{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_5827/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_5827","id":"gutenberg_5827","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/5827","summary":null,"tags":["Category: Philosophy & Ethics","Knowledge, Theory of","Metaphysics","Nobel Prizes in Literature","Philosophy","Philosophy -- Introductions"],"text":"THE PROBLEMS OF PHILOSOPHY\n\n\nBy Bertrand Russell\n\n\n\n\nPREFACE\n\nIn the following pages I have confined myself in the main to those\nproblems of philosophy in regard to which I thought it possible to say\nsomething positive and constructive, since merely negative criticism\nseemed out of place. For this reason, theory of knowledge occupies a\nlarger space than metaphysics in the present volume, and some topics\nmuch discussed by philosophers are treated very briefly, if at all.\n\nI have derived valuable assistance from unpublished writings of G. E.\nMoore and J. M. Keynes: from the former, as regards the relations\nof sense-data to physical objects, and from the latter as regards\nprobability and induction. I have also profited greatly by the\ncriticisms and suggestions of Professor Gilbert Murray.\n\n1912\n\n\n\n\nCHAPTER I. APPEARANCE AND REALITY\n\nIs there any knowledge in the world which is so certain that no\nreasonable man could doubt it? This question, which at first sight might\nnot seem difficult, is really one of the most difficult that can\nbe asked. When we have realized the obstacles in the way of a\nstraightforward and confident answer, we shall be well launched on the\nstudy of philosophy--for philosophy is merely the attempt to answer\nsuch ultimate questions, not carelessly and dogmatically, as we do in\nordinary life and even in the sciences, but critically, after exploring\nall that makes such questions puzzling, and after realizing all the\nvagueness and confusion that underlie our ordinary ideas.\n\nIn daily life, we assume as certain many things which, on a closer\nscrutiny, are found to be so full of apparent contradictions that only a\ngreat amount of thought enables us to know what it is that we really may\nbelieve. In the search for certainty, it is natural to begin with our\npresent experiences, and in some sense, no doubt, knowledge is to be\nderived from them. But any statement as to what it is that our immediate\nexperiences make us know is very likely to be wrong. It seems to me that\nI am now sitting in a chair, at a table of a certain shape, on which I\nsee sheets of paper with writing or print. By turning my head I see out\nof the window buildings and clouds and the sun. I believe that the sun\nis about ninety-three million miles from the earth; that it is a hot\nglobe many times bigger than the earth; that, owing to the earth's\nrotation, it rises every morning, and will continue to do so for an\nindefinite time in the future. I believe that, if any other normal\nperson comes into my room, he will see the same chairs and tables and\nbooks and papers as I see, and that the table which I see is the same as\nthe table which I feel pressing against my arm. All this seems to be\nso evident as to be hardly worth stating, except in answer to a man who\ndoubts whether I know anything. Yet all this may be reasonably doubted,\nand all of it requires much careful discussion before we can be sure\nthat we have stated it in a form that is wholly true.\n\nTo make our difficulties plain, let us concentrate attention on the\ntable. To the eye it is oblong, brown and shiny, to the touch it is\nsmooth and cool and hard; when I tap it, it gives out a wooden sound.\nAny one else who sees and feels and hears the table will agree with this\ndescription, so that it might seem as if no difficulty would arise;\nbut as soon as we try to be more precise our troubles begin. Although\nI believe that the table is 'really' of the same colour all over, the\nparts that reflect the light look much brighter than the other parts,\nand some parts look white because of reflected light. I know that, if\nI move, the parts that reflect the light will be different, so that the\napparent distribution of colours on the table will change. It follows\nthat if several people are looking at the table at the same moment, no\ntwo of them will see exactly the same distribution of colours, because\nno two can see it from exactly the same point of view, and any change in\nthe point of view makes some change in the way the light is reflected.\n\nFor most practical purposes these differences are unimportant, but to\nthe painter they are all-important: the painter has to unlearn the habit\nof thinking that things seem to have the colour which common sense says\nthey 'really' have, and to learn the habit of seeing things as they\nappear. Here we have already the beginning of one of the distinctions\nthat cause most trouble in philosophy--the distinction between\n'appearance' and 'reality', between what things seem to be and what they\nare. The painter wants to know what things seem to be, the practical man\nand the philosopher want to know what they are; but the philosopher's\nwish to know this is stronger than the practical man's, and is more\ntroubled by knowledge as to the difficulties of answering the question.\n\nTo return to the table. It is evident from what we have found, that\nthere is no colour which pre-eminently appears to be _the_ colour of the\ntable, or even of any one particular part of the table--it appears to\nbe of different colours from different points of view, and there is\nno reason for regarding some of these as more really its colour than\nothers. And we know that even from a given point of view the colour will\nseem different by artificial light, or to a colour-blind man, or to a\nman wearing blue spectacles, while in the dark there will be no colour\nat all, though to touch and hearing the table will be unchanged. This\ncolour is not something which is inherent in the table, but something\ndepending upon the table and the spectator and the way the light falls\non the table. When, in ordinary life, we speak of _the_ colour of the\ntable, we only mean the sort of colour which it will seem to have to a\nnormal spectator from an ordinary point of view under usual conditions\nof light. But the other colours which appear under other conditions\nhave just as good a right to be considered real; and therefore, to avoid\nfavouritism, we are compelled to deny that, in itself, the table has any\none particular colour.\n\nThe same thing applies to the texture. With the naked eye one can see\nthe grain, but otherwise the table looks smooth and even. If we looked\nat it through a microscope, we should see roughnesses and hills and\nvalleys, and all sorts of differences that are imperceptible to the\nnaked eye. Which of these is the 'real' table? We are naturally tempted\nto say that what we see through the microscope is more real, but that in\nturn would be changed by a still more powerful microscope. If, then, we\ncannot trust what we see with the naked eye, why should we trust what we\nsee through a microscope? Thus, again, the confidence in our senses with\nwhich we began deserts us.\n\nThe shape of the table is no better. We are all in the habit of judging\nas to the 'real' shapes of things, and we do this so unreflectingly that\nwe come to think we actually see the real shapes. But, in fact, as we\nall have to learn if we try to draw, a given thing looks different\nin shape from every different point of view. If our table is 'really'\nrectangular, it will look, from almost all points of view, as if it had\ntwo acute angles and two obtuse angles. If opposite sides are parallel,\nthey will look as if they converged to a point away from the spectator;\nif they are of equal length, they will look as if the nearer side were\nlonger. All these things are not commonly noticed in looking at a table,\nbecause experience has taught us to construct the 'real' shape from the\napparent shape, and the 'real' shape is what interests us as practical\nmen. But the 'real' shape is not what we see; it is something inferred\nfrom what we see. And what we see is constantly changing in shape as we\nmove about the room; so that here again the senses seem not to give us\nthe truth about the table itself, but only about the appearance of the\ntable.\n\nSimilar difficulties arise when we consider the sense of touch. It is\ntrue that the table always gives us a sensation of hardness, and we feel\nthat it resists pressure. But the sensation we obtain depends upon how\nhard we press the table and also upon what part of the body we press\nwith; thus the various sensations due to various pressures or various\nparts of the body cannot be supposed to reveal _directly_ any definite\nproperty of the table, but at most to be _signs_ of some property which\nperhaps _causes_ all the sensations, but is not actually apparent in any\nof them. And the same applies still more obviously to the sounds which\ncan be elicited by rapping the table.\n\nThus it becomes evident that the real table, if there is one, is not the\nsame as what we immediately experience by sight or touch or hearing. The\nreal table, if there is one, is not _immediately_ known to us at all,\nbut must be an inference from what is immediately known. Hence, two very\ndifficult questions at once arise; namely, (1) Is there a real table at\nall? (2) If so, what sort of object can it be?\n\nIt will help us in considering these questions to have a few simple\nterms of which the meaning is definite and clear. Let us give the name\nof 'sense-data' to the things that are immediately known in sensation:\nsuch things as colours, sounds, smells, hardnesses, roughnesses, and\nso on. We shall give the name 'sensation' to the experience of being\nimmediately aware of these things. Thus, whenever we see a colour,\nwe have a sensation _of_ the colour, but the colour itself is a\nsense-datum, not a sensation. The colour is that _of_ which we are\nimmediately aware, and the awareness itself is the sensation. It is\nplain that if we are to know anything about the table, it must be\nby means of the sense-data--brown colour, oblong shape, smoothness,\netc.--which we associate with the table; but, for the reasons which have\nbeen given, we cannot say that the table is the sense-data, or even\nthat the sense-data are directly properties of the table. Thus a problem\narises as to the relation of the sense-data to the real table, supposing\nthere is such a thing.\n\nThe real table, if it exists, we will call a 'physical object'. Thus\nwe have to consider the relation of sense-data to physical objects.\nThe collection of all physical objects is called 'matter'. Thus our two\nquestions may be re-stated as follows: (1) Is there any such thing as\nmatter? (2) If so, what is its nature?\n\nThe philosopher who first brought prominently forward the reasons\nfor regarding the immediate objects of our senses as not existing\nindependently of us was Bishop Berkeley (1685-1753). His _Three\nDialogues between Hylas and Philonous, in Opposition to Sceptics and\nAtheists_, undertake to prove that there is no such thing as matter at\nall, and that the world consists of nothing but minds and their ideas.\nHylas has hitherto believed in matter, but he is no match for Philonous,\nwho mercilessly drives him into contradictions and paradoxes, and makes\nhis own denial of matter seem, in the end, as if it were almost common\nsense. The arguments employed are of very different value: some are\nimportant and sound, others are confused or quibbling. But Berkeley\nretains the merit of having shown that the existence of matter is\ncapable of being denied without absurdity, and that if there are any\nthings that exist independently of us they cannot be the immediate\nobjects of our sensations.\n\nThere are two different questions involved when we ask whether matter\nexists, and it is important to keep them clear. We commonly mean by\n'matter' something which is opposed to 'mind', something which we think\nof as occupying space and as radically incapable of any sort of thought\nor consciousness. It is chiefly in this sense that Berkeley denies\nmatter; that is to say, he does not deny that the sense-data which we\ncommonly take as signs of the existence of the table are really signs\nof the existence of _something_ independent of us, but he does deny\nthat this something is non-mental, that it is neither mind nor ideas\nentertained by some mind. He admits that there must be something which\ncontinues to exist when we go out of the room or shut our eyes, and that\nwhat we call seeing the table does really give us reason for believing\nin something which persists even when we are not seeing it. But he\nthinks that this something cannot be radically different in nature from\nwhat we see, and cannot be independent of seeing altogether, though it\nmust be independent of _our_ seeing. He is thus led to regard the 'real'\ntable as an idea in the mind of God. Such an idea has the required\npermanence and independence of ourselves, without being--as matter would\notherwise be--something quite unknowable, in the sense that we can only\ninfer it, and can never be directly and immediately aware of it.\n\nOther philosophers since Berkeley have also held that, although the\ntable does not depend for its existence upon being seen by me, it does\ndepend upon being seen (or otherwise apprehended in sensation) by\n_some_ mind--not necessarily the mind of God, but more often the whole\ncollective mind of the universe. This they hold, as Berkeley does,\nchiefly because they think there can be nothing real--or at any rate\nnothing known to be real except minds and their thoughts and feelings.\nWe might state the argument by which they support their view in some\nsuch way as this: 'Whatever can be thought of is an idea in the mind of\nthe person thinking of it; therefore nothing can be thought of except\nideas in minds; therefore anything else is inconceivable, and what is\ninconceivable cannot exist.'\n\nSuch an argument, in my opinion, is fallacious; and of course those who\nadvance it do not put it so shortly or so crudely. But whether valid or\nnot, the argument has been very widely advanced in one form or another;\nand very many philosophers, perhaps a majority, have held that there is\nnothing real except minds and their ideas. Such philosophers are called\n'idealists'. When they come to explaining matter, they either say, like\nBerkeley, that matter is really nothing but a collection of ideas,\nor they say, like Leibniz (1646-1716), that what appears as matter is\nreally a collection of more or less rudimentary minds.\n\nBut these philosophers, though they deny matter as opposed to mind,\nnevertheless, in another sense, admit matter. It will be remembered that\nwe asked two questions; namely, (1) Is there a real table at all? (2) If\nso, what sort of object can it be? Now both Berkeley and Leibniz admit\nthat there is a real table, but Berkeley says it is certain ideas in the\nmind of God, and Leibniz says it is a colony of souls. Thus both of them\nanswer our first question in the affirmative, and only diverge from the\nviews of ordinary mortals in their answer to our second question. In\nfact, almost all philosophers seem to be agreed that there is a real\ntable: they almost all agree that, however much our sense-data--colour,\nshape, smoothness, etc.--may depend upon us, yet their occurrence is\na sign of something existing independently of us, something differing,\nperhaps, completely from our sense-data, and yet to be regarded as\ncausing those sense-data whenever we are in a suitable relation to the\nreal table.\n\nNow obviously this point in which the philosophers are agreed--the view\nthat there _is_ a real table, whatever its nature may be--is vitally\nimportant, and it will be worth while to consider what reasons there are\nfor accepting this view before we go on to the further question as\nto the nature of the real table. Our next chapter, therefore, will be\nconcerned with the reasons for supposing that there is a real table at\nall.\n\nBefore we go farther it will be well to consider for a moment what it\nis that we have discovered so far. It has appeared that, if we take any\ncommon object of the sort that is supposed to be known by the senses,\nwhat the senses _immediately_ tell us is not the truth about the object\nas it is apart from us, but only the truth about certain sense-data\nwhich, so far as we can see, depend upon the relations between us and\nthe object. Thus what we directly see and feel is merely 'appearance',\nwhich we believe to be a sign of some 'reality' behind. But if the\nreality is not what appears, have we any means of knowing whether there\nis any reality at all? And if so, have we any means of finding out what\nit is like?\n\nSuch questions are bewildering, and it is difficult to know that even\nthe strangest hypotheses may not be true. Thus our familiar table,\nwhich has roused but the slightest thoughts in us hitherto, has become a\nproblem full of surprising possibilities. The one thing we know about it\nis that it is not what it seems. Beyond this modest result, so far, we\nhave the most complete liberty of conjecture. Leibniz tells us it is a\ncommunity of souls: Berkeley tells us it is an idea in the mind of God;\nsober science, scarcely less wonderful, tells us it is a vast collection\nof electric charges in violent motion.\n\nAmong these surprising possibilities, doubt suggests that perhaps there\nis no table at all. Philosophy, if it cannot _answer_ so many questions\nas we could wish, has at least the power of _asking_ questions which\nincrease the interest of the world, and show the strangeness and wonder\nlying just below the surface even in the commonest things of daily life.\n\n\n\nCHAPTER II. THE EXISTENCE OF MATTER\n\nIn this chapter we have to ask ourselves whether, in any sense at all,\nthere is such a thing as matter. Is there a table which has a certain\nintrinsic nature, and continues to exist when I am not looking, or is\nthe table merely a product of my imagination, a dream-table in a very\nprolonged dream? This question is of the greatest importance. For if\nwe cannot be sure of the independent existence of objects, we cannot\nbe sure of the independent existence of other people's bodies, and\ntherefore still less of other people's minds, since we have no grounds\nfor believing in their minds except such as are derived from observing\ntheir bodies. Thus if we cannot be sure of the independent existence of\nobjects, we shall be left alone in a desert--it may be that the whole\nouter world is nothing but a dream, and that we alone exist. This is an\nuncomfortable possibility; but although it cannot be strictly proved to\nbe false, there is not the slightest reason to suppose that it is true.\nIn this chapter we have to see why this is the case.\n\nBefore we embark upon doubtful matters, let us try to find some more\nor less fixed point from which to start. Although we are doubting the\nphysical existence of the table, we are not doubting the existence\nof the sense-data which made us think there was a table; we are not\ndoubting that, while we look, a certain colour and shape appear to us,\nand while we press, a certain sensation of hardness is experienced by\nus. All this, which is psychological, we are not calling in question.\nIn fact, whatever else may be doubtful, some at least of our immediate\nexperiences seem absolutely certain.\n\nDescartes (1596-1650), the founder of modern philosophy, invented a\nmethod which may still be used with profit--the method of systematic\ndoubt. He determined that he would believe nothing which he did not see\nquite clearly and distinctly to be true. Whatever he could bring himself\nto doubt, he would doubt, until he saw reason for not doubting it.\nBy applying this method he gradually became convinced that the only\nexistence of which he could be _quite_ certain was his own. He imagined\na deceitful demon, who presented unreal things to his senses in a\nperpetual phantasmagoria; it might be very improbable that such a demon\nexisted, but still it was possible, and therefore doubt concerning\nthings perceived by the senses was possible.\n\nBut doubt concerning his own existence was not possible, for if he did\nnot exist, no demon could deceive him. If he doubted, he must exist; if\nhe had any experiences whatever, he must exist. Thus his own existence\nwas an absolute certainty to him. 'I think, therefore I am,' he said\n(_Cogito, ergo sum_); and on the basis of this certainty he set to work\nto build up again the world of knowledge which his doubt had laid in\nruins. By inventing the method of doubt, and by showing that subjective\nthings are the most certain, Descartes performed a great service to\nphilosophy, and one which makes him still useful to all students of the\nsubject.\n\nBut some care is needed in using Descartes' argument. 'I think,\ntherefore I am' says rather more than is strictly certain. It might seem\nas though we were quite sure of being the same person to-day as we were\nyesterday, and this is no doubt true in some sense. But the real Self is\nas hard to arrive at as the real table, and does not seem to have that\nabsolute, convincing certainty that belongs to particular experiences.\nWhen I look at my table and see a certain brown colour, what is quite\ncertain at once is not '_I_ am seeing a brown colour', but rather,\n'a brown colour is being seen'. This of course involves something (or\nsomebody) which (or who) sees the brown colour; but it does not of\nitself involve that more or less permanent person whom we call 'I'. So\nfar as immediate certainty goes, it might be that the something which\nsees the brown colour is quite momentary, and not the same as the\nsomething which has some different experience the next moment.\n\nThus it is our particular thoughts and feelings that have primitive\ncertainty. And this applies to dreams and hallucinations as well as to\nnormal perceptions: when we dream or see a ghost, we certainly do have\nthe sensations we think we have, but for various reasons it is held that\nno physical object corresponds to these sensations. Thus the certainty\nof our knowledge of our own experiences does not have to be limited in\nany way to allow for exceptional cases. Here, therefore, we have, for\nwhat it is worth, a solid basis from which to begin our pursuit of\nknowledge.\n\nThe problem we have to consider is this: Granted that we are certain of\nour own sense-data, have we any reason for regarding them as signs of\nthe existence of something else, which we can call the physical object?\nWhen we have enumerated all the sense-data which we should naturally\nregard as connected with the table, have we said all there is to say\nabout the table, or is there still something else--something not a\nsense-datum, something which persists when we go out of the room? Common\nsense unhesitatingly answers that there is. What can be bought and sold\nand pushed about and have a cloth laid on it, and so on, cannot be\na _mere_ collection of sense-data. If the cloth completely hides the\ntable, we shall derive no sense-data from the table, and therefore, if\nthe table were merely sense-data, it would have ceased to exist, and\nthe cloth would be suspended in empty air, resting, by a miracle, in\nthe place where the table formerly was. This seems plainly absurd; but\nwhoever wishes to become a philosopher must learn not to be frightened\nby absurdities.\n\nOne great reason why it is felt that we must secure a physical object\nin addition to the sense-data, is that we want the same object for\ndifferent people. When ten people are sitting round a dinner-table,\nit seems preposterous to maintain that they are not seeing the same\ntablecloth, the same knives and forks and spoons and glasses. But the\nsense-data are private to each separate person; what is immediately\npresent to the sight of one is not immediately present to the sight of\nanother: they all see things from slightly different points of view, and\ntherefore see them slightly differently. Thus, if there are to be public\nneutral objects, which can be in some sense known to many different\npeople, there must be something over and above the private and\nparticular sense-data which appear to various people. What reason, then,\nhave we for believing that there are such public neutral objects?\n\nThe first answer that naturally occurs to one is that, although\ndifferent people may see the table slightly differently, still they all\nsee more or less similar things when they look at the table, and\nthe variations in what they see follow the laws of perspective and\nreflection of light, so that it is easy to arrive at a permanent object\nunderlying all the different people's sense-data. I bought my table from\nthe former occupant of my room; I could not buy _his_ sense-data,\nwhich died when he went away, but I could and did buy the confident\nexpectation of more or less similar sense-data. Thus it is the fact that\ndifferent people have similar sense-data, and that one person in a given\nplace at different times has similar sense-data, which makes us suppose\nthat over and above the sense-data there is a permanent public object\nwhich underlies or causes the sense-data of various people at various\ntimes.\n\nNow in so far as the above considerations depend upon supposing that\nthere are other people besides ourselves, they beg the very question at\nissue. Other people are represented to me by certain sense-data, such as\nthe sight of them or the sound of their voices, and if I had no\nreason to believe that there were physical objects independent of my\nsense-data, I should have no reason to believe that other people exist\nexcept as part of my dream. Thus, when we are trying to show that there\nmust be objects independent of our own sense-data, we cannot appeal to\nthe testimony of other people, since this testimony itself consists of\nsense-data, and does not reveal other people's experiences unless our\nown sense-data are signs of things existing independently of us. We must\ntherefore, if possible, find, in our own purely private experiences,\ncharacteristics which show, or tend to show, that there are in the world\nthings other than ourselves and our private experiences.\n\nIn one sense it must be admitted that we can never prove the existence\nof things other than ourselves and our experiences. No logical absurdity\nresults from the hypothesis that the world consists of myself and my\nthoughts and feelings and sensations, and that everything else is mere\nfancy. In dreams a very complicated world may seem to be present, and\nyet on waking we find it was a delusion; that is to say, we find that\nthe sense-data in the dream do not appear to have corresponded with such\nphysical objects as we should naturally infer from our sense-data. (It\nis true that, when the physical world is assumed, it is possible to\nfind physical causes for the sense-data in dreams: a door banging, for\ninstance, may cause us to dream of a naval engagement. But although, in\nthis case, there is a physical cause for the sense-data, there is not a\nphysical object corresponding to the sense-data in the way in which an\nactual naval battle would correspond.) There is no logical impossibility\nin the supposition that the whole of life is a dream, in which we\nourselves create all the objects that come before us. But although this\nis not logically impossible, there is no reason whatever to suppose that\nit is true; and it is, in fact, a less simple hypothesis, viewed as a\nmeans of accounting for the facts of our own life, than the common-sense\nhypothesis that there really are objects independent of us, whose action\non us causes our sensations.\n\nThe way in which simplicity comes in from supposing that there really\nare physical objects is easily seen. If the cat appears at one moment in\none part of the room, and at another in another part, it is natural\nto suppose that it has moved from the one to the other, passing over\na series of intermediate positions. But if it is merely a set of\nsense-data, it cannot have ever been in any place where I did not see\nit; thus we shall have to suppose that it did not exist at all while I\nwas not looking, but suddenly sprang into being in a new place. If\nthe cat exists whether I see it or not, we can understand from our own\nexperience how it gets hungry between one meal and the next; but if\nit does not exist when I am not seeing it, it seems odd that appetite\nshould grow during non-existence as fast as during existence. And if the\ncat consists only of sense-data, it cannot be hungry, since no hunger\nbut my own can be a sense-datum to me. Thus the behaviour of the\nsense-data which represent the cat to me, though it seems quite natural\nwhen regarded as an expression of hunger, becomes utterly inexplicable\nwhen regarded as mere movements and changes of patches of colour, which\nare as incapable of hunger as a triangle is of playing football.\n\nBut the difficulty in the case of the cat is nothing compared to the\ndifficulty in the case of human beings. When human beings speak--that\nis, when we hear certain noises which we associate with ideas, and\nsimultaneously see certain motions of lips and expressions of face--it\nis very difficult to suppose that what we hear is not the expression\nof a thought, as we know it would be if we emitted the same sounds. Of\ncourse similar things happen in dreams, where we are mistaken as to the\nexistence of other people. But dreams are more or less suggested by what\nwe call waking life, and are capable of being more or less accounted for\non scientific principles if we assume that there really is a physical\nworld. Thus every principle of simplicity urges us to adopt the natural\nview, that there really are objects other than ourselves and our\nsense-data which have an existence not dependent upon our perceiving\nthem.\n\nOf course it is not by argument that we originally come by our belief in\nan independent external world. We find this belief ready in ourselves as\nsoon as we begin to reflect: it is what may be called an _instinctive_\nbelief. We should never have been led to question this belief but for\nthe fact that, at any rate in the case of sight, it seems as if the\nsense-datum itself were instinctively believed to be the independent\nobject, whereas argument shows that the object cannot be identical\nwith the sense-datum. This discovery, however--which is not at all\nparadoxical in the case of taste and smell and sound, and only slightly\nso in the case of touch--leaves undiminished our instinctive belief that\nthere _are_ objects _corresponding_ to our sense-data. Since this belief\ndoes not lead to any difficulties, but on the contrary tends to simplify\nand systematize our account of our experiences, there seems no good\nreason for rejecting it. We may therefore admit--though with a slight\ndoubt derived from dreams--that the external world does really exist,\nand is not wholly dependent for its existence upon our continuing to\nperceive it.