{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/wikisource_Tractatus_Logico_Philosophicus_4/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/wikisource_Tractatus_Logico_Philosophicus_4","id":"wikisource_Tractatus_Logico_Philosophicus_4","license":"Public Domain / CC-BY-SA (see source)","rights_basis":"wikisource_site_inclusion_policy","source":"wikisource","source_url":"https://en.wikisource.org/wiki/Tractatus_Logico-Philosophicus/4","summary":null,"tags":["Pages_using_automatic_headers","Subpages"],"text":"4 The thought is the significant proposition.\n\n4.001 The totality of propositions is the language.\n\n4.002 Man possesses the capacity of constructing languages, in which every sense can be expressed, without having an idea how and what each word means\u2014just as one speaks without knowing how the single sounds are produced.\n\nColloquial language is a part of the human organism and is not less complicated than it.\n\nFrom it it is humanly impossible to gather immediately the logic of language.\n\nLanguage disguises the thought; so that from the external form of the clothes one cannot infer the form of the thought they clothe, because the external form of the clothes is constructed with quite another object than to let the form of the body be recognized.\n\nThe silent adjustments to understand colloquial language are enormously complicated.\n\n4.003 Most propositions and questions, that have been written about philosophical matters, are not false, but senseless. We cannot, therefore, answer questions of this kind at all, but only state their senselessness. Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language.\n\n(They are of the same kind as the question whether the Good is more or less identical than the Beautiful.)\n\nAnd so it is not to be wondered at that the deepest problems are really no problems.\n\n4.0031 All philosophy is \u201cCritique of language\u201d (but not at all in Mauthner\u2019s sense). Russell\u2019s merit is to have shown that the apparent logical form of the proposition need not be its real form.\n\n4.01 The proposition is a picture of reality.\n\nThe proposition is a model of the reality as we think it is.\n\n4.011 At the first glance the proposition\u2014say as it stands printed on paper\u2014does not seem to be picture of the reality of which it treats. But nor does the musical score appear at first sight to be a picture of a musical piece; nor does our phonetic spelling (letters) seem to be a picture of our spoken language. And yet these symbolisms prove to be pictures\u2014even in the ordinary sense of the word\u2014of what they represent.\n\n4.012 It is obvious that we perceive a proposition of the form aRb as a picture. Here the sign is obviously a likeness of the signified.\n\n4.013 And if we penetrate to the essence of this pictorial nature we see that this is not disturbed by apparent irregularities (like the use of \u266f and \u266d in the score).\n\nFor these irregularities also picture what they are to express; only in another way.\n\n4.014 The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation, which holds between language and the world.\n\nTo all of them the logical structure is common.\n\n(Like the two youths, their two horses and their lilies in the story. They are all in a certain sense one.)\n\n4.0141 In the fact that there is a general rule by which the musician is able to read the symphony out of the score, and that there is a rule by which one could reconstruct the symphony from the line on a gramophone record and from this again\u2014by means of the first rule\u2014construct the score, herein lies the internal similarity between these things which at first sight seem to be entirely different. And the rule is the law of projection which projects the symphony into the language of the musical score. It is the rule of translation of this language into the language of the gramophone record.\n\n4.015 The possibility of all similes, of all the imagery of our language, rests on the logic of representation.\n\n4.016 In order to understand the essence of the proposition, consider hieroglyphic writing, which pictures the facts it describes.\n\nAnd from it came the alphabet without the essence of the representation being lost.\n\n4.02 This we see from the fact that we understand the sense of the propositional sign, without having had it explained to us.\n\n4.021 The proposition is a picture of reality, for I know the state of affairs presented by it, if I understand the proposition. And I understand the proposition, without its sense having been explained to me.\n\n4.022 The proposition shows its sense.