently,\nnot only as separated, but also as occupying separate places, the\nconception of space must be placed as the foundation. Therefore, the\nconception of space cannot be obtained by experience from the relations\nof the external phenomenon, but this external experience itself is\npossible only by this conception.\"[48]\n\n[48] Kant, _Transc. \u00c6st\u0153\u0153h._ I. Absch. \u00a7 2, 1.\n\nThere is a great confusion of ideas here. What are the conditions which\nare necessary to the phenomenon of the sensation of the extended? We\nare not here treating of the appreciation of dimensions, but merely of\nextension as represented or conceived. I do not see how this phenomenon\nrequires any thing _a priori_, except the sensitive faculty which,\nin fact, exists _a priori_, that is to say, is a primitive fact of\nour soul in its relations to the organization of the body which is\nunited to it, and of the other bodies which surround it. Under certain\nconditions of our organization, and of the bodies which affect it, the\nsoul receives the impressions of sight or touch, and with them the\nimpression of extension. This extension is not presented to the mind in\nthe abstract, or as separated from the other sensation which accompany\nit, but as united with them. The mind does not reflect, then, upon the\nposition of the objects, but it has an intuition of the arrangement\nof the parts. So long as the fact is confined to mere sensation, it\nis common to the learned and the unlearned, to the old and the young,\nand even to all animals. This requires nothing _a priori_ except\nthe sensitive faculty, which simply means that a being, in order to\nperceive, must have the faculty of perceiving, and should hardly\ndeserve to be announced as a discovery of philosophy.\n\n109. There is no such discovery in Kant's doctrine of space, for on the\none side he asserts a well known fact, that the intuition of space is\na necessary subjective condition, without which it is impossible for us\nto perceive things, one _outside_ of another; and on the other side he\nfalls into idealism, inasmuch as he denies this extension all reality,\nand regards things and their position in space as pure _phenomena_,\nor mere appearances. The fact which he asserts is true at bottom;\nfor it is, in fact, impossible to perceive things as distinct among\nthemselves, and as outside of us, without the intuition of space; but,\nat the same time, it is not accurately expressed, for the intuition\nof space is this perception itself; and, consequently, he ought to\nhave said that they are identical, not that one is an indispensable\ncondition of the other.\n\n110. Prior to the impressions, there is no such intuition, and if\nwe regard it as a pure intuition and separated from intellectual\nconception, we can only conceive it as accompanied by some\nrepresentation of one of the five senses. Let us imagine a pure space\nwithout any of these representations, without even that mysterious\nvagueness which we imagine in the most distant regions of the universe.\nThe imagination finds no object; the intuition ceases; there remains\nonly the purely intellectual conceptions which we form of extension,\nthe ideas of an order of possible beings, and the assertion or denial\nof this order, according to our opinion of the reality or non-reality\nof space.\n\n111. It is evident that a series of pure sensations cannot produce a\ngeneral idea. Science requires some other foundation. The phenomena\nleave traces of the sensible object in the memory, and are so connected\nwith each other, that the representation of one cannot be repeated\nwithout exciting the representation of the other, but they produce no\ngeneral result which could serve as the basis of geometry. A dog sees\na man stoop, and make a certain motion, and is immediately struck with\na stone, which causes in him a sensation of pain; when the dog sees\nanother man perform the motion, he runs away; because the sensations of\nthe motions are connected in his memory with the sensation of pain, and\nhis natural instinct of avoiding pain inspires him to fly.\n\n112. When these sensations are produced in an intelligent being, they\nexcite other internal phenomena, distinct from the mere sensitive\nintuition. Whether general ideas already exist in our mind, or are\nformed by the aid of sensation, it is certain that they are developed\nin the presence of sensation. Thus, in the present case we not only\nhave the sensitive intuition of extension, but we also perceive\nsomething which is common to all extended objects. Extension ceases\nto be a particular object, and becomes a general form applicable\nto all extended things. There is then a perception of extension in\nitself, although there is no intuition of the extended; we then begin\nto reflect upon the idea and analyze it, and deduce from it those\nprinciples, which are the fruitful germs from the infinite development\nof which is produced the tree of science called geometry.\n\n113. This transition from the sensation to the idea, from the\ncontingent to the necessary, from the particular fact to the general\nscience, presents important considerations on the origin and nature of\nideas, and the high character of the human mind.\n\nKant seems to have confounded the imagination of space with the idea\nof space, and notwithstanding his attempts at analysis, he is not so\nprofound as he thinks, when he considers space as the receptacle of\nphenomena. This a very common idea, and all that Kant has done is to\ndestroy its objectiveness, making space a purely subjective condition.\nAccording to this philosopher, the world is the sum of the appearances\nwhich are presented to our mind; and just as we imagine in the\nexternal world an unlimited receptacle which contains every thing, but\nis distinct from what it contains, so he has placed space within us as\na preliminary condition, as a form of the phenomena, as a capacity in\nwhich we may distribute and classify them.\n\n114. In this he confounds, I say, the vague imagination with the idea.\nThe limit between the two is strongly marked. When we see an object we\nhave the sensation and intuition of extension. The space perceived or\nsensed is, in this case, the extension itself perceived. We imagine a\nmultitude of extended objects, and a capacity which contains them all.\nWe imagine this capacity as the immensity of the ethereal regions, a\nboundless abyss, a dark region beyond the limits of creation. So far\nthere is no idea, there is only an imagination arising from the fact\nthat when we begin to see bodies we do not see the air which surrounds\nthem, and the transparency of the air permits us to see distant\nobjects, and thus from our infancy we are accustomed to imagine an\nempty capacity in which all bodies are placed, but which is distinct\nfrom them.\n\nBut this is not the idea of space; it is only an imagination of it, a\nsort of rude, sensible idea, probably common to man and the beasts. The\ntrue idea, and the only one deserving the name, is that which our mind\npossesses when it conceives extension in itself, without any mixture of\nsensation, and which is, as it were, the seed of the whole science of\ngeometry.\n\n115. It should be observed that the word representation as applied to\npurely intellectual ideas must be taken in a purely metaphorical sense,\nunless we eliminate from its meaning all that relates to the sensible\norder. We know objects by ideas, but they are not represented to us.\nRepresentation, properly speaking, occurs only in the imagination\nwhich necessarily relates to sensible things. If I demonstrate the\nproperties of a triangle, it is clear that I must know the triangle,\nthat I must have an idea of it; but this idea is not the natural\nrepresentation which is presented to me like a figure in a painting.\nAll the world, even irrational animals have this representation, yet we\ncannot say that brutes have the idea of a triangle. This representation\nhas no degrees of perfection, but is equally perfect in all. Any\none who imagines three lines with an area enclosed, possesses the\nrepresentation of a triangle with as much perfection as Archimedes; but\nthe same cannot be said of the idea of a triangle, which is evidently\nsusceptible of various degrees of perfection.\n\n116. The representation of a triangle is always limited to a certain\nsize and figure. When we imagine a triangle, it is always with such\nor such extension and with greater or smaller angles. The imagination\nrepresenting an obtuse angled triangle sees something very different\nfrom an acute or right angled triangle. But the idea of the triangle\nin itself is not subject to any particular size or figure; it\nextends to all triangular figures of every size. The general idea of\ntriangle abstracts necessarily all species of triangles, whilst the\nrepresentation of a triangle is necessarily the representation of a\ntriangle of a determinate species. Therefore the representation and the\nidea are very different, even in relation to sensible objects.\n\n117. It is the same with space. Its representation is not its idea. The\nrepresentation is always presented to us as something determinate, with\na clearness like that of the air illuminated by the sun, or a blackness\nlike the darkness of night. There is nothing of this sort in the idea,\nor when we reason upon extension and distances.\n\nThe idea of space is one; its representations are many. The idea is\ncommon to the blind man and to him who sees. For both it is equally the\nbasis of geometry, but the representation is very different in these\ntwo. The latter represents space as a confused reproduction of the\nsensations of sight; the blind man can only represent it as a confused\nrepetition of the sensations of touch.\n\nThe representation of space is only indefinite, and even this\nprogressively. The imagination runs over one space after another, but\nit cannot at once represent a space without limits; it can no more do\nthis than the sight can take in an endless object. The imagination is\na sort of interior sight, it reaches a certain point, but there it\nfinds a limit. It can, it is true, pass beyond this limit, and expand\nstill farther, but only successively, and always with the condition of\nencountering a new limit. Space is not represented as infinite, but as\nindefinite, that is to say, that after a given limit there is always\nmore space, but we can never advance so far as to imagine an infinite\ntotality. It is the contrary with the idea; we conceive instantaneously\nwhat is meant by infinite space, we dispute on its possibility or\nimpossibility, we distinguish it perfectly from indefinite space, we\nask if it has in reality limits or not, calling it in the first case\nfinite, in the latter infinite. We see in the word indefinite the\nimpossibility of finding limits, but at the same time we distinguish\nbetween the existence of these limits, and finding them. All this shows\nthat the idea is very different from the representation.\n\nTo regard space as a mere condition of sensibility is to confound the\ntwo aspects under which extension should be considered, as the basis of\nsensations, and as idea; as the field of all sensible representations,\nand as the origin of geometry. I have often insisted on this\ndistinction, and shall never weary of repeating it; because it is the\nline which divides the sensible from the purely intellectual order, and\nsensations from ideas.\n\n\n\n\nCHAPTER XVII.\n\nINABILITY OF KANT'S DOCTRINE TO SOLVE THE PROBLEM OF THE POSSIBILITY OF\nEXPERIENCE.\n\n\n118. I think that Kant's _Transcendental \u00c6sthetics_, or theory of\nsensibility, is not sufficiently transcendental. It is too much\nconfined to the empirical part, and does not rise to the height which\nwe should expect from the title. The problem of the possibility of\nexperience which Kant proposed to solve, either is not at all touched\nby his doctrine, or else it is solved in a strictly idealist sense.\nIt leaves the problem untouched, if we consider only what relates to\nobservation; for he only repeats what we already knew in establishing\nthe fact of the _exteriority_ of things; it solves the problem in a\nstrictly idealist sense, inasmuch as these things are only considered\nas phenomena or appearances.\n\n119. A purely subjective space either does not explain the problems\nof the external world, or it denies them in denying all reality. What\nprogress has philosophy made by affirming that space is a purely\nsubjective condition? Before Kant, did we, perchance, not know that we\nhad perception of external phenomena? The difficulty was not in the\nexistence of this perception attested by consciousness; but in its\nvalue to prove the existence of an external world, in relation with it.\nThe difficulty was in the objective, not the subjective part of the\nperception.\n\n120. To say that the perception is nothing more than a condition of\nthe subject, is to cut the knot instead of untying it. It does not\nexplain the manner of the possibility of experience, but denies this\npossibility.\n\nWhat is experience if there is only the subject? There will be the\n_phenomenon_ or _appearance_ of objectiveness, but nature is then only\na mere appearance, and there is nothing in reality which corresponds\nto our experimental perceptions. We then have experience reduced to\nthe perception of appearances; and as even this purely phenomenal\nexperience is only possible by virtue of a purely subjective condition,\nthe intuition of space; all experience remains purely subjective, and\nwe find ourselves holding the system of Fichte, admitting the _me_ as\nthe primitive fact, the development of which constitutes the universe.\nThus the system of Fichte follows from Kant's doctrine; the former has\nonly carried out the principles of his master.\n\n121. In order to make the connection between the two doctrines still\nclearer, we shall make some further reflections on Kant's system. If\nspace is something purely subjective, a condition of the sensibility\nand of the possibility of experience, it follows that the mind instead\nof receiving any thing from the object, creates whatever is in the\nobject, or rather, whatever we consider as in it. Things in themselves\nare not extended; extension is only a form with which the mind clothes\nthem. In the same manner, they are not colored, sonorous, tasteful,\nor odorous, except inasmuch as we transfer to them that which is\nin ourselves alone. Every thing being reduced to mere appearances,\nthere is in the external world not even the principle of causality of\nsubjective extension; the mind gives it to objects, does not receive\nit from them. These objects are pure phenomena; and, consequently, the\nsoul only sees what it contains in itself, it knows no other world than\nthat which is its own creation. Thus, we see the real world spring from\nthe _me_; or, rather, the real world is only the ideal creation of the\nmind. On this supposition, the laws of nature are only the laws of our\nown mind, and instead of seeking for the types of our ideas in nature,\nwe ought to regard our ideas as the generative principle of all that\nexists, or seems to exist; and the laws of the universe are merely the\nsubjective condition of the _me_ applied to phenomena.\n\n122. Some of the disciples of Kant show no fear of his idealist\ntendencies; in fact they accept them without any hesitation, as may be\nseen by the comparisons which they use in explaining his doctrine. If\na seal be applied to a piece of soft wax, it will leave its impression\non the wax; if we suppose the seal to be capable of perception, it\nwould see its mark on the wax, and attribute to the object what it had\nitself given it. If a vase full of water were capable of perception,\nit would attribute to the water the form, which in reality is only the\nform of the vase itself, and is communicated from it to the water. In\na similar manner the mind constructs the external world, giving to it\nits impression and form, and then believing it has received from the\nexternal world what it has itself communicated to it.\n\n123. Still we must confess that Kant, in the second edition of his\n_Critic of Pure Reason_, rejects these conclusions, and expressly\ncombats idealism. There is no necessity of examining how far the second\nedition contradicts the first: it is sufficient for me to inform the\nreader that this contradiction exists, and that in the first edition\nthere are expressions which so plainly lead to idealism, that it is\nimpossible not to be surprised on finding the same author in the second\nedition of his work strongly opposing the idealist system. I have\npointed out the consequences of the doctrine; if the author understood\nit in a different sense from that which his words expressed, this is\nmerely a personal, not a philosophical question.(31)\n\n\n\n\nCHAPTER XVIII.\n\nTHE PROBLEM OF SENSIBLE EXPERIENCE.\n\n\n124. The great problem of philosophy does not consist in the\nexplanation of the possibility of experience; but in establishing the\nreason of the consciousness of experience, as experience. Experience in\nitself is a fact of our soul attested by consciousness, but _to know_\nthat this fact is a fact of experience, is something very different\nfrom mere experience; for, by knowing this, we pass from the subjective\nto the objective, referring to the external world what we experience\nwithin us.\n\nWe refer objects to different points of space, and regard them as\noutside of, and distinct from, each other: to say that the instinct by\nwhich we so regard them is a condition of the subject and of sensible\nexperience is to establish a sterile fact. The difficulty is in knowing\nwhy we have this instinct; why the representation of an extension is in\nour soul; and why this subjective extension in a simple being should\nbe presented to our perception as the image of something external and\nreally extended.\n\n125. Transcendental esthetics may determine the following problems:\n\nI. To explain what is the subjective representation of extension,\nabstracted from all that is objective.\n\nII. Why this representation is found in our soul.\n\nIII. Why a simple being contains in itself the representation of\nmultiplicity, and an unextended being the representation of extension.\n\nIV. Why and how we pass from ideal to real extension.\n\nV. To determine how far we may apply to extension what is true of the\nother sensations, which are considered as phenomena of our soul,\nhaving no external object like them, and no other correspondence with\nthe external world than the relation of effects to their cause.\n\n126. What is the subjective representation of extension, abstracted\nfrom all that is objective? It is a fact of our soul; no further\nexplanation is possible; he that has it, knows what it is; he that has\nit not, does not, except intelligences of a higher order, which know\nwhat this representation is, without experiencing it as we do.\n\n127. I do not pretend that it is possible to explain why the\nrepresentation of extension is found in our soul; we might as well ask\nwhy we are intelligent and sensible beings. The only reason _a priori_\nwhich we can give, is that God has so created us. This representation\nmay be found in us, and it is so found, for we experience it; but this\ninternal experience is the limit of philosophy; immediate observation\ncan go no farther back. Reason raises us to the knowledge of a cause\nwhich created us, but not to a phenomenon which is the source of the\nphenomena of experience.\n\n128. Why a simple being contains in itself the representation of\nmultiplicity, and an unextended being the representation of extension,\nis the problem of intelligence, which, because it is intelligence, is\none and simple, and capable of perceiving multiplicity and composition.\n\n129. We pass from ideal to real extension by a natural and irresistible\nimpulse, which is confirmed by the assent of reason. This has been\ndemonstrated in the first book, and also in the second when treating of\nthe objectiveness of sensations.\n\n130. Of the five problems the last remains. We must determine how far\nwe may apply to extension what is true of the other sensations, which\nare considered as phenomena of our soul, having no external object like\nthem, and no other correspondence with the external world than the\nrelation of effects to their cause.\n\n131. The solution of this problem settles the question for or against\nthe idealists. If we may apply to extension what is true of the other\nsensations, idealism triumphs, and the real world, if it exists, is a\nbeing which has no resemblance to the world which we think.\n\nI have proved in treating of sensations[49] that extension is something\nreal, and independent of our sensations, and I have shown[50] that it\nrepresents multiplicity and continuity. This is sufficient to overthrow\nidealism, and also to explain, to a certain extent, what extension\nconsists in; but as the idea of space, which is closely connected\nwith extension, had not then been examined, it was not possible for\nus to rise above the order of phenomena and regard extension under a\ntranscendental aspect, examining it in itself, abstracted from all its\nrelations with the world of appearances. This is what I propose to do\nin the following chapters.\n\n[49] Bk. II., Chs. VII., VIII., and IX., and Bk. III., Ch. IV.\n\n[50] Bk. II., Ch. VIII., and Bk. III., Ch. VI.\n\n132. We come now to a more cragged path; we have to distinguish the\nreality from appearance; our understanding, which is always accompanied\nby sensible representations, must now depart from them, and place\nitself in opposition to a condition to which it is naturally subjected\nin the exercise of its functions.\n\n\n\n\nCHAPTER XIX.\n\nEXTENSION ABSTRACTED FROM PHENOMENA.\n\n\n133. That which is extended is not one being only; it is a collection\nof beings. Extension necessarily contains parts, some outside of, and\nconsequently distinct from, others. Their union is not identity; for,\nthe very fact that they are united, supposes them distinct, since any\nthing is not united with itself.\n\nIt would seem from this that extension in itself and distinguished from\nthe things extended, is nothing; to imagine extension as a being whose\nreal nature can be investigated is to resign one's self to be the sport\nof one's fancy.\n\nExtension is not identified in particular with any one of the beings\nwhich compose it, but it is the _result_ of their union. This is\nequally true whether we consider extension composed of unextended\npoints, or of points that are extended but infinitely divisible.\nIf we suppose the points unextended, it is evident that they are\nnot extension, because extended and unextended are contradictory.\nNeither are these points identified with extension, if we suppose\nthem extended; for extension implies a whole, and a whole cannot be\nidentified with any of its parts. If a line be four feet long, there\ncannot be identity between the whole line and one of its parts a foot\nlong. We may suppose these parts, instead of a foot, to be only an inch\nin length, and we may divide them _ad infinitum_, but we shall never\nfind any of these parts equal to any of its subdivisions. Therefore,\nextension is not identical with any of the particular beings which\ncompose it.\n\n134. The idea of multiplicity being involved in the idea of extension,\nit would seem that extension ought to be considered, not as a being in\nitself, but as the result of a union of many beings. This result is\nwhat we call continuity. We have already seen[51] that multiplicity\nis not sufficient to constitute extension. It enters into the idea of\nnumber, and yet number does not represent any thing extended. We also\nconceive a union of acts, faculties, activities, substances, and beings\nof various classes, without conceiving extension, and yet multiplicity\nis a part of all these conceptions.\n\n[51] Bk. II. Chap. VIII.\n\n135. Therefore continuity is necessary, in order to complete the idea\nof extension. What, then, is continuity? It is the position of parts\noutside of, but joined to other parts. But what is the meaning of\nthe terms, _outside of_, and _joined to_? Inside and outside, joined\nand separated, imply extension, they presuppose that which is to be\nexplained; the thing to be defined enters into the definition in the\nsame sense in which it is to be defined. Exactly; for, to explain the\ncontinuity of extension is the same as to show the meaning of the terms\ninside and outside, joined and separated.\n\n136. We must not forget this observation, unless we wish to accept the\nexplanations which are found in almost all the books on the subject.\nTo define extension by the words _inside_ and _outside_, is not to add\nany thing, under a philosophic aspect; it is merely to express the\nsame thing in different words. Without doubt this language would be\nthe simplest, if all we wanted was to establish the phenomenon only,\nbut philosophy will not be satisfied with it. It is a practical, not\na speculative, explanation. The same may be said of the definition\nof extension by space or places. What is extension?--the occupation\nof place:--but, what is a place?--a portion of space terminated by\ncertain surfaces:--what is space?--the extension in which bodies\nare placed, or the capacity to receive them. But even admitting the\nexistence of space as something absolute, what is the capacity of\nbodies to fill space? Who does not see that this is to define a thing\nby itself, a vicious circle? The extension of space is explained by the\ncapacity of _receiving_; the extension of bodies by the capacity of\n_filling_. The idea of extension remains untouched; it is not defined,\nit is merely expressed in different words, but which mean the same\nthing.\n\nTo suppose the existence of space as something absolute, does not help\nthe question, and is, besides, an entirely gratuitous supposition.\nTo take the extension of space as a term by relation to which we may\nexplain the extension of bodies, is to suppose that to be found which\nwe are looking for.\n\nWe run into the same error if we try to explain the words inside and\noutside, by referring them to distinct points in space, we should\ndefine a thing by itself; for, we have the same difficulty with respect\nto space to determine the meaning of inside and outside, joined and\nseparated, and contiguous and distant. If we presuppose the extension\nof space as something absolute, and try to explain other extensions by\nrelation to this, we only make the illusion more complete. We have to\nexplain extension in itself, the extension of space must be explained\nas well as the rest; to presuppose it is to assume the question already\nsolved, not to solve it.\n\n137. Extension in relation to its dimensions seems to be independent\nof the thing extended in the same place. An extension may remain\nabsolutely fixed with the same dimensions, notwithstanding the change\nof place of the thing extended. If we suppose a series of objects to\npass over a fixed visual field, the things extended vary incessantly,\nbut the extension remains the same. If we suppose a very large object\nto pass before a window, it changes continually; for the part which we\nsee at the instant A is not the part which we see at the instant B, but\nthe extension has not varied in its dimensions. This regards surfaces\nonly, but the same doctrine may be applied to solids. A space may be\nsuccessively filled with a variety of objects, but its capacity remains\nthe same. There is no identity between the object and the extension\nwhich contains it; for any number of objects of the same size may\noccupy the same place; neither is the air, or any surrounding object,\nidentified with the extension; for these, too, may change without\naffecting the extension in which the object is contained.\n\n138. Though the dimensions remain fixed while the objects vary, it does\nnot follow that extension is purely subjective, even though we suppose\nthat the objects which vary cannot be distinguished. If the contrary\nwere maintained, the change of the dimensions would prove them to be\nobjective; and the argument might be retorted against our adversaries.\nThat the dimensions are fixed shows that different objects may produce\nsimilar impressions; and therefore we can form an idea of a determinate\ndimension or figure, without reference to the particular object to\nwhich it does, or may correspond. No one will deny that we have the\nrepresentation of dimensions, without necessarily referring them to any\nthing in particular; but what we wish to determine is, whether these\ndimensions exist in reality, and what is their nature, independently of\ntheir relations to us.\n\n139. If we admit that continuity has no external object either in\npure space or in bodies, what becomes of the corporeal world? It is\nindeed to a collection of beings which in one way or another, and in a\ncertain order, act upon our being.\n\nThe difficulties against the realization of phenomenal continuity\nare not destroyed by appealing to the necessities of the corporeal\norganization of sensible beings. If any one should ask how external\nbeings can act upon us, and affect our organs, if they have not in\nthem the continuity with which they are presented to us; such a one\nwould show that he does not understand the state of the question. For\nit is evident that if we should take from the external world all real\ncontinuity, leaving only the phenomenal, we should at the same time\ntake it from our own organization, which is but a part of the universe.\nThere is here a mutual relation and sort of parallelism of phenomena\nand realities which mutually complete and explain each other. If the\nuniverse is a collection of beings acting upon us in a certain order,\nour organization is another collection of beings, receiving their\ninfluence in the same order. Either both are inexplicable, or else the\nexplanation of one involves the explanation of the other. If that order\nis fixed and constant, and its correspondence remains the same, nothing\nis changed, no matter what hypothesis is assumed in order to explain\nthe phenomenon.\n\n140. The object of our searches here, is the reality subject to the\ncondition of explaining the phenomenon, and not contradicting the order\nof our ideas.