\n\nThe argument which has led us to this conclusion is doubtless less\nstrong than we could wish, but it is typical of many philosophical\narguments, and it is therefore worth while to consider briefly its\ngeneral character and validity. All knowledge, we find, must be built\nup upon our instinctive beliefs, and if these are rejected, nothing\nis left. But among our instinctive beliefs some are much stronger than\nothers, while many have, by habit and association, become entangled with\nother beliefs, not really instinctive, but falsely supposed to be part\nof what is believed instinctively.\n\nPhilosophy should show us the hierarchy of our instinctive beliefs,\nbeginning with those we hold most strongly, and presenting each as much\nisolated and as free from irrelevant additions as possible. It should\ntake care to show that, in the form in which they are finally set forth,\nour instinctive beliefs do not clash, but form a harmonious system.\nThere can never be any reason for rejecting one instinctive belief\nexcept that it clashes with others; thus, if they are found to\nharmonize, the whole system becomes worthy of acceptance.\n\nIt is of course _possible_ that all or any of our beliefs may be\nmistaken, and therefore all ought to be held with at least some slight\nelement of doubt. But we cannot have _reason_ to reject a belief except\non the ground of some other belief. Hence, by organizing our instinctive\nbeliefs and their consequences, by considering which among them is most\npossible, if necessary, to modify or abandon, we can arrive, on the\nbasis of accepting as our sole data what we instinctively believe, at an\norderly systematic organization of our knowledge, in which, though the\n_possibility_ of error remains, its likelihood is diminished by the\ninterrelation of the parts and by the critical scrutiny which has\npreceded acquiescence.\n\nThis function, at least, philosophy can perform. Most philosophers,\nrightly or wrongly, believe that philosophy can do much more than\nthis--that it can give us knowledge, not otherwise attainable,\nconcerning the universe as a whole, and concerning the nature of\nultimate reality. Whether this be the case or not, the more modest\nfunction we have spoken of can certainly be performed by philosophy, and\ncertainly suffices, for those who have once begun to doubt the adequacy\nof common sense, to justify the arduous and difficult labours that\nphilosophical problems involve.\n\n\n\nCHAPTER III. THE NATURE OF MATTER\n\nIn the preceding chapter we agreed, though without being able to\nfind demonstrative reasons, that it is rational to believe that our\nsense-data--for example, those which we regard as associated with my\ntable--are really signs of the existence of something independent of us\nand our perceptions. That is to say, over and above the sensations of\ncolour, hardness, noise, and so on, which make up the appearance of\nthe table to me, I assume that there is something else, of which these\nthings are appearances. The colour ceases to exist if I shut my eyes,\nthe sensation of hardness ceases to exist if I remove my arm from\ncontact with the table, the sound ceases to exist if I cease to rap the\ntable with my knuckles. But I do not believe that when all these things\ncease the table ceases. On the contrary, I believe that it is because\nthe table exists continuously that all these sense-data will reappear\nwhen I open my eyes, replace my arm, and begin again to rap with my\nknuckles. The question we have to consider in this chapter is: What\nis the nature of this real table, which persists independently of my\nperception of it?\n\nTo this question physical science gives an answer, somewhat incomplete\nit is true, and in part still very hypothetical, but yet deserving of\nrespect so far as it goes. Physical science, more or less unconsciously,\nhas drifted into the view that all natural phenomena ought to be reduced\nto motions. Light and heat and sound are all due to wave-motions, which\ntravel from the body emitting them to the person who sees light or feels\nheat or hears sound. That which has the wave-motion is either aether or\n'gross matter', but in either case is what the philosopher would call\nmatter. The only properties which science assigns to it are position in\nspace, and the power of motion according to the laws of motion. Science\ndoes not deny that it _may_ have other properties; but if so, such other\nproperties are not useful to the man of science, and in no way assist\nhim in explaining the phenomena.\n\nIt is sometimes said that 'light _is_ a form of wave-motion', but this\nis misleading, for the light which we immediately see, which we know\ndirectly by means of our senses, is _not_ a form of wave-motion, but\nsomething quite different--something which we all know if we are not\nblind, though we cannot describe it so as to convey our knowledge to a\nman who is blind. A wave-motion, on the contrary, could quite well be\ndescribed to a blind man, since he can acquire a knowledge of space by\nthe sense of touch; and he can experience a wave-motion by a sea voyage\nalmost as well as we can. But this, which a blind man can understand, is\nnot what we mean by _light_: we mean by _light_ just that which a blind\nman can never understand, and which we can never describe to him.\n\nNow this something, which all of us who are not blind know, is not,\naccording to science, really to be found in the outer world: it is\nsomething caused by the action of certain waves upon the eyes and nerves\nand brain of the person who sees the light. When it is said that light\n_is_ waves, what is really meant is that waves are the physical cause of\nour sensations of light. But light itself, the thing which seeing people\nexperience and blind people do not, is not supposed by science to form\nany part of the world that is independent of us and our senses. And very\nsimilar remarks would apply to other kinds of sensations.\n\nIt is not only colours and sounds and so on that are absent from the\nscientific world of matter, but also _space_ as we get it through sight\nor touch. It is essential to science that its matter should be in _a_\nspace, but the space in which it is cannot be exactly the space we see\nor feel. To begin with, space as we see it is not the same as space as\nwe get it by the sense of touch; it is only by experience in infancy\nthat we learn how to touch things we see, or how to get a sight of\nthings which we feel touching us. But the space of science is neutral as\nbetween touch and sight; thus it cannot be either the space of touch or\nthe space of sight.\n\nAgain, different people see the same object as of different shapes,\naccording to their point of view. A circular coin, for example, though\nwe should always _judge_ it to be circular, will _look_ oval unless we\nare straight in front of it. When we judge that it _is_ circular, we are\njudging that it has a real shape which is not its apparent shape, but\nbelongs to it intrinsically apart from its appearance. But this real\nshape, which is what concerns science, must be in a real space, not\nthe same as anybody's _apparent_ space. The real space is public, the\napparent space is private to the percipient. In different people's\n_private_ spaces the same object seems to have different shapes; thus\nthe real space, in which it has its real shape, must be different from\nthe private spaces. The space of science, therefore, though _connected_\nwith the spaces we see and feel, is not identical with them, and the\nmanner of its connexion requires investigation.\n\nWe agreed provisionally that physical objects cannot be quite like\nour sense-data, but may be regarded as _causing_ our sensations.\nThese physical objects are in the space of science, which we may call\n'physical' space. It is important to notice that, if our sensations\nare to be caused by physical objects, there must be a physical space\ncontaining these objects and our sense-organs and nerves and brain. We\nget a sensation of touch from an object when we are in contact with it;\nthat is to say, when some part of our body occupies a place in physical\nspace quite close to the space occupied by the object. We see an object\n(roughly speaking) when no opaque body is between the object and our\neyes in physical space. Similarly, we only hear or smell or taste an\nobject when we are sufficiently near to it, or when it touches the\ntongue, or has some suitable position in physical space relatively to\nour body. We cannot begin to state what different sensations we shall\nderive from a given object under different circumstances unless we\nregard the object and our body as both in one physical space, for it is\nmainly the relative positions of the object and our body that determine\nwhat sensations we shall derive from the object.\n\nNow our sense-data are situated in our private spaces, either the space\nof sight or the space of touch or such vaguer spaces as other senses\nmay give us. If, as science and common sense assume, there is one public\nall-embracing physical space in which physical objects are, the relative\npositions of physical objects in physical space must more or less\ncorrespond to the relative positions of sense-data in our private\nspaces. There is no difficulty in supposing this to be the case. If we\nsee on a road one house nearer to us than another, our other senses will\nbear out the view that it is nearer; for example, it will be reached\nsooner if we walk along the road. Other people will agree that the house\nwhich looks nearer to us is nearer; the ordnance map will take the\nsame view; and thus everything points to a spatial relation between the\nhouses corresponding to the relation between the sense-data which we see\nwhen we look at the houses. Thus we may assume that there is a physical\nspace in which physical objects have spatial relations corresponding to\nthose which the corresponding sense-data have in our private spaces. It\nis this physical space which is dealt with in geometry and assumed in\nphysics and astronomy.\n\nAssuming that there is physical space, and that it does thus correspond\nto private spaces, what can we know about it? We can know _only_ what is\nrequired in order to secure the correspondence. That is to say, we can\nknow nothing of what it is like in itself, but we can know the sort\nof arrangement of physical objects which results from their spatial\nrelations. We can know, for example, that the earth and moon and sun\nare in one straight line during an eclipse, though we cannot know what\na physical straight line is in itself, as we know the look of a straight\nline in our visual space. Thus we come to know much more about the\n_relations_ of distances in physical space than about the distances\nthemselves; we may know that one distance is greater than another, or\nthat it is along the same straight line as the other, but we cannot have\nthat immediate acquaintance with physical distances that we have with\ndistances in our private spaces, or with colours or sounds or other\nsense-data. We can know all those things about physical space which a\nman born blind might know through other people about the space of sight;\nbut the kind of things which a man born blind could never know about the\nspace of sight we also cannot know about physical space. We can know the\nproperties of the relations required to preserve the correspondence with\nsense-data, but we cannot know the nature of the terms between which the\nrelations hold.\n\nWith regard to time, our _feeling_ of duration or of the lapse of time\nis notoriously an unsafe guide as to the time that has elapsed by the\nclock. Times when we are bored or suffering pain pass slowly, times when\nwe are agreeably occupied pass quickly, and times when we are sleeping\npass almost as if they did not exist. Thus, in so far as time is\nconstituted by duration, there is the same necessity for distinguishing\na public and a private time as there was in the case of space. But in so\nfar as time consists in an _order_ of before and after, there is no need\nto make such a distinction; the time-order which events seem to have is,\nso far as we can see, the same as the time-order which they do have. At\nany rate no reason can be given for supposing that the two orders are\nnot the same. The same is usually true of space: if a regiment of men\nare marching along a road, the shape of the regiment will look different\nfrom different points of view, but the men will appear arranged in the\nsame order from all points of view. Hence we regard the order as true\nalso in physical space, whereas the shape is only supposed to correspond\nto the physical space so far as is required for the preservation of the\norder.\n\nIn saying that the time-order which events seem to have is the same as\nthe time-order which they really have, it is necessary to guard against\na possible misunderstanding. It must not be supposed that the various\nstates of different physical objects have the same time-order as the\nsense-data which constitute the perceptions of those objects. Considered\nas physical objects, the thunder and lightning are simultaneous; that is\nto say, the lightning is simultaneous with the disturbance of the air in\nthe place where the disturbance begins, namely, where the lightning\nis. But the sense-datum which we call hearing the thunder does not take\nplace until the disturbance of the air has travelled as far as to where\nwe are. Similarly, it takes about eight minutes for the sun's light\nto reach us; thus, when we see the sun we are seeing the sun of eight\nminutes ago. So far as our sense-data afford evidence as to the physical\nsun they afford evidence as to the physical sun of eight minutes ago; if\nthe physical sun had ceased to exist within the last eight minutes, that\nwould make no difference to the sense-data which we call 'seeing\nthe sun'. This affords a fresh illustration of the necessity of\ndistinguishing between sense-data and physical objects.\n\nWhat we have found as regards space is much the same as what we find\nin relation to the correspondence of the sense-data with their\nphysical counterparts. If one object looks blue and another red, we may\nreasonably presume that there is some corresponding difference between\nthe physical objects; if two objects both look blue, we may presume a\ncorresponding similarity. But we cannot hope to be acquainted directly\nwith the quality in the physical object which makes it look blue or red.\nScience tells us that this quality is a certain sort of wave-motion, and\nthis sounds familiar, because we think of wave-motions in the space we\nsee. But the wave-motions must really be in physical space, with which\nwe have no direct acquaintance; thus the real wave-motions have not that\nfamiliarity which we might have supposed them to have. And what holds\nfor colours is closely similar to what holds for other sense-data. Thus\nwe find that, although the _relations_ of physical objects have all\nsorts of knowable properties, derived from their correspondence with the\nrelations of sense-data, the physical objects themselves remain unknown\nin their intrinsic nature, so far at least as can be discovered by means\nof the senses. The question remains whether there is any other method of\ndiscovering the intrinsic nature of physical objects.\n\nThe most natural, though not ultimately the most defensible, hypothesis\nto adopt in the first instance, at any rate as regards visual\nsense-data, would be that, though physical objects cannot, for the\nreasons we have been considering, be _exactly_ like sense-data, yet they\nmay be more or less like. According to this view, physical objects will,\nfor example, really have colours, and we might, by good luck, see an\nobject as of the colour it really is. The colour which an object seems\nto have at any given moment will in general be very similar, though\nnot quite the same, from many different points of view; we might thus\nsuppose the 'real' colour to be a sort of medium colour, intermediate\nbetween the various shades which appear from the different points of\nview.\n\nSuch a theory is perhaps not capable of being definitely refuted, but\nit can be shown to be groundless. To begin with, it is plain that the\ncolour we see depends only upon the nature of the light-waves that\nstrike the eye, and is therefore modified by the medium intervening\nbetween us and the object, as well as by the manner in which light is\nreflected from the object in the direction of the eye. The intervening\nair alters colours unless it is perfectly clear, and any strong\nreflection will alter them completely. Thus the colour we see is a\nresult of the ray as it reaches the eye, and not simply a property of\nthe object from which the ray comes. Hence, also, provided certain waves\nreach the eye, we shall see a certain colour, whether the object from\nwhich the waves start has any colour or not. Thus it is quite gratuitous\nto suppose that physical objects have colours, and therefore there is no\njustification for making such a supposition. Exactly similar arguments\nwill apply to other sense-data.\n\nIt remains to ask whether there are any general philosophical arguments\nenabling us to say that, if matter is real, it must be of such and such\na nature. As explained above, very many philosophers, perhaps most, have\nheld that whatever is real must be in some sense mental, or at any rate\nthat whatever we can know anything about must be in some sense mental.\nSuch philosophers are called 'idealists'. Idealists tell us that what\nappears as matter is really something mental; namely, either (as Leibniz\nheld) more or less rudimentary minds, or (as Berkeley contended) ideas\nin the minds which, as we should commonly say, 'perceive' the matter.\nThus idealists deny the existence of matter as something intrinsically\ndifferent from mind, though they do not deny that our sense-data are\nsigns of something which exists independently of our private sensations.\nIn the following chapter we shall consider briefly the reasons--in my\nopinion fallacious--which idealists advance in favour of their theory.\n\n\n\nCHAPTER IV. IDEALISM\n\nThe word 'idealism' is used by different philosophers in somewhat\ndifferent senses. We shall understand by it the doctrine that whatever\nexists, or at any rate whatever can be known to exist, must be in\nsome sense mental. This doctrine, which is very widely held among\nphilosophers, has several forms, and is advocated on several different\ngrounds. The doctrine is so widely held, and so interesting in itself,\nthat even the briefest survey of philosophy must give some account of\nit.\n\nThose who are unaccustomed to philosophical speculation may be inclined\nto dismiss such a doctrine as obviously absurd. There is no doubt that\ncommon sense regards tables and chairs and the sun and moon and material\nobjects generally as something radically different from minds and the\ncontents of minds, and as having an existence which might continue if\nminds ceased. We think of matter as having existed long before there\nwere any minds, and it is hard to think of it as a mere product of\nmental activity. But whether true or false, idealism is not to be\ndismissed as obviously absurd.\n\nWe have seen that, even if physical objects do have an independent\nexistence, they must differ very widely from sense-data, and can only\nhave a _correspondence_ with sense-data, in the same sort of way in\nwhich a catalogue has a correspondence with the things catalogued. Hence\ncommon sense leaves us completely in the dark as to the true intrinsic\nnature of physical objects, and if there were good reason to regard them\nas mental, we could not legitimately reject this opinion merely because\nit strikes us as strange. The truth about physical objects _must_ be\nstrange. It may be unattainable, but if any philosopher believes that\nhe has attained it, the fact that what he offers as the truth is strange\nought not to be made a ground of objection to his opinion.\n\nThe grounds on which idealism is advocated are generally grounds derived\nfrom the theory of knowledge, that is to say, from a discussion of the\nconditions which things must satisfy in order that we may be able to\nknow them. The first serious attempt to establish idealism on such\ngrounds was that of Bishop Berkeley. He proved first, by arguments which\nwere largely valid, that our sense-data cannot be supposed to have an\nexistence independent of us, but must be, in part at least, 'in' the\nmind, in the sense that their existence would not continue if there were\nno seeing or hearing or touching or smelling or tasting. So far, his\ncontention was almost certainly valid, even if some of his arguments\nwere not so. But he went on to argue that sense-data were the only\nthings of whose existence our perceptions could assure us; and that\nto be known is to be 'in' a mind, and therefore to be mental. Hence he\nconcluded that nothing can ever be known except what is in some mind,\nand that whatever is known without being in my mind must be in some\nother mind.\n\nIn order to understand his argument, it is necessary to understand his\nuse of the word 'idea'. He gives the name 'idea' to anything which\nis _immediately_ known, as, for example, sense-data are known. Thus a\nparticular colour which we see is an idea; so is a voice which we hear,\nand so on. But the term is not wholly confined to sense-data. There will\nalso be things remembered or imagined, for with such things also we have\nimmediate acquaintance at the moment of remembering or imagining. All\nsuch immediate data he calls 'ideas'.\n\nHe then proceeds to consider common objects, such as a tree, for\ninstance. He shows that all we know immediately when we 'perceive' the\ntree consists of ideas in his sense of the word, and he argues that\nthere is not the slightest ground for supposing that there is anything\nreal about the tree except what is perceived. Its being, he says,\nconsists in being perceived: in the Latin of the schoolmen its '_esse_'\nis '_percipi_'. He fully admits that the tree must continue to exist\neven when we shut our eyes or when no human being is near it. But this\ncontinued existence, he says, is due to the fact that God continues to\nperceive it; the 'real' tree, which corresponds to what we called the\nphysical object, consists of ideas in the mind of God, ideas more or\nless like those we have when we see the tree, but differing in the fact\nthat they are permanent in God's mind so long as the tree continues\nto exist. All our perceptions, according to him, consist in a\npartial participation in God's perceptions, and it is because of this\nparticipation that different people see more or less the same tree. Thus\napart from minds and their ideas there is nothing in the world, nor is\nit possible that anything else should ever be known, since whatever is\nknown is necessarily an idea.\n\nThere are in this argument a good many fallacies which have been\nimportant in the history of philosophy, and which it will be as well to\nbring to light. In the first place, there is a confusion engendered by\nthe use of the word 'idea'. We think of an idea as essentially something\nin somebody's mind, and thus when we are told that a tree consists\nentirely of ideas, it is natural to suppose that, if so, the tree\nmust be entirely in minds. But the notion of being 'in' the mind is\nambiguous. We speak of bearing a person in mind, not meaning that the\nperson is in our minds, but that a thought of him is in our minds. When\na man says that some business he had to arrange went clean out of his\nmind, he does not mean to imply that the business itself was ever in his\nmind, but only that a thought of the business was formerly in his mind,\nbut afterwards ceased to be in his mind. And so when Berkeley says that\nthe tree must be in our minds if we can know it, all that he really has\na right to say is that a thought of the tree must be in our minds. To\nargue that the tree itself must be in our minds is like arguing that a\nperson whom we bear in mind is himself in our minds. This confusion\nmay seem too gross to have been really committed by any competent\nphilosopher, but various attendant circumstances rendered it possible.\nIn order to see how it was possible, we must go more deeply into the\nquestion as to the nature of ideas.\n\nBefore taking up the general question of the nature of ideas, we must\ndisentangle two entirely separate questions which arise concerning\nsense-data and physical objects. We saw that, for various reasons of\ndetail, Berkeley was right in treating the sense-data which constitute\nour perception of the tree as more or less subjective, in the sense that\nthey depend upon us as much as upon the tree, and would not exist if the\ntree were not being perceived. But this is an entirely different point\nfrom the one by which Berkeley seeks to prove that whatever can be\nimmediately known must be in a mind. For this purpose arguments of\ndetail as to the dependence of sense-data upon us are useless. It is\nnecessary to prove, generally, that by being known, things are shown to\nbe mental. This is what Berkeley believes himself to have done. It\nis this question, and not our previous question as to the difference\nbetween sense-data and the physical object, that must now concern us.\n\nTaking the word 'idea' in Berkeley's sense, there are two quite distinct\nthings to be considered whenever an idea is before the mind. There is\non the one hand the thing of which we are aware--say the colour of my\ntable--and on the other hand the actual awareness itself, the mental act\nof apprehending the thing. The mental act is undoubtedly mental, but is\nthere any reason to suppose that the thing apprehended is in any sense\nmental? Our previous arguments concerning the colour did not prove it to\nbe mental; they only proved that its existence depends upon the relation\nof our sense organs to the physical object--in our case, the table. That\nis to say, they proved that a certain colour will exist, in a certain\nlight, if a normal eye is placed at a certain point relatively to\nthe table. They did not prove that the colour is in the mind of the\npercipient.\n\nBerkeley's view, that obviously the colour must be in the mind, seems\nto depend for its plausibility upon confusing the thing apprehended\nwith the act of apprehension. Either of these might be called an 'idea';\nprobably either would have been called an idea by Berkeley. The act\nis undoubtedly in the mind; hence, when we are thinking of the act,\nwe readily assent to the view that ideas must be in the mind. Then,\nforgetting that this was only true when ideas were taken as acts of\napprehension, we transfer the proposition that 'ideas are in the mind'\nto ideas in the other sense, i.e. to the things apprehended by our acts\nof apprehension. Thus, by an unconscious equivocation, we arrive at the\nconclusion that whatever we can apprehend must be in our minds. This\nseems to be the true analysis of Berkeley's argument, and the ultimate\nfallacy upon which it rests.\n\nThis question of the distinction between act and object in our\napprehending of things is vitally important, since our whole power of\nacquiring knowledge is bound up with it. The faculty of being acquainted\nwith things other than itself is the main characteristic of a mind.\nAcquaintance with objects essentially consists in a relation between the\nmind and something other than the mind; it is this that constitutes the\nmind's power of knowing things. If we say that the things known must be\nin the mind, we are either unduly limiting the mind's power of knowing,\nor we are uttering a mere tautology. We are uttering a mere tautology if\nwe mean by '_in_ the mind' the same as by '_before_ the mind', i.e. if\nwe mean merely being apprehended by the mind. But if we mean this, we\nshall have to admit that what, _in this sense_, is in the mind,\nmay nevertheless be not mental. Thus when we realize the nature of\nknowledge, Berkeley's argument is seen to be wrong in substance as well\nas in form, and his grounds for supposing that 'ideas'--i.e. the objects\napprehended--must be mental, are found to have no validity whatever.\nHence his grounds in favour of idealism may be dismissed. It remains to\nsee whether there are any other grounds.\n\nIt is often said, as though it were a self-evident truism, that we\ncannot know that anything exists which we do not know. It is inferred\nthat whatever can in any way be relevant to our experience must be at\nleast capable of being known by us; whence it follows that if matter\nwere essentially something with which we could not become acquainted,\nmatter would be something which we could not know to exist, and which\ncould have for us no importance whatever. It is generally also implied,\nfor reasons which remain obscure, that what can have no importance for\nus cannot be real, and that therefore matter, if it is not composed of\nminds or of mental ideas, is impossible and a mere chimaera.\n\nTo go into this argument fully at our present stage would be impossible,\nsince it raises points requiring a considerable preliminary discussion;\nbut certain reasons for rejecting the argument may be noticed at\nonce. To begin at the end: there is no reason why what cannot have any\n_practical_ importance for us should not be real. It is true that,\nif _theoretical_ importance is included, everything real is of _some_\nimportance to us, since, as persons desirous of knowing the truth about\nthe universe, we have some interest in everything that the universe\ncontains. But if this sort of interest is included, it is not the case\nthat matter has no importance for us, provided it exists even if we\ncannot know that it exists. We can, obviously, suspect that it may\nexist, and wonder whether it does; hence it is connected with our desire\nfor knowledge, and has the importance of either satisfying or thwarting\nthis desire.\n\nAgain, it is by no means a truism, and is in fact false, that we cannot\nknow that anything exists which we do not know. The word 'know' is here\nused in two different senses. (1) In its first use it is applicable to\nthe sort of knowledge which is opposed to error, the sense in which\nwhat we know is _true_, the sense which applies to our beliefs and\nconvictions, i.e. to what are called _judgements_. In this sense of the\nword we know _that_ something is the case. This sort of knowledge may\nbe described as knowledge of _truths_. (2) In the second use of the word\n'know' above, the word applies to our knowledge of _things_, which we\nmay call _acquaintance_. This is the sense in which we know sense-data.\n(The distinction involved is roughly that between _savoir_ and\n_conna\u00eetre_ in French, or between _wissen_ and _kennen_ in German.)