\n\nThe proposition shows how things stand, if it is true. And it says, that they do so stand.\n\n4.023 The proposition determines reality to this extent, that one only needs to say \u201cYes\u201d or \u201cNo\u201d to it to make it agree with reality.\n\nReality must therefore be completely described by the proposition.\n\nA proposition is the description of a fact.\n\nAs the description of an object describes it by its external properties so propositions describe reality by its internal properties.\n\nThe proposition constructs a world with the help of a logical scaffolding, and therefore one can actually see in the proposition all the logical features possessed by reality if it is true. One can draw conclusions from a false proposition.\n\n4.024 To understand a proposition means to know what is the case, if it is true.\n\n(One can therefore understand it without knowing whether it is true or not.)\n\nOne understands it if one understands it constituent parts.\n\n4.025The translation of one language into another is not a process of translating each proposition of the one into a proposition of the other, but only the constituent parts of propositions are translated.\n\n(And the dictionary does not only translate substantives but also adverbs and conjunctions, etc., and it treats them all alike.)\n\n4.026 The meanings of the simple signs (the words) must be explained to us, if we are to understand them.\n\nBy means of propositions we explain ourselves.\n\n4.027 It is essential to propositions, that they can communicate a new sense to us.\n\n4.03 A proposition must communicate a new sense with old words.\n\nThe proposition communicates to us a state of affairs, therefore it must be essentially connected with the state of affairs.\n\nAnd the connexion is, in fact, that it is its logical picture.\n\nThe proposition only asserts something, in so far as it is a picture.\n\n4.031 In the proposition a state of affairs is, as it were, put together for the sake of experiment.\n\nOne can say, instead of, This proposition has such and such a sense, This proposition represents such and such a state of affairs.\n\n4.0311 One name stands for one thing, and another for another thing, and they are connected together. And so the whole, like a living picture, presents the atomic fact.\n\n4.0312 The possibility of propositions is based upon the principle of the representation of objects by signs.\n\nMy fundamental thought is that the \u201clogical constants\u201d do not represent. That the logic of the facts cannot be represented.\n\n4.032 The proposition is a picture of its state of affairs, only in so far as it is logically articulated. (Even the proposition \u201cambulo\u201d is composite, for its stem gives a different sense with another termination, or its termination with another stem.)\n\n4.04 In the proposition there must be exactly as many thing distinguishable as there are in the state of affairs, which it represents.\n\nThey must both possess the same logical (mathematical) multiplicity (cf. Hertz\u2019s Mechanics, on Dynamic Models).\n\n4.041 This mathematical multiplicity naturally cannot in its turn be represented. One cannot get outside it in the representation.\n\n4.0411 If we tried, for example, to express what is expressed by \u201c(x).fx\u201d by putting an index before fx, like: \u201cGen.fx\u201d, it would not do, we should not know what was generalized. If we tried to show it by an index g, like: \u201cf(xg)\u201d it would not do\u2014we should not know the scope of the generalization.\n\nIf we were to try it by introducing a mark in the argument places, like \u201c(G, G).F(G, G)\u201d, it would not do\u2014we could not determine the identity of the variables, etc.\n\nAll these ways of symbolizing are inadequate because they have not the necessary mathematical multiplicity.\n\n4.0412 For the same reason the idealist explanation of the seeing of spatial relations through \u201cspatial spectacles\u201d does not do, because it cannot explain the multiplicity of these relations.\n\n4.05 Reality is compared with the proposition.\n\n4.06 Propositions can be true or false only by being pictures of the reality.\n\n4.061 If one does not observe that propositions have a sense independent of the facts, one can easily believe that true and false are two relations between signs and things signified with equal rights.\n\nOne could, then, for example, say that \u201cp\u201d signifies in the true way what \u201c~p\u201d signifies in the false way, etc.\n\n4.062 Can we not make ourselves understood by means of false propositions as hitherto with true ones, so long as we know that they are meant to be false? No! For a proposition is true, if what we assert by means of it is the case; and if by \u201cp\u201d we mean ~p, and what we mean is the case, then \u201cp\u201d in the new conception is true and not false.