\n\nIt might be objected to those who take from the external world the\nphenomenal or apparent qualities of continuity, that they destroy\ngeometry, which is based on the idea of phenomenal continuity. But this\nobjection cannot stand; for it supposes the idea of geometry to be\nphenomenal, whereas it is transcendental. We have already shown that\nthe idea of extension is not a sensation, but a pure idea, and that the\nimaginary representations by which it is made sensible are not the\nidea, but only the forms with which the idea is clothed.\n\n141. All phenomenal extension is presented to us with a certain\nmagnitude; geometry abstracts all magnitude. Its theorems and problems\nrelate to figures in general abstracted absolutely from their size,\nand when the size is taken into consideration it is only in so far\nas relative. Of two triangles of equal bases that which has greater\naltitude has the greater surface. Here the word _greater_ relates to\nsize, it is true; but to a relative, not to any absolute size; the\nquestion is not of the magnitudes themselves, but of their _relation_.\nConsequently, the theorem is equally true whether the triangles are\nimmense, or infinitely small. Therefore, geometry abstracts absolutely\nall magnitudes considered as phenomena, and makes use of them only\nin order to assist the intellectual perception by the sensible\nrepresentation.\n\n142. This is an important truth, and I shall explain it further when\ncombating Condillac's system in the treatise on ideas, where I shall\nshow that even the ideas which we have of bodies neither are, nor can\nbe, a transformed sensation. According to these principles, geometry\nis a science which makes its pure ideas sensible by a phenomenal\nrepresentation. This representation is necessary so long as geometry\nis a human science, and man is subject to phenomena; but geometry in\nitself and in all its purity has no need of such representations.\n\n143. In order that this doctrine may seem less strange, and may be more\nreadily accepted, I will ask, whether pure spirits possess the science\nof geometry? We must answer in the affirmative; for, otherwise we\nshould be forced to conclude that God, the author of the universe and\ngreatest of geometricians, does not know geometry. Does God, then, have\nthese representations, by the aid of which we imagine extension? No;\nthese representations are a sort of continuation of sensibility which\nGod has not; they are the exercise of the internal sense, which is not\nfound in God. St. Thomas calls them _phantasmata_, and says they are\nnot found in God, or in pure spirits, nor even in the soul separated\nfrom the body. Therefore, the science of geometry is possible, and does\nreally exist without sensible representations, and, consequently, we\nmay distinguish two extensions, the one phenomenal, and the other real,\nwithout thereby destroying either the phenomenon or the reality, so\nlong as we admit the correspondence between them; so long as we do not\nbreak the thread which unites our being with those around us; so long\nas the conditions of our being harmonize with those of the external\nworld.(32)\n\n\n\n\nCHAPTER XX.\n\nARE THERE ABSOLUTE MAGNITUDES?\n\n\n144. The preceding doctrine will seem much more probable if we reflect\nthat all purely intellectual perceptions of extension may be reduced\nto the knowledge of order and relation. There is nothing absolute in\nthe eyes of science, not even of mathematical science. The absolute, in\nrelation to extension, is an ignorant fancy which the observation of\nthe phenomena is sufficient to dissipate.\n\nIn the order of appearances there are no absolute magnitudes; all are\nrelations. We can not even form an idea of a magnitude, unless with\nreference to another which serves for a measure. The absolute is found\nonly in number, and never in extension; a magnitude is absolute, not\nin itself, but only by being numbered. A surface two feet square,\npresents two distinct ideas; the number of its parts, and the kind of\nparts. The number is a fixed idea, but the kind is purely relative. I\nwill try to make this clearer.\n\n145. When I speak of a surface four feet square, the number four is a\nsimple, fixed, and unchangeable idea; but I can explain a square foot\nonly by relations. If I am asked what is a square foot, I can answer\nonly by comparison with a square rod or a square inch; but if I am\nagain asked what is a square rod or a square inch, I am again forced\nto recur to other measures which are greater or smaller; I can nowhere\nfind a fixed magnitude.\n\n146. If there were some fixed measure it might be some dimension\nof the body, my hand, or foot, or arm. But who does not see that\nthe dimensions of my body are not a universal measure, and that the\nhands, or feet, or arms, of all men are not equal? And even in the\nsame individual they are subject to a thousand changes more or less\nperceptible. Shall we take for our fixed measure the radius of the\nearth, or of a heavenly body? But one has no claim to preference before\nthe other. Every one knows that astronomers take sometimes the radius\nof the earth, and sometimes the radius of its orbit as the unity of\nmeasure. If we suppose these radii to be greater or smaller, can we not\nequally in either case take them as the measure? They are preferred\nbecause they do not change.\n\nBut even astronomers regard these magnitudes as purely relative, and at\none time consider them infinitely large, at another infinitely small,\naccording to the point of view from which they look at them. The radius\nof the earth's orbit is considered infinite in comparison with a small\ninequality on the earth's surface, and infinitely small when compared\nwith the distance of the fixed stars.\n\nWe can form no idea of these measures except by comparison with those\nin constant use. What idea should we have of the magnitude of the\nradius of the earth if we did not know how many million measures it is\nequal to? What idea should we have in turn of these measures if we had\nnothing constant to which we could refer them?\n\n147. There is something absolute in magnitudes, it may be objected;\nfor a foot is a certain length which we both see and touch, and cannot\nbe greater or smaller; the surface of a square yard is in like manner\nsomething definite which we see and which we touch; and the same may\nbe applied to solids. There is no necessity of going farther to find\nthat which is so clearly presented to us in sensible intuition. This\nobjection supposes that there is something fixed and constant in\nintuition; this is false. I appeal to experience.\n\nIt is probable that men see the same magnitudes very differently\naccording to the disposition of their eyes. No one is ignorant that\nthis happens when the objects are at a distance; for, then, one sees\nclearly what another cannot even distinguish; to one it is a surface,\nwhile to another it is not even so much as a point. We all know what a\ngreat variety there is in the size of objects when looked at through\ndifferently graduated glasses. From all this we conclude that there is\nnothing fixed in phenomenal magnitude; but that every thing is subject\nto continual changes.\n\nWhen we look through a microscope objects which were before invisible,\ntake large dimensions; and as the microscope may be infinitely\nperfected, it is not absurd to suppose that there are animals to whom\nwhat is invisible to us appears larger than the whole earth. The\nconstruction of the eye may also be considered in an inverse sense, and\nas infinite perfection is also possible in this case, it is possible\nthat magnitudes which to us are immense may be invisible to other\nbeings. To this eye of colossal vision the terrestrial globe would\nperhaps be an imperceptible atom. This is no more than what happens by\nthe interposition of distance; immense masses in the firmament seem to\nus to be only small specks of light.\n\n148. It must now be very evident that there is nothing absolute in\nmagnitudes of sight; but that all is relative, and that objects\nappear to us greater or less, according to habit, the construction\nof our organs, and other circumstances. The variety of appearances\nis in accordance with philosophy; since no necessary relation can\nbe discovered between the size of the organ and the object. What\nconnection is there between a narrow surface like the retina of our eye\nand the immense surfaces which are painted on it?\n\n149. From sight we may pass to touch, but we find no reason of the\nfixity of phenomenal magnitude. The sense of touch gives us the ideas\nof magnitudes by relation to the time it takes to pass over them, and\nto the velocity of our motion. The ideas of time and velocity are\nalso relative; they refer to the space passed over. When we measure\nvelocity we say that it is the space divided by the time; in measuring\ntime we say that it is the space divided by the velocity; and we\nmeasure space by multiplying the velocity by the time. All these ideas\nare correlative, and are measured by each other, and by their mutual\nrelations. This shows that these ideas have nothing absolute; their\nwhole character is that of a relation which is incomplete, or rather\ndoes not exist, if one of the terms is wanting.\n\n150. We shall find it equally impossible to determine these measures\nby the impressions which the motion causes in us. If for example we\npropose to measure the degree of velocity, by the agitation which\nwe feel in our body, we shall find that the measure varies with the\nagitation, but this agitation depends on the degree of force exerted,\nand still more on the strength of the subject. Thus a little child is\nobliged to run till he is almost out of breath, to keep up with his\nfather who is walking fast.\n\nThe impossibility of any fixed measure by means of impressions will\nbe still more apparent if we compare the motion of a horse with the\nmotion of a microscopic animal. The distance which a horse would pass\nover almost without any sensible motion, would require the microscopic\nanimal to display its whole activity, and run perhaps a whole day.\nThe horse would scarce believe he had changed his place, whereas the\npoor animalcule would at night be overcome by fatigue like one who has\ntravelled a long journey. Compare now the motion of the horse with the\nmotion of those fabulous giants who piled up mountains to scale the\nheavens; a single step of one of those giants would be a long distance\nfor the horse to travel.\n\n151. Art seems to be in accordance with science on this point. In art,\nsize is nothing, the only thing which is regarded is the proportion\nor relation. A skilful miniature represents a person as clearly as a\npainting the size of life. The same principle is applied to all the\nobjects embraced by art, the artistic thought never refers directly to\nthe size; proportion, the _relative_ is all that is attended to; the\nabsolute counts for nothing. We see the system of relations transferred\nto the order of appearances, inasmuch as they affect the faculties\nsusceptible of pleasure; reason is thus admirably harmonized with\nsentiment, in the same manner as we have found intellect harmonized\nwith the senses.\n\n\n\n\nCHAPTER XXI.\n\nPURE INTELLIGIBILITY OF THE EXTENDED WORLD.\n\n\n152. Objects in themselves do not change their nature, by the\nvariety of appearances which they produce in us. A polygon turning\nwith rapidity has the appearance of a circle; the stars appear like\nsmall points; and considering the various classes of objects, we\nmay observe that there is a great variety of appearances depending\non circumstances. The nature of a being does not consist in what it\nappears, but in what it is. Suppose there were no sensitive being\nin the world, the present order of sensibility would disappear; for\nwithout sensitive beings there would be no representations. What would\nthe world be in that case? This is a great problem of metaphysics.\n\n153. A pure spirit,--the existence of which we must always suppose;\nfor, though all finite beings were annihilated, there would still\nremain the infinite being which is God,--a pure spirit would know\nthe extended world _just as it is in itself_, and would not have\nthe sensible representations either external or internal, which we\nhave. This is certain, unless we mean to attribute imagination and\nsensibility to pure spirits, and even to God himself.\n\nOn this supposition I ask, what would a pure spirit know of the\nexternal world? or, to speak more properly, since the existence of\nsuch a spirit is certain and its intelligence infinite, what does this\nspirit know of the external world?\n\n154. That which this spirit knows of the world is the world, because\nhe cannot be deceived. But this spirit does not know the world under\nany sensible form. Therefore the world may be known without any of the\nforms of sensibility, and consequently may be the object of a pure\nintelligence.\n\nThere is no difficulty on this point in what regards sensations. It is\nonly necessary that we should say that the pure spirit knows perfectly\nthe principle of causality which resides in the object, and produces\nthe impressions which we experience. There is no need of attributing to\nthe intelligent spirit any sensation of the thing understood.\n\nThis question is more difficult when we come to explain what relates\nto extension. For, if we say that the spirit only knows the principle\nof causality of the subjective representation of the extended, it\nfollows that there is no true extension in the objects, because the\nspirit sees all that there is, and if the spirit does not see it, it\nis because it is not. We fall into Berkeley's idealism; an external\nworld without extension is not the world of common sense, but the\nworld of the idealists. If, on the other hand, we say that this pure\nspirit does know extension, we seem to attribute to the spirit sensible\nrepresentation; because the extension represented seems to involve\nsensible representation. What is an extension with lines, surfaces, and\nfigures? And these objects, as we understand them, are sensible; if,\nhowever, they be taken in another sense, the extension of the world\nwill be of another nature, it will be something of which we have no\nidea; and here again we fall into idealism.\n\n155. To solve this difficulty, which is really a serious one, it is\nnecessary to recollect the distinction on which I insisted so earnestly\nbetween extension as sensation and extension as idea. The former can\nbecome subjective only in a sensible being; the second may be, and\nis, subjective in a purely intellectual being. Extension as sensation\nis something subjective, it is an appearance; its object exists in\nreality, but without including in its essence any thing more than\nis necessary in order to produce the sensation. Extension as idea is\nalso subjective; but it has a real object which corresponds to it, and\nsatisfies all the conditions of the idea.\n\n156. Does not this theory seem to establish two geometries? We must\ndistinguish. The scientific and the pure ideal geometry will remain the\nsame, save the difference of the intelligences which possess it. But\nnotwithstanding this difference, what is true in one is true in the\nother. Empirical geometry as the representative part of geometry will\nbe different: we have the idea only of our own.\n\n157. In fact we observe two parts in geometry even in ourselves; the\none purely scientific, the other of sensible representation. The\nformer includes the connection of ideas; the latter the images and\nparticular cases by means of which we make the ideas sensible: the\nfirst is the ground; the second is the form. But although the two\nare different, we cannot separate them entirely: we cannot have the\ngeometrical idea without the sensible representation, we understand\nit only _per conversionem ad phantasmata_, as say the scholastics.\nThus the two orders of geometry, the sensible and the intellectual,\nthough different, are always joined in us; whether because the pure\ngeometrical idea arises from the sensible, or is excited by it, or\nbecause this is perhaps a necessary primitive condition imposed on our\nmind by its union with the body.\n\n158. This shows how the pure geometry may be separated from the\nsensible, and how it may exist in pure intellectual beings, without any\nof the forms which represent the geometrical idea in sensible beings.\n\n159. But what becomes of extension in itself and stripped of all\nsensible form? When we speak of extension stripped of all sensible\nform, we do not mean to deprive it of its capacity to be perceived\nby the senses, we merely abstract the relations of this capacity to\nsensible beings. Extension is then reduced, not to an imaginary space,\nnor to an eternal and infinite being, but to an order of beings, to\nthe sum of their constant relations subject to necessary laws. What\nthen are these relations? I know not. But I know that they exist and\nthat these necessary laws exist. That they exist in reality I know by\nexperience, which gives testimony of their existence; that they are\npossible, I know on the authority of my ideas, the connection of which\nforces my assent to their intrinsical evidence.\n\n160. That this evidence touches but one aspect of the object, is true;\nthat there are many things in the object which we do not know, is\nlikewise true; but this only proves that our science is incomplete, not\nthat it is illusory or false.\n\n161. It is difficult for us to conceive the pure intelligibility of\nthe sensible world, both because our ideas are always accompanied by\nrepresentations of the imagination, and because we try to explain it by\nsimple addition and subtraction of parts, as though all the problems\nof the universe could be reduced to expressions of lines, surfaces,\nand solids. Geometry plays an important part in all that regards the\nappreciation of the phenomena of nature; but when we want to penetrate\nto the essence of things, we must lay aside geometry and take up\nmetaphysics.\n\nThere is no more seductive philosophy than that which reduces the\nworld to motions and figures, but at the same time there is none\nmore superficial. A slight reflection on the reality of things shows\nthe insufficiency of such a system. For, though the imagination be\nsatisfied with it, the understanding is not, and it takes a noble\nrevenge on its unfaithful companion, when, forcing the imagination to\nfix itself upon objects, the understanding sinks it in an ocean of\ndarkness and contradiction. Those who laugh at the forms, the acts, the\nforces, and other such expressions used with more or less exactness\nin different schools, ought to reflect that even in the physical\nworld there is something more than is perceived by the senses; and\nthat even sensible phenomena cannot be explained by mere sensible\nrepresentations. Physical science is not complete until it calls to its\naid metaphysics.\n\nThe best proof of this will be found in the next chapter, where we\nshall see the imagination entangled in its own representations.\n\n\n\n\nCHAPTER XXII.\n\nINFINITE DIVISIBILITY.\n\n\n162. The divisibility of matter is a question that torments\nphilosophers. Matter is divisible because it is extended, and there is\nno extension without parts. These parts are extended or are not: if\nthey are, they are again divisible; if they are not, they are simple,\nand in the division of matter we must come to unextended points.\n\nThis last consequence can be avoided only by recourse to the infinite\ndivisibility of matter, and even this is a means of escaping the\ndifficulty rather than a true solution. I intimated elsewhere[52] that\ninfinite divisibility seems to suppose the very thing which it denies.\nDivision does not make the parts, it supposes them; that which is\nsimple cannot be divided; therefore, the parts which may be divided\npre-exist in the infinitely divisible composition.\n\n[52] Chap. v.\n\nLet us imagine God to exert his infinite power in dividing, will he\nexhaust divisibility? If you say no, you seem to place limits to his\nomnipotence; if you say yes, we shall have arrived at simple points,\nas otherwise the divisibility would not be exhausted.\n\nEven supposing that God does not make this division, his infinite\nintelligence certainly sees all the parts into which the composite\nis divisible; these parts must be simple, or else the infinite\nintelligence would not see the limit of divisibility. If you answer\nthat this limit does not exist, and therefore cannot be seen, I reply\nthat we must then admit an infinite number of parts in each portion\nof matter; there would, in this case, be no limit of divisibility,\nbecause the number of parts would be inexhaustible; but this infinite\nnumber would be seen by the infinite intelligence, as it is, and all\nthese parts would be known as they are. The difficulty still remains;\nthese parts are simple or composite; if simple, the opinion which we\nare opposing does, at least, admit unextended points; if composite,\nthe same argument may be repeated; they are again divisible. We shall\nthen have a new infinite number in each one of the parts of the first\ninfinite number; but as this series of infinities must be always known\nto the infinite intelligence, we must come to simple points, or else\nsay that the infinite intelligence does not know all that there is in\nmatter.\n\nIt does not mend the matter to say that the parts are not actual but\nonly possible. In the first place, possible parts are existing parts,\nbecause, if the parts are not real, there must be real simplicity, and\nconsequently, indivisibility. Secondly, if they are possible, they may\nbe made to exist by the intervention of an infinite power; and then\nwhat are these parts? they are either extended or unextended, and the\nmatter returns to where it was before.\n\n163. Some say that a mathematical quantity, or a body mathematically\nconsidered, is infinitely divisible, but that natural bodies are not,\nbecause their natural form requires a determinate quantity. This is the\nexplanation which was given in the schools; but it is very clear that\nthere is no ground for affirming that these natural bodies require a\ncertain quantity, beyond which division is impossible. This cannot be\nproved either _a priori_ nor _a posteriori_: not _a priori_, because we\ndo not know the essence of bodies, and cannot say that there is a point\nwhere the natural form requires the limit of divisibility; neither can\nit be proved _a posteriori_, because the means of observation at our\ndisposal are so coarse, that it is impossible for us to reach the last\nlimit of division and discover a part which cannot be divided. Besides,\nwhen we reach this quantity beyond which division cannot go, we have a\ntrue quantity, by the supposition; if it is quantity it is extended; if\nit is extended it has parts; if it has parts it is divisible. Therefore\nthere is no reason for saying that there is any natural form which\nlimits division.\n\n164. The distinction between a natural and a mathematical body is\nnot admissible in what relates to division. This is a result of the\nnature of extension, which is real in natural bodies, and ideal in\nmathematical. That the parts in natural bodies are not actual but\npossible, may be understood in two ways; it may mean that they are\nnot actually separated; or, that they are not distinct. That they are\nnot separated has no bearing on the question; for division may be\nconceived without separating the parts. But, if they are not distinct,\nthe division is impossible; for it cannot even be conceived where the\nthings are not distinct.\n\n165. This distinction seems to have originated in the attempt to avoid\nthe necessity of admitting infinite divisibility in natural bodies.\nBut the difficulty still remaining with regard to mathematical bodies,\nthe philosophical mystery still subsists. It consists in this, that\nno limit can be assigned to division so long as there is any thing\nextended; and, on the other hand, if, in order to assign this limit,\nwe come to simple points, then it is impossible to reconstitute\nextension. The difficulty arises from the very nature of extended\nthings, whether realized or only conceived; the real order escapes\nnone of the difficulties of the ideal. If ideal extension cannot be\nconstituted out of unextended points, neither can real extension; if\nideal extension has no limit to its divisibility until we come to\nsimple points, the same is also true of real extension; for in both it\nis a result of the essence of extension, and inseparable from it.\n\n\n\n\nCHAPTER XXIII.\n\nUNEXTENDED POINTS.\n\n\n166. There are two strong arguments against the existence of unextended\npoints: the first is, that we must suppose them infinite in number, for\notherwise it does not seem possible to arrive at the simple, starting\nfrom the extended: the second is, that even supposing them infinite in\nnumber they are incapable of producing extension. These arguments are\nso powerful as to excuse all the aberrations of the contrary opinion,\nwhich, however strange they may seem, are not more strange than the\nsimple forming extension, and the smallest portion of matter containing\nan infinite number of parts.\n\n167. It does not seem possible to arrive at unextended points unless by\nan infinite division. The unextended is zero in the order of extension,\nand in order to arrive at zero by a decreasing geometrical progression\nit must be continued _ad infinitum_. Mathematical calculation presents\na sensible image of this. When two parts are united they must have a\nside where they touch, and another where they are not in contact.\nIf we separate the interior side from the exterior we have two new\nsides, one which touches and another which does not. Continuing the\ndivision the same thing happens again; we must, therefore, pass\nthrough an infinite series in order to arrive at the unextended,\nwhich is equivalent to saying that we shall never arrive there. To\ncontinue the division _ad infinitum_ we must suppose infinite parts,\nand consequently the existence of an actual infinite number. From the\nmoment that we suppose this infinite number to exist it seems to become\nfinite, since we already see a limit to the division, and also other\nnumbers greater than it. Let us suppose that this infinite number of\nparts is found in a cubic inch; there are numbers which are greater\nthan this which we suppose infinite; a cubic foot, for example, will\ncontain 1,728 times the infinite number of parts contained in the cubic\ninch.\n\nThus the opinion of unextended points seeking to avoid infinite\ndivision, runs into it; just as its adversaries trying to escape from\nunextended points are forced to acknowledge their existence. The\nimagination loses itself and the understanding is confused.\n\n168. The other objection is not less unanswerable. Suppose we have\narrived at unextended points, how shall we reconstitute extension? The\nunextended has no dimensions; therefore, no matter how many unextended\npoints we may take, we can never form extension with them. Let us\nimagine two points to be united, as neither of them alone occupies\nany place, neither will they both together. We cannot say that they\npenetrate each other; for penetration cannot exist without extension.\nWe must admit that these parts being zero in the order of extension,\ntheir sum can never give extension, no matter how many of them we may\nadd together.\n\n169. It is certain that a sum of zeros can give only zero for the\nresult, but mathematicians admit that there are certain expressions\nequal to zero, which multiplied by an infinite quantity will give a\nfinite quantity for the product. 0 + 0 + 0 + 0 + N \u00d7 0 = 0; but if we\ntake 0/M = 0, and multiply it by the expression M/0 = 0, we shall have\n(0/M) \u00d7 (M/0) = (0 \u00d7 M)/(M \u00d7 0) = 0/0 which is equal to any finite\nquantity, which we may express by A. This is shown by the principles of\nelementary algebra only; if we pass to the transcendental we have dz/dx\n= o/o = B; B expressing the differential coefficient which may be equal\nto a finite value. Can these mathematical doctrines serve to explain\nthe generation of the extended from unextended points? I think not.\n\nIt is evident that, multiplication being only addition shortened, if\nan infinite addition of zeros can give only zero; multiplication can\ngive no other result, although the other factor be infinite. Why then\ndo mathematical results say the contrary? This contradiction is not\ntrue, but only apparent. In the multiplication of the infinitesimal by\nthe infinite we may obtain a finite quantity for product, because the\ninfinitesimal is not regarded as a true zero, but as a quantity less\nthan all imaginable quantities, but still it is something. If this\ncondition were wanting, all the operations would be absurd, because\nthey would turn upon a pure nothing. Shall we therefore say that the\nequation, dz/dx = o/o, is only approximate? No; for it expresses the\nrelation of the limit of the decrement, which is equal to B only\nwhen the differentials are equal to zero. But as geometricians only\nconsider the limit in itself, they pass over all the intervals of the\ndecrement, and place themselves at once at the point of true exactness.\nWhy then operate on these quantities? Because the operations are a\nsort of algebraic language, and mark the course that has been followed\nin the calculations, and recall the connection of the limit with the\nquantity to which it refers.\n\n170. Unity which is not number produces number; why then cannot points\nwithout extension produce extension? There is a great disparity between\nthe two cases. The unextended, as such, involves only the negative\nidea of extension; but in unity, although number is denied, this\nnegation does not constitute its nature. No one ever defined unity\nto be the negation of number, yet we always define the unextended to\nbe that which has no extension. Unity is any being taken in general,\nwithout considering its divisibility; number is a collection of\nunities; therefore the idea of number involves the idea of unity, of\nan _undivided_ being, number being nothing more than the repetition\nof this unity. It belongs to the essence of all number that it can be\nresolved into unity; it contains unity in a determinate manner. But the\nextended can not be resolved into the unextended, unless by proceeding\n_ad infinitum_, or else by some process of decomposition which we know\nnothing of.\n\n\n\n\nCHAPTER XXIV.\n\nA CONJECTURE ON THE TRANSCENDENTAL NOTION OF EXTENSION.\n\n\n171. The arguments for or against unextended points, for or against\nthe infinite divisibility of matter seem equally conclusive.