\n\nThus the statement which seemed like a truism becomes, when re-stated,\nthe following: 'We can never truly judge that something with which we\nare not acquainted exists.' This is by no means a truism, but on the\ncontrary a palpable falsehood. I have not the honour to be acquainted\nwith the Emperor of China, but I truly judge that he exists. It may\nbe said, of course, that I judge this because of other people's\nacquaintance with him. This, however, would be an irrelevant retort,\nsince, if the principle were true, I could not know that any one else\nis acquainted with him. But further: there is no reason why I should not\nknow of the existence of something with which nobody is acquainted. This\npoint is important, and demands elucidation.\n\nIf I am acquainted with a thing which exists, my acquaintance gives\nme the knowledge that it exists. But it is not true that, conversely,\nwhenever I can know that a thing of a certain sort exists, I or some one\nelse must be acquainted with the thing. What happens, in cases where I\nhave true judgement without acquaintance, is that the thing is known to\nme by _description_, and that, in virtue of some general principle, the\nexistence of a thing answering to this description can be inferred\nfrom the existence of something with which I am acquainted. In order\nto understand this point fully, it will be well first to deal with\nthe difference between knowledge by acquaintance and knowledge by\ndescription, and then to consider what knowledge of general principles,\nif any, has the same kind of certainty as our knowledge of the existence\nof our own experiences. These subjects will be dealt with in the\nfollowing chapters.\n\n\n\nCHAPTER V. KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION\n\nIn the preceding chapter we saw that there are two sorts of knowledge:\nknowledge of things, and knowledge of truths. In this chapter we shall\nbe concerned exclusively with knowledge of things, of which in turn we\nshall have to distinguish two kinds. Knowledge of things, when it is\nof the kind we call knowledge by _acquaintance_, is essentially simpler\nthan any knowledge of truths, and logically independent of knowledge\nof truths, though it would be rash to assume that human beings ever,\nin fact, have acquaintance with things without at the same time knowing\nsome truth about them. Knowledge of things by _description_, on the\ncontrary, always involves, as we shall find in the course of the present\nchapter, some knowledge of truths as its source and ground. But first of\nall we must make clear what we mean by 'acquaintance' and what we mean\nby 'description'.\n\nWe shall say that we have _acquaintance_ with anything of which we are\ndirectly aware, without the intermediary of any process of inference\nor any knowledge of truths. Thus in the presence of my table I am\nacquainted with the sense-data that make up the appearance of my\ntable--its colour, shape, hardness, smoothness, etc.; all these are\nthings of which I am immediately conscious when I am seeing and touching\nmy table. The particular shade of colour that I am seeing may have many\nthings said about it--I may say that it is brown, that it is rather\ndark, and so on. But such statements, though they make me know truths\nabout the colour, do not make me know the colour itself any better\nthan I did before so far as concerns knowledge of the colour itself, as\nopposed to knowledge of truths about it, I know the colour perfectly and\ncompletely when I see it, and no further knowledge of it itself is even\ntheoretically possible. Thus the sense-data which make up the\nappearance of my table are things with which I have acquaintance, things\nimmediately known to me just as they are.\n\nMy knowledge of the table as a physical object, on the contrary, is not\ndirect knowledge. Such as it is, it is obtained through acquaintance\nwith the sense-data that make up the appearance of the table. We have\nseen that it is possible, without absurdity, to doubt whether there is\na table at all, whereas it is not possible to doubt the sense-data. My\nknowledge of the table is of the kind which we shall call 'knowledge\nby description'. The table is 'the physical object which causes\nsuch-and-such sense-data'. This describes the table by means of the\nsense-data. In order to know anything at all about the table, we must\nknow truths connecting it with things with which we have acquaintance:\nwe must know that 'such-and-such sense-data are caused by a physical\nobject'. There is no state of mind in which we are directly aware of the\ntable; all our knowledge of the table is really knowledge of truths, and\nthe actual thing which is the table is not, strictly speaking, known\nto us at all. We know a description, and we know that there is just one\nobject to which this description applies, though the object itself is\nnot directly known to us. In such a case, we say that our knowledge of\nthe object is knowledge by description.\n\nAll our knowledge, both knowledge of things and knowledge of truths,\nrests upon acquaintance as its foundation. It is therefore important to\nconsider what kinds of things there are with which we have acquaintance.\n\nSense-data, as we have already seen, are among the things with which\nwe are acquainted; in fact, they supply the most obvious and striking\nexample of knowledge by acquaintance. But if they were the sole example,\nour knowledge would be very much more restricted than it is. We should\nonly know what is now present to our senses: we could not know anything\nabout the past--not even that there was a past--nor could we know any\ntruths about our sense-data, for all knowledge of truths, as we shall\nshow, demands acquaintance with things which are of an essentially\ndifferent character from sense-data, the things which are sometimes\ncalled 'abstract ideas', but which we shall call 'universals'. We have\ntherefore to consider acquaintance with other things besides sense-data\nif we are to obtain any tolerably adequate analysis of our knowledge.\n\nThe first extension beyond sense-data to be considered is acquaintance\nby _memory_. It is obvious that we often remember what we have seen or\nheard or had otherwise present to our senses, and that in such cases we\nare still immediately aware of what we remember, in spite of the fact\nthat it appears as past and not as present. This immediate knowledge by\nmemory is the source of all our knowledge concerning the past: without\nit, there could be no knowledge of the past by inference, since we\nshould never know that there was anything past to be inferred.\n\nThe next extension to be considered is acquaintance by _introspection_.\nWe are not only aware of things, but we are often aware of being aware\nof them. When I see the sun, I am often aware of my seeing the sun; thus\n'my seeing the sun' is an object with which I have acquaintance. When\nI desire food, I may be aware of my desire for food; thus 'my desiring\nfood' is an object with which I am acquainted. Similarly we may be\naware of our feeling pleasure or pain, and generally of the events which\nhappen in our minds. This kind of acquaintance, which may be called\nself-consciousness, is the source of all our knowledge of mental things.\nIt is obvious that it is only what goes on in our own minds that can be\nthus known immediately. What goes on in the minds of others is known\nto us through our perception of their bodies, that is, through the\nsense-data in us which are associated with their bodies. But for our\nacquaintance with the contents of our own minds, we should be unable to\nimagine the minds of others, and therefore we could never arrive at\nthe knowledge that they have minds. It seems natural to suppose that\nself-consciousness is one of the things that distinguish men from\nanimals: animals, we may suppose, though they have acquaintance with\nsense-data, never become aware of this acquaintance. I do not mean\nthat they _doubt_ whether they exist, but that they have never become\nconscious of the fact that they have sensations and feelings, nor\ntherefore of the fact that they, the subjects of their sensations and\nfeelings, exist.\n\nWe have spoken of acquaintance with the contents of our minds as\n_self_-consciousness, but it is not, of course, consciousness of our\n_self_: it is consciousness of particular thoughts and feelings. The\nquestion whether we are also acquainted with our bare selves, as opposed\nto particular thoughts and feelings, is a very difficult one, upon which\nit would be rash to speak positively. When we try to look into ourselves\nwe always seem to come upon some particular thought or feeling, and not\nupon the 'I' which has the thought or feeling. Nevertheless there are\nsome reasons for thinking that we are acquainted with the 'I', though\nthe acquaintance is hard to disentangle from other things. To make clear\nwhat sort of reason there is, let us consider for a moment what our\nacquaintance with particular thoughts really involves.\n\nWhen I am acquainted with 'my seeing the sun', it seems plain that I am\nacquainted with two different things in relation to each other. On the\none hand there is the sense-datum which represents the sun to me, on the\nother hand there is that which sees this sense-datum. All acquaintance,\nsuch as my acquaintance with the sense-datum which represents the sun,\nseems obviously a relation between the person acquainted and the object\nwith which the person is acquainted. When a case of acquaintance is one\nwith which I can be acquainted (as I am acquainted with my acquaintance\nwith the sense-datum representing the sun), it is plain that the person\nacquainted is myself. Thus, when I am acquainted with my\nseeing the sun, the whole fact with which I am acquainted is\n'Self-acquainted-with-sense-datum'.\n\nFurther, we know the truth 'I am acquainted with this sense-datum'. It\nis hard to see how we could know this truth, or even understand what is\nmeant by it, unless we were acquainted with something which we call 'I'.\nIt does not seem necessary to suppose that we are acquainted with a more\nor less permanent person, the same to-day as yesterday, but it does seem\nas though we must be acquainted with that thing, whatever its nature,\nwhich sees the sun and has acquaintance with sense-data. Thus, in some\nsense it would seem we must be acquainted with our Selves as opposed\nto our particular experiences. But the question is difficult, and\ncomplicated arguments can be adduced on either side. Hence, although\nacquaintance with ourselves seems _probably_ to occur, it is not wise to\nassert that it undoubtedly does occur.\n\nWe may therefore sum up as follows what has been said concerning\nacquaintance with things that exist. We have acquaintance in sensation\nwith the data of the outer senses, and in introspection with the data of\nwhat may be called the inner sense--thoughts, feelings, desires, etc.;\nwe have acquaintance in memory with things which have been data either\nof the outer senses or of the inner sense. Further, it is probable,\nthough not certain, that we have acquaintance with Self, as that which\nis aware of things or has desires towards things.\n\nIn addition to our acquaintance with particular existing things, we also\nhave acquaintance with what we shall call _universals_, that is to say,\ngeneral ideas, such as _whiteness_, _diversity_, _brotherhood_, and so\non. Every complete sentence must contain at least one word which stands\nfor a universal, since all verbs have a meaning which is universal. We\nshall return to universals later on, in Chapter IX; for the present, it\nis only necessary to guard against the supposition that whatever we can\nbe acquainted with must be something particular and existent. Awareness\nof universals is called _conceiving_, and a universal of which we are\naware is called a _concept_.\n\nIt will be seen that among the objects with which we are acquainted\nare not included physical objects (as opposed to sense-data), nor other\npeople's minds. These things are known to us by what I call 'knowledge\nby description', which we must now consider.\n\nBy a 'description' I mean any phrase of the form 'a so-and-so' or\n'the so-and-so'. A phrase of the form 'a so-and-so' I shall call an\n'ambiguous' description; a phrase of the form 'the so-and-so' (in the\nsingular) I shall call a 'definite' description. Thus 'a man' is an\nambiguous description, and 'the man with the iron mask' is a definite\ndescription. There are various problems connected with ambiguous\ndescriptions, but I pass them by, since they do not directly concern\nthe matter we are discussing, which is the nature of our knowledge\nconcerning objects in cases where we know that there is an object\nanswering to a definite description, though we are not acquainted with\nany such object. This is a matter which is concerned exclusively with\ndefinite descriptions. I shall therefore, in the sequel, speak simply of\n'descriptions' when I mean 'definite descriptions'. Thus a description\nwill mean any phrase of the form 'the so-and-so' in the singular.\n\nWe shall say that an object is 'known by description' when we know that\nit is 'the so-and-so', i.e. when we know that there is one object, and\nno more, having a certain property; and it will generally be implied\nthat we do not have knowledge of the same object by acquaintance. We\nknow that the man with the iron mask existed, and many propositions\nare known about him; but we do not know who he was. We know that the\ncandidate who gets the most votes will be elected, and in this case we\nare very likely also acquainted (in the only sense in which one can\nbe acquainted with some one else) with the man who is, in fact, the\ncandidate who will get most votes; but we do not know which of the\ncandidates he is, i.e. we do not know any proposition of the form 'A is\nthe candidate who will get most votes' where A is one of the candidates\nby name. We shall say that we have 'merely descriptive knowledge' of the\nso-and-so when, although we know that the so-and-so exists, and although\nwe may possibly be acquainted with the object which is, in fact, the\nso-and-so, yet we do not know any proposition '_a_ is the so-and-so',\nwhere _a_ is something with which we are acquainted.\n\nWhen we say 'the so-and-so exists', we mean that there is just one\nobject which is the so-and-so. The proposition '_a_ is the so-and-so'\nmeans that _a_ has the property so-and-so, and nothing else has. 'Mr.\nA. is the Unionist candidate for this constituency' means 'Mr. A. is\na Unionist candidate for this constituency, and no one else is'. 'The\nUnionist candidate for this constituency exists' means 'some one is a\nUnionist candidate for this constituency, and no one else is'. Thus,\nwhen we are acquainted with an object which is the so-and-so, we know\nthat the so-and-so exists; but we may know that the so-and-so exists\nwhen we are not acquainted with any object which we know to be the\nso-and-so, and even when we are not acquainted with any object which, in\nfact, is the so-and-so.\n\nCommon words, even proper names, are usually really descriptions. That\nis to say, the thought in the mind of a person using a proper name\ncorrectly can generally only be expressed explicitly if we replace the\nproper name by a description. Moreover, the description required to\nexpress the thought will vary for different people, or for the same\nperson at different times. The only thing constant (so long as the name\nis rightly used) is the object to which the name applies. But so long as\nthis remains constant, the particular description involved usually makes\nno difference to the truth or falsehood of the proposition in which the\nname appears.\n\nLet us take some illustrations. Suppose some statement made about\nBismarck. Assuming that there is such a thing as direct acquaintance\nwith oneself, Bismarck himself might have used his name directly to\ndesignate the particular person with whom he was acquainted. In this\ncase, if he made a judgement about himself, he himself might be a\nconstituent of the judgement. Here the proper name has the direct use\nwhich it always wishes to have, as simply standing for a certain object,\nand not for a description of the object. But if a person who knew\nBismarck made a judgement about him, the case is different. What this\nperson was acquainted with were certain sense-data which he connected\n(rightly, we will suppose) with Bismarck's body. His body, as a physical\nobject, and still more his mind, were only known as the body and the\nmind connected with these sense-data. That is, they were known by\ndescription. It is, of course, very much a matter of chance which\ncharacteristics of a man's appearance will come into a friend's mind\nwhen he thinks of him; thus the description actually in the friend's\nmind is accidental. The essential point is that he knows that the\nvarious descriptions all apply to the same entity, in spite of not being\nacquainted with the entity in question.\n\nWhen we, who did not know Bismarck, make a judgement about him, the\ndescription in our minds will probably be some more or less vague mass\nof historical knowledge--far more, in most cases, than is required to\nidentify him. But, for the sake of illustration, let us assume that we\nthink of him as 'the first Chancellor of the German Empire'. Here all\nthe words are abstract except 'German'. The word 'German' will, again,\nhave different meanings for different people. To some it will recall\ntravels in Germany, to some the look of Germany on the map, and so on.\nBut if we are to obtain a description which we know to be applicable,\nwe shall be compelled, at some point, to bring in a reference to a\nparticular with which we are acquainted. Such reference is involved in\nany mention of past, present, and future (as opposed to definite dates),\nor of here and there, or of what others have told us. Thus it would seem\nthat, in some way or other, a description known to be applicable to a\nparticular must involve some reference to a particular with which we\nare acquainted, if our knowledge about the thing described is not to be\nmerely what follows _logically_ from the description. For example, 'the\nmost long-lived of men' is a description involving only universals,\nwhich must apply to some man, but we can make no judgements concerning\nthis man which involve knowledge about him beyond what the description\ngives. If, however, we say, 'The first Chancellor of the German Empire\nwas an astute diplomatist', we can only be assured of the truth of our\njudgement in virtue of something with which we are acquainted--usually a\ntestimony heard or read. Apart from the information we convey to others,\napart from the fact about the actual Bismarck, which gives importance\nto our judgement, the thought we really have contains the one or more\nparticulars involved, and otherwise consists wholly of concepts.\n\nAll names of places--London, England, Europe, the Earth, the Solar\nSystem--similarly involve, when used, descriptions which start from some\none or more particulars with which we are acquainted. I suspect that\neven the Universe, as considered by metaphysics, involves such a\nconnexion with particulars. In logic, on the contrary, where we are\nconcerned not merely with what does exist, but with whatever might or\ncould exist or be, no reference to actual particulars is involved.\n\nIt would seem that, when we make a statement about something only known\nby description, we often _intend_ to make our statement, not in the form\ninvolving the description, but about the actual thing described. That\nis to say, when we say anything about Bismarck, we should like, if we\ncould, to make the judgement which Bismarck alone can make, namely,\nthe judgement of which he himself is a constituent. In this we are\nnecessarily defeated, since the actual Bismarck is unknown to us. But\nwe know that there is an object B, called Bismarck, and that B was an\nastute diplomatist. We can thus _describe_ the proposition we should\nlike to affirm, namely, 'B was an astute diplomatist', where B is the\nobject which was Bismarck. If we are describing Bismarck as 'the first\nChancellor of the German Empire', the proposition we should like to\naffirm may be described as 'the proposition asserting, concerning the\nactual object which was the first Chancellor of the German Empire, that\nthis object was an astute diplomatist'. What enables us to communicate\nin spite of the varying descriptions we employ is that we know there is\na true proposition concerning the actual Bismarck, and that however we\nmay vary the description (so long as the description is correct) the\nproposition described is still the same. This proposition, which is\ndescribed and is known to be true, is what interests us; but we are not\nacquainted with the proposition itself, and do not know it, though we\nknow it is true.\n\nIt will be seen that there are various stages in the removal from\nacquaintance with particulars: there is Bismarck to people who knew him;\nBismarck to those who only know of him through history; the man with\nthe iron mask; the longest-lived of men. These are progressively further\nremoved from acquaintance with particulars; the first comes as near to\nacquaintance as is possible in regard to another person; in the second,\nwe shall still be said to know 'who Bismarck was'; in the third, we do\nnot know who was the man with the iron mask, though we can know many\npropositions about him which are not logically deducible from the fact\nthat he wore an iron mask; in the fourth, finally, we know nothing\nbeyond what is logically deducible from the definition of the man. There\nis a similar hierarchy in the region of universals. Many universals,\nlike many particulars, are only known to us by description. But here,\nas in the case of particulars, knowledge concerning what is known by\ndescription is ultimately reducible to knowledge concerning what is\nknown by acquaintance.\n\nThe fundamental principle in the analysis of propositions containing\ndescriptions is this: _Every proposition which we can understand must be\ncomposed wholly of constituents with which we are acquainted_.\n\nWe shall not at this stage attempt to answer all the objections which\nmay be urged against this fundamental principle. For the present, we\nshall merely point out that, in some way or other, it must be possible\nto meet these objections, for it is scarcely conceivable that we can\nmake a judgement or entertain a supposition without knowing what it is\nthat we are judging or supposing about. We must attach _some_ meaning\nto the words we use, if we are to speak significantly and not utter mere\nnoise; and the meaning we attach to our words must be something with\nwhich we are acquainted. Thus when, for example, we make a statement\nabout Julius Caesar, it is plain that Julius Caesar himself is not\nbefore our minds, since we are not acquainted with him. We have in mind\nsome description of Julius Caesar: 'the man who was assassinated on the\nIdes of March', 'the founder of the Roman Empire', or, perhaps, merely\n'the man whose name was _Julius Caesar_'. (In this last description,\n_Julius Caesar_ is a noise or shape with which we are acquainted.)\nThus our statement does not mean quite what it seems to mean, but means\nsomething involving, instead of Julius Caesar, some description of him\nwhich is composed wholly of particulars and universals with which we are\nacquainted.\n\nThe chief importance of knowledge by description is that it enables us\nto pass beyond the limits of our private experience. In spite of the\nfact that we can only know truths which are wholly composed of terms\nwhich we have experienced in acquaintance, we can yet have knowledge by\ndescription of things which we have never experienced. In view of the\nvery narrow range of our immediate experience, this result is vital, and\nuntil it is understood, much of our knowledge must remain mysterious and\ntherefore doubtful.\n\n\n\nCHAPTER VI. ON INDUCTION\n\nIn almost all our previous discussions we have been concerned in\nthe attempt to get clear as to our data in the way of knowledge of\nexistence. What things are there in the universe whose existence is\nknown to us owing to our being acquainted with them? So far, our answer\nhas been that we are acquainted with our sense-data, and, probably,\nwith ourselves. These we know to exist. And past sense-data which\nare remembered are known to have existed in the past. This knowledge\nsupplies our data.\n\nBut if we are to be able to draw inferences from these data--if we are\nto know of the existence of matter, of other people, of the past before\nour individual memory begins, or of the future, we must know general\nprinciples of some kind by means of which such inferences can be drawn.\nIt must be known to us that the existence of some one sort of thing, A,\nis a sign of the existence of some other sort of thing, B, either at\nthe same time as A or at some earlier or later time, as, for example,\nthunder is a sign of the earlier existence of lightning. If this were\nnot known to us, we could never extend our knowledge beyond the\nsphere of our private experience; and this sphere, as we have seen, is\nexceedingly limited. The question we have now to consider is whether\nsuch an extension is possible, and if so, how it is effected.\n\nLet us take as an illustration a matter about which none of us, in fact,\nfeel the slightest doubt. We are all convinced that the sun will rise\nto-morrow. Why? Is this belief a mere blind outcome of past experience,\nor can it be justified as a reasonable belief? It is not easy to find\na test by which to judge whether a belief of this kind is reasonable or\nnot, but we can at least ascertain what sort of general beliefs would\nsuffice, if true, to justify the judgement that the sun will rise\nto-morrow, and the many other similar judgements upon which our actions\nare based.\n\nIt is obvious that if we are asked why we believe that the sun will rise\nto-morrow, we shall naturally answer 'Because it always has risen every\nday'. We have a firm belief that it will rise in the future, because it\nhas risen in the past. If we are challenged as to why we believe that\nit will continue to rise as heretofore, we may appeal to the laws of\nmotion: the earth, we shall say, is a freely rotating body, and such\nbodies do not cease to rotate unless something interferes from outside,\nand there is nothing outside to interfere with the earth between now and\nto-morrow. Of course it might be doubted whether we are quite certain\nthat there is nothing outside to interfere, but this is not the\ninteresting doubt. The interesting doubt is as to whether the laws\nof motion will remain in operation until to-morrow. If this doubt is\nraised, we find ourselves in the same position as when the doubt about\nthe sunrise was first raised.\n\nThe _only_ reason for believing that the laws of motion will remain in\noperation is that they have operated hitherto, so far as our knowledge\nof the past enables us to judge. It is true that we have a greater body\nof evidence from the past in favour of the laws of motion than we have\nin favour of the sunrise, because the sunrise is merely a particular\ncase of fulfilment of the laws of motion, and there are countless other\nparticular cases. But the real question is: Do _any_ number of cases\nof a law being fulfilled in the past afford evidence that it will be\nfulfilled in the future? If not, it becomes plain that we have no ground\nwhatever for expecting the sun to rise to-morrow, or for expecting the\nbread we shall eat at our next meal not to poison us, or for any of the\nother scarcely conscious expectations that control our daily lives. It\nis to be observed that all such expectations are only _probable_; thus\nwe have not to seek for a proof that they _must_ be fulfilled, but\nonly for some reason in favour of the view that they are _likely_ to be\nfulfilled.\n\nNow in dealing with this question we must, to begin with, make an\nimportant distinction, without which we should soon become involved\nin hopeless confusions. Experience has shown us that, hitherto, the\nfrequent repetition of some uniform succession or coexistence has been a\n_cause_ of our expecting the same succession or coexistence on the next\noccasion. Food that has a certain appearance generally has a certain\ntaste, and it is a severe shock to our expectations when the familiar\nappearance is found to be associated with an unusual taste. Things which\nwe see become associated, by habit, with certain tactile sensations\nwhich we expect if we touch them; one of the horrors of a ghost (in\nmany ghost-stories) is that it fails to give us any sensations of touch.\nUneducated people who go abroad for the first time are so surprised as\nto be incredulous when they find their native language not understood.\n\nAnd this kind of association is not confined to men; in animals also it\nis very strong. A horse which has been often driven along a certain\nroad resists the attempt to drive him in a different direction. Domestic\nanimals expect food when they see the person who usually feeds them. We\nknow that all these rather crude expectations of uniformity are liable\nto be misleading. The man who has fed the chicken every day throughout\nits life at last wrings its neck instead, showing that more refined\nviews as to the uniformity of nature would have been useful to the\nchicken.\n\nBut in spite of the misleadingness of such expectations, they\nnevertheless exist. The mere fact that something has happened a certain\nnumber of times causes animals and men to expect that it will happen\nagain. Thus our instincts certainly cause us to believe that the sun\nwill rise to-morrow, but we may be in no better a position than the\nchicken which unexpectedly has its neck wrung. We have therefore to\ndistinguish the fact that past uniformities _cause_ expectations as to\nthe future, from the question whether there is any reasonable ground for\ngiving weight to such expectations after the question of their validity\nhas been raised.\n\nThe problem we have to discuss is whether there is any reason for\nbelieving in what is called 'the uniformity of nature'. The belief in\nthe uniformity of nature is the belief that everything that has happened\nor will happen is an instance of some general law to which there are no\nexceptions. The crude expectations which we have been considering are\nall subject to exceptions, and therefore liable to disappoint those who\nentertain them. But science habitually assumes, at least as a working\nhypothesis, that general rules which have exceptions can be replaced by\ngeneral rules which have no exceptions. 'Unsupported bodies in air fall'\nis a general rule to which balloons and aeroplanes are exceptions. But\nthe laws of motion and the law of gravitation, which account for the\nfact that most bodies fall, also account for the fact that balloons and\naeroplanes can rise; thus the laws of motion and the law of gravitation\nare not subject to these exceptions.