\n\n4.0621 That, however, the signs \u201cp\u201d and \u201c~p\u201d can say the same thing is important, for it shows that the sign \u201c~\u201d corresponds to nothing in reality.\n\nThat negation occurs in a proposition, is no characteristic of its sense (~ ~p=p).\n\nThe propositions \u201cp\u201d and \u201c~p\u201d have opposite senses, but to them corresponds one and the same reality.\n\n4.063 An illustration to explain the concept of truth. A black spot on white paper; the form of the spot can be described by saying of each point of the plane whether it is white or black. To the fact that a point is black corresponds a positive fact; to the fact that a point is white (not black), a negative fact. If I indicate a point of the plane (a truth-value in Frege\u2019s terminology), this corresponds to the assumption proposed for judgment, etc. etc.\n\nBut to be able to say that a point is black or white, I must first know under what conditions a point is called white or black; in order to be able to say \u201cp\u201d is true (or false) I must have determined under what conditions I call \u201cp\u201d true, and thereby I determine the sense of the proposition.\n\nThe point at which the simile breaks down is this: we can indicate a point on the paper, without knowing what white and black are; but to a proposition without a sense corresponds nothing at all, for it signifies no thing (truth-value) whose properties are called \u201cfalse\u201d or \u201ctrue\u201d; the verb of the proposition is not \u201cis true\u201d or \u201cis false\u201d\u2014as Frege thought\u2014but that which \u201cis true\u201d must already contain the verb.\n\n4.064 Every proposition must already have a sense; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc.\n\n4.0641 One could say, the denial is already related to the logical place determined by the proposition that is denied.\n\nThe denying proposition determines a logical place other than does the proposition denied.\n\nThe denying proposition determines a logical place, with the help of the logical place of the proposition denied, by saying that it lies outside the latter place.\n\nThat one can deny again the denied proposition, shows that what is denied is already a proposition and not merely the preliminary to a proposition.\n\n4.1 A proposition presents the existence and non-existence of atomic facts.\n\n4.11 The totality of true propositions is the total natural science (or the totality of the natural sciences).\n\n4.111 Philosophy is not one of the natural sciences.\n\n(The word \u201cphilosophy\u201d must mean something which stands above or below, but not beside the natural sciences.)\n\n4.112 The object of philosophy is the logical clarification of thoughts.\n\nPhilosophy is not a theory but an activity.\n\nA philosophical work consists essentially of elucidations.\n\nThe result of philosophy is not a number of \u201cphilosophical propositions\u201d, but to make propositions clear.\n\nPhilosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred.\n\n4.1121 Psychology is no nearer related to philosophy, than is any other natural science.\n\nThe theory of knowledge is the philosophy of psychology.\n\nDoes not my study of sign-language correspond to the study of thought processes which philosophers held to be so essential to the philosophy of logic? Only they got entangled for the most part in unessential psychological investigations, and there is an analogous danger for my method.\n\n4.1122 The Darwinian theory has no more to do with philosophy than has any other hypothesis of natural science.\n\n4.113 Philosophy limits the disputable sphere of natural science.\n\n4.114 It should limit the thinkable and thereby the unthinkable.\n\nIt should limit the unthinkable from within through the thinkable.\n\n4.115 It will mean the unspeakable by clearly displaying the speakable.\n\n4.116 Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly.\n\n4.12 Propositions can represent the whole reality, but they cannot represent what they must have in common with reality in order to be able to represent it\u2014the logical form.\n\nTo be able to represent the logical form, we should have to be able to put ourselves with the propositions outside logic, that is outside the world.\n\n4.121 Propositions cannot represent the logical form: this mirrors itself in the propositions.\n\nThat which mirrors itself in language, language cannot represent.\n\nThat which expresses itself in language, we cannot express by language.\n\nThe propositions show the logical form of reality.