\nThe understanding is afraid that it has met with contradictory\ndemonstrations; it thinks it discovers absurdities in infinite\ndivisibility, and absurdities in limiting it; absurdities in denying\nunextended points, and absurdities in admitting them. It is invincible\nattacking an opinion, but its strength is turned into weakness as\nsoon as it attempts to establish or defend any thing of its own. Yet\nreason can never contradict itself; two contradictory demonstrations\nwould be the contradiction of reason, and would produce its ruin;\nthe contradiction can, therefore, only be apparent. But who shall\nflatter himself that he can untie the knot? Excessive confidence on\nthis point is a sure proof that one has not understood the true state\nof the question, and such vanity would be punished by the conviction\nof ignorance. With all these reserves I now proceed to make a few\nobservations on this mysterious subject.\n\n172. I am inclined to believe that in all investigations on the\nfirst elements of matter, there is an error which renders any result\nimpossible. You wish to know whether extension may be produced from\nunextended points, and the method which you employ consists in\nimagining them already approached, and then trying to see if any part\nof space can be filled by them. This seems to me like trying to make a\ndenial correspond to an affirmation. The unextended point represents\nnothing determinate to us except the denial of extension; when,\ntherefore, we ask if this point joined with others like it can occupy\nspace, we ask if the unextended can be extended. Our imagination makes\nus presuppose extension in the very act in which we wish to examine\nits primitive generation. Space, such as we conceive it, is a true\nextension; and, as has been shown, is the idea of extension in general;\nto imagine, therefore, that the unextended can fill space, is to change\nnon-extension into extension. It is true that this is precisely what is\nrequired, and in this consists the whole difficulty; but the error is\nin attempting to solve it by a juxtaposition which makes these points\nboth unextended and extended, an evident contradiction.\n\n173. In order to know how extension is generated, it would be necessary\nto free ourselves from all sensible representations, and from all\nideas which are in the least degree affected by the phenomenon, and to\ncontemplate it with an eye as simple, a look as penetrating, as that\nof a pure spirit. It would be necessary to take from all geometrical\nideas all phenomenal forms, all representations of the imagination,\nand present them to the imagination purified from all mixture with the\nsensible order. It would be necessary to know how far extension, real\ncontinuity, agrees with the phenomenal. It would, in fine, be necessary\nto eliminate from the object perceived, all that relates to the subject\nwhich perceives it.\n\n174. In extension, as we have already seen, there are two things to\nbe considered; multiplicity, and continuity. As to the first, there\nis no objection to supposing that it may be the result of unextended\npoints, since number results from various units whether they are\nsimple or composite. But the difficulty is with regard to continuity,\nwhich sensible intuition clearly presents to us as the basis of the\nrepresentations of the imagination, but the nature of which is a\npuzzle to the understanding. It may perhaps be said that continuity,\nabstracted from the sensible representation, and considered only in\nthe transcendental order, is, in its reality and as it appears to a\npure spirit, nothing more than the constant relation of many beings,\nwhich are of a nature to produce in a sensitive being the phenomenon of\nrepresentation, and to be perceived in the intuition which we call the\nrepresentation of space.\n\nAccording to this hypothesis extension in the external world is real,\nnot only as a principle of causality of our impressions, but also as\nan object subject to the necessary relations which we conceive.\n\n175. But, then, it will be asked, is the external world such as\nwe imagine it? To this we must answer, in accordance with what we\nhave said when treating of sensations, that it is necessary to take\nfrom sensations all that is subjective, and which by an innocent\nillustration we look upon as objective; we may then say that extension\nreally exists outside of us and independent of our sensations;\nconsidered in itself, it exists free from all sensible representation,\nand in the same manner in which a pure spirit may perceive it.\n\n176. We see no objection which can reasonably be made to this theory\nwhich affirms the reality of the corporeal world, at the same time that\nit settles the difficulties of idealism. To give my opinion in a few\nwords, I say: That extension in itself, exists such as God knows it,\nand in the cognition of God there is no mixture of any of the sensible\nrepresentations which always accompany man's perception. That which is\npositive in extension is multiplicity, together with a certain constant\norder; continuity is nothing more than this constant order, in so far\nas sensibly represented in us, it is a purely subjective phenomenon\nwhich does not at all affect the reality.\n\n177. We may even assign a reason why sensible intuition has been given\nto us. Our soul is united to an organized body,--that is to say, a\ncollection of beings bound together by constant relation to each other\nand to the other bodies of the universe. In order that the harmony\nmight not be interrupted, and that the soul which presides over this\norganization might rightly exercise its functions, there was need of\na continued representation of this collection of the relations of our\nown and other bodies. This representation must be simultaneous and\nindependent of intellectual combinations; for otherwise the animal\nfaculties could not be exercised with the promptness and perseverance\nwhich the satisfaction of the necessities of life demands. Therefore\nit is that all sensible beings, even those which have not reason, have\nbeen endowed with this intuition of extension or space: which is like\nan unlimited field on which the different parts of the universe are\nrepresented.\n\n\n\n\nCHAPTER XXV.\n\nHARMONY OF THE REAL, PHENOMENAL, AND IDEAL ORDERS.\n\n\n178. We may consider two natures in the external world, the one real,\nthe other phenomenal; the first is particular and absolute, the second\nis relative to the being which perceives the phenomenon; by the first\nthe world is, by the second it _appears_. A pure intellectual being\nknows the world as it _is_; a sensitive being experiences it as it\n_appears_. We can discover this duality in ourselves; in so far as we\nare sensitive beings, we experience the phenomenon, but in so far as\nintelligent, although we do not know the reality, we attempt to reach\nit by reasoning and conjecture.\n\n179. The external world in its real nature, abstracted from the\nphenomenal, is not an illusion. Its existence is known to us not by\nphenomena only, but by principles of pure intelligence which are\nsuperior to all that is individual and contingent. These principles,\nbased on the data of experience,--that is, on sensations the existence\nof which we know from consciousness, assure us that the objectiveness\nof sensations, or the reality of the external world, is a truth.\n\n180. This distinction between the essential and the accidental, and\nbetween the absolute and the relative, was admitted in the schools.\nExtension was considered not as the essence, but as an accident\nof bodies; the relations of bodies to our senses are not founded\nimmediately on their essence, but on their accidents. Matter and\nsubstantial form united constitute the essence of bodies; the matter\nreceiving the form, and the form actuating the matter. Neither the\nmatter nor the substantial form can be immediately perceived by the\nsenses, because this perception requires the determination of figure\nand other accidents distinct from the essence of body.\n\nTherefore the scholastics distinguished sensible objects into three\nclasses; particular, common, and accidental, _proprium, commune, et\nper accidens_. The particular is that which appears immediately to\nthe senses, and is only perceived by one of them, as color, sound,\ntaste, and smell. The common is that which is perceived by more than\none sense, as figure, which is the object of sight and of touch. The\naccidental is that which is not directly perceived by any of the\nsenses, but is hidden under sensible qualities, by means of which\nit is discovered, as are substances. The sensible _per accidens_ is\nconnected with sensible qualities; but they do not present it to the\nunderstanding as an image presents the original, but as a sign the\nsignified. Hence they did not consider the sensible _per accidens_ as\nproceeding from the _species_ and reducing the sensitive faculty to\nact: it was intelligible rather than sensible.\n\n181. In the corporeal universe considered _in its essence_, there\nis no necessity of supposing any thing resembling the sensible\nrepresentation, but we must suppose the object to correspond to the\nidea; for otherwise we should have to admit that geometrical truths may\nbe contradicted by experience.\n\n182. Although extension is an order of beings of which we cannot form\na perfect conception, because we cannot purify our ideas from all\nsensible form, still this order must correspond to our ideas, and even\nto our sensible representations, so far as is necessary to prove the\ntruth of the ideas.\n\nIt is evident that although the phenomenal order is distinct from the\nreal, it depends on it, and is connected with it by constant laws.\nIf we suppose that there is no parallel between the reality and the\nphenomenon, and that the reality has not all the conditions necessary\nto satisfy the demands of the phenomenon, there can be no reason why\nthe phenomena should be subject to constant laws, and why experience\nshould not suffer continual confusion. Without a fixed and constant\ncorrespondence between the reality and the appearance, the world\nbecomes a chaos to us, and all regular and constant experience becomes\nimpossible.\n\n183. Let us examine this at greater length. One of the elementary\npropositions of geometry says: \"When two straight lines intersect each\nother, the opposite or vertical angles, which they form, are equal.\"\nIn order to demonstrate this, I must have the internal intuition of\ntwo lines intersecting each other. But the geometrical proposition is\nnot confined to any particular intuition, but embraces all that can be\nimagined, without any limit to their number, or any determination as to\nthe measure of the angles, the length of the lines, or their position\nin space.\n\nHere the pure idea extends to an infinity of cases, whereas the\nsensible intuition represents them only one at a time, and isolated\nif represented successively. The understanding is not limited to the\naffirmation of this relation between the ideas, but applies it to the\nreality, and says: Whenever the conditions of this ideal order are\nrealized, that which I see in my ideas is true in reality, and the\nrelation expressed will be more or less exact in proportion to the\nexactness of the realization of the conditions; the more delicate\nthe real lines are, that is, the more they approach the condition of\nright lines, the nearer will the relation of the two angles approach\nto perfect equality. This conviction is founded on the principle of\ncontradiction, which would be false if the proposition were not true;\nand it is confirmed by experience, so far as it touches the conditions\nof the ideal order.\n\n184. What is there in reality which corresponds to this proposition? An\nexisting or real line is an order of beings; two lines which intersect\neach other are two orders of beings with a determinate relation; the\nangle is the result of this relation, or, rather, it is the relation\nitself; the equality of the opposite angle is the correspondence of\nthese relations in the ratio of equality by the continuation of the\nsame order in another sense. These relations between the orders and the\nbeings, and the correspondence of these orders to each other, is what\ncorresponds in reality to the pure geometrical idea, or to the idea\nseparated from all sensible representation. Since the relations of the\nidea have their corresponding objects in the relations of the reality,\ngeometry exists not only in the ideal order, but also in the real.\nSince the phenomenon or sensible representation is subject to the same\nconditions as the idea, because the order of phenomena presents certain\nrelations of the same nature as the relations of the idea and the fact;\nthe idea, the phenomenon, and the reality agree, and it is explained\nwhy the intellectual order is confirmed by experience, and experience\nreceives with confidence the direction it gives.\n\n185. This harmony must have a cause; we must look for a principle which\nis the sufficient reason of this wonderful agreement between things so\ndistinct. Here new problems arise which overwhelm the understanding,\nbut at the same time expand and invigorate it by the grandeur of the\nspectacle presented to its view, and the immensity of the field opened\nto its investigations.\n\n\n\n\nCHAPTER XXVI.\n\nCHARACTER OF THE RELATIONS OF THE REAL ORDER TO THE PHENOMENAL.\n\n\n186. Is the agreement of the idea, the phenomenon, and the reality\nnecessary, is it founded on the essence of things, or has it been\nfreely established by the will of the Creator?\n\nIf the world had no other reality than that expressed by the sensible\nrepresentation, if the appearances were an exact copy of the essence\nof things, we should have to say that this agreement is unalterable,\nthat things are what they appear, and that if we suppose them to exist,\nit is absolutely necessary that they should be just what they appear;\nfor nothing can be in contradiction with its constitutive notion. That\nwhich now is extended, would be necessarily extended, and could not but\nbe extended in the _same manner_ in which it appears to us, and under\nthe _same conditions_; the relation of bodies to each other would be\nnecessarily subject to the same phenomenal laws, and all which does not\ncome under this order would be a contradiction, and beyond the limit of\nomnipotence.\n\n187. Bodies are presented to us in the sensible intuition with a\ndeterminate magnitude, and in a certain fixed relation which we\ncalculate by comparison with an immovable extension, such as we imagine\nspace. By magnitude, bodies occupy a certain space, determinate,\nthough changeable by motion; by the relation of magnitudes they occupy\na greater or smaller place, and mutually exclude each other; this\nexclusion is called impenetrability. The question to be examined here\nis, whether the determination of magnitudes, and their relation in\nrespect to the occupation of place, are things absolutely necessary, so\nthat their alteration involves a contradiction, or not. I answer that\nthey are not.\n\n188. Relation to place considered as a portion of pure space,\nmeans nothing; for I have already shown that this space is only\nan abstraction of our understanding, and that in itself it has no\nreality,--it is nothing. Therefore the relation to it must be nothing\nalso, because the relation is destroyed if one of the terms is nothing.\nTherefore, the relations of bodies to place can only be the relations\nof bodies to one another.\n\n189. This is the principal thing to be noticed in this question.\nThe understanding gets confused when it begins by supposing space\nan absolute nature with necessary relation to all bodies. We must\nremember the doctrine of the chapters,[53] where we explained how the\nidea of space is generated in us, what object corresponds to this idea\nin reality, and how; and we shall easily perceive that the absolute\nand essential relations which we think we discover between bodies\nand a _vacant and real_ capacity, are illusions of our imagination,\nin consequence of our not sufficiently purifying the ideal order by\nseparating from it all sensible impressions. We cannot understand so\nmuch as the meaning of these questions, if we do not make an attempt at\nthis separation as far as is possible to our nature. If this is done,\nthen the questions proposed in the following chapters will appear very\nphilosophical, and their solution will seem probable, if not true; but\nthey must seem absurd, if we confound the pure intellectual order with\nthe sensible. We cannot admit the idealism which destroys the real\nworld; but the empiricism which annihilates the ideal order, is equally\nobjectionable. If we cannot rise above the sensible representations,\nlet us renounce philosophy, give up thinking, and confine ourselves to\nsensation.\n\n[53] XII., XIII., XIV., and XV.\n\n\n\n\nCHAPTER XXVII.\n\nWHETHER EVERY THING MUST BE IN SOME PLACE.\n\n\n190. Is it necessary that whatever exists should be in some place?\nThis question may seem strange, but it is profoundly philosophical.\n_To be_ is not the same as _to be in a place_. To be, whether taken\nsubstantively as signifying to exist, or copulatively, as expressing\nthe relation of the predicate to the subject, does not involve the\nidea of being in a place. The relation of an object to place is not\nnecessary to it; for it is not contained in the notion of object. It is\nsomething added to the object, whether it is given to the object with\nmore or less foundation by ourselves, or the object has it in reality\nby communication from some other.\n\nThe imagination can represent nothing which does not occupy a place,\nbut the understanding may conceive things that are not situated in\nany place. When we reflect on the essence of objects, what position\ndoes our mind give them? The intellectual act is always accompanied\nby sensible representations, which sometimes assist it, and sometimes\nembarrass and confuse it; but in either case the act of the\nunderstanding is always distinct from these representations.\n\n191. There is no reason for saying that every thing must occupy a\nplace. The imagination cannot see how any thing can exist otherwise,\nbut the understanding finds no absurdity in it, and it is in accordance\nwith the principles of philosophy. If place considered in itself is\nonly a part of space terminated by a surface, and space abstracted from\nbodies is nothing, the relation to place or to points in space must be\nnothing. We must have bodies in order to have a term of the relation;\ntherefore, if we suppose a being which has no relation to bodies, it is\nnot necessary that it should be in any place.\n\n192. The relation of a being to bodies may be of three kinds: that of\ncommensuration, as is the relation of lines, surfaces, and solids to\neach other; that of generation, as we conceive the line generated by\nthe point; and that of action in general, as we conceive the relation\nof pure spirits to matter. The first cannot exist if the object has\nno dimensions; for then it cannot be measured; the second can exist\nonly in unextended or infinitesimal points, from which extension is\ngenerated; therefore these two relations can only exist between bodies,\nor their generative elements. Therefore, nothing which is not a body or\nan element of body, can occupy _place_ under either of these aspects.\nAs to the third relation, that of action of a cause upon a body, it\nmay be found in all agents capable of acting upon matter; but it is\nevident that the position which results from this, is something very\ndifferent from that which we conceive in bodies or their elements; it\nis something of a wholly distinct order, and belongs rather to the pure\nidea of causality than to the intuition of space.\n\n193. We can conceive a being which is not a body, nor an element of\nbody, and which does not exercise any action on bodies; in this case,\nthis being has none of the three relations of which we have spoken,\nconsequently it is not in any place, and to say that it is here, or\nthat it is there, that it is near or distant, would be using words\nwithout meaning.\n\n194. Viewed from the point of this doctrine, the following questions\nare easy to answer:\n\nWhere must a pure spirit be which has no relation of causality nor\ninfluence of any kind upon the corporeal world? Nowhere. The answer\nwill not seem strange to one who understands that the question is\nabsurd. In the case supposed, there is no _where_, for this involves a\nrelation and there are no relations here.\n\nWhere would the pure spirits be if the world did not exist? Nowhere,\nunless we have a mind to say they would be in themselves. But, the word\n_to be_ does not mean the position of which we are speaking here, but\nonly the existence of the spirit, or its identity with itself.\n\nWhere was God before the world was created? _He was_, but he was not in\n_any place_; for he has no parts.\n\n195. I wish here to expose an error of Kant. This philosopher believed\nthat space was conceived by us as a condition of all existence in\ngeneral, and on this he founded one of his arguments that space was a\npurely subjective form. In the second edition of his _Critic of pure\nReason_, explaining the subjectiveness of space, he seems to hold,\nthat we do not even conceive things in the pure intellectual order,\nwithout referring them to space. He observes that in natural theology,\nwhen treating of things which cannot be the object of intuition either\nfor us or for themselves, we are very careful not to attribute to\nthis intuition or manner of perception time and space, which are the\nconditions of human intuition. \"But,\" he adds, \"by what right do we\nproceed thus, when time and space have already been established as\nthe forms of things in themselves, and conditions of their existence\n_a priori_, subsisting still after all else has been annihilated by\nthought? As conditions of all existence in general, they must be the\nconditions of the existence of God. If we do not make space and time\nthe objective forms of _all_ things, it _only remains_ for us to make\nthem the subjective forms of our mode of intuition, as well internal\nas external.\" Kant is right in saying that space and time ought not\nto be considered as real forms, not susceptible of annihilation, and\ntherefore necessary and eternal; but I do not see the necessity of the\ndisjunctive by which he asserts that if we do not make space and time\nthe objective forms of _all_ things, we must make them the subjective\nforms, and that, otherwise, we should make space and time conditions of\nthe existence of God.\n\n196. We regard space as an actual condition of things, which occupy\nplace, but not of all things. We conceive existence in pure spirits\nwithout the necessity of any relation to place, and, consequently,\nindependent of all position in space.\n\nOn this point, as on all relating to the pure intellectual order, we\nfind in the theologians doctrines which are highly important, and\ndeserve to be consulted by all who wish to go deeply into philosophical\nquestions. The author of the _Critic of Pure Reason_ would have found\nthere some observations which would have cleared up the difficulties\nwhich embarrassed him. He would have found how incorrect it is to\nsay that space is a condition of the existence of all things, in the\nbeautiful as well as profound theory by which many of the scholastics\nexplain the presence of God in the corporeal world, and the presence of\nthe angels in different places, their motion from one point to another\nwithout passing through the intermediate points, and the manner in\nwhich the soul is wholly in the whole body and in every part of the\nbody. In these works, unfortunately so little consulted, the German\nphilosopher would have learned that the presence of a spirit in a\nplace is something different from the presence of a body, and has no\nrelation to the intuition of space, whether regarded as the basis of\nsensible representations or as a geometrical idea.\n\n197. St. Thomas[54] asks if God is in all things, and answers that he\nis. In proving this assertion he does not consider the necessity of\nevery thing being in some place, but on the contrary seems rather to\nforget the idea of space, and regards only causality.\n\n[54] _Sum. Theol._ P. I., Q. viii., Art. 1.\n\n\"As God,\" he says, \"is being itself by his essence, created being must\nbe his effect, as to burn is the effect of fire. But God causes this\neffect in things not only when they begin to be, but as long as they\nare preserved in being; thus the light is caused in the air by the sun\nas long as air remains illuminated. As long therefore as things retain\ntheir being, God is necessarily present to them, according to the\nmanner in which they have their being. But being is that which is most\ninternal, and most closely inherent in every thing because it is the\nform of all that is in it, God therefore is in all things internally.\"\n\nTo be situated in space is to be contained in it; so, at least, we\nconceive whatever we consider situated in space. St. Thomas rejects\nthis meaning as applied to spiritual beings, and says, that although\ncorporeal beings are contained in things, spiritual beings on the\ncontrary contain the things in which they are.\n\nIn the second article he asks whether God is in all places (_ubique_);\nand, he says, that as God is in all things, giving them being and\nthe power of acting, so he is in all places giving them being and\ncapacity (_virtutem locativam_). He states as an objection that\nincorporeal things are not in any place, and answers in the following\nphilosophical words: \"Incorporeal things are not in place by the\ncontact of measurable quantity, like bodies; but by the contact of\nactivity (_virtutis_).\" Then explaining how the indivisible can be in\ndifferent places, he says: \"The indivisible is of two kinds; first,\nit is the limit of the continued, as a point in permanent things, and\na moment in successive things. The indivisible in permanent things,\ncannot be in different parts of place or in different places, because\nit has a determinate position; and in the same manner the indivisible\nin action or in motion cannot be in different parts of time, because\nit has a determinate order in action or motion. But there is another\nindivisible which is _beyond all kind of continuation_, and in this\nsense incorporeal substances, as God, the angels, and the soul, are\ncalled indivisible. The indivisible in this manner, is not applied to\nthe continued as _any thing which belongs to it_, but only as reaching\nit by its activity; therefore as its activity may extend to one or\nmany, to the small or to the great, it may be in one place or in many\nplaces, in a small place or in a great place.\"\n\nWhat can be clearer, relatively to the intuition of space, than that\nwhen any thing is in a place it cannot be out of that place? But the\nholy Doctor, rising above sensible representations, boldly maintains\nthat God may be whole in the whole, and in every part of the whole,\nas the soul is whole in every part of the body. And why? Because\nwhat is called totality in corporeal things relates to quantity, but\nthe totality of incorporeal things relates to essence, and cannot be\nmeasured by quantity, and is not confined to any place.\n\nIn the _Treatise on the Angels_,[55] he says that the expression to be\nin place is used equivocally (_\u0153quivoce_),[56] when applied to angels\nand bodies. Bodies are in place by the contact of measurable quantity,\nbut angels by virtual quantity, that is to say, by the action which\nthey may exercise upon a body. We cannot, therefore, say that an angel\nhas a position in the continued (_quod habeat situm in continuo_). In\nthe _Treatise on the Soul_[57] he maintains that the soul is whole\nin every part of the body. He distinguishes the totality of essence\nfrom the totality of quantity, and makes use of an argument similar\nto that which he used with respect to the angels. The more we reflect\non this doctrine the more profound it appears; those who have made\nlight of it, have shown that they never penetrated beyond the surface\nin all that concerns the relations of spiritual to corporeal things.\nIt is generally dangerous to laugh at opinions held by great men;\nfor if they are not certain, they have, at least, powerful arguments\nin their favor. Nothing is more contrary to sensible representations\nthan the possibility of any thing being in different places at the\nsame time, but we shall find nothing more in conformity with the\nprinciples of sound philosophy than this possibility, after we have\nprofoundly analyzed the relations of extension with unextended things,\nand discovered the difference between the position of quantity and the\nposition of causality.\n\n[55] _Sum. Theol._ Q. LII., Art. I.\n\n[56] Dialecticians understand by an _equivocal_ term one which in\ndifferent things has an entirely different meaning. They give as an\nexample the term LION which is applied _equivocally_ to an animal, or\na constellation. \u00c6quivoca sunt quorum nomen commune est, et ratio per\nnomen significata, simpliciter diversa, is the scholastic definition.\n\n[57] _Sum. Theol._ Q. lxxvi., Art. 8.\n\n198. From these doctrines it may be concluded, that to be in space\nis not a general condition of all existences, even according to the\nmanner of existences; for we can conceive existences without relation\nto any place. Many have confounded imagination with understanding\non this point, and believed that what is impossible for the former\nis equally so for the latter. It is certain that we can _imagine_\nnothing without referring it to points of space, and even in purely\nintellectual objects there is always a sensible representation, but\nthe understanding regards these representations as false and does\nnot conform to them. As imagination is a sort of continuation of\nsensibility, or an internal sense, and the basis of sensations is\nextension; it is impossible for us to exercise this internal sense,\nwithout the presence of space, which, as we have shown, is only the\nidea of extension in general. Position in space is consequently a\ngeneral condition of all things, as perceived by the senses, but not as\nperceived by the intellect.\n\n\n\n\nCHAPTER XXVIII.\n\nCONTINGENCY OF CORPOREAL RELATIONS.\n\n\n199. Position in place is the relation of a body to other bodies.