\n\nThe belief that the sun will rise to-morrow might be falsified if the\nearth came suddenly into contact with a large body which destroyed its\nrotation; but the laws of motion and the law of gravitation would not\nbe infringed by such an event. The business of science is to find\nuniformities, such as the laws of motion and the law of gravitation,\nto which, so far as our experience extends, there are no exceptions.\nIn this search science has been remarkably successful, and it may be\nconceded that such uniformities have held hitherto. This brings us back\nto the question: Have we any reason, assuming that they have always held\nin the past, to suppose that they will hold in the future?\n\nIt has been argued that we have reason to know that the future will\nresemble the past, because what was the future has constantly become the\npast, and has always been found to resemble the past, so that we really\nhave experience of the future, namely of times which were formerly\nfuture, which we may call past futures. But such an argument really begs\nthe very question at issue. We have experience of past futures, but not\nof future futures, and the question is: Will future futures resemble\npast futures? This question is not to be answered by an argument which\nstarts from past futures alone. We have therefore still to seek for some\nprinciple which shall enable us to know that the future will follow the\nsame laws as the past.\n\nThe reference to the future in this question is not essential. The same\nquestion arises when we apply the laws that work in our experience to\npast things of which we have no experience--as, for example, in geology,\nor in theories as to the origin of the Solar System. The question we\nreally have to ask is: 'When two things have been found to be often\nassociated, and no instance is known of the one occurring without the\nother, does the occurrence of one of the two, in a fresh instance, give\nany good ground for expecting the other?' On our answer to this question\nmust depend the validity of the whole of our expectations as to the\nfuture, the whole of the results obtained by induction, and in fact\npractically all the beliefs upon which our daily life is based.\n\nIt must be conceded, to begin with, that the fact that two things have\nbeen found often together and never apart does not, by itself, suffice\nto _prove_ demonstratively that they will be found together in the next\ncase we examine. The most we can hope is that the oftener things are\nfound together, the more probable it becomes that they will be found\ntogether another time, and that, if they have been found together often\nenough, the probability will amount _almost_ to certainty. It can\nnever quite reach certainty, because we know that in spite of frequent\nrepetitions there sometimes is a failure at the last, as in the case\nof the chicken whose neck is wrung. Thus probability is all we ought to\nseek.\n\nIt might be urged, as against the view we are advocating, that we\nknow all natural phenomena to be subject to the reign of law, and that\nsometimes, on the basis of observation, we can see that only one law\ncan possibly fit the facts of the case. Now to this view there are two\nanswers. The first is that, even if _some_ law which has no exceptions\napplies to our case, we can never, in practice, be sure that we have\ndiscovered that law and not one to which there are exceptions. The\nsecond is that the reign of law would seem to be itself only probable,\nand that our belief that it will hold in the future, or in unexamined\ncases in the past, is itself based upon the very principle we are\nexamining.\n\nThe principle we are examining may be called the _principle of\ninduction_, and its two parts may be stated as follows:\n\n(a) When a thing of a certain sort A has been found to be associated\nwith a thing of a certain other sort B, and has never been found\ndissociated from a thing of the sort B, the greater the number of cases\nin which A and B have been associated, the greater is the probability\nthat they will be associated in a fresh case in which one of them is\nknown to be present;\n\n(b) Under the same circumstances, a sufficient number of cases of\nassociation will make the probability of a fresh association nearly a\ncertainty, and will make it approach certainty without limit.\n\nAs just stated, the principle applies only to the verification of our\nexpectation in a single fresh instance. But we want also to know that\nthere is a probability in favour of the general law that things of the\nsort A are _always_ associated with things of the sort B, provided a\nsufficient number of cases of association are known, and no cases of\nfailure of association are known. The probability of the general law is\nobviously less than the probability of the particular case, since if the\ngeneral law is true, the particular case must also be true, whereas\nthe particular case may be true without the general law being true.\nNevertheless the probability of the general law is increased by\nrepetitions, just as the probability of the particular case is. We may\ntherefore repeat the two parts of our principle as regards the general\nlaw, thus:\n\n(a) The greater the number of cases in which a thing of the sort A has\nbeen found associated with a thing of the sort B, the more probable it\nis (if no cases of failure of association are known) that A is always\nassociated with B;\n\nb) Under the same circumstances, a sufficient number of cases of the\nassociation of A with B will make it nearly certain that A is always\nassociated with B, and will make this general law approach certainty\nwithout limit.\n\nIt should be noted that probability is always relative to certain data.\nIn our case, the data are merely the known cases of coexistence of A and\nB. There may be other data, which _might_ be taken into account, which\nwould gravely alter the probability. For example, a man who had seen a\ngreat many white swans might argue, by our principle, that on the\ndata it was _probable_ that all swans were white, and this might be a\nperfectly sound argument. The argument is not disproved by the fact that\nsome swans are black, because a thing may very well happen in spite of\nthe fact that some data render it improbable. In the case of the swans,\na man might know that colour is a very variable characteristic in many\nspecies of animals, and that, therefore, an induction as to colour is\npeculiarly liable to error. But this knowledge would be a fresh datum,\nby no means proving that the probability relatively to our previous data\nhad been wrongly estimated. The fact, therefore, that things often fail\nto fulfil our expectations is no evidence that our expectations will not\n_probably_ be fulfilled in a given case or a given class of cases. Thus\nour inductive principle is at any rate not capable of being _disproved_\nby an appeal to experience.\n\nThe inductive principle, however, is equally incapable of being _proved_\nby an appeal to experience. Experience might conceivably confirm\nthe inductive principle as regards the cases that have been already\nexamined; but as regards unexamined cases, it is the inductive principle\nalone that can justify any inference from what has been examined to what\nhas not been examined. All arguments which, on the basis of experience,\nargue as to the future or the unexperienced parts of the past or\npresent, assume the inductive principle; hence we can never use\nexperience to prove the inductive principle without begging the\nquestion. Thus we must either accept the inductive principle on the\nground of its intrinsic evidence, or forgo all justification of our\nexpectations about the future. If the principle is unsound, we have no\nreason to expect the sun to rise to-morrow, to expect bread to be more\nnourishing than a stone, or to expect that if we throw ourselves off\nthe roof we shall fall. When we see what looks like our best friend\napproaching us, we shall have no reason to suppose that his body is not\ninhabited by the mind of our worst enemy or of some total stranger. All\nour conduct is based upon associations which have worked in the past,\nand which we therefore regard as likely to work in the future; and this\nlikelihood is dependent for its validity upon the inductive principle.\n\nThe general principles of science, such as the belief in the reign\nof law, and the belief that every event must have a cause, are as\ncompletely dependent upon the inductive principle as are the beliefs of\ndaily life All such general principles are believed because mankind have\nfound innumerable instances of their truth and no instances of their\nfalsehood. But this affords no evidence for their truth in the future,\nunless the inductive principle is assumed.\n\nThus all knowledge which, on a basis of experience tells us something\nabout what is not experienced, is based upon a belief which experience\ncan neither confirm nor confute, yet which, at least in its more\nconcrete applications, appears to be as firmly rooted in us as many\nof the facts of experience. The existence and justification of such\nbeliefs--for the inductive principle, as we shall see, is not the only\nexample--raises some of the most difficult and most debated problems of\nphilosophy. We will, in the next chapter, consider briefly what may be\nsaid to account for such knowledge, and what is its scope and its degree\nof certainty.\n\n\n\nCHAPTER VII. ON OUR KNOWLEDGE OF GENERAL PRINCIPLES\n\nWe saw in the preceding chapter that the principle of induction, while\nnecessary to the validity of all arguments based on experience,\nis itself not capable of being proved by experience, and yet is\nunhesitatingly believed by every one, at least in all its concrete\napplications. In these characteristics the principle of induction does\nnot stand alone. There are a number of other principles which cannot be\nproved or disproved by experience, but are used in arguments which start\nfrom what is experienced.\n\nSome of these principles have even greater evidence than the principle\nof induction, and the knowledge of them has the same degree of certainty\nas the knowledge of the existence of sense-data. They constitute the\nmeans of drawing inferences from what is given in sensation; and if what\nwe infer is to be true, it is just as necessary that our principles\nof inference should be true as it is that our data should be true. The\nprinciples of inference are apt to be overlooked because of their\nvery obviousness--the assumption involved is assented to without our\nrealizing that it is an assumption. But it is very important to realize\nthe use of principles of inference, if a correct theory of knowledge\nis to be obtained; for our knowledge of them raises interesting and\ndifficult questions.\n\nIn all our knowledge of general principles, what actually happens\nis that first of all we realize some particular application of the\nprinciple, and then we realize that the particularity is irrelevant, and\nthat there is a generality which may equally truly be affirmed. This is\nof course familiar in such matters as teaching arithmetic: 'two and\ntwo are four' is first learnt in the case of some particular pair of\ncouples, and then in some other particular case, and so on, until at\nlast it becomes possible to see that it is true of any pair of couples.\nThe same thing happens with logical principles. Suppose two men are\ndiscussing what day of the month it is. One of them says, 'At least you\nwill admit that _if_ yesterday was the 15th to-day must be the 16th.'\n'Yes', says the other, 'I admit that.' 'And you know', the first\ncontinues, 'that yesterday was the 15th, because you dined with Jones,\nand your diary will tell you that was on the 15th.' 'Yes', says the\nsecond; 'therefore to-day _is_ the 16th.'\n\nNow such an argument is not hard to follow; and if it is granted that\nits premisses are true in fact, no one will deny that the conclusion\nmust also be true. But it depends for its truth upon an instance of a\ngeneral logical principle. The logical principle is as follows: 'Suppose\nit known that _if_ this is true, then that is true. Suppose it also\nknown that this _is_ true, then it follows that that is true.' When it\nis the case that if this is true, that is true, we shall say that this\n'implies' that, and that that 'follows from' this. Thus our principle\nstates that if this implies that, and this is true, then that is true.\nIn other words, 'anything implied by a true proposition is true', or\n'whatever follows from a true proposition is true'.\n\nThis principle is really involved--at least, concrete instances of it\nare involved--in all demonstrations. Whenever one thing which we believe\nis used to prove something else, which we consequently believe, this\nprinciple is relevant. If any one asks: 'Why should I accept the results\nof valid arguments based on true premisses?' we can only answer by\nappealing to our principle. In fact, the truth of the principle is\nimpossible to doubt, and its obviousness is so great that at first sight\nit seems almost trivial. Such principles, however, are not trivial to\nthe philosopher, for they show that we may have indubitable knowledge\nwhich is in no way derived from objects of sense.\n\nThe above principle is merely one of a certain number of self-evident\nlogical principles. Some at least of these principles must be granted\nbefore any argument or proof becomes possible. When some of them have\nbeen granted, others can be proved, though these others, so long as they\nare simple, are just as obvious as the principles taken for granted. For\nno very good reason, three of these principles have been singled out by\ntradition under the name of 'Laws of Thought'.\n\nThey are as follows:\n\n(1) _The law of identity_: 'Whatever is, is.'\n\n(2) _The law of contradiction_: 'Nothing can both be and not be.'\n\n(3) _The law of excluded middle_: 'Everything must either be or not be.'\n\nThese three laws are samples of self-evident logical principles, but\nare not really more fundamental or more self-evident than various other\nsimilar principles: for instance, the one we considered just now, which\nstates that what follows from a true premiss is true. The name 'laws of\nthought' is also misleading, for what is important is not the fact that\nwe think in accordance with these laws, but the fact that things behave\nin accordance with them; in other words, the fact that when we think in\naccordance with them we think _truly_. But this is a large question, to\nwhich we must return at a later stage.\n\nIn addition to the logical principles which enable us to prove from\na given premiss that something is _certainly_ true, there are other\nlogical principles which enable us to prove, from a given premiss,\nthat there is a greater or less probability that something is true. An\nexample of such principles--perhaps the most important example is the\ninductive principle, which we considered in the preceding chapter.\n\nOne of the great historic controversies in philosophy is the controversy\nbetween the two schools called respectively 'empiricists' and\n'rationalists'. The empiricists--who are best represented by the\nBritish philosophers, Locke, Berkeley, and Hume--maintained that all\nour knowledge is derived from experience; the rationalists--who are\nrepresented by the Continental philosophers of the seventeenth century,\nespecially Descartes and Leibniz--maintained that, in addition to what\nwe know by experience, there are certain 'innate ideas' and 'innate\nprinciples', which we know independently of experience. It has now\nbecome possible to decide with some confidence as to the truth or\nfalsehood of these opposing schools. It must be admitted, for the\nreasons already stated, that logical principles are known to us, and\ncannot be themselves proved by experience, since all proof presupposes\nthem. In this, therefore, which was the most important point of the\ncontroversy, the rationalists were in the right.\n\nOn the other hand, even that part of our knowledge which is _logically_\nindependent of experience (in the sense that experience cannot prove\nit) is yet elicited and caused by experience. It is on occasion of\nparticular experiences that we become aware of the general laws which\ntheir connexions exemplify. It would certainly be absurd to suppose that\nthere are innate principles in the sense that babies are born with a\nknowledge of everything which men know and which cannot be deduced from\nwhat is experienced. For this reason, the word 'innate' would not now be\nemployed to describe our knowledge of logical principles. The phrase\n'_a priori_' is less objectionable, and is more usual in modern writers.\nThus, while admitting that all knowledge is elicited and caused by\nexperience, we shall nevertheless hold that some knowledge is _a\npriori_, in the sense that the experience which makes us think of it\ndoes not suffice to prove it, but merely so directs our attention that\nwe see its truth without requiring any proof from experience.\n\nThere is another point of great importance, in which the empiricists\nwere in the right as against the rationalists. Nothing can be known to\n_exist_ except by the help of experience. That is to say, if we wish to\nprove that something of which we have no direct experience exists, we\nmust have among our premisses the existence of one or more things of\nwhich we have direct experience. Our belief that the Emperor of China\nexists, for example, rests upon testimony, and testimony consists,\nin the last analysis, of sense-data seen or heard in reading or being\nspoken to. Rationalists believed that, from general consideration as\nto what must be, they could deduce the existence of this or that in the\nactual world. In this belief they seem to have been mistaken. All the\nknowledge that we can acquire _a priori_ concerning existence seems\nto be hypothetical: it tells us that if one thing exists, another must\nexist, or, more generally, that if one proposition is true, another must\nbe true. This is exemplified by the principles we have already dealt\nwith, such as '_if_ this is true, and this implies that, then that is\ntrue', or '_if_ this and that have been repeatedly found connected, they\nwill probably be connected in the next instance in which one of them is\nfound'. Thus the scope and power of _a priori_ principles is strictly\nlimited. All knowledge that something exists must be in part dependent\non experience. When anything is known immediately, its existence is\nknown by experience alone; when anything is proved to exist, without\nbeing known immediately, both experience and _a priori_ principles must\nbe required in the proof. Knowledge is called _empirical_ when it rests\nwholly or partly upon experience. Thus all knowledge which asserts\nexistence is empirical, and the only _a priori_ knowledge concerning\nexistence is hypothetical, giving connexions among things that exist or\nmay exist, but not giving actual existence.\n\n_A priori_ knowledge is not all of the logical kind we have been\nhitherto considering. Perhaps the most important example of non-logical\n_a priori_ knowledge is knowledge as to ethical value. I am not speaking\nof judgements as to what is useful or as to what is virtuous, for such\njudgements do require empirical premisses; I am speaking of judgements\nas to the intrinsic desirability of things. If something is useful, it\nmust be useful because it secures some end; the end must, if we have\ngone far enough, be valuable on its own account, and not merely because\nit is useful for some further end. Thus all judgements as to what is\nuseful depend upon judgements as to what has value on its own account.\n\nWe judge, for example, that happiness is more desirable than misery,\nknowledge than ignorance, goodwill than hatred, and so on. Such\njudgements must, in part at least, be immediate and _a priori_. Like our\nprevious _a priori_ judgements, they may be elicited by experience, and\nindeed they must be; for it seems not possible to judge whether anything\nis intrinsically valuable unless we have experienced something of\nthe same kind. But it is fairly obvious that they cannot be proved by\nexperience; for the fact that a thing exists or does not exist cannot\nprove either that it is good that it should exist or that it is bad. The\npursuit of this subject belongs to ethics, where the impossibility of\ndeducing what ought to be from what is has to be established. In the\npresent connexion, it is only important to realize that knowledge as to\nwhat is intrinsically of value is _a priori_ in the same sense in\nwhich logic is _a priori_, namely in the sense that the truth of such\nknowledge can be neither proved nor disproved by experience.\n\nAll pure mathematics is _a priori_, like logic. This was strenuously\ndenied by the empirical philosophers, who maintained that experience was\nas much the source of our knowledge of arithmetic as of our knowledge of\ngeography. They maintained that by the repeated experience of seeing two\nthings and two other things, and finding that altogether they made four\nthings, we were led by induction to the conclusion that two things\nand two other things would _always_ make four things altogether. If,\nhowever, this were the source of our knowledge that two and two are\nfour, we should proceed differently, in persuading ourselves of its\ntruth, from the way in which we do actually proceed. In fact, a certain\nnumber of instances are needed to make us think of two abstractly,\nrather than of two coins or two books or two people, or two of any other\nspecified kind. But as soon as we are able to divest our thoughts of\nirrelevant particularity, we become able to see the general principle\nthat two and two are four; any one instance is seen to be _typical_, and\nthe examination of other instances becomes unnecessary.(1)\n\n(1) Cf. A. N. Whitehead, _Introduction to Mathematics_ (Home University\nLibrary).\n\nThe same thing is exemplified in geometry. If we want to prove some\nproperty of _all_ triangles, we draw some one triangle and reason about\nit; but we can avoid making use of any property which it does not share\nwith all other triangles, and thus, from our particular case, we obtain\na general result. We do not, in fact, feel our certainty that two and\ntwo are four increased by fresh instances, because, as soon as we have\nseen the truth of this proposition, our certainty becomes so great as\nto be incapable of growing greater. Moreover, we feel some quality of\nnecessity about the proposition 'two and two are four', which is\nabsent from even the best attested empirical generalizations. Such\ngeneralizations always remain mere facts: we feel that there might be a\nworld in which they were false, though in the actual world they happen\nto be true. In any possible world, on the contrary, we feel that two\nand two would be four: this is not a mere fact, but a necessity to which\neverything actual and possible must conform.\n\nThe case may be made clearer by considering a genuinely-empirical\ngeneralization, such as 'All men are mortal.' It is plain that we\nbelieve this proposition, in the first place, because there is no known\ninstance of men living beyond a certain age, and in the second place\nbecause there seem to be physiological grounds for thinking that an\norganism such as a man's body must sooner or later wear out. Neglecting\nthe second ground, and considering merely our experience of men's\nmortality, it is plain that we should not be content with one quite\nclearly understood instance of a man dying, whereas, in the case of 'two\nand two are four', one instance does suffice, when carefully considered,\nto persuade us that the same must happen in any other instance. Also\nwe can be forced to admit, on reflection, that there may be some doubt,\nhowever slight, as to whether _all_ men are mortal. This may be made\nplain by the attempt to imagine two different worlds, in one of which\nthere are men who are not mortal, while in the other two and two make\nfive. When Swift invites us to consider the race of Struldbugs who never\ndie, we are able to acquiesce in imagination. But a world where two\nand two make five seems quite on a different level. We feel that such a\nworld, if there were one, would upset the whole fabric of our knowledge\nand reduce us to utter doubt.\n\nThe fact is that, in simple mathematical judgements such as 'two and two\nare four', and also in many judgements of logic, we can know the general\nproposition without inferring it from instances, although some instance\nis usually necessary to make clear to us what the general proposition\nmeans. This is why there is real utility in the process of _deduction_,\nwhich goes from the general to the general, or from the general to the\nparticular, as well as in the process of _induction_, which goes from\nthe particular to the particular, or from the particular to the general.\nIt is an old debate among philosophers whether deduction ever gives\n_new_ knowledge. We can now see that in certain cases, at least, it does\ndo so. If we already know that two and two always make four, and we\nknow that Brown and Jones are two, and so are Robinson and Smith, we can\ndeduce that Brown and Jones and Robinson and Smith are four. This is\nnew knowledge, not contained in our premisses, because the general\nproposition, 'two and two are four', never told us there were such\npeople as Brown and Jones and Robinson and Smith, and the particular\npremisses do not tell us that there were four of them, whereas the\nparticular proposition deduced does tell us both these things.\n\nBut the newness of the knowledge is much less certain if we take the\nstock instance of deduction that is always given in books on logic,\nnamely, 'All men are mortal; Socrates is a man, therefore Socrates is\nmortal.' In this case, what we really know beyond reasonable doubt is\nthat certain men, A, B, C, were mortal, since, in fact, they have died.\nIf Socrates is one of these men, it is foolish to go the roundabout way\nthrough 'all men are mortal' to arrive at the conclusion that _probably_\nSocrates is mortal. If Socrates is not one of the men on whom our\ninduction is based, we shall still do better to argue straight from our\nA, B, C, to Socrates, than to go round by the general proposition, 'all\nmen are mortal'. For the probability that Socrates is mortal is greater,\non our data, than the probability that all men are mortal. (This is\nobvious, because if all men are mortal, so is Socrates; but if Socrates\nis mortal, it does not follow that all men are mortal.) Hence we shall\nreach the conclusion that Socrates is mortal with a greater approach to\ncertainty if we make our argument purely inductive than if we go by way\nof 'all men are mortal' and then use deduction.\n\nThis illustrates the difference between general propositions known _a\npriori_ such as 'two and two are four', and empirical generalizations\nsuch as 'all men are mortal'. In regard to the former, deduction is the\nright mode of argument, whereas in regard to the latter, induction is\nalways theoretically preferable, and warrants a greater confidence in\nthe truth of our conclusion, because all empirical generalizations are\nmore uncertain than the instances of them.\n\nWe have now seen that there are propositions known _a priori_, and that\namong them are the propositions of logic and pure mathematics, as well\nas the fundamental propositions of ethics. The question which must\nnext occupy us is this: How is it possible that there should be such\nknowledge? And more particularly, how can there be knowledge of general\npropositions in cases where we have not examined all the instances, and\nindeed never can examine them all, because their number is infinite?\nThese questions, which were first brought prominently forward by\nthe German philosopher Kant (1724-1804), are very difficult, and\nhistorically very important.\n\n\n\nCHAPTER VIII. HOW _A PRIORI_ KNOWLEDGE IS POSSIBLE\n\nImmanuel Kant is generally regarded as the greatest of the modern\nphilosophers. Though he lived through the Seven Years War and the\nFrench Revolution, he never interrupted his teaching of philosophy at\nK\u00f6nigsberg in East Prussia. His most distinctive contribution was the\ninvention of what he called the 'critical' philosophy, which, assuming\nas a datum that there is knowledge of various kinds, inquired how such\nknowledge comes to be possible, and deduced, from the answer to this\ninquiry, many metaphysical results as to the nature of the world.\nWhether these results were valid may well be doubted. But Kant\nundoubtedly deserves credit for two things: first, for having perceived\nthat we have _a priori_ knowledge which is not purely 'analytic', i.e.\nsuch that the opposite would be self-contradictory, and secondly,\nfor having made evident the philosophical importance of the theory of\nknowledge.\n\nBefore the time of Kant, it was generally held that whatever knowledge\nwas _a priori_ must be 'analytic'. What this word means will be best\nillustrated by examples. If I say, 'A bald man is a man', 'A plane\nfigure is a figure', 'A bad poet is a poet', I make a purely analytic\njudgement: the subject spoken about is given as having at least two\nproperties, of which one is singled out to be asserted of it. Such\npropositions as the above are trivial, and would never be enunciated\nin real life except by an orator preparing the way for a piece of\nsophistry. They are called 'analytic' because the predicate is obtained\nby merely analysing the subject. Before the time of Kant it was thought\nthat all judgements of which we could be certain _a priori_ were of this\nkind: that in all of them there was a predicate which was only part\nof the subject of which it was asserted. If this were so, we should be\ninvolved in a definite contradiction if we attempted to deny anything\nthat could be known _a priori_. 'A bald man is not bald' would assert\nand deny baldness of the same man, and would therefore contradict\nitself. Thus according to the philosophers before Kant, the law of\ncontradiction, which asserts that nothing can at the same time have and\nnot have a certain property, sufficed to establish the truth of all _a\npriori_ knowledge.\n\nHume (1711-76), who preceded Kant, accepting the usual view as to what\nmakes knowledge _a priori_, discovered that, in many cases which had\npreviously been supposed analytic, and notably in the case of cause and\neffect, the connexion was really synthetic. Before Hume, rationalists at\nleast had supposed that the effect could be logically deduced from the\ncause, if only we had sufficient knowledge. Hume argued--correctly, as\nwould now be generally admitted--that this could not be done. Hence he\ninferred the far more doubtful proposition that nothing could be known\n_a priori_ about the connexion of cause and effect. Kant, who had been\neducated in the rationalist tradition, was much perturbed by Hume's\nscepticism, and endeavoured to find an answer to it. He perceived that\nnot only the connexion of cause and effect, but all the propositions\nof arithmetic and geometry, are 'synthetic', i.e. not analytic: in\nall these propositions, no analysis of the subject will reveal the\npredicate. His stock instance was the proposition 7 + 5 = 12. He pointed\nout, quite truly, that 7 and 5 have to be put together to give 12: the\nidea of 12 is not contained in them, nor even in the idea of adding them\ntogether. Thus he was led to the conclusion that all pure mathematics,\nthough _a priori_, is synthetic; and this conclusion raised a new\nproblem of which he endeavoured to find the solution.