\n\nThey exhibit it.\n\n4.1211 Thus a proposition \u201cfa\u201d shows that in its sense the object a occurs, two propositions \u201cfa\u201d and \u201cga\u201d that they are both about the same object.\n\nIf two propositions contradict one another, this is shown by their structure; similarly if one follows from another, etc.\n\n4.1212 What can be shown cannot be said.\n\n4.1213 Now we understand our feeling that we are in possession of the right logical conception, if only all is right in our symbolism.\n\n4.122 We can speak in a certain sense of formal properties of objects and atomic facts, or of properties of the structure of facts, and in the same sense of formal relations and relations of structures.\n\n(Instead of property of the structure I also say \u201cinternal property\u201d; instead of relation of structures \u201cinternal relation\u201d.\n\nI introduce these expressions in order to show the reason for the confusion, very widespread among philosophers, between internal relations and proper (external) relations.)\n\nThe holding of such internal properties and relations cannot, however, be asserted by propositions, but it shows itself in the propositions, which present the facts and treat of the objects in question.\n\n4.1221 An internal property of a fact we also call a feature of this fact. (In the sense in which we speak of facial features.)\n\n4.123 A property is internal if it is unthinkable that its object does not possess it.\n\n(This blue colour and that stand in the internal relation of brighter and darker eo ipso. It is unthinkable that these two objects should not stand in this relation.)\n\n(Here to the shifting use of the words \u201cproperty\u201d and \u201crelation\u201d there corresponds the shifting use of the word \u201cobject\u201d.)\n\n4.124 The existence of an internal property of a possible state of affairs is not expressed by a proposition, but it expresses itself in the proposition which presents that state of affairs, by an internal property of this proposition.\n\nIt would be as senseless to ascribe a formal property to a proposition as to deny it the formal property.\n\n4.1241 One cannot distinguish forms from one another by saying that one has this property, the other that: for this assumes that there is a sense in asserting either property of either form.\n\n4.125 The existence of an internal relation between possible states of affairs expresses itself in language by an internal relation between the propositions presenting them.\n\n4.1251 Now this settles the disputed question \u201cwhether all relations are internal or external\u201d.\n\n4.1252 Series which are ordered by internal relations I call formal series.\n\nThe series of numbers is ordered not by an external, but by an internal relation.\n\nSimilarly the series of propositions \u201caRb\u201d,\n\n\u201c(\u2203x):aRx.xRb\u201d,\n\u201c(\u2203x,y):aRx.xRy.yRb\u201d, etc.\n(If b stands in one of these relations to a, I call b a successor of a.)\n\n4.126 In the sense in which we speak of formal properties we can now speak also of formal concepts.\n\n(I introduce this expression in order to make clear the confusion of formal concepts with proper concepts which runs through the whole of the old logic.)\n\nThat anything falls under a formal concept as an object belonging to it, cannot be expressed by a proposition. But it is shown in the symbol for the object itself. (The name shows that it signifies an object, the numerical sign that it signifies a number, etc.)\n\nFormal concepts, cannot, like proper concepts, be presented by a function.\n\nFor their characteristics, the formal properties, are not expressed by the functions.\n\nThe expression of a formal property is a feature of certain symbols.\n\nThe sign that signifies the characteristics of a formal concept is, therefore, a characteristic feature of all symbols, whose meanings fall under the concept. The expression of the formal concept is therefore a propositional variable in which only this characteristic feature is constant.\n\n4.127 The propositional variable signifies the formal concept, and its values signify the objects which fall under this concept.\n\n4.1271 Every variable is the sign of a formal concept.\n\nFor every variable presents a constant form, which all its values possess, and which can be conceived as a formal property of these values.\n\n4.1272 So the variable name \u201cx\u201d is the proper sign of the pseudo-concept object.\n\nWherever the word \u201cobject\u201d (\u201cthing\u201d, \u201centity\u201d, etc.) is rightly used, it is expressed in logical symbolism by the variable name.