\nIs this relation necessary? I distinguish: conditionally, yes;\nessentially, no. God has established this relation, and therefore it is\nnecessary; but God might have ordered it otherwise, and can even now\nchange it, without varying the essence of things.\n\nIf we admit, as we must, a correspondence between the subjective and\nthe objective, or between the appearance and the reality, we cannot\ndeny that the relations of bodies are constant, and this constancy must\nproceed from some necessity. But that the existing order is subject\nto fixed laws, does not prove that these laws have their root in the\nessence of things, in such a manner that, supposing the existence of\nobjects, their relations could not have been very different from what\nthey actually are.\n\n200. In order to assert that the existing order of the universe is\nintrinsically necessary, we must know the essence of things; but this\nis not possible for us, because objects are not immediately present to\nour understanding, and we see them only under one aspect, that which\nplaces them in relation with our sensitive faculties. The best proof of\nour ignorance of the essence of bodies is the great division of opinion\non this subject. Some maintain that the essence of bodies is extension\nor dimensions; and others that extension is merely an accident, not\nonly distinct, but even separable from corporeal substance.\n\nThe great obscurity in which the investigation of the constitutive\nelements of bodies is involved, proves that their essence is unknown\nto us, and that we know nothing of them except their relation to our\nsensibility.\n\n201. It is not necessary that the aspect under which being is presented\nto us should contain its whole nature. To say that bodies contain\nnothing besides what we perceive in them, is to make our faculties\nthe type of things in themselves, a ridiculous pretension in a being\nwhich finds its activity limited at every step and is almost always\npassive in its relations to bodies, and which, in order to exercise\nits faculties externally, is forced to submit to the laws of the\nexternal world, or else to encounter obstacles which are absolutely\ninsurmountable.\n\nIf we are ignorant of the essence of bodies we can have no certain\nknowledge of what is intrinsically necessary in them; with the\nexception of composition, which even the sensible order presents to\nus, and which we cannot take from bodies without seeming to run into\na contradiction. Simplicity and composition in the same object are\nincompatible and contradictory.\n\n202. Hence, in all that pertains to the relations of bodies we must\nabstain from judging absolutely, and speak only conditionally. We may\nsay: \"This happens now; this must happen according to the order now\nestablished;\" but we cannot say: \"This happens, and it is absolutely\nnecessary that it should happen.\" The transition from the first\nproposition to the second, implies the knowledge of what no man can\nknow, that the aspect under which the external world is presented to us\nis the image of its essence.\n\n203. One of the greatest errors of Descartes was, that he did not make\nsufficient account of this difference: he placed the essence of bodies\nin dimensions, which is to confound the real world with the phenomenal,\nand to take one aspect of things for their nature. It is true that\nwhatever affects us has extension, and that extension is the basis of\nthe relations of our sensibility with the external world; but it does\nnot follow that the essence of this world is nothing more than what\nis presented to us in its dimensions. We might as well say that the\nessence of man is the lines which mark his form.\n\n204. The different aspects under which the external world is presented\nto our senses, ought to prevent us from confounding what is absolute\nin it with what is relative. A man deprived of one sense would not\nreason well if he should conclude that the world has no other aspects\nthan those which he perceives. What do we know of the manner in which\nobjects are presented to pure spirits, or of the many other phases\nwhich they might offer to our sensibility?\n\nLet us then leave nature its secrets; and let us not limit omnipotence\nby saying, that the order of the world is so intrinsically necessary\nthat its present relations cannot be changed without contradiction.\nWhen we examine the possibility of a new order of relations between\nthe beings which we call bodies, let us not settle the question too\nquickly, taking for our only type of the possible the vain impotence\nof our faculties. What should we think of a blind man who should laugh\nat those who see, if he heard them speak of the relations of objects\nas seen? Yet we present the same spectacle to a pure spirit when we\ntalk of the impossibility of an order different from what our senses\nperceive.\n\n205. The principles of physical science are in great part conditional;\nfor they are true only on the supposition of the reality of the data\nfurnished by experience. If position and relation to place are not\nessential to bodies, distance and motion are conditional facts true\nonly under certain suppositions. All the natural sciences, as we have\nseen, are reduced to the calculation of extension and motion; they\ndo not reach the essence of things, but are limited to one aspect,\nthat presented by experience. In these sciences there is consequently\nnothing strictly absolute; in this respect, they are far below\nmetaphysics, which knows things that are absolutely necessary. A\nfurther explanation of this doctrine is required, and will be given in\nthe following chapters.\n\n\n\n\nCHAPTER XXIX.\n\nSOLUTION OF TWO DIFFICULTIES.\n\n\n206. Must not the theory which supposes the relations of bodies to be\nvariable, put an end to all the natural sciences? Can there be science\nwithout a necessary object? and can there be a necessity which is\ncompatible with variability?\n\nThe natural sciences have two parts: one physical, and the other\ngeometrical. The first supposes the data furnished by experience;\nthe second forms its calculations relative to these data. Change the\nrelations of external beings, and the data will be different, you will\nhave a new experience producing a new physical science: the calculation\nwill be the same, only new results will be obtained from the new data.\nThe difficulty thus disappears. All the physical sciences are based on\nobservation, all their combinations are made from data furnished by\nexperience; therefore the physical sciences are not wholly absolute,\nbut they have a part which is conditional. The theory of universal\ngravitation is developed as a body of geometrical science, but it\nstarts from the data furnished by experience. Destroy these data and\nfrom a body of physical science it becomes a body of pure geometry. In\nmechanics, the problems of the composition and decomposition of forces\nhave a physical signification, inasmuch as they presuppose the data of\nexperience; suppress these data and there remains only a composition of\nlines which mean nothing when we call them forces. Therefore mechanics\nis only a system of geometrical applications.\n\n207. Here another difficulty arises which is apparently more serious\nthan the other. If the relations of bodies are not essential, but are\nsubject to variation; if our calculations upon them are not founded\nupon data which are intrinsically necessary, it seems that geometry\nis destroyed, or limited in such a way to the ideal order, that it\ncannot be sure that on descending to the field of experience it will\nnot find that false which it regarded as true, and that true which it\nreputed false. For example, the distances of bodies are calculated by\nconsiderations of geometry: if the relation of distance is variable,\nand a body may be in many places at the same time, geometry turns out\nfalse. Such a supposition is no more than the application of the\nforegoing theory; for, if the relations are variable, this variation\nmay affect distance, which is only a relation. I said this difficulty\nwas more serious than the other, because it leaves the field of\nexperience, and attacks the order of our ideas, an order which we\nmust hold to be indestructible, unless we wish to give up our reason.\nWhat would become of our reason if geometry were contradicted by the\nreality? what would become of an order of ideas in contradiction\nto facts? Still I repeat that the force of this difficulty is only\napparent, and if analyzed will be found of no more weight than the\nobjection which we have already answered.\n\nA body which is a hundred yards distant from another, cannot be only\none yard distant; geometry would be opposed to it. But if the relations\nof bodies are variable this proposition can mean nothing with respect\nto the reality. Therefore geometry is false. I admit the consequence;\nbut the principle on which it is based involves a supposition contrary\nto my theory. If you alter or destroy the relations of bodies, you\ndestroy distance, which is a relation, consequently you cannot have\na distance of one hundred yards, nor of one yard, nor any distance\nat all, and if there is no distance there is no contradiction. If,\nthen, you ask how great is the distance between them, your question is\nabsurd; for it supposes a distance, whereas there is no distance at all.\n\n208. This solution rests on a fundamental principle which we ought\nnever to lose sight of. Geometrical truth is true in reality when the\nconditions of geometry exist in reality; if these conditions do not\nexist, there is no real geometry. There is nothing strange in this:\nin fact, the same occurs in the purely ideal order; even there,\ngeometry rests on certain postulates, without which it is impossible.\nTwo triangles with the same base and altitude are equivalent to each\nother. This is a true proposition, but only on the supposition that\nthere are those orders of points which are called lines, and that the\nlines form angles, and are united at three points. If these relations\nare not presupposed, the geometrical theorem has no meaning.\n\n209. Geometry in itself, or in the purely ideal order, is founded\non the principle of contradiction. The truth of this principle\nbeing absolutely necessary, that of geometry is equally so. But the\nprinciple of contradiction, like all purely ideal principles, abstracts\nexistence, and is applied to nothing in practice, unless we suppose\nsome fact to support it. Yes and no at the same time are impossible;\nbut the principle determines nothing for or against either of the\nextremes. It only affirms that one excludes the other; if we suppose\n_yes_, it excludes _no_, and if we suppose _no_, it excludes _yes_;\nthat is to say, it always needs a condition, a datum which only\nexperience can furnish.\n\nIt is the same with geometry. All its theorems and problems refer to\nthe ideal field within us, where there are certain conditions which\nlead to certain results, by virtue of the principle of contradiction:\nwhenever the conditions exist, the results are true; but if the former\nfail the latter are false. Ideal sciences consider the _connection_ of\nconclusions with principles in the order of possibility, but take no\nnote of facts. If the connection is admitted the science is true.\n\n\n\n\nCHAPTER XXX.\n\nPASSIVE SENSIBILITY.\n\n\n210. Active sensibility, or the faculty of perceiving by the senses,\nhas been a subject of great dispute among philosophers. Passive\nsensibility, or the capacity of an object to be perceived, is a\nquestion of not less interest.\n\nCan every thing which exists be perceived by the senses?\n\nBefore answering this question, let us remember that to be perceived by\nthe senses may be understood in two ways: First, it may mean, to cause\nan impression in a sensitive being; and secondly, to be the immediate\nobject of sensible intuition. The first is true of every being capable\nof producing the impression; the second is true only of those beings\nwhich unite the conditions which the intuition supposes.\n\n211. To produce an impression is simply _to cause_; and causality is\nnot repugnant to simple beings. There is, therefore, no absurdity in\nsupposing that pure spirits can produce sensible impressions: were it\notherwise God could not act upon our soul, causing an impression in\nit, without the mediation of bodies. This causality cannot be called\npassive sensibility; the being which has it is not perceived by the\nsenses. The relation of the sensation to the being which produces it\nwould be only that of an effect to its cause.\n\n212. To be the immediate object of sensible intuition, is to be\npresented to this intuition as an original to the copy. Under this\nview, only the extended can be perceived by the senses; that is to\nsay, multiplicity combined with continuity is an absolutely necessary\ncondition of our sensitive faculties in relation to external objects.\n\n213. In this manner, it is a manifest contradiction to say that the\nsimple can be sensible. Instinct and reason force us to suppose a real\nobject of sensible intuition. This intuition is referred to the object\nas to something essentially composite, belonging to the order which\nwe call continuity. If we make this object simple, it ceases to be\nsensible; and we both affirm and deny its sensible objectiveness. It is\na contradiction to suppose a faculty in act, and at the same time to\ndeprive it of the conditions to which its action is necessarily subject.\n\n214. It may be said, that there is no necessity of transferring to the\nobject the conditions of the subject, and therefore a simple object may\nbe presented to the senses. But this is to elude the question at issue.\nFor, either the sensible intuition is referred to the object, or it is\nnot; if it is, the object cannot be simple; if it is not, we fall into\nidealism, which we have so often combated in the course of this work.\n\n215. If you answer, that our soul, which is simple, has the\nrepresentation of the composite, I reply, that the objective\nrepresentation is not the same thing as the subjective perception of\nthe composite; nor the presentation of the object as multiple the\nsame thing as the perception of the multiple. Our soul perceives the\nmultiple, and for this reason must itself be one, or it could not\nperceive that which is multiple. So much for the subjective; as to the\nobjective, we must remark, that our sensible representations do not\nalways proceed from real objects; but they always refer to objects\nwhich are at least possible; that is to say, the intuition is never\nentirely void; and when it has no object in reality, it finds one in\npossibility.\n\n216. The external world, as involving multiplicity, or a collection of\nmany beings, and as susceptible of this order which we call continuity,\nmay be the object of sensible intuition, as we experience in reality.\nBut this passive sensibility is not intrinsically necessary to it:\nI mean that God could so have disposed the collection of beings\nconstituting the universe as not to be sensible. This is based on the\nvariability of the relations of bodies; for, it is evident that if\nthese relations did not exist, or were not subject to the conditions\nrequired by sensible representation, this representation would be\nimpossible, and the world not sensible.\n\n217. Experience confirms this conclusion which is obtained from\ntranscendental philosophy. We find a slight alteration continually\nchanging sensible bodies into insensible, and making sensible those\nthat were insensible. The condensation of the air makes it visible; and\nits rarefaction invisible. A liquid body is tangible, but it ceases to\nbe so when converted into vapor. The same variety which is caused by\nthe alteration of the object may also proceed from a modification of\nthe organ. A proof of this is found in what happens to the sight when\naided by certain instruments. If, then, these transitions from sensible\nto insensible are now possible, without infringement of the fundamental\nlaws of the relations of bodies, why could there not be a radical\nchange in these relations which should make bodies wholly insensible?\n\n218. By the variation of the relations of the beings which compose\nthe corporeal universe, the sensible might become insensible; and, on\nthe other hand, there are many insensible beings which by a different\narrangement might be made sensible. To a certain extent we have\nsomething besides idle conjectures on this matter: facts speak; in\nproportion as the field of experience is expanded, new phenomena are\ndiscovered; thus magnetic attraction, electricity, and galvanism, have\nbeen added to experimental science.\n\nIn these phenomena there are agents at work which are not perceptible\nto the senses; why may they not be disposed in such way as to be\nperceived like other bodies? Where is the limit of these agents? We\nknow not; but reasoning from analogy we may believe that there are many\nothers whose existence is not known to us.\n\nThe perfection of a sensitive organ by means of instruments, is an\narrangement by which we vary the ordinary system of the relations\nof our body to those around us. This perfectibility is indefinite,\nand the farther we advance, the greater do we find its extension. It\nis therefore probable, that in the universe there are many beings\nwhich are imperceptible to our senses, but which a modification of\nour organs, or a change of some of the laws of nature would render\nsensible. What a vast field of bold conjectures and sublime meditations!\n\n\n\n\nCHAPTER XXXI.\n\nPOSSIBILITY OF A GREATER SPHERE IN ACTIVE SENSIBILITY.\n\n\n219. Having treated of passive sensibility in the order of possibles,\na similar question naturally arises with respect to the active\nsensibility of beings subject to different conditions from those of our\nsoul while united to the body.\n\nI speak only of possibility, for, limited to what experience teaches\nus, we know not what may be in the sphere of beings with which we have\nno communication. Whatever we know of them is by divine revelation; and\nthe object of revelation is not to teach us philosophy, but virtue.\n\n220. To examine how far active sensibility is possible in an order\ndifferent from that of our experience, not only raises curious and\ninteresting questions, but it also gives an opportunity to explain\nby new reflections, the nature of this phenomenon in its relations to\nbodily organization. There is a special reason why we should seek to\ninvestigate this question. It consists in the interest inspired by\nevery thing which relates to a state of existence into which we must\nsoon enter. Short are the moments allotted to man to dwell in this\nworld. We all hasten with astonishing rapidity to the final instant\nwhen the fragile organization which envelops our mortal spirit shall\ndissolve, and crumble into dust,--when the being which feels, thinks,\nand wills within us, shall pass to a new state, and be separated from\nthe bodily organization. What will then be its faculties? This is a\nquestion which we cannot be indifferent to; for it concerns us, and the\nstate of our future existence.\n\n221. If we are asked whether a pure spirit is capable of sensible\nperception, we must answer negatively; because we are treating of\nactive sensibility, which is not possible without the mediation of a\nbody. I believe that some explanation of the question may be given. But\nwe must first of all determine the meaning of the words. Sometimes we\nunderstand by a pure spirit, one which is not united to a body; but,\nmore strictly speaking, the term is confined to a spirit which neither\nis united to a body, nor destined to this union. Thus the human soul is\na spirit, but not a pure spirit; for it is either actually united to a\nbody or is destined to this union.\n\nIt might appear at first sight that as we are limiting ourselves to\nthe sphere of possibility, there is no difference between the two\nacceptations of the term; for, if it is not essentially repugnant to\nthe soul when separated from the body, to have sensible intuition, it\nwill not be so to other spirits. The parity is not certain; still, for\nthe present, when speaking of pure spirits in general, I shall include\nsouls separated from bodies.\n\n222. What do we understand by sensing? This word may mean two things.\nIt may mean the receiving of an impression by means of bodily organs;\nor it may mean simply the experiencing of the impression, independently\nof the bodily organ. For example: I see an object. Here is the\naffection called _seeing_, and the mechanism by which the object\ntransmits light to the retina, and a certain impression to the brain.\nThese are two very different things; the first is a fact of my mind;\nthe second a modification of my body.\n\n223. If by sensing is meant the receiving of the impression of a bodily\norgan, it is clear that a spirit which has no body cannot sense; but\nif by it is meant only the subjective affection abstracted from the\nmedium by which it is produced or communicated, then the question is\ndifferent, and the existence or non-existence of bodies cannot affect\nits answer either affirmatively or negatively.\n\n224. The question then becomes this: Can a pure spirit have the various\naffections and representations which we call sensible?\n\nSimplicity is not opposed to the sensitive faculty. Our soul senses,\nand still it is simple. The body aids it in the exercise of the\nsensitive faculties; but this aid is instrumental, not, however, in\nsuch a manner that the soul senses _by the body_, as an action is\nperformed by means of the instrument. That which senses is the soul\nitself, and the instrumental action of the body consists in providing\ncertain conditions from which sensation follows, by a physical or\noccasional influx. Therefore, the simplicity of a pure spirit is no\nargument against the sensitive faculties. Such an argument would prove\ntoo much; consequently, it proves nothing.\n\n225. Hence there would be no _intrinsical_ repugnance in God\ncommunicating to a pure spirit sensitive faculties; whether\nrepresentative like those which place us in relation with the corporeal\nworld, or purely subjective, like those of pleasure or pain.\n\n226. Although in the present order these functions depend on certain\nconditions to which bodies are subject, considered in themselves,\ninasmuch as they are a modification of the soul, they have no essential\nrelation to the corporeal world. It would therefore seem contrary to\nthe principles of sound philosophy to say, that the soul separated\nfrom the body could not experience affections similar to those it has\nin this life. If this is not repugnant to the soul in its separate\nexistence, why should it be so to other spirits?\n\nThe sensitive faculties are a sort of inferior order of perception.\nWe see them in beings united to bodies, but they are not exercised\nimmediately by a bodily organ. So far from contradicting simplicity,\nthey require it; and therefore we have seen[58] that matter is\nincapable of sensation. Many grave philosophers are of opinion that the\ncausality of bodies with respect to sensations, is only occasional.\nThis opinion is founded on the difficulty of explaining how a composite\nbeing can produce affections of any kind in a simple being. Instead\nof a repugnance between simplicity and the sensitive faculties, there\nis, on the contrary, a necessary connection. No composite being can be\nsensitive.\n\n[58] B. II., Ch. II.\n\n227. Perhaps it may now be thought that there is no longer any doubt of\nthe possibility of sensation independently of the bodily organs; and\nthat to hold the contrary, it would be necessary to maintain that God\ncan not produce immediately that which he produces by means of second\ncauses. The observations which we have made may seem to have exhausted\nthe matter, but if we reflect on it, we shall find that we have scarce\nentered on it.\n\nIt must not be forgotten that we are examining the possibility of\nsensitive faculties, in relation to one attribute only, that of\nsimplicity. This greatly limits the question, as it leaves it to be\nsolved under one aspect only. Simplicity is a negative property. When\nwe say that any thing is simple, we deny that it has parts, but we\naffirm none of its properties; we say what it is not, not what it is.\nTherefore, in maintaining that sensitive faculties are not repugnant to\na pure spirit, we ought to restrict the proposition; we should express\nour meaning more exactly, if instead of saying \"sensitive faculties are\nnot repugnant to a pure spirit,\" we should say, \"sensitive faculties\nare not repugnant to the _simplicity_ of a pure spirit.\"\n\n228. This last observation seems to me to present the question in its\ntrue point of view. Any other expression of it seems only to confuse\nideas and raise problems which we have not sufficient data to solve.\nIn fact, how do we know but what the repugnance which does not exist\nbetween sensibility and simplicity, may exist between sensibility and\nsome attribute which we know nothing about? This argument is not valid\nfor the human soul, because we already know that the soul is capable of\nsensing; but it is valid for other spirits, whose essence is unknown to\nus, and the character of whose perceptive faculties experience has not\ndiscovered to us.\n\n229. One of the distinctive marks of sensitive perception is the\nreference to individual objects, not in what concerns their essence,\nbut inasmuch as they are arranged in a certain order, the variations\nof which do not affect their internal nature. Extension itself, which\nboth instinct and reflection teach us to regard as objective, is rather\na result of the relations of the beings which form the composite\nextended object, than those beings themselves. The sensitive faculties\nare the lowest grade in the order of perception. Their sole function\nis to make known to their possessor a certain arrangement of external\nobjects, but they teach him nothing concerning the nature of those\nobjects. Pure spirits are a grade higher in the scale of perceptive\nbeings, and one of the characteristics of intelligence is, that it\npenetrates to the inward nature of things. Therefore it might easily\nhappen that the sensible faculties are repugnant to intelligences of\na higher order than ours, not by reason of their simplicity, but on\naccount of the different manner of their perception.\n\n230. Reasoning by analogy from what takes place within ourselves, we\nare confirmed in this opinion. Sensible representations are often\npowerful auxiliaries to purely intellectual perception; but they just\nas often embarrass and confuse it. In meditating on very abstract\nmatters sensible representations are a hinderance to the understanding,\nfrom which we should be glad to free ourselves. Every one has\nexperienced this to be so. They are like shadows which come between\nthe eye of the intellect and the object: the necessity of continually\nremoving them delays and weakens our perception. Thus, we propose, for\nexample, to think of causality. No sensible representation should find\nplace in this idea in the abstract, yet in spite of all our efforts\nthe representation haunts us. At one time it is the word _causality_,\nwritten or spoken; at another, the image of a man doing something,\nor of any other agent. The sensible representation is always in our\nway, and we cannot free ourselves from its presence. The understanding\nis forced to repeat continually to itself, \"This is not the idea of\ncausality; it is only an image, a comparison, an expression;\" in order\nto defend itself against illusions, which would make it confound the\nparticular with the universal, the contingent with the necessary, the\nphenomenal with the real.\n\n231. We must conclude from this that a repugnance of sensitive\nfaculties to the nature of a pure spirit, might proceed from the\ncharacter of its intelligence, which by reason of its perfection\nrejects the duality of perception which exists in us. The object of\nthe understanding is the essence of the thing understood, _quidditas_,\nas the scholastics called it. Sensible representations tell us nothing\nof this essence. They offer only one aspect of things, and even this\nis limited to the perception of extension; for as regards the other\nsensations, they are a subjective fact which instinct and reason teach\nus to attribute to external causes, rather than a perception of the\nreal disposition of things.\n\n232. This suggests another observation which supports the conjecture\nthat the elevation of intelligence above a certain degree makes it\nincompatible with sensitive faculties. Sensations would tell us nothing\neven of this aspect and disposition of things if they did not have\nextension for their basis. To what should we reduce the corporeal world\nif we supposed it unextended? Since extension, as we have shown,[59]\nalthough the basis of some sensations, is not the direct and immediate\nobject of sensation; that which in the sensitive faculties makes us\nperceive something of the reality of objects, is not strictly sensible.\nTherefore, if it is the character of intellectual perception to know\nthe reality of the object, the more elevated an intelligence is the\nfarther it will be from sensation, and there may be a subject in which\nintellectual faculties are incompatible with sensitive faculties.\n\n[59] Ch. II.\n\n233. We shall better understand the force of this observation by\ncasting a glance at the scale of beings, and noting the difference in\nthem in proportion to their perfection. The isolation of a being is a\nmark of its imperfection. The lowest idea of an object is that which we\nform when we conceive it absolutely limited to existence, completely\ninert, without either internal or external activity. A stone has\nexistence and a determinate form; it is what it was made, and nothing\nmore; it preserves the form which was given to it, but it has no\nactivity to communicate with other beings, no consciousness of what it\nis; in all its relations it is passive; it receives but cannot give.\n\n234. In proportion as beings rise in the scale of perfection, this\nisolation ceases; active properties are combined with the passive;\nsuch we conceive to be the corporeal agents, which, although they do\nnot reach the category of _living beings_, take an active part in the\nproduction of phenomena in the laboratory of nature. In these beings we\nfind besides what they _are_, what they _can do_; their relations with\nother beings are many and varied; their existence is not confined to\nthe circle of their own existence; but it expands and is communicated\nin some way to others.