\n\nThe question which Kant put at the beginning of his philosophy, namely\n'How is pure mathematics possible?' is an interesting and difficult one,\nto which every philosophy which is not purely sceptical must find\nsome answer. The answer of the pure empiricists, that our mathematical\nknowledge is derived by induction from particular instances, we have\nalready seen to be inadequate, for two reasons: first, that the validity\nof the inductive principle itself cannot be proved by induction;\nsecondly, that the general propositions of mathematics, such as 'two\nand two always make four', can obviously be known with certainty by\nconsideration of a single instance, and gain nothing by enumeration of\nother cases in which they have been found to be true. Thus our knowledge\nof the general propositions of mathematics (and the same applies to\nlogic) must be accounted for otherwise than our (merely probable)\nknowledge of empirical generalizations such as 'all men are mortal'.\n\nThe problem arises through the fact that such knowledge is general,\nwhereas all experience is particular. It seems strange that we should\napparently be able to know some truths in advance about particular\nthings of which we have as yet no experience; but it cannot easily be\ndoubted that logic and arithmetic will apply to such things. We do not\nknow who will be the inhabitants of London a hundred years hence; but\nwe know that any two of them and any other two of them will make four of\nthem. This apparent power of anticipating facts about things of which\nwe have no experience is certainly surprising. Kant's solution of the\nproblem, though not valid in my opinion, is interesting. It is, however,\nvery difficult, and is differently understood by different philosophers.\nWe can, therefore, only give the merest outline of it, and even that\nwill be thought misleading by many exponents of Kant's system.\n\nWhat Kant maintained was that in all our experience there are two\nelements to be distinguished, the one due to the object (i.e. to what we\nhave called the 'physical object'), the other due to our own nature. We\nsaw, in discussing matter and sense-data, that the physical object is\ndifferent from the associated sense-data, and that the sense-data are to\nbe regarded as resulting from an interaction between the physical\nobject and ourselves. So far, we are in agreement with Kant. But what\nis distinctive of Kant is the way in which he apportions the shares of\nourselves and the physical object respectively. He considers that the\ncrude material given in sensation--the colour, hardness, etc.--is due\nto the object, and that what we supply is the arrangement in space\nand time, and all the relations between sense-data which result from\ncomparison or from considering one as the cause of the other or in any\nother way. His chief reason in favour of this view is that we seem\nto have _a priori_ knowledge as to space and time and causality and\ncomparison, but not as to the actual crude material of sensation. We can\nbe sure, he says, that anything we shall ever experience must show the\ncharacteristics affirmed of it in our _a priori_ knowledge, because\nthese characteristics are due to our own nature, and therefore\nnothing can ever come into our experience without acquiring these\ncharacteristics.\n\nThe physical object, which he calls the 'thing in itself',(1) he regards\nas essentially unknowable; what can be known is the object as we have it\nin experience, which he calls the 'phenomenon'. The phenomenon, being\na joint product of us and the thing in itself, is sure to have those\ncharacteristics which are due to us, and is therefore sure to conform\nto our _a priori_ knowledge. Hence this knowledge, though true of all\nactual and possible experience, must not be supposed to apply outside\nexperience. Thus in spite of the existence of _a priori_ knowledge, we\ncannot know anything about the thing in itself or about what is not\nan actual or possible object of experience. In this way he tries to\nreconcile and harmonize the contentions of the rationalists with the\narguments of the empiricists.\n\n(1) Kant's 'thing in itself' is identical in _definition_ with\nthe physical object, namely, it is the cause of sensations. In the\nproperties deduced from the definition it is not identical, since Kant\nheld (in spite of some inconsistency as regards cause) that we can know\nthat none of the categories are applicable to the 'thing in itself'.\n\nApart from minor grounds on which Kant's philosophy may be criticized,\nthere is one main objection which seems fatal to any attempt to deal\nwith the problem of _a priori_ knowledge by his method. The thing to\nbe accounted for is our certainty that the facts must always conform to\nlogic and arithmetic. To say that logic and arithmetic are contributed\nby us does not account for this. Our nature is as much a fact of the\nexisting world as anything, and there can be no certainty that it will\nremain constant. It might happen, if Kant is right, that to-morrow\nour nature would so change as to make two and two become five. This\npossibility seems never to have occurred to him, yet it is one which\nutterly destroys the certainty and universality which he is anxious\nto vindicate for arithmetical propositions. It is true that this\npossibility, formally, is inconsistent with the Kantian view that time\nitself is a form imposed by the subject upon phenomena, so that our\nreal Self is not in time and has no to-morrow. But he will still have\nto suppose that the time-order of phenomena is determined by\ncharacteristics of what is behind phenomena, and this suffices for the\nsubstance of our argument.\n\nReflection, moreover, seems to make it clear that, if there is any truth\nin our arithmetical beliefs, they must apply to things equally whether\nwe think of them or not. Two physical objects and two other physical\nobjects must make four physical objects, even if physical objects cannot\nbe experienced. To assert this is certainly within the scope of what\nwe mean when we state that two and two are four. Its truth is just as\nindubitable as the truth of the assertion that two phenomena and two\nother phenomena make four phenomena. Thus Kant's solution unduly limits\nthe scope of _a priori_ propositions, in addition to failing in the\nattempt at explaining their certainty.\n\nApart from the special doctrines advocated by Kant, it is very common\namong philosophers to regard what is _a priori_ as in some sense mental,\nas concerned rather with the way we must think than with any fact of\nthe outer world. We noted in the preceding chapter the three principles\ncommonly called 'laws of thought'. The view which led to their being so\nnamed is a natural one, but there are strong reasons for thinking\nthat it is erroneous. Let us take as an illustration the law of\ncontradiction. This is commonly stated in the form 'Nothing can both be\nand not be', which is intended to express the fact that nothing can at\nonce have and not have a given quality. Thus, for example, if a tree\nis a beech it cannot also be not a beech; if my table is rectangular it\ncannot also be not rectangular, and so on.\n\nNow what makes it natural to call this principle a law of _thought_\nis that it is by thought rather than by outward observation that we\npersuade ourselves of its necessary truth. When we have seen that a tree\nis a beech, we do not need to look again in order to ascertain whether\nit is also not a beech; thought alone makes us know that this is\nimpossible. But the conclusion that the law of contradiction is a law\nof _thought_ is nevertheless erroneous. What we believe, when we believe\nthe law of contradiction, is not that the mind is so made that it must\nbelieve the law of contradiction. _This_ belief is a subsequent result\nof psychological reflection, which presupposes the belief in the law of\ncontradiction. The belief in the law of contradiction is a belief about\nthings, not only about thoughts. It is not, e.g., the belief that if we\n_think_ a certain tree is a beech, we cannot at the same time _think_\nthat it is not a beech; it is the belief that if the tree _is_ a\nbeech, it cannot at the same time _be_ not a beech. Thus the law of\ncontradiction is about things, and not merely about thoughts; and\nalthough belief in the law of contradiction is a thought, the law of\ncontradiction itself is not a thought, but a fact concerning the things\nin the world. If this, which we believe when we believe the law of\ncontradiction, were not true of the things in the world, the fact\nthat we were compelled to _think_ it true would not save the law of\ncontradiction from being false; and this shows that the law is not a law\nof _thought_.\n\nA similar argument applies to any other _a priori_ judgement. When we\njudge that two and two are four, we are not making a judgement about our\nthoughts, but about all actual or possible couples. The fact that our\nminds are so constituted as to believe that two and two are four, though\nit is true, is emphatically not what we assert when we assert that two\nand two are four. And no fact about the constitution of our minds could\nmake it _true_ that two and two are four. Thus our _a priori_ knowledge,\nif it is not erroneous, is not merely knowledge about the constitution\nof our minds, but is applicable to whatever the world may contain, both\nwhat is mental and what is non-mental.\n\nThe fact seems to be that all our _a priori_ knowledge is concerned with\nentities which do not, properly speaking, _exist_, either in the mental\nor in the physical world. These entities are such as can be named by\nparts of speech which are not substantives; they are such entities as\nqualities and relations. Suppose, for instance, that I am in my room. I\nexist, and my room exists; but does 'in' exist? Yet obviously the word\n'in' has a meaning; it denotes a relation which holds between me and my\nroom. This relation is something, although we cannot say that it exists\n_in the same sense_ in which I and my room exist. The relation 'in' is\nsomething which we can think about and understand, for, if we could not\nunderstand it, we could not understand the sentence 'I am in my room'.\nMany philosophers, following Kant, have maintained that relations are\nthe work of the mind, that things in themselves have no relations,\nbut that the mind brings them together in one act of thought and thus\nproduces the relations which it judges them to have.\n\nThis view, however, seems open to objections similar to those which we\nurged before against Kant. It seems plain that it is not thought which\nproduces the truth of the proposition 'I am in my room'. It may be true\nthat an earwig is in my room, even if neither I nor the earwig nor any\none else is aware of this truth; for this truth concerns only the earwig\nand the room, and does not depend upon anything else. Thus relations, as\nwe shall see more fully in the next chapter, must be placed in a world\nwhich is neither mental nor physical. This world is of great importance\nto philosophy, and in particular to the problems of _a priori_\nknowledge. In the next chapter we shall proceed to develop its nature\nand its bearing upon the questions with which we have been dealing.\n\n\n\nCHAPTER IX. THE WORLD OF UNIVERSALS\n\nAt the end of the preceding chapter we saw that such entities as\nrelations appear to have a being which is in some way different from\nthat of physical objects, and also different from that of minds and from\nthat of sense-data. In the present chapter we have to consider what is\nthe nature of this kind of being, and also what objects there are that\nhave this kind of being. We will begin with the latter question.\n\nThe problem with which we are now concerned is a very old one, since it\nwas brought into philosophy by Plato. Plato's 'theory of ideas' is an\nattempt to solve this very problem, and in my opinion it is one of the\nmost successful attempts hitherto made. The theory to be advocated in\nwhat follows is largely Plato's, with merely such modifications as time\nhas shown to be necessary.\n\nThe way the problem arose for Plato was more or less as follows. Let\nus consider, say, such a notion as _justice_. If we ask ourselves what\njustice is, it is natural to proceed by considering this, that, and the\nother just act, with a view to discovering what they have in common.\nThey must all, in some sense, partake of a common nature, which will be\nfound in whatever is just and in nothing else. This common nature, in\nvirtue of which they are all just, will be justice itself, the pure\nessence the admixture of which with facts of ordinary life produces the\nmultiplicity of just acts. Similarly with any other word which may be\napplicable to common facts, such as 'whiteness' for example. The word\nwill be applicable to a number of particular things because they all\nparticipate in a common nature or essence. This pure essence is what\nPlato calls an 'idea' or 'form'. (It must not be supposed that 'ideas',\nin his sense, exist in minds, though they may be apprehended by minds.)\nThe 'idea' _justice_ is not identical with anything that is just: it is\nsomething other than particular things, which particular things partake\nof. Not being particular, it cannot itself exist in the world of sense.\nMoreover it is not fleeting or changeable like the things of sense: it\nis eternally itself, immutable and indestructible.\n\nThus Plato is led to a supra-sensible world, more real than the common\nworld of sense, the unchangeable world of ideas, which alone gives to\nthe world of sense whatever pale reflection of reality may belong to it.\nThe truly real world, for Plato, is the world of ideas; for whatever\nwe may attempt to say about things in the world of sense, we can only\nsucceed in saying that they participate in such and such ideas, which,\ntherefore, constitute all their character. Hence it is easy to pass\non into a mysticism. We may hope, in a mystic illumination, to see the\nideas as we see objects of sense; and we may imagine that the ideas\nexist in heaven. These mystical developments are very natural, but the\nbasis of the theory is in logic, and it is as based in logic that we\nhave to consider it.\n\nThe word 'idea' has acquired, in the course of time, many associations\nwhich are quite misleading when applied to Plato's 'ideas'. We shall\ntherefore use the word 'universal' instead of the word 'idea', to\ndescribe what Plato meant. The essence of the sort of entity that Plato\nmeant is that it is opposed to the particular things that are given in\nsensation. We speak of whatever is given in sensation, or is of the same\nnature as things given in sensation, as a _particular_; by opposition\nto this, a _universal_ will be anything which may be shared by many\nparticulars, and has those characteristics which, as we saw, distinguish\njustice and whiteness from just acts and white things.\n\nWhen we examine common words, we find that, broadly speaking, proper\nnames stand for particulars, while other substantives, adjectives,\nprepositions, and verbs stand for universals. Pronouns stand for\nparticulars, but are ambiguous: it is only by the context or the\ncircumstances that we know what particulars they stand for. The word\n'now' stands for a particular, namely the present moment; but like\npronouns, it stands for an ambiguous particular, because the present is\nalways changing.\n\nIt will be seen that no sentence can be made up without at least one\nword which denotes a universal. The nearest approach would be some such\nstatement as 'I like this'. But even here the word 'like' denotes\na universal, for I may like other things, and other people may like\nthings. Thus all truths involve universals, and all knowledge of truths\ninvolves acquaintance with universals.\n\nSeeing that nearly all the words to be found in the dictionary stand\nfor universals, it is strange that hardly anybody except students of\nphilosophy ever realizes that there are such entities as universals. We\ndo not naturally dwell upon those words in a sentence which do not stand\nfor particulars; and if we are forced to dwell upon a word which stands\nfor a universal, we naturally think of it as standing for some one of\nthe particulars that come under the universal. When, for example, we\nhear the sentence, 'Charles I's head was cut off', we may naturally\nenough think of Charles I, of Charles I's head, and of the operation\nof cutting off _his_ head, which are all particulars; but we do not\nnaturally dwell upon what is meant by the word 'head' or the word\n'cut', which is a universal: We feel such words to be incomplete and\ninsubstantial; they seem to demand a context before anything can be\ndone with them. Hence we succeed in avoiding all notice of universals as\nsuch, until the study of philosophy forces them upon our attention.\n\nEven among philosophers, we may say, broadly, that only those universals\nwhich are named by adjectives or substantives have been much or often\nrecognized, while those named by verbs and prepositions have been\nusually overlooked. This omission has had a very great effect upon\nphilosophy; it is hardly too much to say that most metaphysics, since\nSpinoza, has been largely determined by it. The way this has occurred\nis, in outline, as follows: Speaking generally, adjectives and common\nnouns express qualities or properties of single things, whereas\nprepositions and verbs tend to express relations between two or more\nthings. Thus the neglect of prepositions and verbs led to the belief\nthat every proposition can be regarded as attributing a property to a\nsingle thing, rather than as expressing a relation between two or more\nthings. Hence it was supposed that, ultimately, there can be no such\nentities as relations between things. Hence either there can be only\none thing in the universe, or, if there are many things, they cannot\npossibly interact in any way, since any interaction would be a relation,\nand relations are impossible.\n\nThe first of these views, advocated by Spinoza and held in our own day\nby Bradley and many other philosophers, is called _monism_; the second,\nadvocated by Leibniz but not very common nowadays, is called _monadism_,\nbecause each of the isolated things is called a _monad_. Both these\nopposing philosophies, interesting as they are, result, in my opinion,\nfrom an undue attention to one sort of universals, namely the sort\nrepresented by adjectives and substantives rather than by verbs and\nprepositions.\n\nAs a matter of fact, if any one were anxious to deny altogether that\nthere are such things as universals, we should find that we cannot\nstrictly prove that there are such entities as _qualities_, i.e. the\nuniversals represented by adjectives and substantives, whereas we\ncan prove that there must be _relations_, i.e. the sort of universals\ngenerally represented by verbs and prepositions. Let us take in\nillustration the universal _whiteness_. If we believe that there is such\na universal, we shall say that things are white because they have the\nquality of whiteness. This view, however, was strenuously denied by\nBerkeley and Hume, who have been followed in this by later empiricists.\nThe form which their denial took was to deny that there are such things\nas 'abstract ideas '. When we want to think of whiteness, they said, we\nform an image of some particular white thing, and reason concerning this\nparticular, taking care not to deduce anything concerning it which we\ncannot see to be equally true of any other white thing. As an account of\nour actual mental processes, this is no doubt largely true. In geometry,\nfor example, when we wish to prove something about all triangles, we\ndraw a particular triangle and reason about it, taking care not to use\nany characteristic which it does not share with other triangles. The\nbeginner, in order to avoid error, often finds it useful to draw several\ntriangles, as unlike each other as possible, in order to make sure that\nhis reasoning is equally applicable to all of them. But a difficulty\nemerges as soon as we ask ourselves how we know that a thing is white\nor a triangle. If we wish to avoid the universals _whiteness_ and\n_triangularity_, we shall choose some particular patch of white or some\nparticular triangle, and say that anything is white or a triangle if it\nhas the right sort of resemblance to our chosen particular. But then the\nresemblance required will have to be a universal. Since there are many\nwhite things, the resemblance must hold between many pairs of particular\nwhite things; and this is the characteristic of a universal. It will be\nuseless to say that there is a different resemblance for each pair, for\nthen we shall have to say that these resemblances resemble each other,\nand thus at last we shall be forced to admit resemblance as a universal.\nThe relation of resemblance, therefore, must be a true universal. And\nhaving been forced to admit this universal, we find that it is no longer\nworth while to invent difficult and unplausible theories to avoid the\nadmission of such universals as whiteness and triangularity.\n\nBerkeley and Hume failed to perceive this refutation of their rejection\nof 'abstract ideas', because, like their adversaries, they only thought\nof _qualities_, and altogether ignored _relations_ as universals. We\nhave therefore here another respect in which the rationalists appear to\nhave been in the right as against the empiricists, although, owing to\nthe neglect or denial of relations, the deductions made by rationalists\nwere, if anything, more apt to be mistaken than those made by\nempiricists.\n\nHaving now seen that there must be such entities as universals, the next\npoint to be proved is that their being is not merely mental. By this is\nmeant that whatever being belongs to them is independent of their being\nthought of or in any way apprehended by minds. We have already touched\non this subject at the end of the preceding chapter, but we must now\nconsider more fully what sort of being it is that belongs to universals.\n\nConsider such a proposition as 'Edinburgh is north of London'. Here we\nhave a relation between two places, and it seems plain that the relation\nsubsists independently of our knowledge of it. When we come to know that\nEdinburgh is north of London, we come to know something which has to\ndo only with Edinburgh and London: we do not cause the truth of the\nproposition by coming to know it, on the contrary we merely apprehend a\nfact which was there before we knew it. The part of the earth's surface\nwhere Edinburgh stands would be north of the part where London stands,\neven if there were no human being to know about north and south, and\neven if there were no minds at all in the universe. This is, of course,\ndenied by many philosophers, either for Berkeley's reasons or for\nKant's. But we have already considered these reasons, and decided that\nthey are inadequate. We may therefore now assume it to be true that\nnothing mental is presupposed in the fact that Edinburgh is north of\nLondon. But this fact involves the relation 'north of', which is a\nuniversal; and it would be impossible for the whole fact to involve\nnothing mental if the relation 'north of', which is a constituent part\nof the fact, did involve anything mental. Hence we must admit that the\nrelation, like the terms it relates, is not dependent upon thought, but\nbelongs to the independent world which thought apprehends but does not\ncreate.\n\nThis conclusion, however, is met by the difficulty that the relation\n'north of' does not seem to _exist_ in the same sense in which Edinburgh\nand London exist. If we ask 'Where and when does this relation exist?'\nthe answer must be 'Nowhere and nowhen'. There is no place or time where\nwe can find the relation 'north of'. It does not exist in Edinburgh any\nmore than in London, for it relates the two and is neutral as between\nthem. Nor can we say that it exists at any particular time. Now\neverything that can be apprehended by the senses or by introspection\nexists at some particular time. Hence the relation 'north of' is\nradically different from such things. It is neither in space nor in\ntime, neither material nor mental; yet it is something.\n\nIt is largely the very peculiar kind of being that belongs to universals\nwhich has led many people to suppose that they are really mental. We\ncan think _of_ a universal, and our thinking then exists in a perfectly\nordinary sense, like any other mental act. Suppose, for example, that\nwe are thinking of whiteness. Then _in one sense_ it may be said that\nwhiteness is 'in our mind'. We have here the same ambiguity as we noted\nin discussing Berkeley in Chapter IV. In the strict sense, it is not\nwhiteness that is in our mind, but the act of thinking of whiteness. The\nconnected ambiguity in the word 'idea', which we noted at the same time,\nalso causes confusion here. In one sense of this word, namely the sense\nin which it denotes the _object_ of an act of thought, whiteness is an\n'idea'. Hence, if the ambiguity is not guarded against, we may come to\nthink that whiteness is an 'idea' in the other sense, i.e. an act of\nthought; and thus we come to think that whiteness is mental. But in so\nthinking, we rob it of its essential quality of universality. One man's\nact of thought is necessarily a different thing from another man's; one\nman's act of thought at one time is necessarily a different thing from\nthe same man's act of thought at another time. Hence, if whiteness were\nthe thought as opposed to its object, no two different men could think\nof it, and no one man could think of it twice. That which many different\nthoughts of whiteness have in common is their _object_, and this object\nis different from all of them. Thus universals are not thoughts, though\nwhen known they are the objects of thoughts.\n\nWe shall find it convenient only to speak of things _existing_ when they\nare in time, that is to say, when we can point to some time at which\nthey exist (not excluding the possibility of their existing at all\ntimes). Thus thoughts and feelings, minds and physical objects exist.\nBut universals do not exist in this sense; we shall say that they\n_subsist_ or _have being_, where 'being' is opposed to 'existence'\nas being timeless. The world of universals, therefore, may also be\ndescribed as the world of being. The world of being is unchangeable,\nrigid, exact, delightful to the mathematician, the logician, the builder\nof metaphysical systems, and all who love perfection more than life. The\nworld of existence is fleeting, vague, without sharp boundaries,\nwithout any clear plan or arrangement, but it contains all thoughts and\nfeelings, all the data of sense, and all physical objects, everything\nthat can do either good or harm, everything that makes any difference to\nthe value of life and the world. According to our temperaments, we shall\nprefer the contemplation of the one or of the other. The one we do not\nprefer will probably seem to us a pale shadow of the one we prefer, and\nhardly worthy to be regarded as in any sense real. But the truth is that\nboth have the same claim on our impartial attention, both are real,\nand both are important to the metaphysician. Indeed no sooner have we\ndistinguished the two worlds than it becomes necessary to consider their\nrelations.\n\nBut first of all we must examine our knowledge of universals. This\nconsideration will occupy us in the following chapter, where we shall\nfind that it solves the problem of _a priori_ knowledge, from which we\nwere first led to consider universals.\n\n\n\nCHAPTER X. ON OUR KNOWLEDGE OF UNIVERSALS\n\nIn regard to one man's knowledge at a given time, universals, like\nparticulars, may be divided into those known by acquaintance, those\nknown only by description, and those not known either by acquaintance or\nby description.\n\nLet us consider first the knowledge of universals by acquaintance. It is\nobvious, to begin with, that we are acquainted with such universals as\nwhite, red, black, sweet, sour, loud, hard, etc., i.e. with qualities\nwhich are exemplified in sense-data. When we see a white patch, we are\nacquainted, in the first instance, with the particular patch; but by\nseeing many white patches, we easily learn to abstract the whiteness\nwhich they all have in common, and in learning to do this we are\nlearning to be acquainted with whiteness. A similar process will make us\nacquainted with any other universal of the same sort. Universals of this\nsort may be called 'sensible qualities'. They can be apprehended with\nless effort of abstraction than any others, and they seem less removed\nfrom particulars than other universals are.\n\nWe come next to relations. The easiest relations to apprehend are those\nwhich hold between the different parts of a single complex sense-datum.\nFor example, I can see at a glance the whole of the page on which I\nam writing; thus the whole page is included in one sense-datum. But I\nperceive that some parts of the page are to the left of other parts,\nand some parts are above other parts. The process of abstraction in this\ncase seems to proceed somewhat as follows: I see successively a number\nof sense-data in which one part is to the left of another; I perceive,\nas in the case of different white patches, that all these sense-data\nhave something in common, and by abstraction I find that what they have\nin common is a certain relation between their parts, namely the relation\nwhich I call 'being to the left of'. In this way I become acquainted\nwith the universal relation.\n\nIn like manner I become aware of the relation of before and after in\ntime. Suppose I hear a chime of bells: when the last bell of the chime\nsounds, I can retain the whole chime before my mind, and I can perceive\nthat the earlier bells came before the later ones. Also in memory I\nperceive that what I am remembering came before the present time. From\neither of these sources I can abstract the universal relation of before\nand after, just as I abstracted the universal relation 'being to the\nleft of'. Thus time-relations, like space-relations, are among those\nwith which we are acquainted.\n\nAnother relation with which we become acquainted in much the same way is\nresemblance. If I see simultaneously two shades of green, I can see\nthat they resemble each other; if I also see a shade of red: at the same\ntime, I can see that the two greens have more resemblance to each other\nthan either has to the red. In this way I become acquainted with the\nuniversal _resemblance_ or _similarity_.