\n\nFor example in the proposition \u201cthere are two objects which \u2026\u201d, by \u201c(\u2203x,y)\u2026\u201d.\n\nWherever it is used otherwise, i.e. as a proper concept word, there arise senseless pseudo-propositions.\n\nSo one cannot, e.g. say \u201cThere are objects\u201d as one says \u201cThere are books\u201d. Nor \u201cThere are 100 objects\u201d or \u201cThere are \u21350 objects\u201d.\n\nAnd it is senseless to speak of the number of all objects.\n\nThe same holds of the words \u201cComplex\u201d, \u201cFact\u201d, \u201cFunction\u201d, \u201cNumber\u201d, etc.\n\nThey all signify formal concepts and are presented in logical symbolism by variables, not by functions or classes (as Frege and Russell thought).\n\nExpressions like \u201c1 is a number\u201d, \u201cthere is only one number nought\u201d, and all like them are senseless.\n\n(It is as senseless to say, \u201cthere is only one 1\u201d as it would be to say: 2+2 is at 3 o\u2019clock equal to 4.)\n\n4.12721 The formal concept is already given with an object, which falls under it. One cannot, therefore, introduce both, the objects which fall under a formal concept and the formal concept itself, as primitive ideas. One cannot, therefore, e.g. introduce (as Russell does) the concept of function and also special functions as primitive ideas; or the concept of number and definite numbers.\n\n4.1273 If we want to express in logical symbolism the general proposition \u201cb is a successor of a\u201d we need for this an expression for the general term of the formal series: aRb, (\u2203x):aRx.xRb, (\u2203x,y):aRx.xRy.yRb,\u2026 The general term of a formal series can only be expressed by a variable, for the concept symbolized by \u201cterm of this formal series\u201d is a formal concept. (This Frege and Russell overlooked; the way in which they express general propositions like the above is, therefore, false; it contains a vicious circle.)\n\nWe can determine the general term of the formal series by giving its first term and the general form of the operation, which generates the following term out of the preceding proposition.\n\n4.1274 The question about the existence of a formal concept is senseless. For no proposition can answer such a question.\n\n(For example, one cannot ask: \u201cAre there unanalysable subject-predicate propositions?\u201d)\n\n4.128 The logical forms are anumerical.\n\nTherefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc.\n\n4.2 The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of the atomic facts.\n\n4.21 The simplest proposition, the elementary proposition, asserts the existence of an atomic fact.\n\n4.211 It is a sign of an elementary proposition, that no elementary proposition can contradict it.\n\n4.22 The elementary proposition consists of names. It is a connexion, a concatenation, of names.\n\n4.221 It is obvious that in the analysis of propositions we must come to elementary propositions, which consist of names in immediate combination.\n\nThe question arises here, how the propositional connexion comes to be.\n\n4.2211 Even if the world is infinitely complex, so that every fact consists of an infinite number of atomic facts and every atomic fact is composed of an infinite number of objects, even then there must be objects and atomic facts.\n\n4.23 The name occurs in the proposition only in the context of the elementary proposition.\n\n4.24 The names are the simple symbols, I indicate them by single letters (x, y, z).\n\nThe elementary proposition I write as function of the names, in the form \u201cfx\u201d, \u201c\u03d5(x,y)\u201d, etc.\n\nOr I indicate it by the letters p, q, r.\n\n4.241 If I use two signs with one and the same meaning, I express this by putting between them the sign \u201c=\u201d.\n\n\u201ca=b\u201d means then, that the sign \u201ca\u201d is replaceable by the sign \u201cb\u201d.\n\n(If I introduce by an equation a new sign \u201cb\u201d, by determining that it shall replace a previously known sign \u201ca\u201d, I write the equation\u2014definition \u2014(like Russell) in the form \u201ca=b Def.\u201d. A definition is a symbolic rule.)\n\n4.242 Expressions of the form \u201ca=b\u201d are therefore only expedients in presentation: They assert nothing about the meaning of the signs \u201ca\u201d and \u201cb\u201d.\n\n4.243 Can we understand two names without knowing whether they signify the same thing or two different things? Can we understand a proposition in which two names occur, without knowing if they mean the same or different things?\n\nIf I know the meaning of an English and a synonymous German word, it is impossible for me not to know that they are synonymous, it is impossible for me not to be able to translate them into one another.