\n\n235. In organized beings we find a more expansive nature. Their life\nis a continual expansion. The living being extends in a measure beyond\nthe limits of its own existence; for it bears within it the germs of\nits reproduction. Its existence is not for itself alone, but for others\nalso. It is only an imperceptible link in the great chain of nature;\nbut the vibrations of this link are felt in the remotest confines of\nthe universe.\n\n236. Life is still more extended when it becomes sensation. The\nsensitive being contains in himself, as it were, the universe. By the\nconsciousness of its affections, it places itself in new relations\nwith all that acts upon it. Perception is immanent, that is to say,\nit remains in the subject, but with the subjective is combined the\nobjective, by which the universe is reflected on a point. Being does\nnot then exist in itself alone, it becomes in some manner other things.\nThere is a profound truth in the expression of the scholastics:\n\"That which knows is the thing known.\" There is a certain order in\nsensations; they are more perfect in proportion as they are less\nsubjective; the most noble are those which place us in communication\nwith objects considered in themselves,--those which are not limited\nto the experience of what the objects cause in us, but include the\nknowledge of what the objects are.\n\n237. Extension is the basis of the objectiveness of sensations, but it\nis not the direct and immediate object of sensation. Although extension\nteaches us something of the reality of beings as regards a certain\narrangement of them among themselves, it is not so much the object of a\nsensitive faculty as of intelligence. Here sensation ceases and science\ncommences. Science is not satisfied with what the objects appear. It\npenetrates to the reality; the understanding does not stop with the\nsubjective, but passes to the objective, and when it cannot reach the\nreality, it wanders in the regions of possibility.\n\n238. Thus we see that the perfection of beings is in proportion to\ntheir expansion. Accordingly as they are more perfect, they go farther\nout of their own sphere, and exercise a more extended activity. Hence\nthe highest degree of perception is the least subjective; the lowest is\nsensation, which is limited to the experience of the sentient subject.\nIntelligence which is the highest degree, abstracts experience, and\ngives its whole attention to reality, its proper object.\n\n239. If we could know the intimate nature of pure spirits, perhaps we\nshould find that the sensitive faculties are altogether incompatible\nwith the elevation of their intelligence, and that the analogy founded\non the nature of our perceptions has no value when applied to a more\nperfect order of intelligence. However this may be, we must admit that\nthe question would have been solved in a very incomplete way, if we had\nlimited it to the single aspect of simplicity. These observations on\nthe nature of intelligence ought to make us very cautious in affirming\nto be possible, what we should perhaps see to be impossible, if our\nknowledge of the nature of things were greater.\n\n240. So far we have spoken only of the _intrinsical possibility_; what\nshall we say of the reality? This is a question of fact which can only\nbe solved on data which our experience is unable to furnish, as we are\nnot in immediate communication either with souls separated from bodies,\nor with pure spirits.\n\n241. If we wish to look for an argument to prove that pure spirits\nand souls after they are separated from bodies, have no sensitive\nfaculties, we shall find it in the consideration of the end to which\nthese faculties are destined, better than by attempting to discover\nthe essence of things. The body, to which the soul is united in this\nlife, is an organization subject to the general laws of the corporeal\nuniverse. In order that the soul may rightly exercise its functions,\nit must be in constant communication with its own body and the bodies\naround it; it must have sensible intuition of the relations of\nbodies; it must be notified by pain of any disorder which occurs in\nits body, and guided by the sentiment of pleasure as by an instinct\nwhich, directed and moderated by reason, may point out to it what is\nprofitable or necessary. When the soul is no longer united to the body,\nthere is no reason why it should have these affections, as it does not\nrequire to be directed in its acts. As this applies equally to pure\nspirits, we may form a conjecture as to the cause of the difference\nwhich there must be between the state of our soul in this life, and\nthat of spiritual beings which are not united to bodies.\n\nThis argument, deduced from the final cause, is not to be considered as\na proof; at best it is only a conjecture: for we do not know how far\nthe soul in its separate existence, or pure spirits, may be in relation\nwith bodies; and consequently, we do not know whether these sensible\naffections would be useful or necessary for ends of which we have no\nconception. And even supposing that neither the soul nor pure spirits\nhave any relations with bodies, we are far from sure that sensible\naffections would be useless to them. On the contrary, so far as we can\nform an opinion on the subject, it seems that to take from the soul its\nimagination and sensation, would be to deprive it of two of its most\nbeautiful faculties; for they not only assist the understanding, but\nare often a strong motive of its acts.\n\n242. It is difficult for us to form an idea of pleasure or pain,\nwithout sensible affections. In the purely intellectual will, we\nconceive only _willing_ and _not willing_, acts of a most simple\nrelation, which do not have for us the same meaning as a pleasant or\nunpleasant affection. We often wish a thing in which we experience\npain; and as often find pleasure in what we do not wish. Therefore to\nwish and not to wish do not imply pleasure and displeasure, but are\nindependent of these affections and may exist in opposition to them.\n\n243. It might be said that the cause of this discord is in the\ndisagreement of the sensitive with the intellectual faculties. This\nis true, but it proves nothing against what I have been saying. The\npurely intellectual will, in opposition with the sensible affections,\ndoes not involve pleasure or exclude pain. The will triumphs, it is\ntrue, but it does so by virtue of its freedom. Its triumph is like\nthat of a master obliged to exact obedience by severe punishment, who\nexperiences pain at the very time when he is obtaining the execution of\nhis commands. Who can tell, then, whether the will, after this life,\nwill be accompanied by affections similar to those which it now has,\nbut purified from the grossness of the body which weighs down the soul?\nI see no intrinsical impossibility in it. If questions of philosophy\ncould be solved by sentiment, I should not hesitate to express my\nopinion that this fair and noble union of faculties which we call the\nheart, does not go down to the grave, but flies with the soul to the\nregions of immortality.\n\n244. As to the imagination,--that mysterious faculty which not only\ngives life to the real world, but possesses an inexhaustible activity\nin creating new worlds of its own, displaying before the eyes of the\nsoul rich and splendid panoramas; why should it desert the soul on\nits separation from the body? Why may not the harmony of nature be\nperceived in a similar manner hereafter? Let us not advance opinions\non secrets of which we are ignorant, but, at the same time, let us\nbeware of setting bounds to the omnipotence of God. Sound philosophy\nshould not multiply opinions beyond measure; but neither should\nit circumscribe within the limits of human reason the sphere of\npossibility.\n\n\n\n\nCHAPTER XXXII.\n\nPOSSIBILITY OF THE PENETRATION OF BODIES.\n\n\n245. The more we meditate on the corporeal world, the more we discover\nthe contingency of many of its relations, and the consequent necessity\nof recourse to a higher cause which has established them. Even those\nproperties which seem most absolute cease to appear so when submitted\nto the examination of reason. What more necessary than impenetrability?\nYet from the moment it is carefully analyzed, it becomes reduced\nto a fact of experience not founded on the nature of things, which\nconsequently may exist or cease to exist without any contradiction.\n\n246. Impenetrability is that property of bodies by which two or more\ncannot be in the same place at the same time. For those who do not\nmake pure space a reality independent of bodies this definition has no\nmeaning; for if place like pure space is nothing, to speak of _the same\nplace_ abstracted from bodies, is to speak of nothing. In that case,\nimpenetrability can only be a certain relation either of bodies or of\nideas.\n\n247. Above all, we must distinguish the real order from the purely\nideal. We may consider two kinds of impenetrability; physical\nimpenetrability, and geometrical impenetrability. The physical is that\nwhich we see in nature; the geometrical that which is found in our\nideas. Two balls of metal cannot be in the same place: this is physical\nimpenetrability. The ideas of the two balls present two extensions\nwhich mutually exclude each other in the sensible representation: this\nis geometrical impenetrability. If we imagine two balls which perfectly\ncoincide, they are no longer two, but only one; and if we imagine one\nball to occupy a part of the other, we have a new figure, or, rather,\none is considered as a portion of the other, and is consequently\ncontained in the idea of the other, as a small ball inside of a larger\nball. On either supposition the balls are regarded as penetrating\neach other in whole or in part; but by penetration is here meant\nonly that there are certain parts in one, considered as pure space,\nwhich the other, also considered as pure space, occupies. Geometrical\nimpenetrability exists only when the two objects are supposed to be\nseparated, and only inasmuch as they are separated; in which case\nimpenetrability is absolutely necessary, because penetration would\nbe to confound what is by the supposition separated, and would imply\nseparation and non-separation, which are contradictory. Therefore,\ngeometrical impenetrability is no argument in favor of physical\nimpenetrability; for the former exists only in case it is presupposed\nor required under pain of contradiction. The same would occur in\nreality; for if we suppose two bodies separated, they cannot be in the\nsame place whilst they are separated, without a manifest contradiction.\nOn this point, therefore, the ideal teaches us nothing as to the real.\n\n248. Can penetration exist in reality? Can one ball of metal, for\nexample, enter another ball of metal, as we make one geometrical ball\nenter another? We are not treating of the regular order of things which\nis repugnant to such suppositions, but of the essence of things. On\nthis supposition, I maintain that there is no contradiction in making\nbodies penetrable, and that an analysis of this matter proves that the\nimpenetrability of bodies is not essential.\n\nWe have seen that the idea of place as pure space is an abstraction.\nIt is therefore an entirely imaginary supposition on which we give to\nevery body a certain extension to fill a certain place, necessarily,\nand in such a manner that it is impossible for it to admit another body\ninto the same place at the same time. The position of bodies in general\nis the sum of their relations; the particular extension of each body is\nonly the sum of the relations of its parts among themselves, until we\ncome by an infinite division to unextended or infinitesimal points.\n\nThe sum of the relations of indivisible or infinitesimal beings\nconstitutes what we call extension and space, and all that is contained\nin the vast field of sensible representation. Who can assure us that\nthese relations are not variable? Is our experience, perhaps, the limit\nof the nature of things? Evidently not. The universe was not planned\nafter our experience, but our experience is obtained from the universe.\nTo say that it contains, and can contain only what our experience sees\nin it, is to make the _me_ the type of the universe; to affirm that\nits laws are derived from us, that they are emanations from our being.\nFoolish pride of an imperceptible atom, which appears for an instant\non the great theatre of nature, and goes out like a spark of fire;\nfoolish pride for a spirit which, despite its great idea of its own\nimportance, feels that it is unable to withdraw itself from these laws\nand phenomena, which it pretends to consider as its own creation!\n\n\n\n\nCHAPTER XXXIII.\n\nA TRIUMPH OF RELIGION IN THE FIELD OF PHILOSOPHY.\n\n\n249. There are two things in extended objects: multiplicity and\ncontinuity. The first is absolutely necessary to extension; it supposes\ndistinct parts, and that which is distinct cannot be identical without\nevident contradiction. The continuity represented in the sensible\nimpression is not essential to extension, because it is only the\nresult of a union of relations inseparable in the present order of\nsensibility, but not absolutely necessary in the order of reality.\nTranscendental philosophy rising above sensible representations,\nand leaving phenomena to enter on the contemplation of beings in\nthemselves, nowhere discovers the necessity of these relations, and\nis obliged to consider them as simple facts which might cease to be\nwithout any contradiction. In this manner the correspondence of the\nphenomenon with the reality is saved, and the internal world harmonized\nwith the external, but the subjective conditions of the former are\nnot all transferred to the latter in such a way as to make what is\nnecessary for our representations, absolutely necessary in itself.\n\n250. Arrived at this point of transcendental philosophy, the mind\nbeholds new worlds unfolded to its view. We rejoice to say that this\ndiscovers to us a new proof of the divinity of the Catholic religion,\nand teaches us to distrust that proud philosophy which finds a\ncontradiction in every thing which it cannot understand.\n\n251. There is a mystery which the Church celebrates with august\nceremonies, and the Christian adores with faith and with love. The\nunbeliever sees the holy Tabernacle, and exclaims, in the pride of his\nignorance: \"Here is a monument of superstition; here man adores an\nabsurdity.\"\n\nAs the present is a work of philosophy, not of theology, I might\npass over without answering the objections of infidelity, but the\noccasion seems so well suited for the solution of some difficulties\nbrought by light and superficial thinkers, that I am unwilling to pass\nthem in silence. The nature of the work requires me to be brief in\nthis discussion, though the subject is too important to be entirely\nomitted; the more so, as Catholic writers on philosophy have given\ntheir explanations on these points in what they considered the most\nseasonable place, and most frequently when treating of extension.\n\n252. That the mystery of the Eucharist is a supernatural fact\nincomprehensible to man, and inexplicable by human words, is confessed\nby Catholics and acknowledged by the Church. We cannot, therefore, give\na philosophical reason to explain this secret; no one was ever so vain\nas to attempt it. We can only examine whether the mystery is absurd\nand intrinsically contradictory; for if it were, it would not be a\ntruth but an error, because divine omnipotence does not extend to what\nis absurd. The question is, whether the fact, although beyond the laws\nof nature, is intrinsically possible; for then it belongs to the field\nof criticism. If the incredulous man admits God, he must admit his\nomnipotence; the discussion must then be, not whether God can perform\nthis miracle, but whether he has performed it.\n\n253. The objections brought against the Eucharist may be reduced to the\nfollowing: a body exists without the conditions to which other bodies\nare subject; it produces none of the sensible impressions which we\nreceive from other bodies; and is in many places at the same time. To\nanswer these objections, let us first determine our ideas.\n\n254. The doctrines explained in the theory of sensations in this\nvolume, show how false it is to say that the Eucharist is impossible.\nUnder the sacred species is a body which does not affect our senses;\nhere is a miracle, but not an impossible thing. I have shown that\nthere is no necessary relation between bodies and our sensibility. The\nconnection which now exists cannot be explained by any intrinsical\nproperty of spirits and bodies; we must, therefore, recur to a higher\ncause which freely established these relations. The same cause can\nsuspend them. From this point of view the question becomes this: Can\nthe power of God make a body which shall not produce the phenomena of\nsensibility, and suspend the laws which he was free to establish? Thus\npresented, the question cannot bear two answers. It must be answered in\nthe affirmative, or the omnipotence of God is denied.\n\n255. Those who attempt to show the impossibility of our dogma, must\nprove the following propositions:\n\nI. Passive sensibility is so essential to bodies that they cannot lose\nit without destroying the principle of contradiction.\n\nII. The relations of our organs [to] objects are intrinsically\nimmutable.\n\nIII. The transmission of the impressions of the organ to the sensitive\nfaculties of the soul is equally essential, and can fail under no\nsupposition.\n\nIf they do not prove the truth of these three propositions, all the\nobjections founded on the phenomena of sensibility fall to the ground.\nIf one only is not proved, all the objections are solved; for it is\nevident that the phenomena of sensibility may be altered by three\ncauses:\n\nI. By the absence of the dispositions necessary to the body, that it\nmay be the object of sensibility.\n\nII. By the interruption of the ordinary relations between our organs\nand the body.\n\nIII. By the failure of the transmission of the impressions of the organ\nto the sensitive faculties.\n\nConsequently, if one of the first propositions is false, the doubter is\nreduced to silence.\n\n256. Whoever should attempt to prove these three propositions, not only\nwould fail, but the attempt would prove his ignorance of the phenomena\nof sensibility, and that his philosophy on this point is the notions of\nthe vulgar. It is not necessary to be a philosopher, it is sufficient\nto have acquired a very slight knowledge of philosophy to see that\nsuch an attempt would suppose a complete ignorance of the history of\nphilosophy. At any rate, I need not insist on this point; for I have\ntreated these questions at length in the last two books of this volume.\n\n257. The solution there given ought to suffice to answer satisfactorily\nthe objection founded on the particular state of a body without the\nconditions of extension which we find in others. From the moment\nthat we suppose the correspondence of a body with our senses to be\nsuspended, as these are the only means by which we are informed of\nwhat passes in the external world, it is impossible for us to affirm\nthat there is any absurdity in that of which we have no experience. We\nperceive extension only by sensation, therefore we can say nothing in\nrelation to the extension of an object of which we have no sensation.\nBut although this answer should cut short all objections, I shall not\nconfine myself to this alone.\n\n258. What is extension? In reality it is the sum of the relations of\nthe beings which compose the extended object. These relations, as I\nhave proved, are not intrinsically necessary: therefore God can alter\nthem. Thus this question comes to the same point as the preceding:\ncan the power of God suspend, alter, or entirely take away relations\nwhich are not intrinsically necessary? Evidently it can. The difficulty\nthen is not as to what could have been, but as to what is. Again we\nfind ourselves out of the field of philosophy in that of facts, or the\nexamination of the motives of credibility.\n\n259. The other objection founded on the impossibility of body being in\nseveral places at the same time, though in appearance more difficult,\namounts to the same as the former. To be in a place, as we now\nunderstand it, is to have a particular extension, with the ordinary\nform and relations with respect to the extension of other bodies. If\nwe suppose a body with extension subject to other conditions, without\nthe ordinary relation to the extension of other bodies, we destroy the\nsupposition on which we base the impossibility of a body being at the\nsame time in several places. Therefore, as we have proved that the\nomnipotence of God can alter and even take away these relations, there\nis no contradiction in admitting the destruction of the results which\nproceed from these relations.\n\n260. This is why the distinction of the scholastics between two\nclasses of extension: _in ordine ad se, et in ordine ad locum_,\nor quantitative and sacramental extension, though to the eyes of\na superficial philosophy it might appear to be an empty subtlety,\ninvented for the purpose of avoiding the difficulty, is nevertheless\na profound observation, confirmed by the analysis of the reality and\nthe phenomenon in the sensible order. I do not mean by this to say\nthat when this distinction was made in the schools, they understood\nperfectly all the truth and philosophical nicety which it involves; nor\nthat the distinction was always accompanied by the critical analysis\nwhich belongs to it. At present I abstract the merit of the men and\nregard only the thing. The less philosophical intelligence we suppose\nin those who used the distinction, the more admirable appears that\nreligion which inspires its defenders with fruitful thoughts which\nthe ages to come might unfold. The philosophical schools disputed\nwarmly on extension, on accidents, and on the sensitive faculties: the\nCatholic dogma taught a truth which was contrary to all appearances,\nit stimulated them to examine more profoundly the distance of the\nphenomenon from the reality, the difference between the contingent\nand the necessary; the mystery which the Church taught introduced\ninto philosophy questions which without it would probably never have\noccurred to man's understanding.\n\n261. Bacon expressed a profound truth when he said that a little\nphilosophy carried its possessor from religion, and a great deal of\nphilosophy leads him to it. A careful study of the objections brought\nagainst Christianity, lays bare a truth confirmed by the history of\neighteen centuries; the most weighty objections against Catholicity,\ninstead of proving any thing against it, involve a proof which confirms\nit. The secret for discovering this proof, is to go to the bottom of\nthe objection, and examine it under all its aspects. Original sin is a\nmystery, but it explains the whole world; the Incarnation is a mystery,\nbut it explains the traditions of the human race; faith is full of\nmysteries, but it satisfies one of the greatest necessities of reason;\nthe history of the creation is a mystery, but this mystery clears up\nchaos, throws light on the world, and is the key to the history of\nmankind; all Christianity is a collection of mysteries, but these\nmysteries are connected by a secret union with all that is profound,\ngrand, sublime, or beautiful in heaven or earth; they are connected\nwith the individual, with the family, with society, with God, with the\nunderstanding, with the heart, with languages, sciences, and art. The\ninvestigator who rejects religion and even seeks means to oppose it,\nfinds it at the entrance as at the outlet of the mysterious ways of\nlife; at the cradle of the infant as in the shadow of the tomb; in time\nas in eternity; explaining every thing by a word; listening unmoved to\nthe wanderings of ignorance and the sarcasms of unbelief, patiently\nawaiting till the course of ages shall acknowledge its truth, which\nexisted before all ages.\n\n\n\n\nCHAPTER XXXIV.\n\nCONCLUSION AND SUMMING UP.\n\n\n262. Before passing to another subject, let us fix our attention for a\nfew moments on the nature and origin of the idea of extension. We shall\nthus collect the fruit of the preceding investigations, and prepare the\nway for those which follow.\n\nThe scientific fruitfulness of this idea to our mind proves how\ndistant sensible impressions are from intellectual perception. We\ncannot know whether this idea existed in our mind before the sensible\nimpression; if it did exist we were not conscious of it, and in this\nrespect it is affirming a gratuitous proposition to say that it is an\ninnate idea. What we can safely say, is, that there are two distinct\norders of internal phenomena, that sensation could not have produced\nthe idea, that this idea is immeasurably superior to the external\nimpression, or even the internal sensitive intuition, and that if it\ndid not already exist in the mind, it was not produced by sensation as\nan effect is produced by its cause.\n\n263. Here we make an important transition from the order of sensations,\nto the order of ideas, and discover in our mind a new class of facts.\nIt matters little whether these facts exist before the impression,\nor result from its presence. In the first case, we see in the mind\na deposit of germs which need only the warmth of life in order to\nbe developed; in the second, we find in the mind a fertility which\nproduces these germs. In either case we find a being of a privileged\nnature, a sublime being which by a single leap rises above the region\nof matter, and awakened by the external impression, arises to a new\nlife which this world cannot contain.\n\n264. In this sense there are innate ideas; ideas which sensation could\nnot have produced. In this sense all general and necessary ideas are\ninnate; for sensation could not produce them. Sensation is never any\nthing more than a phenomenon, a particular and contingent fact, and\nconsequently incapable of producing general ideas, or the ideas of the\nnecessary relations of being. Sight, or the imaginary representation\nof a triangle, is a contingent phenomenon which tells us nothing of\nthe necessary relations of the sides and angles to each other. In\norder to perceive these relations, this necessity, something else is\nrequired. This something else, call it innate ideas, force, fecundity,\nor activity of the mind, or any thing you please, exists, and could not\nhave been produced by sensation, but belongs to a higher order distinct\nfrom sensible phenomena.\n\n265. After such long investigations of the phenomena of sensation, we\nat last find an idea; it is the idea of extension, the foundation of\nall the mathematical sciences and of their application to the laws of\nnature.\n\nThe human mind, in all its relations with the material world, seems to\nhave one great idea, that of extension, which, modified in infinite\nways, is the origin of all the sciences which relate to matter. The\nwhole material world rests on this idea, and all knowledge of material\nobjects proceeds from it. It is a pure idea in its necessary relations\nand in its necessary branches. It is a light given to the lord of\ncreation that he may know and admire the prodigies of nature.\n\n266. We find the same wonderful simplicity amidst so complicated a\nmultiplicity in another order of ideas. Hence we infer that the whole\nedifice of the sciences and all human knowledge are founded on a small\nnumber of ideas, perhaps on two alone. These ideas are not sensible\nrepresentations, they are the objects of pure intuitions; they cannot\nbe decomposed, but they may be applied to an infinite variety of\nthings; they are not explained by words, as a union including various\nconceptions; by them a mind acts on another mind, not to teach it any\nthing, but to make it concentrate its activity in order to note what\nit contains within itself, and learn, in a certain measure, what it\nalready knows.\n\nTry to explain extension, the idea by which we perceive this order\nwhich we cannot express in words, but on which we found sensible\nexperience and geometrical science, and you can find no expression.\nWill you define it to be \"parts outside of parts?\" But what are\n_parts_, and what does _outside_ mean, if you have not the idea\nof extension? Take any extended thing, make your mind concentrate\nitself and exercise its activity in generalization. Is this triangle\na quadrilateral? No. Are they both extended? Yes. Is this surface a\nsolid? No. Are they both extended? Yes. Are all triangles different\nfrom quadrilaterals? Yes. Have all surfaces and solids extension? Yes.\nHow do you pass from one fact to all the facts of the same kind, from\nthe contingent to the necessary? Have you explained what extension is?\nNo. Have you shown what there is common to all these different things?\nNo. All that you have done then is to arouse the activity of your mind,\nand to make it direct its attention to the general idea of extension,\nand the mind applies this idea to various things which are different,\nyet have something in common, it applies the different modifications of\nthis idea to various things which have something in common, and finds\nthem different. You have not taught the truths of geometry to the mind,\nbut have awakened them in it, whether they already existed in it, or\nthe mind had the faculty of producing them.\n\n267. Let us now collect the result of the investigations we have made.\nI do not give an equal value to all the propositions which follow. I\nhave explained my opinion of each in its proper place, but I consider\nit well to sum them all up here in order to assist the understanding\nand help the memory.\n\nI. There is immediate certainty of our relations with beings distinct\nfrom us.\n\nII. There is certainty of the existence of an external world.\n\nIII. The external world in relation to us, is only an extended\nbeing which affects us, and is subject to constant laws which we may\ndetermine.\n\nIV. We have the idea of extension.\n\nV. The idea of extension is excited by sensations, but it is not\nconfounded with them.\n\nVI. The idea of extension is the basis of all our cognitions of bodies.\n\nVII. The idea of extension should not be confounded with the imaginary\nrepresentation of extension.\n\nVIII. An extended space which is nothing real, is an absurdity.