\n\nBetween universals, as between particulars, there are relations of which\nwe may be immediately aware. We have just seen that we can perceive\nthat the resemblance between two shades of green is greater than the\nresemblance between a shade of red and a shade of green. Here we are\ndealing with a relation, namely 'greater than', between two relations.\nOur knowledge of such relations, though it requires more power of\nabstraction than is required for perceiving the qualities of sense-data,\nappears to be equally immediate, and (at least in some cases) equally\nindubitable. Thus there is immediate knowledge concerning universals as\nwell as concerning sense-data.\n\nReturning now to the problem of _a priori_ knowledge, which we left\nunsolved when we began the consideration of universals, we find\nourselves in a position to deal with it in a much more satisfactory\nmanner than was possible before. Let us revert to the proposition 'two\nand two are four'. It is fairly obvious, in view of what has been said,\nthat this proposition states a relation between the universal 'two' and\nthe universal 'four'. This suggests a proposition which we shall\nnow endeavour to establish: namely, _All _a priori_ knowledge deals\nexclusively with the relations of universals_. This proposition is\nof great importance, and goes a long way towards solving our previous\ndifficulties concerning _a priori_ knowledge.\n\nThe only case in which it might seem, at first sight, as if our\nproposition were untrue, is the case in which an _a priori_ proposition\nstates that _all_ of one class of particulars belong to some other\nclass, or (what comes to the same thing) that _all_ particulars having\nsome one property also have some other. In this case it might seem\nas though we were dealing with the particulars that have the property\nrather than with the property. The proposition 'two and two are four' is\nreally a case in point, for this may be stated in the form 'any two\nand any other two are four', or 'any collection formed of two twos is a\ncollection of four'. If we can show that such statements as this really\ndeal only with universals, our proposition may be regarded as proved.\n\nOne way of discovering what a proposition deals with is to ask ourselves\nwhat words we must understand--in other words, what objects we must be\nacquainted with--in order to see what the proposition means. As soon as\nwe see what the proposition means, even if we do not yet know whether\nit is true or false, it is evident that we must have acquaintance with\nwhatever is really dealt with by the proposition. By applying this test,\nit appears that many propositions which might seem to be concerned with\nparticulars are really concerned only with universals. In the special\ncase of 'two and two are four', even when we interpret it as meaning\n'any collection formed of two twos is a collection of four', it is plain\nthat we can understand the proposition, i.e. we can see what it is that\nit asserts, as soon as we know what is meant by 'collection' and 'two'\nand 'four'. It is quite unnecessary to know all the couples in the\nworld: if it were necessary, obviously we could never understand the\nproposition, since the couples are infinitely numerous and therefore\ncannot all be known to us. Thus although our general statement _implies_\nstatements about particular couples, _as soon as we know that there are\nsuch particular couples_, yet it does not itself assert or imply that\nthere are such particular couples, and thus fails to make any statement\nwhatever about any actual particular couple. The statement made is about\n'couple', the universal, and not about this or that couple.\n\nThus the statement 'two and two are four' deals exclusively with\nuniversals, and therefore may be known by anybody who is acquainted\nwith the universals concerned and can perceive the relation between them\nwhich the statement asserts. It must be taken as a fact, discovered\nby reflecting upon our knowledge, that we have the power of sometimes\nperceiving such relations between universals, and therefore of sometimes\nknowing general _a priori_ propositions such as those of arithmetic and\nlogic. The thing that seemed mysterious, when we formerly considered\nsuch knowledge, was that it seemed to anticipate and control experience.\nThis, however, we can now see to have been an error. _No_ fact\nconcerning anything capable of being experienced can be known\nindependently of experience. We know _a priori_ that two things and two\nother things together make four things, but we do _not_ know _a priori_\nthat if Brown and Jones are two, and Robinson and Smith are two, then\nBrown and Jones and Robinson and Smith are four. The reason is that this\nproposition cannot be understood at all unless we know that there are\nsuch people as Brown and Jones and Robinson and Smith, and this we can\nonly know by experience. Hence, although our general proposition is _a\npriori_, all its applications to actual particulars involve experience\nand therefore contain an empirical element. In this way what seemed\nmysterious in our _a priori_ knowledge is seen to have been based upon\nan error.\n\nIt will serve to make the point clearer if we contrast our genuine _a\npriori_ judgement with an empirical generalization, such as 'all men are\nmortals'. Here as before, we can _understand_ what the proposition\nmeans as soon as we understand the universals involved, namely _man_ and\n_mortal_. It is obviously unnecessary to have an individual acquaintance\nwith the whole human race in order to understand what our proposition\nmeans. Thus the difference between an _a priori_ general proposition\nand an empirical generalization does not come in the _meaning_ of the\nproposition; it comes in the nature of the _evidence_ for it. In the\nempirical case, the evidence consists in the particular instances.\nWe believe that all men are mortal because we know that there are\ninnumerable instances of men dying, and no instances of their living\nbeyond a certain age. We do not believe it because we see a connexion\nbetween the universal _man_ and the universal _mortal_. It is true that\nif physiology can prove, assuming the general laws that govern living\nbodies, that no living organism can last for ever, that gives a\nconnexion between _man_ and _mortality_ which would enable us to assert\nour proposition without appealing to the special evidence of _men_\ndying. But that only means that our generalization has been subsumed\nunder a wider generalization, for which the evidence is still of the\nsame kind, though more extensive. The progress of science is constantly\nproducing such subsumptions, and therefore giving a constantly wider\ninductive basis for scientific generalizations. But although this gives\na greater _degree_ of certainty, it does not give a different _kind_:\nthe ultimate ground remains inductive, i.e. derived from instances, and\nnot an _a priori_ connexion of universals such as we have in logic and\narithmetic.\n\nTwo opposite points are to be observed concerning _a priori_ general\npropositions. The first is that, if many particular instances are known,\nour general proposition may be arrived at in the first instance by\ninduction, and the connexion of universals may be only subsequently\nperceived. For example, it is known that if we draw perpendiculars\nto the sides of a triangle from the opposite angles, all three\nperpendiculars meet in a point. It would be quite possible to be first\nled to this proposition by actually drawing perpendiculars in many\ncases, and finding that they always met in a point; this experience\nmight lead us to look for the general proof and find it. Such cases are\ncommon in the experience of every mathematician.\n\nThe other point is more interesting, and of more philosophical\nimportance. It is, that we may sometimes know a general proposition in\ncases where we do not know a single instance of it. Take such a case as\nthe following: We know that any two numbers can be multiplied together,\nand will give a third called their _product_. We know that all pairs\nof integers the product of which is less than 100 have been actually\nmultiplied together, and the value of the product recorded in the\nmultiplication table. But we also know that the number of integers is\ninfinite, and that only a finite number of pairs of integers ever have\nbeen or ever will be thought of by human beings. Hence it follows that\nthere are pairs of integers which never have been and never will be\nthought of by human beings, and that all of them deal with integers the\nproduct of which is over 100. Hence we arrive at the proposition:\n'All products of two integers, which never have been and never will\nbe thought of by any human being, are over 100.' Here is a general\nproposition of which the truth is undeniable, and yet, from the very\nnature of the case, we can never give an instance; because any two\nnumbers we may think of are excluded by the terms of the proposition.\n\nThis possibility, of knowledge of general propositions of which no\ninstance can be given, is often denied, because it is not perceived\nthat the knowledge of such propositions only requires a knowledge of the\nrelations of universals, and does not require any knowledge of instances\nof the universals in question. Yet the knowledge of such general\npropositions is quite vital to a great deal of what is generally\nadmitted to be known. For example, we saw, in our early chapters,\nthat knowledge of physical objects, as opposed to sense-data, is only\nobtained by an inference, and that they are not things with which we are\nacquainted. Hence we can never know any proposition of the form 'this\nis a physical object', where 'this' is something immediately known. It\nfollows that all our knowledge concerning physical objects is such that\nno actual instance can be given. We can give instances of the associated\nsense-data, but we cannot give instances of the actual physical objects.\nHence our knowledge as to physical objects depends throughout upon this\npossibility of general knowledge where no instance can be given. And the\nsame applies to our knowledge of other people's minds, or of any other\nclass of things of which no instance is known to us by acquaintance.\n\nWe may now take a survey of the sources of our knowledge, as they have\nappeared in the course of our analysis. We have first to distinguish\nknowledge of things and knowledge of truths. In each there are two\nkinds, one immediate and one derivative. Our immediate knowledge of\nthings, which we called _acquaintance_, consists of two sorts, according\nas the things known are particulars or universals. Among particulars, we\nhave acquaintance with sense-data and (probably) with ourselves. Among\nuniversals, there seems to be no principle by which we can decide which\ncan be known by acquaintance, but it is clear that among those that\ncan be so known are sensible qualities, relations of space and time,\nsimilarity, and certain abstract logical universals. Our derivative\nknowledge of things, which we call knowledge by _description_, always\ninvolves both acquaintance with something and knowledge of truths. Our\nimmediate knowledge of _truths_ may be called _intuitive_ knowledge,\nand the truths so known may be called _self-evident_ truths. Among such\ntruths are included those which merely state what is given in sense, and\nalso certain abstract logical and arithmetical principles, and (though\nwith less certainty) some ethical propositions. Our _derivative_\nknowledge of truths consists of everything that we can deduce from\nself-evident truths by the use of self-evident principles of deduction.\n\nIf the above account is correct, all our knowledge of truths depends\nupon our intuitive knowledge. It therefore becomes important to consider\nthe nature and scope of intuitive knowledge, in much the same way as,\nat an earlier stage, we considered the nature and scope of knowledge by\nacquaintance. But knowledge of truths raises a further problem, which\ndoes not arise in regard to knowledge of things, namely the problem of\n_error_. Some of our beliefs turn out to be erroneous, and therefore\nit becomes necessary to consider how, if at all, we can distinguish\nknowledge from error. This problem does not arise with regard\nto knowledge by acquaintance, for, whatever may be the object of\nacquaintance, even in dreams and hallucinations, there is no error\ninvolved so long as we do not go beyond the immediate object: error can\nonly arise when we regard the immediate object, i.e. the sense-datum,\nas the mark of some physical object. Thus the problems connected\nwith knowledge of truths are more difficult than those connected\nwith knowledge of things. As the first of the problems connected\nwith knowledge of truths, let us examine the nature and scope of our\nintuitive judgements.\n\n\n\nCHAPTER XI. ON INTUITIVE KNOWLEDGE\n\nThere is a common impression that everything that we believe ought to be\ncapable of proof, or at least of being shown to be highly probable. It\nis felt by many that a belief for which no reason can be given is an\nunreasonable belief. In the main, this view is just. Almost all our\ncommon beliefs are either inferred, or capable of being inferred, from\nother beliefs which may be regarded as giving the reason for them. As a\nrule, the reason has been forgotten, or has even never been consciously\npresent to our minds. Few of us ever ask ourselves, for example, what\nreason there is to suppose the food we are just going to eat will not\nturn out to be poison. Yet we feel, when challenged, that a perfectly\ngood reason could be found, even if we are not ready with it at the\nmoment. And in this belief we are usually justified.\n\nBut let us imagine some insistent Socrates, who, whatever reason we\ngive him, continues to demand a reason for the reason. We must sooner\nor later, and probably before very long, be driven to a point where we\ncannot find any further reason, and where it becomes almost certain that\nno further reason is even theoretically discoverable. Starting with the\ncommon beliefs of daily life, we can be driven back from point to point,\nuntil we come to some general principle, or some instance of a general\nprinciple, which seems luminously evident, and is not itself capable\nof being deduced from anything more evident. In most questions of\ndaily life, such as whether our food is likely to be nourishing and not\npoisonous, we shall be driven back to the inductive principle, which we\ndiscussed in Chapter VI. But beyond that, there seems to be no further\nregress. The principle itself is constantly used in our reasoning,\nsometimes consciously, sometimes unconsciously; but there is no\nreasoning which, starting from some simpler self-evident principle,\nleads us to the principle of induction as its conclusion. And the same\nholds for other logical principles. Their truth is evident to us, and we\nemploy them in constructing demonstrations; but they themselves, or at\nleast some of them, are incapable of demonstration.\n\nSelf-evidence, however, is not confined to those among general\nprinciples which are incapable of proof. When a certain number of\nlogical principles have been admitted, the rest can be deduced from\nthem; but the propositions deduced are often just as self-evident as\nthose that were assumed without proof. All arithmetic, moreover, can\nbe deduced from the general principles of logic, yet the simple\npropositions of arithmetic, such as 'two and two are four', are just as\nself-evident as the principles of logic.\n\nIt would seem, also, though this is more disputable, that there are some\nself-evident ethical principles, such as 'we ought to pursue what is\ngood'.\n\nIt should be observed that, in all cases of general principles,\nparticular instances, dealing with familiar things, are more evident\nthan the general principle. For example, the law of contradiction states\nthat nothing can both have a certain property and not have it. This is\nevident as soon as it is understood, but it is not so evident as that a\nparticular rose which we see cannot be both red and not red. (It is of\ncourse possible that parts of the rose may be red and parts not red, or\nthat the rose may be of a shade of pink which we hardly know whether to\ncall red or not; but in the former case it is plain that the rose as a\nwhole is not red, while in the latter case the answer is theoretically\ndefinite as soon as we have decided on a precise definition of 'red'.)\nIt is usually through particular instances that we come to be able to\nsee the general principle. Only those who are practised in dealing with\nabstractions can readily grasp a general principle without the help of\ninstances.\n\nIn addition to general principles, the other kind of self-evident truths\nare those immediately derived from sensation. We will call such truths\n'truths of perception', and the judgements expressing them we will\ncall 'judgements of perception'. But here a certain amount of care\nis required in getting at the precise nature of the truths that are\nself-evident. The actual sense-data are neither true nor false. A\nparticular patch of colour which I see, for example, simply exists: it\nis not the sort of thing that is true or false. It is true that there is\nsuch a patch, true that it has a certain shape and degree of brightness,\ntrue that it is surrounded by certain other colours. But the patch\nitself, like everything else in the world of sense, is of a radically\ndifferent kind from the things that are true or false, and therefore\ncannot properly be said to be _true_. Thus whatever self-evident truths\nmay be obtained from our senses must be different from the sense-data\nfrom which they are obtained.\n\nIt would seem that there are two kinds of self-evident truths of\nperception, though perhaps in the last analysis the two kinds may\ncoalesce. First, there is the kind which simply asserts the _existence_\nof the sense-datum, without in any way analysing it. We see a patch\nof red, and we judge 'there is such-and-such a patch of red', or more\nstrictly 'there is that'; this is one kind of intuitive judgement of\nperception. The other kind arises when the object of sense is complex,\nand we subject it to some degree of analysis. If, for instance, we see a\n_round_ patch of red, we may judge 'that patch of red is round'. This is\nagain a judgement of perception, but it differs from our previous kind.\nIn our present kind we have a single sense-datum which has both colour\nand shape: the colour is red and the shape is round. Our judgement\nanalyses the datum into colour and shape, and then recombines them by\nstating that the red colour is round in shape. Another example of this\nkind of judgement is 'this is to the right of that', where 'this'\nand 'that' are seen simultaneously. In this kind of judgement the\nsense-datum contains constituents which have some relation to each\nother, and the judgement asserts that these constituents have this\nrelation.\n\nAnother class of intuitive judgements, analogous to those of sense and\nyet quite distinct from them, are judgements of _memory_. There is some\ndanger of confusion as to the nature of memory, owing to the fact that\nmemory of an object is apt to be accompanied by an image of the object,\nand yet the image cannot be what constitutes memory. This is easily seen\nby merely noticing that the image is in the present, whereas what is\nremembered is known to be in the past. Moreover, we are certainly able\nto some extent to compare our image with the object remembered, so\nthat we often know, within somewhat wide limits, how far our image is\naccurate; but this would be impossible, unless the object, as opposed to\nthe image, were in some way before the mind. Thus the essence of memory\nis not constituted by the image, but by having immediately before the\nmind an object which is recognized as past. But for the fact of memory\nin this sense, we should not know that there ever was a past at all,\nnor should we be able to understand the word 'past', any more than a man\nborn blind can understand the word 'light'. Thus there must be intuitive\njudgements of memory, and it is upon them, ultimately, that all our\nknowledge of the past depends.\n\nThe case of memory, however, raises a difficulty, for it is notoriously\nfallacious, and thus throws doubt on the trustworthiness of intuitive\njudgements in general. This difficulty is no light one. But let us\nfirst narrow its scope as far as possible. Broadly speaking, memory is\ntrustworthy in proportion to the vividness of the experience and to its\nnearness in time. If the house next door was struck by lightning half a\nminute ago, my memory of what I saw and heard will be so reliable that\nit would be preposterous to doubt whether there had been a flash at\nall. And the same applies to less vivid experiences, so long as they are\nrecent. I am absolutely certain that half a minute ago I was sitting in\nthe same chair in which I am sitting now. Going backward over the day,\nI find things of which I am quite certain, other things of which I am\nalmost certain, other things of which I can become certain by thought\nand by calling up attendant circumstances, and some things of which I\nam by no means certain. I am quite certain that I ate my breakfast this\nmorning, but if I were as indifferent to my breakfast as a philosopher\nshould be, I should be doubtful. As to the conversation at breakfast,\nI can recall some of it easily, some with an effort, some only with a\nlarge element of doubt, and some not at all. Thus there is a continual\ngradation in the degree of self-evidence of what I remember, and a\ncorresponding gradation in the trustworthiness of my memory.\n\nThus the first answer to the difficulty of fallacious memory is to say\nthat memory has degrees of self-evidence, and that these correspond\nto the degrees of its trustworthiness, reaching a limit of perfect\nself-evidence and perfect trustworthiness in our memory of events which\nare recent and vivid.\n\nIt would seem, however, that there are cases of very firm belief in a\nmemory which is wholly false. It is probable that, in these cases, what\nis really remembered, in the sense of being immediately before the mind,\nis something other than what is falsely believed in, though something\ngenerally associated with it. George IV is said to have at last believed\nthat he was at the battle of Waterloo, because he had so often said that\nhe was. In this case, what was immediately remembered was his repeated\nassertion; the belief in what he was asserting (if it existed) would\nbe produced by association with the remembered assertion, and would\ntherefore not be a genuine case of memory. It would seem that cases of\nfallacious memory can probably all be dealt with in this way, i.e. they\ncan be shown to be not cases of memory in the strict sense at all.\n\nOne important point about self-evidence is made clear by the case of\nmemory, and that is, that self-evidence has degrees: it is not a quality\nwhich is simply present or absent, but a quality which may be more or\nless present, in gradations ranging from absolute certainty down to an\nalmost imperceptible faintness. Truths of perception and some of the\nprinciples of logic have the very highest degree of self-evidence;\ntruths of immediate memory have an almost equally high degree. The\ninductive principle has less self-evidence than some of the other\nprinciples of logic, such as 'what follows from a true premiss must be\ntrue'. Memories have a diminishing self-evidence as they become remoter\nand fainter; the truths of logic and mathematics have (broadly speaking)\nless self-evidence as they become more complicated. Judgements of\nintrinsic ethical or aesthetic value are apt to have some self-evidence,\nbut not much.\n\nDegrees of self-evidence are important in the theory of knowledge,\nsince, if propositions may (as seems likely) have some degree of\nself-evidence without being true, it will not be necessary to abandon\nall connexion between self-evidence and truth, but merely to say that,\nwhere there is a conflict, the more self-evident proposition is to be\nretained and the less self-evident rejected.\n\nIt seems, however, highly probable that two different notions are\ncombined in 'self-evidence' as above explained; that one of them,\nwhich corresponds to the highest degree of self-evidence, is really an\ninfallible guarantee of truth, while the other, which corresponds to\nall the other degrees, does not give an infallible guarantee, but only a\ngreater or less presumption. This, however, is only a suggestion, which\nwe cannot as yet develop further. After we have dealt with the nature\nof truth, we shall return to the subject of self-evidence, in connexion\nwith the distinction between knowledge and error.\n\n\n\nCHAPTER XII. TRUTH AND FALSEHOOD\n\nOur knowledge of truths, unlike our knowledge of things, has an\nopposite, namely _error_. So far as things are concerned, we may know\nthem or not know them, but there is no positive state of mind which can\nbe described as erroneous knowledge of things, so long, at any rate,\nas we confine ourselves to knowledge by acquaintance. Whatever we are\nacquainted with must be something; we may draw wrong inferences from\nour acquaintance, but the acquaintance itself cannot be deceptive. Thus\nthere is no dualism as regards acquaintance. But as regards knowledge of\ntruths, there is a dualism. We may believe what is false as well as\nwhat is true. We know that on very many subjects different people\nhold different and incompatible opinions: hence some beliefs must be\nerroneous. Since erroneous beliefs are often held just as strongly\nas true beliefs, it becomes a difficult question how they are to be\ndistinguished from true beliefs. How are we to know, in a given case,\nthat our belief is not erroneous? This is a question of the very\ngreatest difficulty, to which no completely satisfactory answer is\npossible. There is, however, a preliminary question which is rather less\ndifficult, and that is: What do we _mean_ by truth and falsehood? It is\nthis preliminary question which is to be considered in this chapter. In\nthis chapter we are not asking how we can know whether a belief is true\nor false: we are asking what is meant by the question whether a belief\nis true or false. It is to be hoped that a clear answer to this question\nmay help us to obtain an answer to the question what beliefs are\ntrue, but for the present we ask only 'What is truth?' and 'What is\nfalsehood?' not 'What beliefs are true?' and 'What beliefs are false?'\nIt is very important to keep these different questions entirely\nseparate, since any confusion between them is sure to produce an answer\nwhich is not really applicable to either.\n\nThere are three points to observe in the attempt to discover the nature\nof truth, three requisites which any theory must fulfil.\n\n(1) Our theory of truth must be such as to admit of its opposite,\nfalsehood. A good many philosophers have failed adequately to satisfy\nthis condition: they have constructed theories according to which all\nour thinking ought to have been true, and have then had the greatest\ndifficulty in finding a place for falsehood. In this respect our theory\nof belief must differ from our theory of acquaintance, since in the case\nof acquaintance it was not necessary to take account of any opposite.\n\n(2) It seems fairly evident that if there were no beliefs there could\nbe no falsehood, and no truth either, in the sense in which truth is\ncorrelative to falsehood. If we imagine a world of mere matter, there\nwould be no room for falsehood in such a world, and although it would\ncontain what may be called 'facts', it would not contain any truths, in\nthe sense in which truths are things of the same kind as falsehoods.\nIn fact, truth and falsehood are properties of beliefs and statements:\nhence a world of mere matter, since it would contain no beliefs or\nstatements, would also contain no truth or falsehood.\n\n(3) But, as against what we have just said, it is to be observed that\nthe truth or falsehood of a belief always depends upon something which\nlies outside the belief itself. If I believe that Charles I died on the\nscaffold, I believe truly, not because of any intrinsic quality of my\nbelief, which could be discovered by merely examining the belief, but\nbecause of an historical event which happened two and a half centuries\nago. If I believe that Charles I died in his bed, I believe falsely: no\ndegree of vividness in my belief, or of care in arriving at it, prevents\nit from being false, again because of what happened long ago, and not\nbecause of any intrinsic property of my belief. Hence, although truth\nand falsehood are properties of beliefs, they are properties dependent\nupon the relations of the beliefs to other things, not upon any internal\nquality of the beliefs.\n\nThe third of the above requisites leads us to adopt the view--which has\non the whole been commonest among philosophers--that truth consists in\nsome form of correspondence between belief and fact. It is, however, by\nno means an easy matter to discover a form of correspondence to which\nthere are no irrefutable objections. By this partly--and partly by the\nfeeling that, if truth consists in a correspondence of thought with\nsomething outside thought, thought can never know when truth has been\nattained--many philosophers have been led to try to find some definition\nof truth which shall not consist in relation to something wholly outside\nbelief. The most important attempt at a definition of this sort is the\ntheory that truth consists in _coherence_. It is said that the mark of\nfalsehood is failure to cohere in the body of our beliefs, and that it\nis the essence of a truth to form part of the completely rounded system\nwhich is The Truth.\n\nThere is, however, a great difficulty in this view, or rather two great\ndifficulties. The first is that there is no reason to suppose that\nonly _one_ coherent body of beliefs is possible. It may be that, with\nsufficient imagination, a novelist might invent a past for the world\nthat would perfectly fit on to what we know, and yet be quite different\nfrom the real past. In more scientific matters, it is certain that there\nare often two or more hypotheses which account for all the known facts\non some subject, and although, in such cases, men of science endeavour\nto find facts which will rule out all the hypotheses except one, there\nis no reason why they should always succeed.