\n\nExpressions like \u201ca=a\u201d, or expressions deduced from these are neither elementary propositions nor otherwise significant signs. (This will be shown later.)\n\n4.25 If the elementary proposition is true, the atomic fact exists; if it is false the atomic fact does not exist.\n\n4.26 The specification of all true elementary propositions describes the world completely. The world is completely described by the specification of all elementary propositions plus the specification, which of them are true and which false.\n\n4.27 With regard to the existence of n atomic facts there are\n\nK\n\nn\n\n=\n\n\u2211\n\nv\n=\n0\n\nn\n\n(\n\nn\nv\n\n)\n\n{\\displaystyle \\mathbf {K} _{n}=\\sum _{v=0}^{n}{\\binom {n}{v}}}\n\npossibilities.\n\nIt is possible for all combinations of atomic facts to exist, and the others not to exist.\n\n4.28 To these combinations correspond the same number of possibilities of the truth\u2014and falsehood\u2014of n elementary propositions.\n\n4.3 The truth-possibilities of the elementary propositions mean the possibilities of the existence and non-existence of the atomic facts. 4.31 The truth-possibilities can be presented by\nschemata of the following kind (\"T\" means\n\"true\", \"F\" \"false\". The rows of T's and F's\nunder the row of the elementary propositions mean\ntheir truth-possibilities in an easily intelligible\nsymbolism).\n\np\n\nq\n\nr\n\nT\nT\nT\n\nF\nT\nT\n\nT\nF\nT\n\nT\nT\nF\n\nF\nF\nT\n\nF\nT\nF\n\nT\nF\nF\n\nF\nF\nF\n\np\n\nq\n\nT\nT\n\nF\nT\n\nT\nF\n\nF\nF\n\np\n\nT\n\nF\n\n4.4 A proposition is the expression of agreement\nand disagreement with the truth-possibilities of\nthe elementary propositions.\n\n4.41 The truth-possibilities of the elementary propositions are the conditions of the truth and\nfalsehood of the propositions.\n\n.411 It seems probable even at first sight that the\nintroduction of the elementary propositions is\nfundamental for the comprehension of the other\nkinds of propositions. Indeed the comprehension\nof the general propositions depends palpably on\nthat of the elementary propositions.\n\n4.42 With regard to the agreement and disagreement of a proposition with the truth-possibilities of n elementary propositions there are\n\n\u2211\n\nK\n=\n0\n\nK\n\nn\n\n(\n\nK\n\nn\n\n\u03ba\n\n)\n\n=\n\nL\n\nn\n\n{\\displaystyle \\sum _{K=0}^{K_{n}}{K_{n} \\choose \\kappa }=L_{n}}\n\npossibilities.\n\nAgreement with the truth-possibilities can be expressed by co-ordinating with them in the\nschema the mark \"T\" (true).\n\nAbsence of this mark means disagreement.\n\n4.431 The expression of the agreement and disagreement with the truth-possibilities of the elementary-propositions expresses the truth-conditions of the\nproposition.\nThe proposition is the expression of its truth-\nconditions.\n\n(Frege has therefore quite rightly put them at\nthe beginning, as explaining the signs of his\nlogical symbolism. Only Frege's explanation\nof the truth-concept is false: if \"the true\" and\n\"the false\" were real objects and the arguments\nin ~p etc., then the sense of ~p would by no\nmeans be determined by Frege's determination.)\n\n4.44 The sign which arises from the co-ordination of\nthat mark \"T\" with the truth-possibilities is a\npropositional sign.\n\n4.441 It is clear that to the complex of the signs \"F\"\nand \"T\" no object (or complex of objects) corresponds; any more than to horizontal and vertical\nlines or to brackets. There are no \"logical\nobjects\".\n\nSomething analogous holds of course for all\nsigns, which express the same as the schemata of\n\"T\"and \"F\".\n\n4.442 Thus e.g.\n\n\"\n\np\n\nq\n\nT\nT\nT\n\nF\nT\nT\n\nT\nF\n\nF\nF\nT \"\n\n\"\n\nis a propositional sign.\n\n(Frege's assertion sign \" |- \" is logically altogether meaningless; in Frege (and Russell) it only shows\nthat these authors hold as true the propositions\nmarked in this way.\n\n\"|-\" belongs therefore to the propositions no\nmore than does the number of the proposition. A\nproposition cannot possibly assert of itself that it\nis true.)\n\nIf the sequence of the truth-possibilities in the\nschema is once for all determined by a rule of\ncombination, then the last column is by itself an\nexpression of the truth-conditions. If we write\nthis column as a row the propositional sign becomes:\n\"(T\u2014T) (p,q)\" or more plainly: \"(T T F T) (p,q)\".\n\n(The number of places in the left-hand bracket\nis determined by the number of terms in the right-hand bracket.)\n\n4.45 For n elementary propositions there are Ln\npossible groups of truth-conditions.\n\nThe groups of truth-conditions which belong to\nthe truth-possibilities of a number of elementary\npropositions can be ordered in a series.