\n\nIX. Space is nothing real distinguished from the extension of bodies.\n\nX. Where there are no bodies, there are no distances.\n\nXI. Motion is the change of the positions of bodies among themselves.\n\nXII. There is not and cannot be vacuum of any kind.\n\nXIII. The idea of space is the idea of extension in the abstract.\n\nXIV. The imagination of an unlimited space is only an attempt of\nthe imagination to follow the understanding in the abstraction of\nextension. It also arises from our habit of seeing through transparent\nmediums, and moving in fluids whose resistance is not perceptible.\n\nXV. As all that we know of bodies is, that they are extended and affect\nus, whatever has these two conditions is to us a body.\n\nXVI. But as we do not know the essence of bodies, we do not know\nwhether a body can exist without extension.\n\nXVII. Neither do we know what modifications the extension of one body\nmay be subject to, with respect to others.\n\nXVIII. The elements of which bodies are composed are unknown to us.\n\nXIX. The approximation of some bodies to others, and the gravitation\nwhich results from it, seem to be the necessary effect of their present\nrelations.\n\nXX. The necessity of approximation does not suffice to explain the laws\nof motion, or their beginning, or their continuation.\n\nXXI. The idea of space is not an absolutely necessary condition of\nsensation.\n\nXXII. The idea of extension has a real objectiveness.\n\nXXIII. The transition from the subjective to the objective in relation\nto extension is a primitive fact of our nature.\n\nXXIV. Therefore bodily phenomena have a real existence outside of us.\n\nXXV. Therefore a real certainty, scientific as well as phenomenal,\narises from the testimony of the senses.\n\nXXVI. Reason justifies the instinct of nature when it examines the\nrelation of subjectiveness with objectiveness in sensations.\n\nXXVII. Geometry considers extension in the abstract; but with the\ncertainty that when the principle exists in the real order, the\nconsequences cannot fail to be produced, and that the consequences will\nbe more or less exact in proportion as the principle is more or less\nexactly realized.\n\nXXVIII. Notwithstanding our certainty of the existence of the external\nworld we do not know its essence.\n\nXXIX. We do not know what this world is when seen by a pure spirit.\n\nXXX. Sensible intuition, to which our geometry relates, does not\nconstitute the essence of scientific knowledge, and may be separated\nfrom it.\n\nXXXI. A change in the relations of corporeal beings among themselves,\nand with our sensitive faculties, is not intrinsically impossible.\n\n\nNOTES TO BOOK FIRST.\n\n\nON CHAPTER I.\n\n(1) We must distinguish between certainty and truth: there are intimate\nrelations between them, yet they are very different things. Truth is\nthe conformity of the intellect with the object. Certainty is a firm\nassent to a real or apparent truth.\n\nCertainty is not truth, but it must at least have the illusion of\ntruth. We may be certain of what is false, but not unless we believe it\nto be true.\n\nThere is no truth so long as there is no judgment; for without judgment\nthere is only perception, but no comparison of the idea with the thing;\nand without comparison there can be neither conformity nor discrepancy.\nIf we conceive a mountain a thousand miles high, we conceive a thing\nthat does not exist; but we do not err so long as we do not assert the\nexistence of the mountain. If we affirm it, there is opposition between\nour judgment and the reality: this constitutes error. The object of\nthe intellect is truth; therefore, we at least require the illusion\nof truth in order to be certain: our intellect is weak; hence its\ncertainty is liable to error. The first is a law of the intellect, the\nsecond a proof of its frailty.\n\nPhilosophy, or, rather, man, cannot rest content with appearances,\nbut demands reality; if any one be convinced that he has only the\nappearance, or if he even doubt of it, he loses his certainty, for it\nadmits appearances only on condition of their being disguised.\n\n\nON CHAPTER II.\n\n(2) Even Pyrrho did not doubt of every thing as some pretend; he\nadmitted sensations so far as passive, and resigned himself to the\nconsequences of these impressions, and yielded to the necessity of\nconforming in practice to what they indicated. No one ever yet denied\nappearances: it is reality that is disputed; some hold that man must be\ncontent with saying _it appears_; others that he can go so far as to\nsay _it is_. It is useful to preserve this distinction, as it prevents\nconfusion of ideas in the history of philosophy, and conduces to render\nclear the question of certainty. Thus of the three questions: is there\ncertainty? on what is it founded? how is it acquired? the first is\nresolved alike by all the schools, so far as it relates to a fact of\nour soul: by only admitting appearances, they admit the certainty of\nthem.\n\n\nON CHAPTER III.\n\n(3) In order to form clear ideas of the development of the\nunderstanding, and the other faculties of our soul, the reader may\nrefer to what we advanced in our work, entitled _The Criterion_, and\nparticularly to the chapters I., II., III., XII., XIII., XIV., XVIII.,\nand XXII.\n\n\nON CHAPTER IV.\n\n(4) We subjoin the passages from St. Thomas on the unity and\nmultiplicity of ideas, to which we referred in the text. We believe the\nfriends of solid and profound metaphysics will read them with great\npleasure.\n\n\"In omnibus enim substantiis intellectualibus, invenitur virtus\nintellectiva per influentiam divini luminis. Quod quidem in primo\nprincipio est unum et simplex, et quanto magis creatur\u00e6 intellectuales\ndistant a primo principio, tanto magis dividitur illud lumen, et\ndiversificatur, sicut accidit in lineis a centro egredientibus. Et inde\nest quod Deus per suam essentiam omnia intelligit: superiores autem\nintellectualium substantiarum, etsi per plures formas intelligant,\ntamen intelligunt per pauciores et magis universales et virtuosiores ad\ncomprehensionem rerum propter efficaciam virtutis intellectiv\u00e6, qu\u00e6 est\nin eis. In inferioribus autem sunt form\u00e6 plures et minus universales,\net minus efficaces ad comprehensionem rerum, in quantum deficiunt a\nvirtute intellectiva superiorum. Si ergo inferiores substanti\u00e6 haberent\nformas in illa universalitate, in qua habent superiores, quia non sunt\ntant\u00e6 efficaci\u00e6 in intelligendo, non acciperent per eas perfectam\ncognitionem de rebus, sed in quadam communitate, et confusione, quod\naliqualiter apparet in hominibus. Nam qui sunt debilioris intellectus,\nper universales conceptiones magis intelligentium, non accipiunt\nperfectam cognitionem, nisi eis singula in speciali explicentur. (P.\n1^n, Q. 89^2, A. 1\u00b0.)\n\n\"Intellectus quanto est altior et perspicacior tanto ex uno potest\nplura cognoscere. Et quia intellectus divinus est altissimus, per\nunam simplicem essentiam suam omnia cognoscit; nec est ibi aliqua\npluralitas formarum idealium, nisi secundum diversos respectus divin\u00e6\nessenti\u00e6 ad res cognitas; sed in intellectu creato multiplicatur\nsecundum rem quod est unum secundum rem in mente divina, ut non\npossit omnia per unum cognoscere; ita tamen quod quanto intellectus\ncreatus est altior, tanto pauciores habet formas ad plura cognoscenda\nefficaces. Et hoc est quod Dio. dicit, 12, c\u0153. hier. quod superiores\nordines habent scientiam magis universalem in inferioribus. Et in\nlib. de causis dicitur, quod intelligenti\u00e6 superiores habent formas\nmagis universales; hoc tamen observato, quod in infimis angelis sunt\nform\u00e6 adhuc universales in tantum, quod per unam formam possunt\ncognoscere omnia individua unius speciei: ita quod illa species sit\npropria, uniuscujusque particularium secundum diversos respectus ejus\nad particularia, sicut essentia divina efficitur propria similitudo\nsingulorum secundum diversos respectus; sed intellectus humanus qui\nest ultimus in ordine substantiarum intellectualium habet formas\nin tantum particulatas quod non potest per unam speciem nisi unum\nquid cognoscere. Et ideo similitudo speciei existens in intellectu\nhumano non sufficit ad cognoscenda plura singularia; et propter hoc\nintellectui adjuncti sunt sensus quibus singularia accipiat. (Quodlib.\n7, A. 3.)\n\n\"Respondeo dicendum, quod ex hoc sunt in rebus aliqua superiora, quod\nsunt uni primo, quod est Deus, propinquiora et similiora. In Deo\nautem tota plenitudo intellectualis cognitionis continetur in uno,\nscilicet in essentia divina, per quam Deus omnia cognoscit. Qu\u00e6 quidem\nintelligibilis plentitudo, in intelligibilibus creaturis inferiori\nmodo et minus simpliciter invenitur. Unde oportet, quod ea qu\u00e6 Deus\ncognoscit per unam, inferiores intellectus cognoscant per multa; et\ntanto amplius per plura, quanto amplius intellectus inferior fuit. Sic\nigitur quanto angelus fuerit superior, tanto per pauciores species\nuniversitatem intelligibilium apprehendere poterit, et ideo oportet\nquod ejus form\u00e6 sint universaliores, quasi ad plura se extendentes\nunaqu\u00e6que eorum. Et de hoc, exemplum aliqualiter in nobis perspici\npotest: sunt enim quidam, qui veritatem intelligibilem capere non\npossunt; nisi eis particulatim per singula explicatur. Et hoc quidem ex\ndebilitate intellectus eorum contingit. Alii vero qui sunt fortioris\nintellectus, ex paucis multo capere possunt.\" (P.1^a, Q. 55^a A. 3\u00b0.)\n\n\nON CHAPTER V.\n\n(5) Here is the idea of Condillac's man-statue explained by himself:\n\"To gain this object we imagined a statue internally organized like\nourselves, and animated with a mind deprived of every sort of ideas. We\nalso supposed its exterior composed wholly of marble, to allow it the\nuse of none of its senses, and we reserved to ourselves the liberty to\nopen them at our pleasure to the different impressions of which they\nare susceptible.\n\n\"We thought we ought to commence with _smell_, because of all the\nsenses this is the one which least contributes to cognitions of the\nmind. Next we had to examine the others, and after having considered\nthem apart and together, we saw the statue become an animal able to\nattend to its own preservation.\n\n\"The principle that determines the development of its faculties is\nsimple; even sensations contain it; for, all being of necessity either\nagreeable or the contrary, the statue is interested in enjoying some\nand shunning others. The reader will now be convinced that this\ninterest suffices to give occasion to the gradations of the will and\nthe understanding. Judgments, reflection, desires, passions, are only\nsensations variously transformed. This is why it seemed to us useless\nto suppose the soul to have received immediately from nature all the\nsensations with which it is endowed. Nature has given us organs which\nshow us by pleasure or pain what we ought to seek or to avoid; but here\nshe stops, and leaves to experience the task of leading us to contract\nhabits, and finish the work she has commenced.\n\n\"This object is new, and shows all the simplicity of the ways of the\nAuthor of nature. Is it not a thing worthy of our admiration thus to\nsee, from man's sensibility to pleasure or pain, spring up in him\nideas, desires, habits, and talents of various kinds?\"--_Traite des\nSensations._ _Dessein de l'ouvrage._\n\nWhat we admire in Condillac is not his system, but his candor; and\nwe wonder yet more that, for a time, he should have had numerous\nfollowers of his so poor and superficial system. The author proposes\nthe difficulty, that as there is in our soul nothing but transformed\nsensations, it is strange that brutes, which also have sensations,\nshould not be endowed with the same faculties as man. Can the reader\nimagine what profound reason the French philosopher assigned? We doubt\nit very much. It is a curious thought: \"the organ of _touch_ is _less\nperfect_ in brutes, and consequently it cannot be to them an occasional\ncause of all the operations which we observe in ourselves.\" He did well\nto adopt the motto: _nec tamen quasi Pythius Apollo!_\n\n\nON CHAPTER VI.\n\n(6) The works of the scholastics are worth reading on these points.\nTreating of _the object of science_, they are at once exact and\nprofound. It is not easy to think of any thing concerning the\nclassification of truths not explained or indicated by them.\n\n\nON CHAPTER VII.\n\n(7) Let us not be thought to judge too severely of the forms adopted\nby the German philosophers. It is well known how Madame de Sta\u00ebl\nspeaks of them; but happily we can cite in our favor a more competent\njudge. Schelling, one of the chiefs of German philosophy, says: \"The\nGermans have so long philosophized among themselves, as to gradually\ndepart more and more, in their thoughts and their words, from what\nis universally intelligible; and the degree of departure therefrom\nhas almost come at last to be the measure of philosophical ability.\nExamples are not wanting to us. As families which separate from general\nsociety, and live wholly among themselves, among other repulsive\nsingularities, come to use expressions intelligible only to themselves,\nso is it with the Germans in philosophy; and after vain efforts to\nspread the Kantian philosophy out of Germany, they renounced the\nattempt to make themselves intelligible to other nations; they became\naccustomed to regard themselves as the chosen people of philosophy,\nforgetting that the primary end of philosophy,--an end often neglected,\nbut not the less to be sought for on that account,--is to gain\nuniversal consent, by making themselves universally intelligible. This\nis not to say that we must judge works of thought like exercises in\nstyle; but all philosophy not intelligible to all civilized nations,\nand accessible in every language, cannot, for this reason alone, be the\nuniversal and true philosophy.\"--_Schelling's Judgment of V. Cousin,\nand the state of French and German Philosophy in general._ 1834. p. 4.\n\nSchelling flatters himself that German philosophy is about to take a\nbetter course with respect to clearness, and adds: \"The philosophical\nwriter who, for tens of years past, was unable to depart from the terms\nand forms of the school, without loss of his scientific reputation, may\nhereafter emancipate himself from this restraint. He will seek depth of\nthought; and an absolute incapacity to express himself with clearness,\nwill no longer be regarded as the mark of talent and philosophical\ninspiration.\" We have nothing to add to this passage; we would only\nremind its author that: _mutato nomine, de te fabula narratur_.\n\n\nON CHAPTER VIII.\n\n(8) The perusal of Schelling's work on Ideal Transcendentalism leaves\nno doubt as to his view of this identity, which at bottom neither is\nnor can be any thing else than pantheism; yet, for the sake of truth,\nwe will allow that Schelling seems to have modified his doctrine, or\nto have feared its consequences, if we are to consider the indications\nfound in his discourse at the opening of his course of philosophy,\nat Berlin, the 13th of November, 1841. We there find the following\npassage, worthy of the attention of all thinking men: \"The difficulties\nand obstacles of all kinds, against which philosophy contends are\nvisible, and in vain would we attempt to dissemble them. Never was\nthere a more powerful reaction against philosophy on the part of real\nand active life than at this present epoch; and this proves philosophy\nto have penetrated even to the vital questions of society, those\nconcerning which no one can rest indifferent. So long as a philosophy\nis only in the first stages of formation, taking the first steps in its\nmarch, no one cares for it, except philosophers themselves; other men\nawait the last word of philosophy, since it is important to the general\npublic only in its results.\n\n\"We confess that we ought not to take as the practical result of a\nsolid and profoundly meditated philosophy whatever it may please any\nbody to designate as such: were it so, the world would be subjected\nto doctrines the most repugnant to sound morality, even such as sap\nits foundation. No! No one judges of philosophy by the practical\nconclusions drawn by ignorance or presumption. Moreover, lest deception\non this point be possible, the public should reject a philosophy\nwhich has such results, without examining or even judging it in its\nprinciples; it should say that it cannot understand the depth of these\nquestions, or the artificial and intricate march of the arguments;\nbut without pausing here it should promptly decide that a philosophy\nleading to such conclusions cannot be true in its principles. What the\nRoman moralist said of the useful: _nihil utile nisi quod honestum_,\nis equally applicable to the investigation of truth: _no philosophy\nthat respects itself will allow that it leads to irreligion_. Yet\nactual philosophy is in such a state, that, however much it promises\na religious result, no one admits it; for deductions drawn from it\nconvert the dogmas of the Christian religion into a vain phantasmagory.\n\n\"As to this, some of its most faithful disciples are openly agreed; be\nthe suspicion well founded or not, its existence suffices, and this\nopinion is established.\n\n\"But active life in the last result is always right; and so philosophy\nis exposed to great risks. They who war on one philosophy are not far\nfrom condemning all philosophy; they say in their heart, there is no\nlonger philosophy in the world. I myself am not exempt from these\ncondemnations, since _it is pretended that it is I, who first gave\nimpulse to this philosophy which is at present so badly judged of,\nbecause of its religious results_.\n\n\"How shall I defend myself? Certainly I would never attack a philosophy\nfor its last results; but I would judge it in its first principles, as\nevery philosophical mind should. It is moreover well enough known that\nI have shown myself little satisfied with the philosophy of which I\nspeak.\n\n       *       *       *       *       *\n\n\"The moral and spiritual worlds are so divided that any point of union\nfor an instant should be a motive of satisfaction. Besides to destroy,\nis a very sad thing when there is nothing wherewith to replace the\nthing destroyed. 'Do it better yourself,' we say to one who can do\nnothing but criticize.\n\n       *       *       *       *       *\n\n\"I therefore consecrate myself entirely to the mission with which I\nam charged; for you I will live; for you I will labor without ceasing\nwhile there remains in me the breath of life, and while He permits\nme, without whose permission not a hair can fall from our head, and\nyet less a deeply felt word proceed from our mouth. He, without whose\ninspiration not one lucid idea can shine on our mind, nor one thought\nof truth and liberty illumine our soul.\"\n\nThis passage shows the embarrassment of the German philosopher's\nposition, and the irreligious consequences attached to his doctrines.\nIt is consoling to see him pay some homage to truth; but it is\nafflicting to see him still pretend to save its inconsequence.\n\n\nON CHAPTER IX.\n\n(9) In these latter days there have not been wanting some to count\nthe illustrious Malebranche among the partisans of pantheism. We\ncannot conceive how M. Cousin could say; \"Malebranche est avec\nSpinoza le plus grand disciple de Descartes. Comme lui il a tir\u00e9 des\nprincipes de leur commun ma\u00eetre les cons\u00e9quences que ces principes\nrenfermaient. Malebranche est \u00e0 la lettre Spinoza chr\u00e9tien.\"\n(_Fragments Philosophiques._ T. 2^{me}. p. 167. Ed. 3^{ieme}.) We\nrepeat that we cannot conceive how any one, who had read ever so little\nof the great metaphysician's works, should assert such a paradox. The\nslightest glance at his writings suffices to show in them the most\nlofty spiritualism united with profound respect for the dogmas of\nour most holy religion. When we treat of the various philosophical\nsystems of the origin of ideas and the problem of the universe, we\nshall have other occasions to vindicate the wise and pious author of\nthe _Investigation de la Verit\u00e9_. Yet we were unwilling to pass by\nthe present occasion without doing him the justice to defend him from\nimputations, which he would, were he living, repel as intolerable\ncalumnies. Who would have thought when he wrote those works, on every\npage of which we find, God, the mind, the Christian religion, eternal\ntruth, and original sin, with frequent texts from the sacred Scriptures\nand St. Augustine, that he would ever be ranked with Spinoza, with\nthe absurd epithet of _Christian Spinoza_? Such is at times the sad\nlot of great men, thus to be held as chiefs of sects they abhorred.\nMalebranche styled Spinoza, _l'impie de nos jours_, and M. Cousin dares\ncall Malebranche the _Christian_ Spinoza.\n\n\nON CHAPTER X.\n\n(10) We are not ignorant of the difficulties to which Leibnitz's\nsystems are subject; but it is necessary to show that in this great\nman's mind the erroneous doctrines of modern Germans had no place. \"Et\nc'est ainsi,\" he says, in his Monadologie (No. 38), \"que la derni\u00e8re\nraison des choses doit \u00eatre dans une substance necessaire, dans\nlaquelle le d\u00e9tail des changmens ne soit qu'eminemment, comme dans la\nsource, et c'est ce que nous appelons Dieu. Or cette substance \u00e9tant\nune raison suffisante de tout ce d\u00e9tail, lequel est aussi li\u00e9 partout,\nil n'y a qu'un Dieu, et ce Dieu suffit.\n\n\"On peut juger aussi que cette substance supr\u00eame qui est unique,\nuniverselle, et necessaire, n'ayant rien hors d'elle qui en soit\nind\u00e9pendant, et \u00e9tant une suite simple de l'\u00eatre possible, doit \u00eatre\nincapable de limites et contenir tout autant de realit\u00e9 qu'il est\npossible.\n\n\"D'o\u00f9 il s'ensuit, que Dieu est absolument parfait, la perfection\nn'\u00e9tant autre chose, que la grandeur de la realit\u00e9 positive prise\npr\u00e9cis\u00e9ment en mettant \u00e0 part les limites ou bornes dans les choses qui\nen ont. Et l\u00e0, o\u00f9 il n'y a point de bornes, c'est-\u00e0-dire, en Dieu, la\nperfection est absolument infinie.\n\n\"Il s'ensuit aussi que les cr\u00e9atures ont leur perfections de\nl'influence de Dieu, mais qu'elles ont leurs imperfections de leur\nnature propre, incapable d'\u00eatre sans bornes. Car c'est en cela qu'elles\nsont distingu\u00e9es de Dieu.\n\n\"Il est vrai aussi, qu'en Dieu est non seulement la source des\nexistences, mais encore celle des essences, en tant que r\u00e9elles, ou de\nce qu'il y a de r\u00e9el dans la possibilit\u00e9.\"\n\nIn his dissertation on the Platonic philosophy he combats the\npantheistic tendencies of Valentine Weigel, in these words:\n\"Valentinum Weigelium, qui non tantum vitam beatam peculiari libero\nper Deificationem explicat, sed et passim mortem et quietem hujusmodi\ncommendat, vellem cum aliis Quietistis suspicionem similis sententi\u00e6\nnon dedisse. * * * Spinoza aliter eodem tendebat; ei una substantia\nest, Deus; creatur\u00e6 ejus modificationes, et figur\u00e6 in cera continue per\nmotum nascentes et pereuntes. Ita ipsi, perinde ut Almerico, anima non\nsuperest, nisi per suum _esse_ ideale in Deo ut ibi ab \u00e6terno fuit.\n\n\"Sed nihil in Platone animadverto, unde colligam, animos propriam\nsibi substantiam non servare; quod etiam sane philosophanti extra\ncontroversiam est, neque intelligi contraria potest sententia, nisi\nDeum et animam corporea fingas, neque enim aliter ex Deo animas,\ntanquam particulas divellas; sed talis de Deo atque anima notio,\naliunde absurda est.\" (Leibnitz. Epist. ad Hanschium de Philos. Platon.)\n\nSo far was Leibnitz from deeming the tendency to pantheism an elevated\nphilosophy, that, as we have just seen, he considered it the result\nof a rude imagination. It is very remarkable that under an historical\nas under a metaphysical aspect Leibnitz agrees with St. Thomas; both\nexpress the same ideas in very similar words. The holy doctor asks if\nthe soul is made from the substance of God, and there takes occasion\nto examine the origin of the error, and says: \"Respondeo dicendum,\nquod dicere animam esse de substantia Dei, manifestam improbabilitatem\ncontinet. Ut enim ex dictis patet, anima humana est quandoque\nintelligens in potentia, et scientiam quodammodo a rebus acquirit, et\nhabet diversas potentias; qu\u00e6 omnia aliena sunt a Dei natura, qui est\nactus purus, et nihil ab alio accipiens, et nullam in se diversitatem\nhabens, ut supra probatum est.\n\n\"Sed hic error principium habuisse videtur ex duabus positionibus\nantiquorum. Primi enim, qui naturas rerum considerare inceperunt,\nimaginationem transcendere non valentes, nihil pr\u00e6ter corpora esse\nposuerunt. Et ideo Deum dicebant esse quoddam corpus, quod aliorum\ncorporum judicabant esse principium. Et quia animam ponebant esse de\nnatura illius corporis, quod dicebant esse principium, ut dicitur\nin primo de anima, per consequens sequebatur quod anima esset de\nsubstantia Dei. Juxta quam positionem etiam Manich\u00e6i, Deum esse quamdam\nlucem corpoream existimantes, quandam partem illius lucis animam esse\nposuerunt corpori alligatam. Secundo vero processum fuit ad hoc quod\naliqui aliquid incorporeum esse apprehenderunt; non tamen a corpore\nseparatum, sed corporis formam. Unde et Varro dixit quod Deus est\nanima, mundum intuitu, vel motu et ratione gubernans: ut Augu. narrat 7\nde Civit. Dei. Sic igitur illius totalis anim\u00e6 partem, aliqui posuerunt\nanimam hominis: sicut homo est pars totius mundi; non valentes\nintellectu pertingere ad distinguendos spiritualium substantiarum\ngradus, nisi secundum distinctiones corporum. H\u00e6c autem sunt omnia\nimpossibilia, ut supra probatum est, unde manifeste falsum est animam\nesse de substantia Dei.\" (P. 1^a, Q. 90^a, A. 1^o.)\n\n\nON CHAPTER XI.\n\n(11) We often find the intellect identified by the scholastics with\nthe thing known, even when they treat of created intellects; but this\nidentity is limited to the purely ideal order, and denotes only the\nintimate union of the idea and the intellect. It is well known what\nimportance they attached to matters and forms; and this distinction\nis also applied to the phenomena of intelligence. Although the idea\nwas considered as a thing distinct from the intellect, yet, as\nthe intellect is perfected by it, and placed in relation with the\nthing represented, they said that the intellect was the same as the\nthing known. We must thus explain passages in St. Thomas and other\nscholastics, since, although their expressions, if considered in\nisolation, would be inexact, they are not so, if regard be had to the\nmeaning which they attributed to them, and which clearly follows from\ntheir fundamental principles. Thus St. Thomas (Quodlibet. 7 A. 2), to\nprove that the created intellect cannot know many things at the same\ntime, says:\n\n\"Sed quod intellectus simul intelligat plura intelligibilia, primo\net principaliter, est impossibile. Cujus ratio est quia _intellectus\nsecundum actum est omnino, id est, perfecte res intellecta_: ut dicitur\nin 3 de anima. _Quod quidem intelligendum est non quod essentia\nintellectus fiat res intellecta_ vel species ejus; sed quia complete\ninformatur per speciem rei intellect\u00e6, dum eam actu intelligit. Unde\nintellectum simul plura intelligere primo, idem est ac si res una simul\nesset plura. In rebus enim materiabilus videmus quod una res numero non\npotest esse simul plura in actu, sed plura in potentia.\n\n       *       *       *       *       *\n\n\"Unde patet quod sicut una res materialis non potest esse simul plura\nactu, ita unus intellectus non potest simul plura intelligere primo.\nEt hoc est quod Alga, dicit, quod sicut unum corpus non potest simul\nfigurari pluribus figuris; ita unus intellectus non potest simul plura\nintelligere. Nec potest dici quod intellectus informatur perfecte\nsimul pluribus speciebus intelligibilibus, sicut unum corpus simul\ninformatur figura et colore; quia figura et color non sunt form\u00e6\nunius generis, nec in eodem ordine accipiuntur quia non ordinantur ad\nperficiendum in esse unius rationis; sed omnes form\u00e6 intelligibiles in\nquantum hujusmodi, sunt unius generis, et in eodem ordine se habent ad\nintellectum, in quantum perficiunt intellectum in hoc quod est esse\nintellectum in actu. Unde plures species intelligibiles se habent sicut\nfigur\u00e6 plures, vel plures colores, qui simul in actu in eodem esse non\npossunt secundum idem.\"\n\nBy the first passage, we see that the meaning of identity of the\nintellect with the thing known, is the same as explained in the\nbeginning of this note; to wit, the intimate union of the idea\nof intelligible species with the intellect, as the form with its\nmatter,--a form which perfects the intellect, makes it pass from\npotentiality to actuality, and places it in relation with the thing\nrepresented.\n\n\nON CHAPTER XII.\n\n(12) The doctrine of immediate intelligibility is susceptible of still\nfurther illustration; but as this cannot be clearly done without\nexamining at length the nature of ideas, which does not pertain to our\npresent treatise, we shall reserve it for its proper place.\n\n\nON CHAPTER XIII.\n\n(13) Enough, perhaps, was not said in the text to enable all readers to\nform clear and complete ideas of the representation of causality; but\nthis doctrine, as regards the first intelligence, is closely allied to\nthe questions on the foundation of the possibility even of non-existent\nthings,--questions which we cannot here investigate without reversing\nthe order of subjects.\n\n\nON CHAPTER XIV.\n\n(14) The distinction of geometrical and non-geometrical orders of ideas\nis of the utmost importance in ideology. We have given this distinction\nin order that the examination of a truth fundamental among purely ideal\ntruths might not remain incomplete. But its explanation and foundation\nwill be given in our treatise on the of space and extension.\n\n\nON CHAPTER XV.\n\n(15) The word _instinct_, when applied to the intellect, is clearly\ntaken in a different sense than it is when applied to irrational\nanimals. It has here no ignoble meaning; and this is in accordance with\nthe use made of it when divine things are spoken of. One meaning given\nit by the dictionary is, \"_impulse, or movement of the Holy Ghost, in\nspeaking of supernatural inspirations_.\" The Latin, _instinctus_, means\n_inspiration_. Thus: \"Sacro mens _instincta_ furore.\"\n\n\nON CHAPTER XVI.