\n\nIn philosophy, again, it seems not uncommon for two rival hypotheses\nto be both able to account for all the facts. Thus, for example, it is\npossible that life is one long dream, and that the outer world has only\nthat degree of reality that the objects of dreams have; but although\nsuch a view does not seem inconsistent with known facts, there is no\nreason to prefer it to the common-sense view, according to which other\npeople and things do really exist. Thus coherence as the definition\nof truth fails because there is no proof that there can be only one\ncoherent system.\n\nThe other objection to this definition of truth is that it assumes the\nmeaning of 'coherence' known, whereas, in fact, 'coherence' presupposes\nthe truth of the laws of logic. Two propositions are coherent when both\nmay be true, and are incoherent when one at least must be false. Now in\norder to know whether two propositions can both be true, we must\nknow such truths as the law of contradiction. For example, the two\npropositions, 'this tree is a beech' and 'this tree is not a beech',\nare not coherent, because of the law of contradiction. But if the law of\ncontradiction itself were subjected to the test of coherence, we should\nfind that, if we choose to suppose it false, nothing will any longer\nbe incoherent with anything else. Thus the laws of logic supply the\nskeleton or framework within which the test of coherence applies, and\nthey themselves cannot be established by this test.\n\nFor the above two reasons, coherence cannot be accepted as giving the\n_meaning_ of truth, though it is often a most important _test_ of truth\nafter a certain amount of truth has become known.\n\nHence we are driven back to _correspondence with fact_ as constituting\nthe nature of truth. It remains to define precisely what we mean by\n'fact', and what is the nature of the correspondence which must subsist\nbetween belief and fact, in order that belief may be true.\n\nIn accordance with our three requisites, we have to seek a theory of\ntruth which (1) allows truth to have an opposite, namely falsehood, (2)\nmakes truth a property of beliefs, but (3) makes it a property wholly\ndependent upon the relation of the beliefs to outside things.\n\nThe necessity of allowing for falsehood makes it impossible to regard\nbelief as a relation of the mind to a single object, which could be said\nto be what is believed. If belief were so regarded, we should find that,\nlike acquaintance, it would not admit of the opposition of truth and\nfalsehood, but would have to be always true. This may be made clear\nby examples. Othello believes falsely that Desdemona loves Cassio. We\ncannot say that this belief consists in a relation to a single object,\n'Desdemona's love for Cassio', for if there were such an object, the\nbelief would be true. There is in fact no such object, and therefore\nOthello cannot have any relation to such an object. Hence his belief\ncannot possibly consist in a relation to this object.\n\nIt might be said that his belief is a relation to a different object,\nnamely 'that Desdemona loves Cassio'; but it is almost as difficult to\nsuppose that there is such an object as this, when Desdemona does not\nlove Cassio, as it was to suppose that there is 'Desdemona's love for\nCassio'. Hence it will be better to seek for a theory of belief which\ndoes not make it consist in a relation of the mind to a single object.\n\nIt is common to think of relations as though they always held between\ntwo terms, but in fact this is not always the case. Some relations\ndemand three terms, some four, and so on. Take, for instance, the\nrelation 'between'. So long as only two terms come in, the relation\n'between' is impossible: three terms are the smallest number that render\nit possible. York is between London and Edinburgh; but if London and\nEdinburgh were the only places in the world, there could be nothing\nwhich was between one place and another. Similarly _jealousy_ requires\nthree people: there can be no such relation that does not involve three\nat least. Such a proposition as 'A wishes B to promote C's marriage with\nD' involves a relation of four terms; that is to say, A and B and C and\nD all come in, and the relation involved cannot be expressed otherwise\nthan in a form involving all four. Instances might be multiplied\nindefinitely, but enough has been said to show that there are relations\nwhich require more than two terms before they can occur.\n\nThe relation involved in _judging_ or _believing_ must, if falsehood is\nto be duly allowed for, be taken to be a relation between several terms,\nnot between two. When Othello believes that Desdemona loves Cassio, he\nmust not have before his mind a single object, 'Desdemona's love for\nCassio', or 'that Desdemona loves Cassio ', for that would require that\nthere should be objective falsehoods, which subsist independently of\nany minds; and this, though not logically refutable, is a theory to be\navoided if possible. Thus it is easier to account for falsehood if\nwe take judgement to be a relation in which the mind and the various\nobjects concerned all occur severally; that is to say, Desdemona and\nloving and Cassio must all be terms in the relation which subsists when\nOthello believes that Desdemona loves Cassio. This relation, therefore,\nis a relation of four terms, since Othello also is one of the terms of\nthe relation. When we say that it is a relation of four terms, we do not\nmean that Othello has a certain relation to Desdemona, and has the same\nrelation to loving and also to Cassio. This may be true of some other\nrelation than believing; but believing, plainly, is not a relation which\nOthello has to _each_ of the three terms concerned, but to _all_ of\nthem together: there is only one example of the relation of believing\ninvolved, but this one example knits together four terms. Thus the\nactual occurrence, at the moment when Othello is entertaining his\nbelief, is that the relation called 'believing' is knitting together\ninto one complex whole the four terms Othello, Desdemona, loving, and\nCassio. What is called belief or judgement is nothing but this relation\nof believing or judging, which relates a mind to several things other\nthan itself. An _act_ of belief or of judgement is the occurrence\nbetween certain terms at some particular time, of the relation of\nbelieving or judging.\n\nWe are now in a position to understand what it is that distinguishes a\ntrue judgement from a false one. For this purpose we will adopt certain\ndefinitions. In every act of judgement there is a mind which judges, and\nthere are terms concerning which it judges. We will call the mind the\n_subject_ in the judgement, and the remaining terms the _objects_. Thus,\nwhen Othello judges that Desdemona loves Cassio, Othello is the subject,\nwhile the objects are Desdemona and loving and Cassio. The subject and\nthe objects together are called the _constituents_ of the judgement.\nIt will be observed that the relation of judging has what is called a\n'sense' or 'direction'. We may say, metaphorically, that it puts its\nobjects in a certain _order_, which we may indicate by means of the\norder of the words in the sentence. (In an inflected language, the same\nthing will be indicated by inflections, e.g. by the difference between\nnominative and accusative.) Othello's judgement that Cassio loves\nDesdemona differs from his judgement that Desdemona loves Cassio, in\nspite of the fact that it consists of the same constituents, because the\nrelation of judging places the constituents in a different order in the\ntwo cases. Similarly, if Cassio judges that Desdemona loves Othello,\nthe constituents of the judgement are still the same, but their order is\ndifferent. This property of having a 'sense' or 'direction' is one which\nthe relation of judging shares with all other relations. The 'sense'\nof relations is the ultimate source of order and series and a host of\nmathematical concepts; but we need not concern ourselves further with\nthis aspect.\n\nWe spoke of the relation called 'judging' or 'believing' as knitting\ntogether into one complex whole the subject and the objects. In this\nrespect, judging is exactly like every other relation. Whenever a\nrelation holds between two or more terms, it unites the terms into a\ncomplex whole. If Othello loves Desdemona, there is such a complex whole\nas 'Othello's love for Desdemona'. The terms united by the relation may\nbe themselves complex, or may be simple, but the whole which results\nfrom their being united must be complex. Wherever there is a relation\nwhich relates certain terms, there is a complex object formed of the\nunion of those terms; and conversely, wherever there is a complex\nobject, there is a relation which relates its constituents. When an act\nof believing occurs, there is a complex, in which 'believing' is the\nuniting relation, and subject and objects are arranged in a certain\norder by the 'sense' of the relation of believing. Among the objects,\nas we saw in considering 'Othello believes that Desdemona loves Cassio',\none must be a relation--in this instance, the relation 'loving'. But\nthis relation, as it occurs in the act of believing, is not the relation\nwhich creates the unity of the complex whole consisting of the subject\nand the objects. The relation 'loving', as it occurs in the act of\nbelieving, is one of the objects--it is a brick in the structure, not\nthe cement. The cement is the relation 'believing'. When the belief is\n_true_, there is another complex unity, in which the relation which was\none of the objects of the belief relates the other objects. Thus, e.g.,\nif Othello believes _truly_ that Desdemona loves Cassio, then there is\na complex unity, 'Desdemona's love for Cassio', which is composed\nexclusively of the _objects_ of the belief, in the same order as they\nhad in the belief, with the relation which was one of the objects\noccurring now as the cement that binds together the other objects of the\nbelief. On the other hand, when a belief is _false_, there is no such\ncomplex unity composed only of the objects of the belief. If Othello\nbelieves _falsely_ that Desdemona loves Cassio, then there is no such\ncomplex unity as 'Desdemona's love for Cassio'.\n\nThus a belief is _true_ when it _corresponds_ to a certain associated\ncomplex, and _false_ when it does not. Assuming, for the sake of\ndefiniteness, that the objects of the belief are two terms and a\nrelation, the terms being put in a certain order by the 'sense' of\nthe believing, then if the two terms in that order are united by the\nrelation into a complex, the belief is true; if not, it is false. This\nconstitutes the definition of truth and falsehood that we were in search\nof. Judging or believing is a certain complex unity of which a mind is\na constituent; if the remaining constituents, taken in the order which\nthey have in the belief, form a complex unity, then the belief is true;\nif not, it is false.\n\nThus although truth and falsehood are properties of beliefs, yet they\nare in a sense extrinsic properties, for the condition of the truth of\na belief is something not involving beliefs, or (in general) any mind\nat all, but only the _objects_ of the belief. A mind, which believes,\nbelieves truly when there is a _corresponding_ complex not involving the\nmind, but only its objects. This correspondence ensures truth, and its\nabsence entails falsehood. Hence we account simultaneously for the two\nfacts that beliefs (a) depend on minds for their _existence_, (b) do not\ndepend on minds for their _truth_.\n\nWe may restate our theory as follows: If we take such a belief as\n'Othello believes that Desdemona loves Cassio', we will call Desdemona\nand Cassio the _object-terms_, and loving the _object-relation_. If\nthere is a complex unity 'Desdemona's love for Cassio', consisting of\nthe object-terms related by the object-relation in the same order as\nthey have in the belief, then this complex unity is called the _fact\ncorresponding to the belief_. Thus a belief is true when there is a\ncorresponding fact, and is false when there is no corresponding fact.\n\nIt will be seen that minds do not _create_ truth or falsehood. They\ncreate beliefs, but when once the beliefs are created, the mind cannot\nmake them true or false, except in the special case where they concern\nfuture things which are within the power of the person believing, such\nas catching trains. What makes a belief true is a _fact_, and this fact\ndoes not (except in exceptional cases) in any way involve the mind of\nthe person who has the belief.\n\nHaving now decided what we _mean_ by truth and falsehood, we have next\nto consider what ways there are of knowing whether this or that belief\nis true or false. This consideration will occupy the next chapter.\n\n\n\nCHAPTER XIII. KNOWLEDGE, ERROR, AND PROBABLE OPINION\n\nThe question as to what we mean by truth and falsehood, which we\nconsidered in the preceding chapter, is of much less interest than the\nquestion as to how we can know what is true and what is false. This\nquestion will occupy us in the present chapter. There can be no doubt\nthat _some_ of our beliefs are erroneous; thus we are led to inquire\nwhat certainty we can ever have that such and such a belief is not\nerroneous. In other words, can we ever _know_ anything at all, or do we\nmerely sometimes by good luck believe what is true? Before we can attack\nthis question, we must, however, first decide what we mean by 'knowing',\nand this question is not so easy as might be supposed.\n\nAt first sight we might imagine that knowledge could be defined as 'true\nbelief'. When what we believe is true, it might be supposed that we had\nachieved a knowledge of what we believe. But this would not accord\nwith the way in which the word is commonly used. To take a very trivial\ninstance: If a man believes that the late Prime Minister's last name\nbegan with a B, he believes what is true, since the late Prime Minister\nwas Sir Henry Campbell Bannerman. But if he believes that Mr. Balfour\nwas the late Prime Minister, he will still believe that the late Prime\nMinister's last name began with a B, yet this belief, though true,\nwould not be thought to constitute knowledge. If a newspaper, by an\nintelligent anticipation, announces the result of a battle before any\ntelegram giving the result has been received, it may by good fortune\nannounce what afterwards turns out to be the right result, and it may\nproduce belief in some of its less experienced readers. But in spite of\nthe truth of their belief, they cannot be said to have knowledge. Thus\nit is clear that a true belief is not knowledge when it is deduced from\na false belief.\n\nIn like manner, a true belief cannot be called knowledge when it is\ndeduced by a fallacious process of reasoning, even if the premisses from\nwhich it is deduced are true. If I know that all Greeks are men and that\nSocrates was a man, and I infer that Socrates was a Greek, I cannot be\nsaid to _know_ that Socrates was a Greek, because, although my premisses\nand my conclusion are true, the conclusion does not follow from the\npremisses.\n\nBut are we to say that nothing is knowledge except what is validly\ndeduced from true premisses? Obviously we cannot say this. Such a\ndefinition is at once too wide and too narrow. In the first place, it is\ntoo wide, because it is not enough that our premisses should be _true_,\nthey must also be _known_. The man who believes that Mr. Balfour was the\nlate Prime Minister may proceed to draw valid deductions from the true\npremiss that the late Prime Minister's name began with a B, but he\ncannot be said to _know_ the conclusions reached by these deductions.\nThus we shall have to amend our definition by saying that knowledge\nis what is validly deduced from _known_ premisses. This, however, is a\ncircular definition: it assumes that we already know what is meant\nby 'known premisses'. It can, therefore, at best define one sort\nof knowledge, the sort we call derivative, as opposed to intuitive\nknowledge. We may say: '_Derivative_ knowledge is what is validly\ndeduced from premisses known intuitively'. In this statement there is\nno formal defect, but it leaves the definition of _intuitive_ knowledge\nstill to seek.\n\nLeaving on one side, for the moment, the question of intuitive\nknowledge, let us consider the above suggested definition of derivative\nknowledge. The chief objection to it is that it unduly limits knowledge.\nIt constantly happens that people entertain a true belief, which has\ngrown up in them because of some piece of intuitive knowledge from which\nit is capable of being validly inferred, but from which it has not, as a\nmatter of fact, been inferred by any logical process.\n\nTake, for example, the beliefs produced by reading. If the newspapers\nannounce the death of the King, we are fairly well justified in\nbelieving that the King is dead, since this is the sort of announcement\nwhich would not be made if it were false. And we are quite amply\njustified in believing that the newspaper asserts that the King is\ndead. But here the intuitive knowledge upon which our belief is based\nis knowledge of the existence of sense-data derived from looking at\nthe print which gives the news. This knowledge scarcely rises into\nconsciousness, except in a person who cannot read easily. A child may be\naware of the shapes of the letters, and pass gradually and painfully to\na realization of their meaning. But anybody accustomed to reading\npasses at once to what the letters mean, and is not aware, except on\nreflection, that he has derived this knowledge from the sense-data\ncalled seeing the printed letters. Thus although a valid inference from\nthe-letters to their meaning is possible, and _could_ be performed\nby the reader, it is not in fact performed, since he does not in fact\nperform any operation which can be called logical inference. Yet\nit would be absurd to say that the reader does not _know_ that the\nnewspaper announces the King's death.\n\nWe must, therefore, admit as derivative knowledge whatever is the result\nof intuitive knowledge even if by mere association, provided there _is_\na valid logical connexion, and the person in question could become aware\nof this connexion by reflection. There are in fact many ways, besides\nlogical inference, by which we pass from one belief to another: the\npassage from the print to its meaning illustrates these ways. These\nways may be called 'psychological inference'. We shall, then, admit such\npsychological inference as a means of obtaining derivative knowledge,\nprovided there is a discoverable logical inference which runs parallel\nto the psychological inference. This renders our definition of\nderivative knowledge less precise than we could wish, since the word\n'discoverable' is vague: it does not tell us how much reflection may be\nneeded in order to make the discovery. But in fact 'knowledge' is not a\nprecise conception: it merges into 'probable opinion', as we shall\nsee more fully in the course of the present chapter. A very precise\ndefinition, therefore, should not be sought, since any such definition\nmust be more or less misleading.\n\nThe chief difficulty in regard to knowledge, however, does not arise\nover derivative knowledge, but over intuitive knowledge. So long as we\nare dealing with derivative knowledge, we have the test of intuitive\nknowledge to fall back upon. But in regard to intuitive beliefs, it is\nby no means easy to discover any criterion by which to distinguish\nsome as true and others as erroneous. In this question it is scarcely\npossible to reach any very precise result: all our knowledge of truths\nis infected with some degree of doubt, and a theory which ignored this\nfact would be plainly wrong. Something may be done, however, to mitigate\nthe difficulties of the question.\n\nOur theory of truth, to begin with, supplies the possibility of\ndistinguishing certain truths as _self-evident_ in a sense which ensures\ninfallibility. When a belief is true, we said, there is a corresponding\nfact, in which the several objects of the belief form a single complex.\nThe belief is said to constitute _knowledge_ of this fact, provided\nit fulfils those further somewhat vague conditions which we have been\nconsidering in the present chapter. But in regard to any fact, besides\nthe knowledge constituted by belief, we may also have the kind of\nknowledge constituted by _perception_ (taking this word in its widest\npossible sense). For example, if you know the hour of the sunset,\nyou can at that hour know the fact that the sun is setting: this is\nknowledge of the fact by way of knowledge of _truths_; but you can also,\nif the weather is fine, look to the west and actually see the setting\nsun: you then know the same fact by the way of knowledge of _things_.\n\nThus in regard to any complex fact, there are, theoretically, two ways\nin which it may be known: (1) by means of a judgement, in which its\nseveral parts are judged to be related as they are in fact related; (2)\nby means of _acquaintance_ with the complex fact itself, which may (in a\nlarge sense) be called perception, though it is by no means confined to\nobjects of the senses. Now it will be observed that the second way of\nknowing a complex fact, the way of acquaintance, is only possible when\nthere really is such a fact, while the first way, like all judgement,\nis liable to error. The second way gives us the complex whole, and is\ntherefore only possible when its parts do actually have that relation\nwhich makes them combine to form such a complex. The first way, on the\ncontrary, gives us the parts and the relation severally, and demands\nonly the reality of the parts and the relation: the relation may not\nrelate those parts in that way, and yet the judgement may occur.\n\nIt will be remembered that at the end of Chapter XI we suggested that\nthere might be two kinds of self-evidence, one giving an absolute\nguarantee of truth, the other only a partial guarantee. These two kinds\ncan now be distinguished.\n\nWe may say that a truth is self-evident, in the first and most absolute\nsense, when we have acquaintance with the fact which corresponds to\nthe truth. When Othello believes that Desdemona loves Cassio, the\ncorresponding fact, if his belief were true, would be 'Desdemona's\nlove for Cassio'. This would be a fact with which no one could have\nacquaintance except Desdemona; hence in the sense of self-evidence that\nwe are considering, the truth that Desdemona loves Cassio (if it were\na truth) could only be self-evident to Desdemona. All mental facts, and\nall facts concerning sense-data, have this same privacy: there is only\none person to whom they can be self-evident in our present sense, since\nthere is only one person who can be acquainted with the mental things\nor the sense-data concerned. Thus no fact about any particular existing\nthing can be self-evident to more than one person. On the other hand,\nfacts about universals do not have this privacy. Many minds may be\nacquainted with the same universals; hence a relation between universals\nmay be known by acquaintance to many different people. In all cases\nwhere we know by acquaintance a complex fact consisting of certain terms\nin a certain relation, we say that the truth that these terms are so\nrelated has the first or absolute kind of self-evidence, and in these\ncases the judgement that the terms are so related _must_ be true. Thus\nthis sort of self-evidence is an absolute guarantee of truth.\n\nBut although this sort of self-evidence is an absolute guarantee of\ntruth, it does not enable us to be _absolutely_ certain, in the case of\nany given judgement, that the judgement in question is true. Suppose\nwe first perceive the sun shining, which is a complex fact, and thence\nproceed to make the judgement 'the sun is shining'. In passing from\nthe perception to the judgement, it is necessary to analyse the given\ncomplex fact: we have to separate out 'the sun' and 'shining' as\nconstituents of the fact. In this process it is possible to commit\nan error; hence even where a _fact_ has the first or absolute kind of\nself-evidence, a judgement believed to correspond to the fact is not\nabsolutely infallible, because it may not really correspond to the\nfact. But if it does correspond (in the sense explained in the preceding\nchapter), then it _must_ be true.\n\nThe second sort of self-evidence will be that which belongs to\njudgements in the first instance, and is not derived from direct\nperception of a fact as a single complex whole. This second kind of\nself-evidence will have degrees, from the very highest degree down to a\nbare inclination in favour of the belief. Take, for example, the case of\na horse trotting away from us along a hard road. At first our certainty\nthat we hear the hoofs is complete; gradually, if we listen intently,\nthere comes a moment when we think perhaps it was imagination or the\nblind upstairs or our own heartbeats; at last we become doubtful whether\nthere was any noise at all; then we _think_ we no longer hear anything,\nand at last we _know_ we no longer hear anything. In this process, there\nis a continual gradation of self-evidence, from the highest degree to\nthe least, not in the sense-data themselves, but in the judgements based\non them.\n\nOr again: Suppose we are comparing two shades of colour, one blue and\none green. We can be quite sure they are different shades of colour; but\nif the green colour is gradually altered to be more and more like the\nblue, becoming first a blue-green, then a greeny-blue, then blue,\nthere will come a moment when we are doubtful whether we can see any\ndifference, and then a moment when we know that we cannot see any\ndifference. The same thing happens in tuning a musical instrument, or in\nany other case where there is a continuous gradation. Thus self-evidence\nof this sort is a matter of degree; and it seems plain that the higher\ndegrees are more to be trusted than the lower degrees.\n\nIn derivative knowledge our ultimate premisses must have some degree of\nself-evidence, and so must their connexion with the conclusions deduced\nfrom them. Take for example a piece of reasoning in geometry. It is not\nenough that the axioms from which we start should be self-evident: it\nis necessary also that, at each step in the reasoning, the connexion of\npremiss and conclusion should be self-evident. In difficult reasoning,\nthis connexion has often only a very small degree of self-evidence;\nhence errors of reasoning are not improbable where the difficulty is\ngreat.\n\nFrom what has been said it is evident that, both as regards intuitive\nknowledge and as regards derivative knowledge, if we assume that\nintuitive knowledge is trustworthy in proportion to the degree of its\nself-evidence, there will be a gradation in trustworthiness, from the\nexistence of noteworthy sense-data and the simpler truths of logic and\narithmetic, which may be taken as quite certain, down to judgements\nwhich seem only just more probable than their opposites. What we firmly\nbelieve, if it is true, is called _knowledge_, provided it is either\nintuitive or inferred (logically or psychologically) from intuitive\nknowledge from which it follows logically. What we firmly believe, if it\nis not true, is called _error_. What we firmly believe, if it is neither\nknowledge nor error, and also what we believe hesitatingly, because it\nis, or is derived from, something which has not the highest degree of\nself-evidence, may be called _probable opinion_. Thus the greater\npart of what would commonly pass as knowledge is more or less probable\nopinion.\n\nIn regard to probable opinion, we can derive great assistance from\n_coherence_, which we rejected as the _definition_ of truth, but may\noften use as a _criterion_. A body of individually probable opinions,\nif they are mutually coherent, become more probable than any one of them\nwould be individually. It is in this way that many scientific hypotheses\nacquire their probability. They fit into a coherent system of probable\nopinions, and thus become more probable than they would be in isolation.\nThe same thing applies to general philosophical hypotheses. Often in a\nsingle case such hypotheses may seem highly doubtful, while yet, when\nwe consider the order and coherence which they introduce into a mass of\nprobable opinion, they become pretty nearly certain. This applies, in\nparticular, to such matters as the distinction between dreams and\nwaking life. If our dreams, night after night, were as coherent one with\nanother as our days, we should hardly know whether to believe the dreams\nor the waking life. As it is, the test of coherence condemns the\ndreams and confirms the waking life. But this test, though it increases\nprobability where it is successful, never gives absolute certainty,\nunless there is certainty already at some point in the coherent system.\nThus the mere organization of probable opinion will never, by itself,\ntransform it into indubitable knowledge.\n\n\n\nCHAPTER XIV. THE LIMITS OF PHILOSOPHICAL KNOWLEDGE\n\nIn all that we have said hitherto concerning philosophy, we have\nscarcely touched on many matters that occupy a great space in the\nwritings of most philosophers. Most philosophers--or, at any rate, very\nmany--profess to be able to prove, by _a priori_ metaphysical reasoning,\nsuch things as the fundamental dogmas of religion, the essential\nrationality of the universe, the illusoriness of matter, the unreality\nof all evil, and so on. There can be no doubt that the hope of finding\nreason to believe such theses as these has been the chief inspiration of\nmany life-long students of philosophy. This hope, I believe, is vain. It\nwould seem that knowledge concerning the universe as a whole is not to\nbe obtained by metaphysics, and that the proposed proofs that, in virtue\nof the laws of logic such and such things _must_ exist and such and such\nothers cannot, are not capable of surviving a critical scrutiny. In\nthis chapter we shall briefly consider the kind of way in which such\nreasoning is attempted, with a view to discovering whether we can hope\nthat it may be valid.\n\nThe great representative, in modern times, of the kind of view which\nwe wish to examine, was Hegel (1770-1831). Hegel's philosophy is very\ndifficult, and commentators differ as to the true interpretation of it.