\n\n4.46 Among the possible groups of truth-conditions\nthere are two extreme cases.\n\nIn the one case the proposition is true for all the\ntruth-possibilities of the elementary propositions.\nWe say that the truth-conditions are tautological.\n\nIn the second case the proposition is false for all\nthe truth-possibilities. The truth-conditions are\nself-contradictory.\n\nIn the first case we call the proposition a\ntautology, in the second case a contradiction.\n\n4.461 The proposition shows what it says, the\ntautology and the contradiction that they say\nnothing.\n\nThe tautology has no truth-conditions, for it is unconditionally true; and the contradiction is on\nno condition true.\n\nTautology and contradiction are without sense.\n\n(Like the point from which two arrows go out in\nopposite directions.)\n\n(I know, e.g. nothing about the weather, when\nI know that it rains or does not rain.)\n\n4.4611 Tautology and contradiction are, however, not\nnonsensical\u00a0; they are part of the symbolism, in the\nsame way that \"0\" is part of the symbolism of\nArithmetic.\n\n4.462 Tautology and contradiction are not pictures of\nthe reality. They present no possible state of\naffairs. For the one allows every possible state\nof affairs, the other none.\n\nIn the tautology the conditions of agreement\nwith the world \u2014 the presenting relations \u2014 cancel\none another, so that it stands in no presenting\nrelation to reality.\n\n4.463 The truth-conditions determine the range, which\nis left to the facts by the proposition.\n\n(The proposition, the picture, the model, are in\na negative sense like a solid body, which restricts\nthe free movement of another: in a positive sense,\nlike the space limited by solid substance, in which\na body may be placed.)\n\nTautology leaves to reality the whole infinite\nlogical space; contradiction fills the whole logical\nspace and leaves no point to reality. Neither of\nthem, therefore, can in any way determine\nreality.\n\n4.464 The truth of tautology is certain, of propositions\npossible, of contradiction impossible.\n\n(Certain, possible, impossible: here we have\nan indication of that gradation which we need in\nthe theory of probability.)\n\n4.465 The logical product of a tautology and a proposition says the same as the proposition. Therefore that product is identical with the proposition.\nFor the essence of the symbol cannot be altered\nwithout altering its sense.\n\n4.466 To a definite logical combination of signs\ncorresponds a definite logical combination of their\nmeanings; every arbitrary combination only corre-\nsponds to the unconnected signs.\n\nThat is, propositions which are true for every\nstate of affairs cannot be combinations of signs at\nall, for otherwise there could only correspond to\nthem definite combinations of objects.\n\n(And to no logical combination corresponds no\ncombination of the objects.)\n\nTautology and contradiction are the limiting\ncases of the combinations of symbols, namely their\ndissolution.\n\n4.4661 Of course the signs are also combined with one\nanother in the tautology and contradiction, i.e.\nthey stand in relations to one another, but these\nrelations are meaningless, unessential to the\nsymbol.\n\n4.5 Now it appears to be possible to give the\nmost general form of proposition; i.e. to give a\ndescription of the propositions of some one sign\nlanguage, so that every possible sense can be\nexpressed by a symbol, which falls under the\ndescription, and so that every symbol which falls\nunder the description can express a sense, if\nthe meanings of the names are chosen accordingly.\n\nIt is clear that in the description of the most\ngeneral form of proposition only what is essential\nto it may be described \u2014 otherwise it would not be\nthe most general form.\n\nThat there is a general form is proved by the\nfact that there cannot be a proposition whose\nform could not have been foreseen (i.e. constructed). The general form of proposition is: Such and such is the case.\n\n4.51 Suppose all elementary propositions were given me: then we can simply ask: what propositions I can build out of them. And these are all propositions and so are they limited.\n\n4.52 The propositions are everything which follows from the totality of all elementary propositions (of course also from the fact that it is the totality of them all). (So, in some sense, one could say, that all propositions are generalizations of the elementary propositions.)\n\n4.53 The general propositional form is a variable.","title":"Tractatus Logico-Philosophicus/4","tradition":"philosophy-ethics","translated_text":null,"word_count":5162}