\n\n(16) The confusion of ideas upon this point originates in that tendency\nto unity of which we spoke in our Fourth Chapter. We first suppose\nthere must be one only principle, and we ask what it is; whereas,\nbefore inquiring what it is, we should ascertain if there be one only,\nas is supposed. We have already seen that Fichte's system rested on the\nsame supposition. Thus the cause of innocent disputes in the schools\nmay lead to more transcendental errors.\n\n\nON CHAPTER XVII.\n\n(17) We have, we think, faithfully interpreted the thought of\nDescartes, but lest there should be some doubt as to this, we subjoin\na notable passage from his answer to the objections collected by _P\u00e8re\nMersenne_ from various philosophers and theologians, against the\nSecond, Third, Fourth, Fifth, and Sixth Meditations.\n\n\"When we know that we are something that thinks, this first notion _is\ntaken from no syllogisms_; and when any one says: _I think, therefore\nI am_, or exist, _he does not infer_ his existence from thought, as\n_by the force of a syllogism_, but as a thing known by itself; _he\nsees it by a simple inspection of the mind_; for if he deduced it from\na syllogism, he would have to know beforehand this major; whatever\nthinks, is, or exists. On the contrary, this proposition is manifested\nto him by his own sentiment that he cannot think without existing. It\nis a property characteristic of our mind to form general propositions\nfrom the knowledge of particular propositions.\" Descartes does not\nalways explain himself with this clearness; the objections of his\nadversaries made him examine his doctrine more thoroughly, and this\ncontributed to clear up his ideas.\n\n\nON CHAPTER XVIII.\n\n(18) To form an accurate estimate of Descartes' views, let us listen to\nhis own explanation of his system.\n\n\"As the senses sometimes deceive us, I wished to _suppose_ that nothing\nof what they make us imagine appeared; as there are men who are\ndeceived, and make paralogisms even when reasoning upon the simplest\nmatters of geometry, I judged myself as liable to err as they are,\nand I rejected as false all those reasons I had before held to be\ndemonstrations; and also considering that even the thoughts which we\nhave while awake may come to us while asleep, although no one of\nthem may be true, I resolved to _feign_ that all things which had\nentered my mind contained no more truth than illusory dreams. But I\nimmediately observed that, while I wished to think that every thing\nwas false, it was necessary for me, who thought this, to be something;\nand, noting that this truth: I think, therefore I am, was so firm and\nsecure, that the most extravagant suppositions could not shake it, I\njudged that I might, without scruple, receive it as the first truth of\nphilosophy.\"--_Discours sur la M\u00e9thode._ P. 4^{ieme.}\n\nWe said that the doubt of Descartes was a _supposition_, a _fiction_,\nand these are the very terms he himself uses. In his reply to the\nobjections of _P\u00e8re Mersenne_, we find the following confirmatory\nextract: \"I have read with great satisfaction your observations upon my\ntreatise on philosophy, for they show your good-will towards me, your\npiety towards God, and your zeal for the advance of his glory. I cannot\nbut rejoice that you have judged my arguments worthy of your criticism,\nbut also that you say nothing not easily answerable.\n\n\"In the first place, you remind me that I have rejected the ideas\nof phantasms of bodies, _not truly, but only by a mere fiction_, in\norder to conclude that I am something that thinks, fearing, perhaps,\nthat I should believe it followed from this that I am only something\nthat thinks; but I have already shown, in my Second Meditation, that\nI agreed with this, and I said: 'But these things, which I _suppose_\nnot to be, because I do not know them, may not really be any thing\ndifferent from me who know them; of this I can say nothing, I have at\npresent nothing to do with it.'\" * * * * * * *\n\nWe here see that Descartes did not deny his doubt to be a mere fiction;\nhe even says that he does nothing but apply a method, the necessity of\nwhich all philosophers admit.\n\n\"I pray you,\" he continues, \"to remember that with respect to matters\nof the will, I have always made a broad distinction between the\ncontemplation of truth and the uses of life; as regards the latter, I\nam so far from thinking that we must follow only things very clearly\nknown, that I believe we must not always consider even what is most\nprobable, but that we must, among things wholly unknown or uncertain,\nsometimes choose one, and hold firmly to it, so long as we see no\nreason for not doing so, just as if we had chosen it from evident and\ncertain motives, as I have already explained in the _Discours sur la\nM\u00e9thode_; but when we treat only of the contemplation of truth, _who\never doubted that it was necessary to suspend the judgment upon things\nthat are obscure or not distinctly known_?\"\n\nIn what, then, consists Descartes' merit? In having _applied_ a\nrule known to all, and employed by few, and in so doing at the very\ntime that prejudices in favor of the Aristotelian doctrine were the\nstrongest. Descartes plainly says so; his method of doubting is not\nnew, only the application of it was wanting; for, as regards its\nfundamental principle, \"who ever doubted that it was necessary to\nsuspend the judgment upon things that are obscure or not distinctly\nknown?\"\n\nUnderstanding Descartes' method in this sense, that is, taking the\ndoubt as a supposition, a mere fiction, it is not opposed to sound\nreligious and moral principles. The profound philosopher does not seem\nto disdain to set his readers at rest upon this point; he ingenuously\nshows, in commencing his investigations, that his religious belief was\nsafe. \"Finally, as before undertaking to rebuild the house wherein one\nlives, it is not enough to demolish the old one, and provide materials\nand workmen, or to exercise one's self in architecture, and to\ncarefully trace the design of the new house; but it is also necessary\nto have another house in which to live, while the new one is building;\nso that my actions might not be unresolved, like my judgments, and\nthat I might, in the meantime, live as happily as possible, I made a\nprovision for myself; it consists of three or four maxims. The first\nis, to observe the laws and customs of my country, _and constantly\nto preserve the religion in which, by the grace of God, I have been\ninstructed from my infancy_. * * * * * * After having assured myself of\nthese maxims, and laid them aside with _the truths of faith which have\nalways been first in my belief_, I judged that I might freely reject\nthe rest of my opinions.\"--_Discours sur la M\u00e9thode_, P. 3^{ieme.}\n\n\nON CHAPTER XIX.\n\n(19) With respect to the distinction between the testimony of\nconsciousness and that of evidence, as in the analysis of the\nproposition: I think, therefore I am; there can be no doubt that\nDescartes did not express himself with sufficient precision and\nexactness. See, for example, this extract: \"After this, I considered\nin general what is necessary for a proposition to be true and certain;\nfor, although I had not yet met such a one, I nevertheless thought I\nought to know in what this certainty consisted; and observing that\nin the proposition, I think, therefore I am, there is nothing to\nassure me of its truth, except the clear perception that in order\nto think I must be, I judged that I could take it to be a general\nrule that things clearly and distinctly conceived are all true; only\nthere is some difficulty in ascertaining what things we do distinctly\nconceive.\"--_Discours sur la M\u00e9thode._ Partie 4^{me}.\n\n\nON CHAPTER XX.\n\n(20) The _apodictical_ certainty of which Kant speaks in the passage\ncited, is the result of the intrinsic evidence of ideas, or, in other\nwords, it is what the schoolmen called metaphysical certainty.\n\n\nON CHAPTER XXI.\n\n(21) Besides the questions on the principle of contradiction as the\nonly foundation of certainty, there are others as to its scientific\nutility and importance. We shall, when we come to treat of the idea of\n_being_ in general, examine these points at length; wherefore we will\nnow pass them by.\n\n\nON CHAPTER XXII.\n\n(22) We see by a passage from the fourth part of the _Discourse on\nMethod_, by Descartes, cited in note xv., that besides the principle,\nI think, therefore I am, he admitted the principle of the legitimacy\nof evidence; for, asking what is necessary in order that a proposition\nmay be true and certain, he says, that having remarked that if he was\ncertain of the truth of this proposition (I think, therefore I am),\nhe was so only because he saw it to be so; he believed that he could\ntake it to be a general rule _that things known clearly and distinctly\nare all true_. This shows two principles, closely connected, although\nvery unlike, to enter into Descartes' system. The first is the fact\nof consciousness of thought; the second is the general rule of the\nlegitimacy of the criterion of evidence.\n\nIt is also to be remarked that there is here some confusion of ideas,\nwhich we have already pointed out. It is not exact to say that the\nprinciple, I think, therefore I am, is evident: the evidence relates to\nthe _consequence_; but there is, properly speaking, no evidence of the\nact of thought, excepting consciousness. Evidence is a criterion, but\nnot the only one.\n\n\nON CHAPTER XXIII.\n\n(23) What we have said of the second proposition of this chapter is\nindependent of the mode in which the soul and body exercise their\nmutual influence. These questions belong elsewhere. This influence is,\nin every system, a fact attested by experience; and this is all that is\nneeded for what we propose to establish here.\n\n\nON CHAPTER XXIV.\n\n(24) For the better understanding of what we have said in this chapter\non evidence, it will be well to consider what will be advanced in\nchapters XXVI. to XXXI., inclusive.\n\n\nON CHAPTER XXV.\n\n(25) What has been said in this chapter shows the truth of what we said\nin the twenty-fourth chapter, upon the connection of the different\ncriteria, and the necessity of not confining one's self to an exclusive\nphilosophy. Consciousness serves as the basis of the other criteria,\nas an indispensable fact; but if we deny the others, we also deny\nconsciousness.\n\n\nON CHAPTERS XXVI., XXVII., AND XXVIII.\n\n(26) Dugald Stewart in his _Elements of the Philosophy of the\nHuman Mind_, (P. II., C. II., Section 3, \u00a72,) cites a passage from\na dissertation printed at Berlin in 1764, which does not appear\nso unreasonable as he pretends. We subjoin it, because the German\nphilosopher's opinion seems to us the same that we gave in the text.\n\n\"Omnes mathematicorum propositiones sunt identic\u00e6 et representantur hac\nformula, A=A. Sunt veritates identic\u00e6, sub varia forma express\u00e6, imo\nipsum quod dicitur contradictionis principium vario modo enuntiatum\net involutum; si quidem omnes hujus generis propositiones revera in\neo continentur. Secundum nostram autem intelligendi facultatem ea est\npropositionum differentia, quod qu\u00e6dam longa ratiociniorum serie,\nalia autem breviore via, ad primum omnium principiorum reducantur, et\nin illud resolvantur. Sic. v. g. propositio 2+2=4 statim huc cedit:\n1+1+1+1=1+1+1+1; id est, idem est idem; et, proprie loquendo, hoc modo\nenuntiari debet,--si contingat adesse vel existere quatuor entia, tum\nexistunt quatuor entia; nam de existentia non agunt geometr\u00e6, sed\nea hypothetice tantum subintelligitur. Inde summa oritur certitudo\nratiocinia perspicienti; observat nempe idearum identitatem; et h\u00e6c est\nevidentia assensum immediate cogens, quam mathematicam aut geometricam\nvocamus. Mathesi tamen sua natura priva non est et propria; oritur\netenim ex identitatis perceptione, qu\u00e6 locum habere potest, etiamsi\nide\u00e6 non repr\u00e6sentent extensum.\"\n\n\nON CHAPTERS XXX AND XXXI.\n\n(27) We have shown that Dugald Stewart had perhaps in view Vico's\ndoctrine; but without wishing to bring against him the charge he\nbrought against his master, Reid, that of resuscitating the doctrines\nof the Jesuit Buffier, we would, in order that the reader may judge\nwith full knowledge of the cause, subjoin a remarkable extract from\nthe Scotch philosopher, which will show coincidence between some of\nhis doctrines and those of the Neapolitan. Had Stewart read Vico,\nwe are inclined to believe that he would not have complained of\nthe _confusion_ with which various ancient and modern authors have\nexplained this doctrine.\n\n\"The peculiarity of that species of evidence which is called\ndemonstrative, and which so remarkably distinguishes our mathematical\nconclusions from those to which we are led in other branches of\nscience, is a fact which must have arrested the attention of every\nperson who possesses the slightest acquaintance with the elements of\ngeometry. And yet, I am doubtful if a satisfactory account has hitherto\nbeen given of the circumstance in which it arises. Mr. Locke tells us,\nthat 'what constitutes a demonstration is intuitive evidence of every\nstep;' and I readily grant, that if in a single step such evidence\nshould fail, the other parts of the demonstration would be of no value.\nIt does not, however, seem to me that it is on this consideration that\nthe demonstrative evidence of the conclusion depends, not even when\nwe add to it another which is much insisted on by Dr. Reid,--that\n'in demonstrative evidence our first principles must be intuitively\ncertain.' The inaccuracy of this remark I formerly pointed out when\ntreating of the evidence of axioms; on which occasion I also observed,\nthat the first principles of our reasonings in mathematics are not\naxioms, but definitions. It is in this last circumstance (I mean the\npeculiarity of reasoning from definitions) that the true theory of\nmathematical demonstration is to be found; and I shall accordingly\nendeavor to explain it at considerable length, and to state some of the\nmore important consequences to which it leads.\n\n\"That I may not, however, have the appearance of claiming, in behalf\nof the following discussion, an undue share of originality, it is\nnecessary for me to remark that the leading idea which it contains has\nbeen repeatedly started, and even to a certain length prosecuted, by\ndifferent writers, ancient as well as modern; but that, in all of them,\nit has been so blended with collateral considerations, although foreign\nto the point in question, as to divert the attention both of writer and\nreader, from that single principle on which the solution of the problem\nhinges. * * * * * * *\n\n\"It was already remarked, in the first chapter of this part, that\nwhereas, in all other sciences, the propositions which we attempt\nto establish, express facts real or supposed,--in mathematics, the\npropositions which we demonstrate only assert a connection between\ncertain suppositions and certain consequences. Our reasonings,\ntherefore, in mathematics, are directed to an object essentially\ndifferent from what we have in view, in any other employment of our\nintellectual faculties;--not to ascertain truths with respect to\nactual existences, but to trace the logical filiation of consequences\nwhich follow from an assumed hypothesis. If, from this hypothesis,\nwe reason with correctness, nothing, it is manifest, can be wanting\nto complete the evidence of the result; as this result only asserts\na necessary connection between the supposition and the conclusion.\nIn the other sciences, admitting that every ambiguity of language\nwere removed, and that every step of our deductions were rigorously\naccurate, our conclusions would still be attended with more or less of\nuncertainty, being ultimately founded on principles which may, or may\nnot, correspond exactly with the fact.\" (_Elements of the Philosophy of\nthe Human Mind._ P. II., C. II., S. 3, \u00a7 1.)\n\nThis is exactly Vico's doctrine of the cause of the difference in the\ndegrees of evidence and certainty; although he makes a general system,\nin order to explain the problem of intelligence, what the Scotchman\nonly assigns as a fact to show the reason of mathematical evidence.\nP\u00e8re Buffier (Trait. des prem. V\u00e9rit\u00e9s, P. I., C. II.) explains the\nsame thing with great clearness.\n\nWe have said that, considering the indefatigable laboriousness which\ndistinguishes the Germans, it would not be strange if they had read the\nscholastics. In confirmation of this, we notice that Leibnitz urgently\nrecommends the reading of them, and the more modern Germans are not\nlikely to forget the advice of so able an author.\n\nAmong various passages of Leibnitz, we select the following extract,\nbecause it seems to us rather curious: \"Truth is more spread than one\nwould believe; but it is often colored, also often covered over, and\neven weakened, mutilated, and corrupted by additions which spoil it,\nor render it less useful. By observing the traces of truth in the\nancients, or, to speak more generally, in all who have preceded us,\nwe dig gold from dirt, and draw the diamond from its mine, light from\ndarkness, and this would really be _perennis qu\u00e6dam Philosophia_.\n\n\"It may even be said that some progress would be observable in\nknowledge. The Orientals have great and beautiful ideas of the\nDivinity; the Greeks added reasoning and a form of science; the Fathers\nof the Church rejected whatever was bad in Greek philosophy; but the\nscholastics labored to usefully employ whatever was acceptable in\nPagan philosophy. I have frequently said: _aurum latere in stercore\nillo scholastico barbariei_, and I wish we could find some one versed\nin the Irish and Spanish philosophy, to cull from it what is good; I am\nsure he would find his labor repaid by many and beautiful truths. There\nwas once a Swiss who _mathematized_ scholastically; his works are but\nlittle known; although, from what I have seen of them, I should judge\nthem to be profound and worthy of consideration.\" (Lettre 3^{ieme} \u00e0 M.\nRemond de Montmort.)\n\nThus speaks Leibnitz, one of the most eminent men of modern times, and\nof whom Fontenelle said: \"He led the van in all the sciences.\" See,\nthen, if he was wrong in recommending the study of those authors to all\ndesirous of acquiring a profound knowledge of philosophy. This study,\nsetting aside its intrinsic utility, is of great advantage in judging,\nwith knowledge of the cause, a school, which, whatever its worth,\noccupies a page in the history of the human mind.\n\n\nON CHAPTER XXXII.\n\n(28)The author to whom I allude (317) is Fenelon, who, under the name\nof common sense, includes also the criterion of evidence, as may be\nseen by this extract: \"What is common sense? Does it not consist in\nthe first notions which all men have of the same things? This common\nsense, which always and everywhere is the same, which precedes all\nexamination, and even holds it in ridicule on certain questions, in\nwhich one laughs instead of examining; which renders man unable to\ndoubt, no matter how great his efforts may be; this sense which belongs\nto all men, which only waits to be consulted in order to discover\nitself and show us the _evidence_ or the absurdity of the question, _is\nnot this what I call my ideas_? Here, then, are these general ideas\nor notions which I cannot contradict or examine, but according to\nwhich I examine and judge every thing, so that, instead of replying, I\nlaugh when any thing is proposed clearly in opposition to what these\n_immutable ideas_ represent.\"--_Existence de Dieu_, P. II., v. 33.\n\nThere is no doubt that Fenelon speaks of evidence in this extract,\nsince, besides using this very term, he refers to immutable ideas; by\ncommon sense he understands the general ideas by which we judge of all\nthings, or in other words, the ideas from which evidence proceeds.\n\n\n\n\nNOTE TO BOOK SECOND.\n\n\nON CHAPTER II.\n\n(29) The immateriality of the souls of brutes is not a discovery of\nmodern philosophy, the scholastics maintained it, and carried their\nideas on this subject so far as to assert that no vital principle can\nbe a body. In this sense they taught that even the principle of life,\nor the soul of plants, was something superior to the body. St. Thomas\n(P. I., Q. LXXV., A. I.) asks, in general, if the soul is a body:\n\"Utrum anima sit corpus,\" and answers as follows:\n\n\"Respondeo dicendum, quod ad inquirendum de natura anim\u00e6, oportet\npr\u00e6supponere, _quod anima dicitur esse primum principium vit\u00e6_, in iis\nqu\u00e6 apud nos vivunt. Animata enim viventia dicimus, res vero inanimatas\nvita carentes; vita autem maxime manifestatur duplici opere, scilicet\ncognitionis, et motus. Horum autem principium antiqui philosophi\nimaginationem transcendere non valentes, aliquod corpus ponebant,\nsola corpora res esse dicentes, et quod non est corpus, nihil esse,\net secundum hoc, animam aliquod corpus esse dicebant. Hujus autem\nopinionis falsitas, licet multipliciter ostendi possit, tamen uno\nutemur, quo etiam communius et certius patet animam corpus non esse.\nManifestum est enim, quod non quodcumque vitalis operationis principium\nest anima; sic enim oculus esset anima, cum sit quoddam principium\nvisionis, et idem esset dicendum de aliis anim\u00e6 instrumentis: sed\nprimum principium vit\u00e6 dicimus esse animam. Quamvis autem aliquod\ncorpus possit esse quoddam principium vit\u00e6, sicut cor est principium\nvit\u00e6 in animali; tamen non potest esse primum principium vit\u00e6 aliquod\ncorpus. Manifestum est enim, quod esse principium vit\u00e6, vel vivens, non\nconvenit corpori ex hoc quod est corpus, alioquin omne corpus esset\nvivens, aut principium vit\u00e6, convenit igitur alicui corpori quod sit\nvivens, vel etiam principium vit\u00e6, per hoc quod est tale corpus. Quod\nautem est actu tale, habet hoc ab aliquo principio, quod dicitur actus\nejus. _Anima igitur qu\u00e6 est primum principium vit\u00e6, non est corpus, sed\ncorporis actus_, sicut calor qui est principium calefactionis, non est\ncorpus, sed quidam corporis actus.\"\n\nNotwithstanding this doctrine, it might still be doubted whether matter\ndoes not enter as a component element in the soul, although the soul\nitself is not corporeal, and, therefore, the holy doctor (Ib., A.\n5) asks if the soul is composed of matter and form; and here he is\nspeaking of the soul in general as the principle of life, and not of\nthe intellectual soul alone. He answers in the negative, as follows:\n\n\"Respondeo dicendum, quod _anima non habet materiam_, et hoc potest\nconsiderari dupliciter. _Primo quidem, ex ratione anim\u00e6 in communi_,\nest enim de ratione anim\u00e6, quod sit forma alicujus corporis. Aut\nigitur est forma secundum se totam, aut secundum aliquam partem sui.\nSi secundum se totam, impossibile est quod pars ejus sit materia, si\ndicatur materia aliquid ejus in potentia tantum, quia forma, in quantum\nforma, est actus. Id autem quod est in potentia tantum, non potest esse\npars actus, cum potentia repugnet actui, utpote contra actum divisa. Si\nautem sit forma secundum aliquam partem sui, illam partem dicemus esse\nanimam, et illam materiam cujus primo est actus, dicemus esse primum\nanimatum. Secundo specialiter ex ratione human\u00e6 anim\u00e6, in quantum est\nintellectiva.\"\n\nAlthough these passages are clear enough, there is another where it is\nexpressly asserted that the souls of perfect animals are absolutely\nindivisible, so that division can be predicated of them neither _per\nse_ nor _per accidens_. He asks, (Q. LXXVI., art. 8,) if the soul in\ngeneral is in any part of the body; and he answers, yes: distinguishing\nbetween essential and quantitative totality:\n\n\"Sed forma, qu\u00e6 requirit diversitatem in partibus, sicut est anima, _et\npr\u00e6cipue animalium perfectorum_, non equaliter se habet ad totum et\nad partes; unde _non dividitur per accidens, scilicet per divisionem\nquantitatis_. Sic ergo totalitas quantitativa, non potest attribui\nanim\u00e6, nec per se, nec per accidens. Sed totalitas secunda, qu\u00e6\nattenditur secundum rationis et essenti\u00e6 perfectionem, proprie et per\nse, convenit formis.\"\n\nIt seems, however, that this doctrine of St. Thomas met with\nopposition, from some persons who could not conceive how the soul of\nbrutes could be inextensive, as they regarded this as the exclusive\nproperty of the intellectual soul. Cardinal Gaetano, in his comments\non St. Thomas, undertakes his defence. He shows that he understood the\ndoctrine of St. Thomas concerning the indivisibility of the souls of\nbrutes, in its strictest sense. He gives the objection in the following\nwords:\n\n\"Dubium secundo est circa candem totalitatem quoniam S. Thomas a\ncommuni opinione discordare videtur hoc in loco, eo quod ponat _pr\u00e6ter\nanimam intellectivam_, aliquam aliam formam in materia _inextensam,\nscilicet animam sensitivam animalium perfectorum_, cum tamen vix\npossit sustineri, quod anima intellectiva de foris veniens, informet\nsecundum esse, et sit inextensa.\"\n\nInstead of more or less plausible interpretations of the text in order\nto solve the objection, the learned commentator boldly maintains the\nindivisibility of the souls of brutes, and treats almost with contempt\nthose who think differently:\n\n\"Ad secundum dubium dicitur, quod doctrina hic tradita, _est quidem\ncontra modernorum communem phantasiam, sed non contra philosophicas\nrationes, parum est autem de horum aucthoritate curandum_. Cum autem\ndicitur, quod sine ratione hoc est dictum, respondetur quod ratio\ninsinuata est a posteriori, quia scilicet diversam totaliter habet\nhabitudinem ad totum et partem ipsa forma ex propria ratione. Si enim\nhabet totaliter diversam habitudinem ad totum et ad partes, _hoc\nprovenit ex indivisibilitate form\u00e6_. Quia si divideretur forma ad\ndivisionem totius, jam pars form\u00e6 proportionaretur parti corporis, et\ncum pars quantitativa form\u00e6 sit tota essentia form\u00e6, ergo ipsa forma\nsecundum rationem su\u00e6 essenti\u00e6 non habet totaliter diversam habitudinem\nad totum et ad partes: sed utrumque, scilicet tam totum quam partem\nrespicit, ut proportionatum perfectible. Et confirmari potest ista\nratio, quia forma extensa ex vi solius divisionis, non desinit esse\nsecundum illam partem quam habet in parte decisa: imo qu\u00e6 quodammodo\nerat per modum potenti\u00e6, perficitur, et fit actu seorsum, ut patet\nin formis naturalibus, ergo a destructione consequentis, si ex sola\ndivisione pars decisa non potest retinere eandem speciem, _ergo non\nerat extensa et divisibilis ad divisionem subjecti_. * *\n\n * * * * * * * *\n\n_Non est ergo sine ratione dictum, quod anim\u00e6 aliqu\u00e6 pr\u00e6ter\nintellectivam sunt tant\u00e6 perfectionis quod sunt inextens\u00e6, tam per se\nquam per accidens_: quamquam potenti\u00e6 omnes earum sint extens\u00e6 per\naccidens: qualitates enim, sunt corporis partibus accommodat\u00e6.\"\n\n\n\n\nNOTES TO BOOK THIRD.\n\n\nON CHAPTER X.\n\n(30) Leibnitz and Clarke had a very interesting dispute on space,\nfrom which I shall extract a few passages. Leibnitz wrote a letter to\nthe Princess of Wales, in which he repeated the expression of Newton,\nthat space was the organ which God uses in his sensations of things.\nLeibnitz argued against this opinion, that if God, in order to perceive\nthings, needs any medium, they do not depend entirely on him, and are\nnot produced by him.\n\n\n_Clarke Answered_:\n\n\"M. le chevalier Newton ne dit pas que l'espace est l'organe dont Dieu\nse sert pour apercevoir les choses; il ne dit pas non plus que Dieu\nait besoin d'aucun moyen pour les apercevoir. Au contraire, il dit\nque Dieu, \u00e9tant pr\u00e9sent partout, aper\u00e7oit les choses par sa pr\u00e9sence\nimm\u00e9diate, dans tout l'espace o\u00f9 elles sont, sans l'intervention ou\nle secours d'aucun organe ou d'aucun moyen. Pour rendre cela plus\nintelligible, il l'\u00e9claircit par une comparaison. Il dit que comme\nl'\u00e2me, \u00e9tant imm\u00e9diatement pr\u00e9sente aux images qui se forment dans le\ncerveau par le moyen des organes des sens, voit ces images comme si\nelles \u00e9taient les choses m\u00eames qu'elles repr\u00e9sentent; de m\u00eame Dieu voit\ntout par sa pr\u00e9sence imm\u00e9diate, \u00e9tant actuellement pr\u00e9sent aux choses\nm\u00eames, \u00e0 toutes les choses qui sont dans l'univers, comme l'\u00e2me est\npr\u00e9sente \u00e0 toutes les images qui se forment dans le cerveau. M. Newton\nconsid\u00e8re le cerveau et les organes des sens comme le moyen par lequel\nces images sont form\u00e9es, et non comme le moyen par lequel l'\u00e2me voit ou\naper\u00e7oit ces images lorsqu'elles sont ainsi form\u00e9es. Et dans l'univers\nil ne consid\u00e8re pas les choses comme si elles \u00e9taient des images\nform\u00e9es par un certain moyen ou par des organes, mais comme des choses\nr\u00e9elles que Dieu lui-m\u00eame a form\u00e9es et qu'il voit dans tous les lieux\no\u00f9 elles sont sans l'intervention d'aucun moyen. C'est tout ce que M.\nNewton a voulu dire par la comparaison dont il s'est servi lorsqu'il\nsuppose que l'espace infini est, pour ainsi dire, le _sensorium_ de\nl'Etre qui est pr\u00e9sent partout.\"\n\n_Leibnitz Replied_:\n\n\"Il se trouve express\u00e9ment dans l'appendice de l'_Optique_ de M. Newton\nque l'espace est le _sensorium_ de Dieu. Or le mot _sensorium_ a\ntoujours signifi\u00e9 l'organe de la sensation. Permis \u00e0 lui et \u00e0 ses amis\nde s'expliquer maintenant tout autrement, je ne m'y oppose pas.\n\n\"On suppose que la pr\u00e9sence de l'\u00e2me suffit pour qu'elle s'aper\u00e7oive\nde se qui se passe dans le cerveau; mais c'est justement ce que le P.\nMalebranche et toute l'\u00e9cole cart\u00e9sienne nient et ont raison de nier.\nIl faut toute autre chose que la seule pr\u00e9sence pour qu'une chose\nrepr\u00e9sente ce qui se passe dans l'autre. Il faut pour cela quelque\ncommunication explicable, quelque mani\u00e8re d'influence. L'espace, selon\nM. Newton, est intimement pr\u00e9sent au corps qu'il contient, et qui est\ncommensur\u00e9 avec lui; s'ensuit-il pour cela que l'espace s'aper\u00e7oive de\nce qui se passe dans le corps, et qu'il s'en souvienne apr\u00e8s que le\ncorps en sera sorti? Outre que l'\u00e2me \u00e9tant indivisible, sa pr\u00e9sence\nimm\u00e9diate, qu'on pourrait s'imaginer dans le corps, ne serait que dans\nun point. Comment donc s'apercevrait-elle de ce qui se fait hors de\nce point? Je pr\u00e9tends d'\u00eatre le premier qui ait montr\u00e9 comment l'\u00e2me\ns'aper\u00e7oit de ce qui se passe dans le corps.