\nAccording to the interpretation I shall adopt, which is that of many, if\nnot most, of the commentators and has the merit of giving an interesting\nand important type of philosophy, his main thesis is that everything\nshort of the Whole is obviously fragmentary, and obviously incapable of\nexisting without the complement supplied by the rest of the world. Just\nas a comparative anatomist, from a single bone, sees what kind of animal\nthe whole must have been, so the metaphysician, according to Hegel,\nsees, from any one piece of reality, what the whole of reality must\nbe--at least in its large outlines. Every apparently separate piece of\nreality has, as it were, hooks which grapple it to the next piece;\nthe next piece, in turn, has fresh hooks, and so on, until the whole\nuniverse is reconstructed. This essential incompleteness appears,\naccording to Hegel, equally in the world of thought and in the world of\nthings. In the world of thought, if we take any idea which is\nabstract or incomplete, we find, on examination, that if we forget\nits incompleteness, we become involved in contradictions; these\ncontradictions turn the idea in question into its opposite, or\nantithesis; and in order to escape, we have to find a new, less\nincomplete idea, which is the synthesis of our original idea and its\nantithesis. This new idea, though less incomplete than the idea we\nstarted with, will be found, nevertheless, to be still not wholly\ncomplete, but to pass into its antithesis, with which it must be\ncombined in a new synthesis. In this way Hegel advances until he reaches\nthe 'Absolute Idea', which, according to him, has no incompleteness,\nno opposite, and no need of further development. The Absolute Idea,\ntherefore, is adequate to describe Absolute Reality; but all lower ideas\nonly describe reality as it appears to a partial view, not as it is\nto one who simultaneously surveys the Whole. Thus Hegel reaches the\nconclusion that Absolute Reality forms one single harmonious system, not\nin space or time, not in any degree evil, wholly rational, and wholly\nspiritual. Any appearance to the contrary, in the world we know, can be\nproved logically--so he believes--to be entirely due to our fragmentary\npiecemeal view of the universe. If we saw the universe whole, as we may\nsuppose God sees it, space and time and matter and evil and all striving\nand struggling would disappear, and we should see instead an eternal\nperfect unchanging spiritual unity.\n\nIn this conception, there is undeniably something sublime, something to\nwhich we could wish to yield assent. Nevertheless, when the arguments\nin support of it are carefully examined, they appear to involve much\nconfusion and many unwarrantable assumptions. The fundamental tenet\nupon which the system is built up is that what is incomplete must be not\nself-subsistent, but must need the support of other things before it can\nexist. It is held that whatever has relations to things outside itself\nmust contain some reference to those outside things in its own nature,\nand could not, therefore, be what it is if those outside things did not\nexist. A man's nature, for example, is constituted by his memories and\nthe rest of his knowledge, by his loves and hatreds, and so on; thus,\nbut for the objects which he knows or loves or hates, he could not be\nwhat he is. He is essentially and obviously a fragment: taken as the\nsum-total of reality he would be self-contradictory.\n\nThis whole point of view, however, turns upon the notion of the 'nature'\nof a thing, which seems to mean 'all the truths about the thing'. It is\nof course the case that a truth which connects one thing with another\nthing could not subsist if the other thing did not subsist. But a\ntruth about a thing is not part of the thing itself, although it must,\naccording to the above usage, be part of the 'nature' of the thing.\nIf we mean by a thing's 'nature' all the truths about the thing, then\nplainly we cannot know a thing's 'nature' unless we know all the thing's\nrelations to all the other things in the universe. But if the word\n'nature' is used in this sense, we shall have to hold that the thing\nmay be known when its 'nature' is not known, or at any rate is not known\ncompletely. There is a confusion, when this use of the word 'nature' is\nemployed, between knowledge of things and knowledge of truths. We may\nhave knowledge of a thing by acquaintance even if we know very few\npropositions about it--theoretically we need not know any propositions\nabout it. Thus, acquaintance with a thing does not involve knowledge of\nits 'nature' in the above sense. And although acquaintance with a thing\nis involved in our knowing any one proposition about a thing, knowledge\nof its 'nature', in the above sense, is not involved. Hence, (1)\nacquaintance with a thing does not logically involve a knowledge of its\nrelations, and (2) a knowledge of some of its relations does not involve\na knowledge of all of its relations nor a knowledge of its 'nature' in\nthe above sense. I may be acquainted, for example, with my toothache,\nand this knowledge may be as complete as knowledge by acquaintance ever\ncan be, without knowing all that the dentist (who is not acquainted\nwith it) can tell me about its cause, and without therefore knowing its\n'nature' in the above sense. Thus the fact that a thing has relations\ndoes not prove that its relations are logically necessary. That is to\nsay, from the mere fact that it is the thing it is we cannot deduce\nthat it must have the various relations which in fact it has. This only\n_seems_ to follow because we know it already.\n\nIt follows that we cannot prove that the universe as a whole forms a\nsingle harmonious system such as Hegel believes that it forms. And if we\ncannot prove this, we also cannot prove the unreality of space and time\nand matter and evil, for this is deduced by Hegel from the fragmentary\nand relational character of these things. Thus we are left to the\npiecemeal investigation of the world, and are unable to know the\ncharacters of those parts of the universe that are remote from our\nexperience. This result, disappointing as it is to those whose hopes\nhave been raised by the systems of philosophers, is in harmony with\nthe inductive and scientific temper of our age, and is borne out by the\nwhole examination of human knowledge which has occupied our previous\nchapters.\n\nMost of the great ambitious attempts of metaphysicians have proceeded by\nthe attempt to prove that such and such apparent features of the actual\nworld were self-contradictory, and therefore could not be real. The\nwhole tendency of modern thought, however, is more and more in the\ndirection of showing that the supposed contradictions were illusory, and\nthat very little can be proved _a priori_ from considerations of what\n_must_ be. A good illustration of this is afforded by space and\ntime. Space and time appear to be infinite in extent, and infinitely\ndivisible. If we travel along a straight line in either direction, it\nis difficult to believe that we shall finally reach a last point,\nbeyond which there is nothing, not even empty space. Similarly, if in\nimagination we travel backwards or forwards in time, it is difficult to\nbelieve that we shall reach a first or last time, with not even empty\ntime beyond it. Thus space and time appear to be infinite in extent.\n\nAgain, if we take any two points on a line, it seems evident that there\nmust be other points between them however small the distance between\nthem may be: every distance can be halved, and the halves can be halved\nagain, and so on _ad infinitum_. In time, similarly, however little\ntime may elapse between two moments, it seems evident that there will be\nother moments between them. Thus space and time appear to be infinitely\ndivisible. But as against these apparent facts--infinite extent and\ninfinite divisibility--philosophers have advanced arguments tending to\nshow that there could be no infinite collections of things, and that\ntherefore the number of points in space, or of instants in time, must\nbe finite. Thus a contradiction emerged between the apparent nature of\nspace and time and the supposed impossibility of infinite collections.\n\nKant, who first emphasized this contradiction, deduced the impossibility\nof space and time, which he declared to be merely subjective; and since\nhis time very many philosophers have believed that space and time are\nmere appearance, not characteristic of the world as it really is. Now,\nhowever, owing to the labours of the mathematicians, notably Georg\nCantor, it has appeared that the impossibility of infinite collections\nwas a mistake. They are not in fact self-contradictory, but only\ncontradictory of certain rather obstinate mental prejudices. Hence the\nreasons for regarding space and time as unreal have become inoperative,\nand one of the great sources of metaphysical constructions is dried up.\n\nThe mathematicians, however, have not been content with showing that\nspace as it is commonly supposed to be is possible; they have shown also\nthat many other forms of space are equally possible, so far as logic\ncan show. Some of Euclid's axioms, which appear to common sense to be\nnecessary, and were formerly supposed to be necessary by philosophers,\nare now known to derive their appearance of necessity from our mere\nfamiliarity with actual space, and not from any _a priori_ logical\nfoundation. By imagining worlds in which these axioms are false, the\nmathematicians have used logic to loosen the prejudices of common\nsense, and to show the possibility of spaces differing--some more, some\nless--from that in which we live. And some of these spaces differ so\nlittle from Euclidean space, where distances such as we can measure are\nconcerned, that it is impossible to discover by observation whether our\nactual space is strictly Euclidean or of one of these other kinds.\nThus the position is completely reversed. Formerly it appeared that\nexperience left only one kind of space to logic, and logic showed this\none kind to be impossible. Now, logic presents many kinds of space as\npossible apart from experience, and experience only partially decides\nbetween them. Thus, while our knowledge of what is has become less\nthan it was formerly supposed to be, our knowledge of what may be is\nenormously increased. Instead of being shut in within narrow walls, of\nwhich every nook and cranny could be explored, we find ourselves in an\nopen world of free possibilities, where much remains unknown because\nthere is so much to know.\n\nWhat has happened in the case of space and time has happened, to some\nextent, in other directions as well. The attempt to prescribe to the\nuniverse by means of _a priori_ principles has broken down; logic,\ninstead of being, as formerly, the bar to possibilities, has become the\ngreat liberator of the imagination, presenting innumerable alternatives\nwhich are closed to unreflective common sense, and leaving to experience\nthe task of deciding, where decision is possible, between the many\nworlds which logic offers for our choice. Thus knowledge as to what\nexists becomes limited to what we can learn from experience--not to\nwhat we can actually experience, for, as we have seen, there is much\nknowledge by description concerning things of which we have no direct\nexperience. But in all cases of knowledge by description, we need some\nconnexion of universals, enabling us, from such and such a datum, to\ninfer an object of a certain sort as implied by our datum. Thus in\nregard to physical objects, for example, the principle that sense-data\nare signs of physical objects is itself a connexion of universals; and\nit is only in virtue of this principle that experience enables us to\nacquire knowledge concerning physical objects. The same applies to\nthe law of causality, or, to descend to what is less general, to such\nprinciples as the law of gravitation.\n\nPrinciples such as the law of gravitation are proved, or rather are\nrendered highly probable, by a combination of experience with some\nwholly _a priori_ principle, such as the principle of induction. Thus\nour intuitive knowledge, which is the source of all our other knowledge\nof truths, is of two sorts: pure empirical knowledge, which tells us of\nthe existence and some of the properties of particular things with\nwhich we are acquainted, and pure _a priori_ knowledge, which gives us\nconnexions between universals, and enables us to draw inferences from\nthe particular facts given in empirical knowledge. Our derivative\nknowledge always depends upon some pure _a priori_ knowledge and usually\nalso depends upon some pure empirical knowledge.\n\nPhilosophical knowledge, if what has been said above is true, does not\ndiffer essentially from scientific knowledge; there is no special\nsource of wisdom which is open to philosophy but not to science, and the\nresults obtained by philosophy are not radically different from those\nobtained from science. The essential characteristic of philosophy,\nwhich makes it a study distinct from science, is criticism. It examines\ncritically the principles employed in science and in daily life; it\nsearches out any inconsistencies there may be in these principles,\nand it only accepts them when, as the result of a critical inquiry, no\nreason for rejecting them has appeared. If, as many philosophers have\nbelieved, the principles underlying the sciences were capable, when\ndisengaged from irrelevant detail, of giving us knowledge concerning\nthe universe as a whole, such knowledge would have the same claim on our\nbelief as scientific knowledge has; but our inquiry has not revealed any\nsuch knowledge, and therefore, as regards the special doctrines of the\nbolder metaphysicians, has had a mainly negative result. But as regards\nwhat would be commonly accepted as knowledge, our result is in the main\npositive: we have seldom found reason to reject such knowledge as the\nresult of our criticism, and we have seen no reason to suppose man\nincapable of the kind of knowledge which he is generally believed to\npossess.\n\nWhen, however, we speak of philosophy as a _criticism_ of knowledge, it\nis necessary to impose a certain limitation. If we adopt the attitude\nof the complete sceptic, placing ourselves wholly outside all knowledge,\nand asking, from this outside position, to be compelled to return within\nthe circle of knowledge, we are demanding what is impossible, and our\nscepticism can never be refuted. For all refutation must begin with\nsome piece of knowledge which the disputants share; from blank doubt,\nno argument can begin. Hence the criticism of knowledge which philosophy\nemploys must not be of this destructive kind, if any result is to be\nachieved. Against this absolute scepticism, no _logical_ argument can be\nadvanced. But it is not difficult to see that scepticism of this kind\nis unreasonable. Descartes' 'methodical doubt', with which modern\nphilosophy began, is not of this kind, but is rather the kind of\ncriticism which we are asserting to be the essence of philosophy. His\n'methodical doubt' consisted in doubting whatever seemed doubtful; in\npausing, with each apparent piece of knowledge, to ask himself whether,\non reflection, he could feel certain that he really knew it. This is the\nkind of criticism which constitutes philosophy. Some knowledge, such as\nknowledge of the existence of our sense-data, appears quite indubitable,\nhowever calmly and thoroughly we reflect upon it. In regard to such\nknowledge, philosophical criticism does not require that we should\nabstain from belief. But there are beliefs--such, for example, as the\nbelief that physical objects exactly resemble our sense-data--which are\nentertained until we begin to reflect, but are found to melt away\nwhen subjected to a close inquiry. Such beliefs philosophy will bid us\nreject, unless some new line of argument is found to support them.\nBut to reject the beliefs which do not appear open to any objections,\nhowever closely we examine them, is not reasonable, and is not what\nphilosophy advocates.\n\nThe criticism aimed at, in a word, is not that which, without reason,\ndetermines to reject, but that which considers each piece of apparent\nknowledge on its merits, and retains whatever still appears to be\nknowledge when this consideration is completed. That some risk of error\nremains must be admitted, since human beings are fallible. Philosophy\nmay claim justly that it diminishes the risk of error, and that in some\ncases it renders the risk so small as to be practically negligible. To\ndo more than this is not possible in a world where mistakes must occur;\nand more than this no prudent advocate of philosophy would claim to have\nperformed.\n\n\n\nCHAPTER XV. THE VALUE OF PHILOSOPHY\n\nHaving now come to the end of our brief and very incomplete review of\nthe problems of philosophy, it will be well to consider, in conclusion,\nwhat is the value of philosophy and why it ought to be studied. It is\nthe more necessary to consider this question, in view of the fact that\nmany men, under the influence of science or of practical affairs, are\ninclined to doubt whether philosophy is anything better than innocent\nbut useless trifling, hair-splitting distinctions, and controversies on\nmatters concerning which knowledge is impossible.\n\nThis view of philosophy appears to result, partly from a wrong\nconception of the ends of life, partly from a wrong conception of the\nkind of goods which philosophy strives to achieve. Physical science,\nthrough the medium of inventions, is useful to innumerable people who\nare wholly ignorant of it; thus the study of physical science is to\nbe recommended, not only, or primarily, because of the effect on the\nstudent, but rather because of the effect on mankind in general. Thus\nutility does not belong to philosophy. If the study of philosophy has\nany value at all for others than students of philosophy, it must be only\nindirectly, through its effects upon the lives of those who study it.\nIt is in these effects, therefore, if anywhere, that the value of\nphilosophy must be primarily sought.\n\nBut further, if we are not to fail in our endeavour to determine the\nvalue of philosophy, we must first free our minds from the prejudices\nof what are wrongly called 'practical' men. The 'practical' man, as\nthis word is often used, is one who recognizes only material needs, who\nrealizes that men must have food for the body, but is oblivious of the\nnecessity of providing food for the mind. If all men were well off, if\npoverty and disease had been reduced to their lowest possible point,\nthere would still remain much to be done to produce a valuable society;\nand even in the existing world the goods of the mind are at least as\nimportant as the goods of the body. It is exclusively among the goods of\nthe mind that the value of philosophy is to be found; and only those who\nare not indifferent to these goods can be persuaded that the study of\nphilosophy is not a waste of time.\n\nPhilosophy, like all other studies, aims primarily at knowledge. The\nknowledge it aims at is the kind of knowledge which gives unity and\nsystem to the body of the sciences, and the kind which results from a\ncritical examination of the grounds of our convictions, prejudices, and\nbeliefs. But it cannot be maintained that philosophy has had any very\ngreat measure of success in its attempts to provide definite answers to\nits questions. If you ask a mathematician, a mineralogist, a historian,\nor any other man of learning, what definite body of truths has been\nascertained by his science, his answer will last as long as you are\nwilling to listen. But if you put the same question to a philosopher, he\nwill, if he is candid, have to confess that his study has not achieved\npositive results such as have been achieved by other sciences. It is\ntrue that this is partly accounted for by the fact that, as soon as\ndefinite knowledge concerning any subject becomes possible, this subject\nceases to be called philosophy, and becomes a separate science. The\nwhole study of the heavens, which now belongs to astronomy, was once\nincluded in philosophy; Newton's great work was called 'the mathematical\nprinciples of natural philosophy'. Similarly, the study of the human\nmind, which was a part of philosophy, has now been separated from\nphilosophy and has become the science of psychology. Thus, to a great\nextent, the uncertainty of philosophy is more apparent than real: those\nquestions which are already capable of definite answers are placed in\nthe sciences, while those only to which, at present, no definite answer\ncan be given, remain to form the residue which is called philosophy.\n\nThis is, however, only a part of the truth concerning the uncertainty of\nphilosophy. There are many questions--and among them those that are of\nthe profoundest interest to our spiritual life--which, so far as we\ncan see, must remain insoluble to the human intellect unless its powers\nbecome of quite a different order from what they are now. Has the\nuniverse any unity of plan or purpose, or is it a fortuitous concourse\nof atoms? Is consciousness a permanent part of the universe, giving\nhope of indefinite growth in wisdom, or is it a transitory accident on\na small planet on which life must ultimately become impossible? Are good\nand evil of importance to the universe or only to man? Such questions\nare asked by philosophy, and variously answered by various philosophers.\nBut it would seem that, whether answers be otherwise discoverable or\nnot, the answers suggested by philosophy are none of them demonstrably\ntrue. Yet, however slight may be the hope of discovering an answer, it\nis part of the business of philosophy to continue the consideration of\nsuch questions, to make us aware of their importance, to examine all the\napproaches to them, and to keep alive that speculative interest in the\nuniverse which is apt to be killed by confining ourselves to definitely\nascertainable knowledge.\n\nMany philosophers, it is true, have held that philosophy could establish\nthe truth of certain answers to such fundamental questions. They have\nsupposed that what is of most importance in religious beliefs could be\nproved by strict demonstration to be true. In order to judge of such\nattempts, it is necessary to take a survey of human knowledge, and to\nform an opinion as to its methods and its limitations. On such a subject\nit would be unwise to pronounce dogmatically; but if the investigations\nof our previous chapters have not led us astray, we shall be compelled\nto renounce the hope of finding philosophical proofs of religious\nbeliefs. We cannot, therefore, include as part of the value of\nphilosophy any definite set of answers to such questions. Hence, once\nmore, the value of philosophy must not depend upon any supposed body of\ndefinitely ascertainable knowledge to be acquired by those who study it.\n\nThe value of philosophy is, in fact, to be sought largely in its very\nuncertainty. The man who has no tincture of philosophy goes through\nlife imprisoned in the prejudices derived from common sense, from the\nhabitual beliefs of his age or his nation, and from convictions which\nhave grown up in his mind without the co-operation or consent of his\ndeliberate reason. To such a man the world tends to become definite,\nfinite, obvious; common objects rouse no questions, and unfamiliar\npossibilities are contemptuously rejected. As soon as we begin to\nphilosophize, on the contrary, we find, as we saw in our opening\nchapters, that even the most everyday things lead to problems to which\nonly very incomplete answers can be given. Philosophy, though unable to\ntell us with certainty what is the true answer to the doubts which it\nraises, is able to suggest many possibilities which enlarge our thoughts\nand free them from the tyranny of custom. Thus, while diminishing our\nfeeling of certainty as to what things are, it greatly increases our\nknowledge as to what they may be; it removes the somewhat arrogant\ndogmatism of those who have never travelled into the region of\nliberating doubt, and it keeps alive our sense of wonder by showing\nfamiliar things in an unfamiliar aspect.\n\nApart from its utility in showing unsuspected possibilities, philosophy\nhas a value--perhaps its chief value--through the greatness of the\nobjects which it contemplates, and the freedom from narrow and personal\naims resulting from this contemplation. The life of the instinctive\nman is shut up within the circle of his private interests: family and\nfriends may be included, but the outer world is not regarded except\nas it may help or hinder what comes within the circle of instinctive\nwishes. In such a life there is something feverish and confined, in\ncomparison with which the philosophic life is calm and free. The private\nworld of instinctive interests is a small one, set in the midst of a\ngreat and powerful world which must, sooner or later, lay our private\nworld in ruins. Unless we can so enlarge our interests as to include the\nwhole outer world, we remain like a garrison in a beleagured fortress,\nknowing that the enemy prevents escape and that ultimate surrender is\ninevitable. In such a life there is no peace, but a constant strife\nbetween the insistence of desire and the powerlessness of will. In one\nway or another, if our life is to be great and free, we must escape this\nprison and this strife.\n\nOne way of escape is by philosophic contemplation. Philosophic\ncontemplation does not, in its widest survey, divide the universe into\ntwo hostile camps--friends and foes, helpful and hostile, good and\nbad--it views the whole impartially. Philosophic contemplation, when it\nis unalloyed, does not aim at proving that the rest of the universe is\nakin to man. All acquisition of knowledge is an enlargement of the Self,\nbut this enlargement is best attained when it is not directly sought. It\nis obtained when the desire for knowledge is alone operative, by a study\nwhich does not wish in advance that its objects should have this or that\ncharacter, but adapts the Self to the characters which it finds in its\nobjects. This enlargement of Self is not obtained when, taking the Self\nas it is, we try to show that the world is so similar to this Self that\nknowledge of it is possible without any admission of what seems alien.\nThe desire to prove this is a form of self-assertion and, like all\nself-assertion, it is an obstacle to the growth of Self which it\ndesires, and of which the Self knows that it is capable. Self-assertion,\nin philosophic speculation as elsewhere, views the world as a means to\nits own ends; thus it makes the world of less account than Self, and the\nSelf sets bounds to the greatness of its goods. In contemplation, on\nthe contrary, we start from the not-Self, and through its greatness the\nboundaries of Self are enlarged; through the infinity of the universe\nthe mind which contemplates it achieves some share in infinity.\n\nFor this reason greatness of soul is not fostered by those philosophies\nwhich assimilate the universe to Man. Knowledge is a form of union\nof Self and not-Self; like all union, it is impaired by dominion, and\ntherefore by any attempt to force the universe into conformity with\nwhat we find in ourselves. There is a widespread philosophical tendency\ntowards the view which tells us that Man is the measure of all things,\nthat truth is man-made, that space and time and the world of universals\nare properties of the mind, and that, if there be anything not created\nby the mind, it is unknowable and of no account for us. This view, if\nour previous discussions were correct, is untrue; but in addition to\nbeing untrue, it has the effect of robbing philosophic contemplation of\nall that gives it value, since it fetters contemplation to Self. What\nit calls knowledge is not a union with the not-Self, but a set of\nprejudices, habits, and desires, making an impenetrable veil between\nus and the world beyond. The man who finds pleasure in such a theory of\nknowledge is like the man who never leaves the domestic circle for fear\nhis word might not be law.\n\nThe true philosophic contemplation, on the contrary, finds its\nsatisfaction in every enlargement of the not-Self, in everything\nthat magnifies the objects contemplated, and thereby the subject\ncontemplating. Everything, in contemplation, that is personal or\nprivate, everything that depends upon habit, self-interest, or desire,\ndistorts the object, and hence impairs the union which the intellect\nseeks. By thus making a barrier between subject and object, such\npersonal and private things become a prison to the intellect. The free\nintellect will see as God might see, without a _here_ and _now_,\nwithout hopes and fears, without the trammels of customary beliefs\nand traditional prejudices, calmly, dispassionately, in the sole and\nexclusive desire of knowledge--knowledge as impersonal, as purely\ncontemplative, as it is possible for man to attain. Hence also the free\nintellect will value more the abstract and universal knowledge into\nwhich the accidents of private history do not enter, than the knowledge\nbrought by the senses, and dependent, as such knowledge must be, upon\nan exclusive and personal point of view and a body whose sense-organs\ndistort as much as they reveal.\n\nThe mind which has become accustomed to the freedom and impartiality of\nphilosophic contemplation will preserve something of the same freedom\nand impartiality in the world of action and emotion. It will view\nits purposes and desires as parts of the whole, with the absence of\ninsistence that results from seeing them as infinitesimal fragments in\na world of which all the rest is unaffected by any one man's deeds. The\nimpartiality which, in contemplation, is the unalloyed desire for truth,\nis the very same quality of mind which, in action, is justice, and in\nemotion is that universal love which can be given to all, and not only\nto those who are judged useful or admirable. Thus contemplation enlarges\nnot only the objects of our thoughts, but also the objects of our\nactions and our affections: it makes us citizens of the universe, not\nonly of one walled city at war with all the rest. In this citizenship\nof the universe consists man's true freedom, and his liberation from the\nthraldom of narrow hopes and fears.\n\nThus, to sum up our discussion of the value of philosophy; Philosophy\nis to be studied, not for the sake of any definite answers to its\nquestions, since no definite answers can, as a rule, be known to be\ntrue, but rather for the sake of the questions themselves; because\nthese questions enlarge our conception of what is possible, enrich\nour intellectual imagination and diminish the dogmatic assurance which\ncloses the mind against speculation; but above all because, through the\ngreatness of the universe which philosophy contemplates, the mind also\nis rendered great, and becomes capable of that union with the universe\nwhich constitutes its highest good.\n\n\n\n\nBIBLIOGRAPHICAL NOTE\n\nThe student who wishes to acquire an elementary knowledge of philosophy\nwill find it both easier and more profitable to read some of the works\nof the great philosophers than to attempt to derive an all-round view\nfrom handbooks. The following are specially recommended:\n\n     Plato: _Republic_, especially Books VI and VII.\n     Descartes: _Meditations_.\n     Spinoza: _Ethics_.\n     Leibniz: _The Monadology_.\n     Berkeley: _Three Dialogues between Hylas and Philonous_.\n     Hume: _Enquiry concerning Human Understanding_.\n     Kant: _Prolegomena to any Future Metaphysic_.","title":"The Problems of Philosophy","tradition":"philosophy-ethics","translated_text":null,"word_count":42756}