\n\n\"La raison pourquoi Dieu s'aper\u00e7oit de tout n'est pas sa simple\npr\u00e9sence, mais encore son op\u00e9ration; c'est parce qu'il conserve les\nchoses par une action qui produit continuellement ce qu'il y a de bont\u00e9\net de perfection en elles. Mais les \u00e2mes n'ayant point d'influence\nimm\u00e9diate sur les corps, ni les corps sur les \u00e2mes, leur correspondance\nmutuelle ne saurait \u00eatre expliqu\u00e9e par la pr\u00e9sence.\"\n\n\n_Clarke Answered_:\n\n\"Le mot de _sensorium_ ne signifie pas proprement l'organe, mais le\nlieu de la sensation. L'\u0153il, l'oreille, etc., sont des organes, mais\nce ne sont pas des _sensoria_. D'ailleurs M. le chevalier Newton ne\ndit pas que l'espace est un _sensorium_, mais qu'il est (par voie de\ncomparaison) _pour ainsi dire_ le _sensorium_, etc.\n\n\"On n'a jamais suppos\u00e9 que la pr\u00e9sence de l'\u00e2me suffit pour la\nperception; on a dit seulement que cette pr\u00e9sence est n\u00e9cessaire afin\nque l'\u00e2me aper\u00e7oive. Si l'\u00e2me n'\u00e9tait pas pr\u00e9sente aux images des\nchoses qui sont aper\u00e7ues, elle ne pourrait pas les apercevoir; mais sa\npr\u00e9sence ne suffit pas, \u00e0 moins qu'elle ne soit aussi une substance\nvivante. Les substances inanim\u00e9es, quoique pr\u00e9sentes, n'aper\u00e7oivent\nrien; et une substance vivante n'est capable de perception que dans\nle lieu o\u00f9 elle est pr\u00e9sente; soit aux choses m\u00eames, comme Dieu est\npr\u00e9sent \u00e0 tout l'univers; soit aux images des choses, comme l'\u00e2me leur\nest pr\u00e9sente dans son _sensorium_. Il est impossible qu'une chose\nagisse ou que quelque sujet agisse sur elle dans un lieu o\u00f9 elle n'est\npas pr\u00e9sente, comme il est impossible qu'elle soit dans un lieu o\u00f9 elle\nn'est pas. Quoique l'\u00e2me soit indivisible, il ne s'ensuit pas qu'elle\nn'est pr\u00e9sente que dans un seul point. L'espace fini ou infini es\nabsolument indivisible, m\u00eame par la pens\u00e9e; car on ne peut s'imaginer\nque ses parties se s\u00e9parent l'une de l'autre sans s'imaginer qu'elles\nsortent, pour ainsi dire, hors d'elle-m\u00eames; et cependant l'espace\nn'est pas un simple point.\n\n\"Dieu n'aper\u00e7oit pas les choses par sa simple pr\u00e9sence, ni parce qu'il\nagit sur elles, mais parce qu'il est non-seulement partout, mais encore\nun \u00eatre vivant et intelligent. On doit dire la m\u00eame chose de l'\u00e2me,\ndans sa petite sph\u00e8re, ce n'est point par sa simple pr\u00e9sence, mais\nparce qu'elle est une substance vivante, qu'elle aper\u00e7oit les images\nauxquelles elle est pr\u00e9sente, et qu'elle ne saurait apercevoir sans\nleur \u00eatre pr\u00e9sente.\"\n\n\n_Reply of Leibnitz._\n\n\"Ces messieurs soutiennent donc que l'_espace_ est un _\u00eatre r\u00e9el\nabsolu_; mais cela les m\u00e8ne \u00e0 de grandes difficult\u00e9s, car il para\u00eet que\ncet \u00eatre doit \u00eatre \u00e9ternel et infini. C'est pourquoi il y en a qui out\ncru que c'\u00e9tait Dieu lui-m\u00eame, ou bien son attribut, son immensit\u00e9.\nMais comme il a des parties, ce n'est pas une chose qui puisse convenir\n\u00e0 Dieu.\n\n\"Pour moi, j'ai marqu\u00e9 plus d'une fois que je tenais l'espace pour\nquelque chose de _purement relatif_, comme le temps, pour un _ordre\ndes coexistences_, comme le temps est un _ordre de successions_. Car\nl'espace marque, en terms de possibilit\u00e9, un ordre des choses qui\nexistent en m\u00eame temps, en tant qu'elles existent ensemble, sans entrer\ndans leurs mani\u00e8res d'exister. Et lorsqu'on voit plusieurs choses\nensemble, on s'aper\u00e7oit de cet ordre des choses entre elles.\n\n\"Pour r\u00e9futer l'imagination de ceux qui prennent l'espace pour une\nsubstance, ou du moins pour quelque \u00eatre absolu, j'ai plusieurs\nd\u00e9monstrations; mais je ne veux me servir \u00e0 pr\u00e9sent que de celle dont\non me fournit ici l'occasion. Je dis donc que si l'espace \u00e9tait un\n\u00eatre absolu, il arriverait quelque chose dont il serait impossible\nqu'il y e\u00fbt une raison suffisante, ce qui est contre notre axiome.\nVoici comment je le prouve. L'espace est quelque chose d'uniforme\nabsolument; et sans les choses y plac\u00e9es, un point de l'espace ne\ndiff\u00e8re absolument en rien d'un autre point de l'espace. Or il suit de\ncela (suppos\u00e9 que l'espace soit quelque chose en lui-m\u00eame outre l'ordre\ndes corps entre eux) qu'il est impossible qu'il y ait une raison\npourquoi Dieu, gardant les m\u00eames situations des corps entre eux, ait\nplac\u00e9 les corps dans l'espace ainsi et non autrement; et pourquoi tout\nn'a pas \u00e9t\u00e9 pris \u00e0 rebours (par exemple), par un \u00e9change de l'orient\net de l'occident. Mais si l'espace n'est autre chose que cet ordre ou\nrapport, et n'est rien du tout sans les corps, que la possibilit\u00e9,\nd'en mettre, ces deux \u00e9tats, l'un tel qu'il est, l'autre suppos\u00e9 \u00e0\nrebours, ne diff\u00e9reraient point entre eux. Leur diff\u00e9rence ne se trouve\ndonc que dans notre supposition chim\u00e9rique de la r\u00e9alit\u00e9 de l'espace en\nlui-m\u00eame. Mais dans la v\u00e9rit\u00e9, l'un serait justement la m\u00eame chose que\nl'autre, comme ils sont absolument indiscernables; et par cons\u00e9quent il\nn'y a pas lieu de demander la raison de la pr\u00e9f\u00e9rence de l'un \u00e0 l'autre.\n\n\"Il en est de m\u00eame du temps. Suppos\u00e9 que quelqu'un demande pourquoi\nDieu n'a pas tout cr\u00e9\u00e9 un an plus t\u00f4t, et que ce m\u00eame personnage\nveuille inf\u00e9rer de l\u00e0 que Dieu a fait quelque chose dont il n'est\npas possible qu'il y ait une raison pourquoi il a fait ainsi plut\u00f4t\nqu'autrement: on lui r\u00e9pondrait que son illation serait vraie, si le\ntemps \u00e9tait quelque chose, hors des choses temporelles; car il serait\nimpossible qu'il y e\u00fbt des raisons pourquoi les choses eussent \u00e9t\u00e9\nappliqu\u00e9es plut\u00f4t \u00e0 de tels instants qu'\u00e0 d'autres, leur succession\ndemeurant la m\u00eame. Mais cela m\u00eame prouve que les instants hors des\nchoses ne sont rien, et qu'ils ne consistent que dans leur ordre\nsuccessif; lequel demeurant le m\u00eame, l'un des deux \u00e9tats, comme celui\nde l'anticipation imagin\u00e9e, ne diff\u00e9rait en rien, et ne saurait \u00eatre\ndiscern\u00e9 de l'autre qui est maintenant....\n\n\"Il sera difficile de nous faire accroire que, dans l'usage ordinaire,\n_sensorium_ ne signifie pas l'organe de la sensation....\n\n\"La simple pr\u00e9sence d'une substance m\u00eame anim\u00e9e ne suffit pas pour\nla perception; un aveugle et m\u00eame un distrait ne voit point. Il faut\nexpliquer comment l'\u00e2me s'aper\u00e7oit de ce qui est hors d'elle.\n\n\"Dieu n'est pas pr\u00e9sent aux choses par situation, mais par essence; sa\npr\u00e9sence se manifeste par son op\u00e9ration imm\u00e9diate. La pr\u00e9sence de l'\u00e2me\nest toute d'une autre nature. Dire qu'elle est diffuse par le corps,\nc'est la rendre \u00e9tendue et divisible; dire qu'elle est tout enti\u00e8re en\nchaque partie de quelque corps, c'est la rendre divisible d'elle-m\u00eame.\nL'attacher \u00e0 un point, la r\u00e9pandre par plusieurs points, tout cela ne\nsont qu'expressions abusives, _Idola Tribus_.\"\n\n\n_Clarke's Answer_:\n\n\"Il est indubitable que rien n'existe sans qu'il y ait une _raison\nsuffisante_ de son existence, et que rien n'existe d'une certaine\nmani\u00e8re plut\u00f4t que d'une autre, sans qu'il y ait aussi une _raison\nsuffisante_ de cette mani\u00e8re d'exister. Mais \u00e0 l'\u00e9gard des choses\nqui sont indiff\u00e9rentes en elles-m\u00eames, la _simple volont\u00e9_ est une\nraison suffisante pour leur donner l'existence, ou pour les faire\nexister d'une certaine mani\u00e8re; et cette volont\u00e9 n'a pas besoin d'\u00eatre\nd\u00e9termin\u00e9e per une cause \u00e9trang\u00e8re....\n\n\"L'espace n'est pas une substance, un \u00eatre \u00e9ternel et infini, mais une\npropri\u00e9t\u00e9 ou une suite de l'existence d'un \u00eatre infini et \u00e9ternel.\nL'espace infini est l'immensit\u00e9 mais l'immensit\u00e9 n'est pas Dieu;[60]\ndonc l'espace infini n'est pas Dieu. Ce que l'on dit ici de l'espace\nn'est point une difficult\u00e9. L'espace infini est absolument et\nessentiellement indivisible, et c'est une contradiction dans les termes\nque de supposer qu'il soit divis\u00e9; car il faudrait qu'il y e\u00fbt un\nespace entre les parties que l'on suppose divis\u00e9s; ce qui est supposer\nque l'espace est divis\u00e9 et non divis\u00e9 en m\u00eame temps.[61] ...\n\n[60] In this proposition Clarke is either inexact and obscure, or else\nhe falls into a serious error. The immensity of God is God himself.\nEvery attribute of God is God.\n\n[61] Here Clarke confounds _divisibility_ with _separability_. See\nchapters X. and XI. of this book.\n\n\"Il ne s'agit pas de savoir ce que Goclenius[62] entend par le mot de\n_sensorium_, mais en quel sens M. le chevalier Newton s'est servi de\nce mot dans son livre. Si _Goclenius_ croit que l'\u0153il, l'oreille, ou\nquelque autre organe des sens est le _sensorium_, il se trompe. Mais\nquand un auteur emploie un terme d'art et qu'il d\u00e9clare en quel sens il\ns'en sert, \u00e0 quoi bon rechercher de quelle mani\u00e8re d'autres \u00e9crivains\nont entendu ce m\u00eame terme? _Scapula_ traduit le mot dont il s'agit ici,\n_domicilium_, c'est-\u00e0-dire le lieu ou l'\u00e2me r\u00e9side.\"\n\n[62] Goclenius is the author of a philosophical dictionary quoted by\nLeibnitz.\n\n\n_Reply of Leibnitz:_\n\n\"Si l'espace infini est l'immensit\u00e9, l'espace fini sera l'oppos\u00e9 de\nl'immensit\u00e9, c'est-\u00e0-dire la mensurabilit\u00e9 ou l'\u00e9tendue born\u00e9e. Or\nl'\u00e9tendue doit \u00eatre l'affection d'un \u00e9tendu. Mais si cet espace est\nvide, il sera un attribut sans sujet, une \u00e9tendue d'aucun \u00e9tendu. C'est\npourquoi, en faisant de l'espace une propri\u00e9t\u00e9, l'on tombe dans mon\nsentiment, qui le fait un ordre des choses et non pas quelque chose\nd'absolu.\n\n\"Si l'espace est une r\u00e9alit\u00e9 absolue, bien loin d'\u00eatre une propri\u00e9t\u00e9 ou\naccidentalit\u00e9 oppos\u00e9e \u00e0 la substance, il sera plus subsistant que les\nsubstances. Dieu ne le saurait d\u00e9truire, ni m\u00eame changer en rien. Il\nest non-seulement immense dans le tout, mais encore immuable et \u00e9ternel\nen chaque partie. Il y aura une infinit\u00e9 de choses \u00e9ternelles hors de\nDieu.\n\n\"Dire que l'espace infini est sans parties, c'est dire que les espaces\nfinis ne le composent point, et que l'espace infini pourrait subsister\nquand tous les espaces finis seraient r\u00e9duits \u00e0 rien. Ce serait comme\nsi l'on disait, dans la supposition cart\u00e9sienne, d'un univers \u00e9tendu\nsans bornes, que cet univers pourrait subsister quand tous les corps\nqui le composent seraient r\u00e9duits \u00e0 rien ...\n\n\"Je serais bien aise de voir le passage d'un philosophe qui prenne\n_sensorium_ autrement que _Goclenius_.\n\n\"Si _Scapula_ dit que _sensorium_ est la place o\u00f9 l'entendement r\u00e9side,\nil entendra l'organe de la sensation interne; ainsi il ne s'\u00e9loignera\npoint de Goclenius.\n\n\"_Sensorium_ a toujours \u00e9t\u00e9 l'organe de la sensation. La glande pin\u00e9ale\nserait, selon Descartes, le _sensorium_ dans le sens qu'on rapporte de\n_Scapula_.\n\n\"Il n'y a gu\u00e8re d'expression moins convenable sur se sujet que celle\nqui donne \u00e0 Dieu un _sensorium_: il semble qu'elle le fait l'\u00e2me du\nmonde. Et on aurait bien de la peine \u00e0 donner \u00e0 l'usage que M. _Newton_\nfait de ce mot un sens qui le puisse justifier.\"\n\n\n_Clarke's Answer:_\n\n\"On revient encore ici \u00e0 l'usage du mot de _sensorium_, quoique M.\nNewton se soit servi d'un correctif lorsqu'il a employ\u00e9 ce mot. Il\nn'est pas n\u00e9cessaire de rien ajouter \u00e0 ce que j'ai dit sur cela ...\n\n\"L'espace destitu\u00e9 de corps est une propri\u00e9t\u00e9 d'une substance\nimmat\u00e9rielle; l'espace n'est pas born\u00e9 par les corps, mais il existe\n\u00e9galement dans les corps et hors des corps. L'espace n'est pas renferm\u00e9\nentre les corps; mais les corps \u00e9tant dans l'espace immense sont\neux-m\u00eames born\u00e9s par leurs propres dimensions.\n\n\"L'espace vide n'est pas un attribut sans sujet; car par cet espace\nnous n'entendons pas un espace o\u00f9 il n'y a rien, mais un espace sans\ncorps. Dieu est certainement pr\u00e9sent dans tout l'espace vide, et\npeut-\u00eatre qu'il y a aussi dans cet espace plusieurs autres substances\nqui ne sont pas mat\u00e9rielles, et qui par cons\u00e9quent ne peuvent \u00eatre\ntangibles ni aper\u00e7ues par aucun de nos sens.\n\n\"L'espace n'est pas une substance, mais un attribut; et si c'est un\nattribut d'un \u00eatre n\u00e9cessaire, il doit (comme tous les autres attributs\nd'un \u00eatre n\u00e9cessaire) exister plus n\u00e9cessairement que les substances\nm\u00eames, qui ne sont pas n\u00e9cessaires. L'espace est immense, immuable\net \u00e9ternel; et l'on doit dire la m\u00eame chose de la dur\u00e9e. Mais il ne\ns'ensuit pas de l\u00e0 qu'il n'y ait rien d'\u00e9ternel hors de Dieu, car\nl'espace et la dur\u00e9e ne sont pas hors de Dieu, ce sont des suites\nimm\u00e9diates et n\u00e9cessaires de son existence, sans lesquelles il ne\nserait point \u00e9ternel et pr\u00e9sent partout.\n\n\"Les infinis ne sont compos\u00e9s de finis que comme les finis sont\ncompos\u00e9s d'infinit\u00e9simes; j'ai fait voir ci-dessus en quel sens on peut\ndire que l'espace a des parties ou qu'il n'en a pas. Les parties dans\nle sens que l'on donne \u00e0 ce mot, lorsqu'on l'applique au corps, sont\ns\u00e9parables, compos\u00e9es, d\u00e9sunies, ind\u00e9pendantes les unes des autres et\ncapables de mouvement. Mais quoique l'imagination puisse en quelque\nmani\u00e8re concevoir des parties dans l'espace infini, cependant, comme\nces parties, improprement ainsi dites, sont essentiellement immobiles\net ins\u00e9parables les unes des autres, il s'ensuit que cet espace est\nessentiellement simple et absolument indivisible.\"[63]\n\n[63] Here Clarke falls again into the confusion we have spoken of, and\nmaking _divisibility_ the same thing as _separability_, he asserts\ncontradictory propositions.\n\n\n_Reply of Leibnitz:_\n\n\"Comme j'avais object\u00e9 que l'espace pris pour quelque chose de r\u00e9el\net d'absolu, sans les corps, serait une chose \u00e9ternelle, impassible,\nind\u00e9pendante de Dieu, on a t\u00e2ch\u00e9 d'\u00e9luder cette difficult\u00e9 en disant\nque l'espace est une propri\u00e9t\u00e9 de Dieu. J'ai oppos\u00e9 \u00e0 cela, dans mon\n\u00e9crit pr\u00e9c\u00e9dent, que la propri\u00e9t\u00e9 de Dieu est l'immensit\u00e9; mais que\nl'espace, qui est souvent commensur\u00e9 avec les corps, et l'immensit\u00e9 de\nDieu, n'est pas la m\u00eame chose.\n\n\"J'ai encore object\u00e9 que, si l'espace est une propri\u00e9t\u00e9, et si l'espace\ninfini est l'immensit\u00e9 de Dieu, l'espace fini sera l'\u00e9tendue ou la\nmensurabilit\u00e9 de quelque chose finie. Ainsi l'espace occup\u00e9 par un\ncorps sera l'\u00e9tendue de ce corps, chose absurde, puisqu'un corps peut\nchanger d'espace, mais qu'il ne peut point quitter son \u00e9tendue.\n\n\"J'ai encore demand\u00e9: si l'espace est une propri\u00e9t\u00e9, de quelle chose\nsera donc la propri\u00e9t\u00e9, un espace vuide born\u00e9, tel qu'on s'imagine dans\nle r\u00e9cipient \u00e9puis\u00e9 air? Il ne para\u00eet point raisonnable de dire que cet\nespace vuide, rond ou quarr\u00e9, soit une propri\u00e9t\u00e9 de Dieu. Sera-ce donc\npeut-\u00eatre la propri\u00e9t\u00e9 de quelques substances immat\u00e9rielles, \u00e9tendues,\nimaginaires, qu'on se figure (se semble) dans les espaces imaginaires?\n\n\"Si l'espace est la propri\u00e9t\u00e9 ou l'affection de la substance qui est\ndans l'espace, le m\u00eame espace sera tant\u00f4t l'affection d'un corps,\ntant\u00f4t d'un autre corps, tant\u00f4t d'une substance immat\u00e9rielle, tant\u00f4t,\npeut-\u00eatre, de Dieu, quand il est vuide de toute autre substance\nmat\u00e9rielle ou immat\u00e9rielle. Mais voil\u00e0 une \u00e9trange propri\u00e9t\u00e9 ou\naffection, qui passe de sujet en sujet. Les sujets quitteront ainsi\nleurs accidents comme un habit, afin que d'autres sujets s'en puissent\nrev\u00eatir. Apr\u00e8s cela comment distinguera-t-on les accidents et les\nsubstances?\n\n\"Que si les espaces born\u00e9s qui y sont, et si l'espace infini est la\npropri\u00e9t\u00e9 de Dieu, il faut (chose \u00e9trange) que la propri\u00e9t\u00e9 de Dieu\nsoit compos\u00e9e des affections des cr\u00e9atures; car tous les espaces finis,\npris ensemble, composent l'espace infini.\n\n\"Que si l'on nie que l'espace born\u00e9 soit une affection des choses\nborn\u00e9es, il ne sera pas raisonnable non plus que l'espace infini soit\nl'affection ou la propri\u00e9t\u00e9 d'une chose infinie. J'avais insinu\u00e9 toutes\nces difficult\u00e9s dans mon \u00e9crit pr\u00e9c\u00e9dent, mais il ne para\u00eet point qu'on\nait t\u00e2ch\u00e9 d'y satisfaire.\n\n\"J'ai encore d'autres raisons contre l'\u00e9trange imagination que l'espace\nest une propri\u00e9t\u00e9 de Dieu. Si cela est, l'espace entre dans l'essence\nde Dieu. Or l'espace a des parties; donc il y aurait des parties dans\nl'essence de Dieu, _spectatum admissi_.\n\n\"De plus des espaces sont tant\u00f4t vuides, tant\u00f4t remplis; donc il y aura\ndans l'essence de Dieu des parties tant\u00f4t vuides, tant\u00f4t remplies,\net par cons\u00e9quent sujettes \u00e0 un changement perp\u00e9tuel. Les corps\nremplissant l'espace rempliraient une partie de l'essence de Dieu, et y\nseraient commensur\u00e9s; et, dans la supposition du vuide, une partie de\nl'essence sera dans le r\u00e9cipient. Ce dieu \u00e0 parties ressemblera fort au\ndieu sto\u00efcien, qui \u00e9tait l'univers entier, consid\u00e9r\u00e9 comme un animal\ndivin.\n\n\"Si l'espace infini est l'immensit\u00e9 de Dieu, le temps infini sera\nl'\u00e9ternit\u00e9 de Dieu; il faudra donc dire que ce qui est dans l'espace\nest dans l'immensit\u00e9 de Dieu, et par cons\u00e9quent dans son essence; et\nque ce qui est dans le temps est dans l'\u00e9ternit\u00e9 de Dieu. Phrases\n\u00e9tranges, et qui font bien conna\u00eetre qu'on abuse des termes.\n\n\"En voici encore une autre instance. L'immensit\u00e9 de Dieu fait que Dieu\nest dans tous les espaces. Mais si Dieu est dans l'espace, comment\npeut-on dire que l'espace est en Dieu, ou qu'il est sa propri\u00e9t\u00e9?\nOn a bien ou\u00ef dire que la propri\u00e9t\u00e9 soit dans le sujet; mais on n'a\njamais ou\u00ef dire que le sujet soit dans la propri\u00e9t\u00e9. De m\u00eame, Dieu\nexiste en chaque temps, comment donc le temps est-il dans Dieu, et\ncomment peut-il \u00eatre une propri\u00e9t\u00e9 de Dieu? Ce sont des _alloglossies\nperp\u00e9tuelles_....\n\n\"Comme j'avais object\u00e9 que l'espace a des parties, on cherche un autre\n\u00e9chappatoire en s'\u00e9loignant du sens re\u00e7u des termes, et soutenant\nque l'espace n'a point de parties; parce que ses parties ne sont\npoint s\u00e9parables et ne sauraient \u00eatre \u00e9loign\u00e9es les unes des autres\npar discerption. Mais il suffit que l'espace ait des parties, soit\nque ces parties soient s\u00e9parables ou non; et on les peut assigner\ndans l'espace, soit par les corps qui y sont, soit par les lignes ou\nsurfaces qu'on peut mener....\n\n\"On s'excuse de n'avoir point dit que l'espace est le _sensorium_ de\nDieu, mais seulement _comme_ son _sensorium_. Il semble que l'un est\naussi peu convenable et aussi peu intelligible que l'autre....\n\n\"Si Dieu sent ce qui ce passe dans le monde, par le moyen d'un\n_sensorium_, il semble que les choses agissent sur lui, et qu'ainsi\nil est comme on con\u00e7oit l'_\u00e2me du monde_. On m'impute de r\u00e9p\u00e9ter les\nobjections, sans prendre connaissance des r\u00e9ponses; mais je ne vois\npoint qu'on ait satisfait \u00e0 cette difficult\u00e9; on ferait mieux de\nrenoncer tout \u00e0 fait \u00e0 ce _sensorium_ pr\u00e9tendu.\"\n\nFor the rest of this interesting discussion, I refer the reader to the\nworks of Leibnitz. These extracts may serve to show what importance\neminent philosophers attributed to the questions on space.\n\n\nON CHAPTER XVII.\n\n(31) In order that the reader may form a perfect conception of Kant's\nopinion of space, and judge for himself whether there is or not the\ncontradiction which we have intimated, I extract a few passages from\nhis works.\n\n\"The transcendental conception of phenomena[64] in space is a critical\nobservation that, in general _nothing_ perceived in space _is any thing\nin itself_; that space is, moreover, a form of things, and would belong\nto them if considered in themselves; but that objects in themselves are\nwholly unknown to us, and those things which we call _external objects,\nare only the pure representations of our sensibility_, whose form is\nspace, and whose true correlative, that is to say, the thing in itself,\nis for this reason wholly unknown, and will always remain so; for\nexperience can tell us nothing of it.\n\n[64] Kant defines phenomenon, \"the indeterminate object of an empirical\nintuition.\" He calls empirical intuition, \"that which relates to an\nobject by means of sensation.\" He understands by sensation, \"the\neffect of an object on the representative faculty, in so far as we are\naffected by it.\"--_Transcend. \u00c6sthet._ I.\n\n * * * * * * * *\n\n\"It is altogether certain, and not merely possible or probable, that\nspace and time, as the necessary conditions of all experience, both\ninternal and external, are purely subjective conditions of all our\nintuitions. It is therefore equally certain that _all objects in\nrelation with space and time, are only simple phenomena and not things\nin themselves_, if considered according to the manner in which they\nare given us. Much may be said _a priori_ of the form of objects, but\nnothing of the thing in itself, which serves as the ground of these\nphenomena.\"--_Transc. \u00c6sth._ I.\n\nThis doctrine of Kant's brought upon him the charge of idealism, and\ndrew from the German philosopher explanations which some look upon as a\nmanifest contradiction.\n\nHere is how Kant defends himself from idealism: \"When I say that in\nspace and time the intuitions of external objects, and of the mind,\nrepresent these two things as they affect our senses, _I do not mean\nto say that objects are a pure appearance_; for in the phenomenon,\nthe objects, and even the properties which we attribute to them, are\nalways considered as something really given; but that as this quality\nof being given depends only on the manner of perception of the subject\nin its relation with the object given, this object as phenomenon, is\ndifferent from what it is as object in itself. _I do not say that\nbodies merely seem_ to be external, or that my soul _merely seems_ to\nhave been given me in consciousness. When I assert that the qualities\nof space and time (in conformity to which I place the body and the\nsoul as the condition of their existence) exist only in my mode of\nintuition, and not in the objects themselves, I should do wrong to\nconvert into a mere appearance what I must take for a phenomenon;\nbut this does not occur, if my principle of the ideality of all our\nsensible intuitions is admitted. On the contrary, if an objective\nreality is given to all these forms of sensible representations,\nevery thing is inevitably converted into a pure appearance; for,\nif space and time are considered as qualities which, as to their\npossibility, must be found in the things themselves, and we reflect\non the absurdities which follow, since two infinite things, which can\nneither be substances, nor any thing inherent in a substance, but which\nare still something existent, and even the necessary condition of the\nexistence of all things would still subsist, though all the rest were\nannihilated, we cannot blame Berkeley for reducing bodies to a mere\nappearance.\"--_Ibid._ 2d Edition.\n\nIn the _Transcendental Logic_ there is also a reputation of idealism.\nThere Kant establishes this theorem:\n\n\"The mere consciousness of my own existence, empirically determined,\nproves the existence of objects outside of me in space.\"\n\nIt is not possible for me to give here the doctrines of Kant's\n_Transcendental Logic_; it is enough to have given his remarks on the\nreality of objects; others call them retractations or contradictions,\nand give various causes for them, which, however, do not belong to the\nfield of philosophy.\n\n\nON CHAPTER XIX.\n\n(32) The scholastics always carefully separated the sensible order\nfrom the intelligible. Kant was not the first to discover the\nlimits which divide the intelligible from the sensible, things in\nthemselves as objects of the understanding, _noumena_, as he calls\nthem, from things as represented in sensible intuition, _phenomena_.\nThe scholastics were so far from regarding sensible representations\nas sufficient for intelligence, that they denied that they were\nintelligible. The intellect might know sensible things, but it was\nnecessary for it to abstract them from material conditions. On account\nof its limitation, it required the intuition of objects in sensible\nrepresentation, _conversio ad phantasmata_; but these intuitions were\nnot the intellectual act, they were only its necessary conditions.\nHence proceeded the theory of the _intellectus agens_, which some have\nlaughed at, because they did not understand it. This hypothesis has\nstrong reasons in its favor, whatever may be its intrinsic value, if,\nsetting aside the form in which it is expressed, we attend only to its\nideological profoundness.\n\nIn reading some passages in Kant's _Transcendental Logic_ on\nphenomena and noumena, on the necessity of sensible intuition in pure\nconceptions, and the distinction of the intuition from the conception,\nand on the sensible and intelligible worlds corresponding to the\nsensitive and intellective faculties, we might suppose that the German\nphilosopher had read the scholastics. True, he departed from their\ndoctrines, but what of that? The authors from whom we learn the most,\nare not always those whose opinions we follow.\n\nIn the treatise on ideas, I shall have occasion to explain my opinion\non this point; for the present I shall only make a few extracts from\nSt. Thomas, the most illustrious representative of the scholastic\nphilosophy. The reader will find that he clearly explains our necessity\nof sensible representations, (_phantasmata_,) and the line which\ndivides these representations from the purely intellectual order.\n\n\"(Pars 1, Q. LXXIX., art. 3.) Sed quia Aristoteles non posuit formas\nrerum naturalium subsistere sine materia, _form\u00e6 autem in materia\nexistentes non sunt intelligibiles actu_; sequebatur, quod natur\u00e6, seu\nform\u00e6 rerum sensibilium, quas intelligimus, non essent intelligibiles\nactu. Nihil autem reducitur de potentia in actum, nisi per aliquod\nens actu: sicut sensus fit in actu per sensibile in actu. Oportet\nigitur ponere aliquam virtutem ex parte intellectus, qu\u00e6 faceret\nintelligibilia in actu per abstractionem specierum a _conditionibus\nmaterialibus_. Et h\u00e6c est necessitas ponendi intellectum agentem.\n\n\"(P. 1, Q. LXXIX., art. 4). Ad cujus evidentiam considerandum est,\nquod supra animam intellectivam humanam, necesse est ponere aliquem\nsuperiorem intellectum, a quo anima virtutem intelligendi obtineat.\n\n * * * * * * * *\n\n\"Nihil autem est perfectius in inferioribus rebus anima humana.\nUnde oportet dicere, quod in ipsa sit aliqua virtus derivata a\nsuperiori intellectu, per quam possit _phantasmata illustrare_. Et\nhoc experimento cognoscimus, dum percipimus _nos abstrahere formas\nuniversales a conditionibus particularibus, quod est facere actu\nintelligibilia_.\n\n\"(P. 1. Q., LXXXIV., art. 1.) Hoc autem necessarium non est: quia\netiam in ipsis sensibilibus videmus, quod forma alio modo est in uno\nsensibilium, quam in altero; puta cum in uno est albedo intensior, in\nalio remissior, ut cum in uno est albedo cum dulcedine, in alio sine\ndulcedine. Et per hunc etiam modum, forma sensibilis alio modo est in\nre, qu\u00e6 est extra animam, et alio modo in sensu, qui suspicit formas\nsensibilium absque materia, sicut colorem auri sine auro. Et similiter\nintellectus species corporum, qu\u00e6 sunt materiales et mobiles, recipit\nimmaterialiter, et immobiliter, secundum modum suum, nam receptum est\nin recipiente per modum recipientis. Dicendum est ergo, quod anima per\nintellectum cognoscit corpora, _cognitione immateriali, universali et\nnecessaria_.\n\n\"(P. I, Q. LXXXIV., art. 6.) Et ideo ad causandam intellectualem\noperationem secundum Aristotelem non sufficit sola impressio\nsensibilium corporum, sed requiritur aliquid nobilius, quia agens est\nhonorabilius patiente, ut ipse dicit. Non autem quod intellectualis\noperatio causetur ex sola impressione aliquarum rerum superiorum,\nut Plato posuit, sed illud superius, et nobilius agens, quod vocat\nintellectum agentem, de quo jam supra diximus quod _facit phantasmata\na sensibus accepta intelligibilia in actu_, per modum abstractionis\ncuiusdam. Secundum hoc ergo, ex parte phantasmatum intellectualis\noperatio a sensu causatur. Sed quia phantasmata non sufficiunt immutare\nintellectum possibilem, sed oportet quod fiant intelligibilia actu\nper intellectum agentem, non potest dici quod sensibilis cognitio\nsit totalis, et perfecta causa intellectualis cognitionis, sed magis\nquodammodo est materia caus\u00e6.\"\n\n\nEND OF VOL. I.\n\n\n\n\n       *       *       *       *       *\n\n\n\n\nTranscriber's note:\n\nObvious typographical errors have been silently corrected.\n\nHyphenation has been standardised.\n\nVariations in spelling, punctuation and accents are as in the original.\n\nRepetition of the titles of Books 2 and 3 has been removed.\n\nFootnotes, identified thus [1], are placed at the end of paragraph.\nReferences to the \"Notes on Chapters\" are identified thus (1) at the end\nof the chapter as in the original.\n\nPage 433, para 154, \"There is no need of attributing to the inligent\nspirit....\" Inligent corrected to intelligent.\n\nPage 486, \"II. The relations of our organs [to] objects are\nintrinsically immutable.\" The to has been added.","title":"Fundamental Philosophy, Vol. 1 (of 2)","tradition":"philosophy-ethics","translated_text":null,"word_count":167883}