 Section 0 of Tractatus logico philosophicus. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Recording by Jeffrey Edwards. Tractatus logico philosophicus by Ludwig Wittgenstein, translated by C.K. Ogden. Section 0. Introduction by Bertrand Russell. Mr. Wittgenstein's Tractatus logico philosophicus, whether or not it proved to give the ultimate truth on the matters with which it deals, certainly deserves, by its breadth and scope and profundity, to be considered an important event in the philosophical world. Starting from the principles of symbolism and the relations which are necessary between words and things in any language, it applies the result of this inquiry to various departments of traditional philosophy, showing in each case how traditional philosophy and traditional solutions arise out of ignorance of the principles of symbolism and out of misuse of language. The logical structure of propositions and the nature of logical inference are first dealt with. Hence we pass successively to Theory of Knowledge, Principles of Physics, Ethics, and finally to the Mystical. Bracket das Mustischa. Close Bracket. In order to understand Mr. Wittgenstein's book, it is necessary to realize what is the problem with which he is concerned. In the part of his theory which deals with symbolism, he is concerned with the conditions which would have to be fulfilled by a logically perfect language. There are various problems as regards language. First, there is the problem, what actually occurs in our minds when we use language with the intention of meaning something by it. This problem belongs to psychology. Secondly, there is the problem as to what is the relation subsisting between thoughts, words, or sentences, and that which they refer to or mean. This problem belongs to epistemology. Thirdly, there is the problem of using sentences so as to convey truth rather than falsehood. This belongs to the special sciences dealing with the subject matter of the sentences in question. Fourthly, there is the question, what relation must one fact, bracket, such as a sentence, close bracket, have to another in order to be capable of being a symbol for that other. This last is a logical question and is the one with which Mr. Wittgenstein is concerned. He is concerned with the conditions for accurate symbolism, i.e. for symbolism in which a sentence, quotes, means something quite definite. In practice, language is always more or less vague, so that what we assert is never quite precise. Thus, logic has two problems to deal with in regard to symbolism. One, the conditions for sense rather than nonsense in combinations of words. Two, the conditions for uniqueness of meaning or reference in symbols or combinations of symbols. A logically perfect language has rules of syntax which prevent nonsense and has single symbols which always have a definite and unique meaning. Mr. Wittgenstein is concerned with the conditions for a logically perfect language, not that any language is logically perfect, or that we believe ourselves capable, here and now, of constructing a logically perfect language, but that the whole function of language is to have meaning, and it only fulfills this function in proportion as it approaches to the ideal language which we postulate. The essential business of language is to assert or deny facts. Given the syntax of language, the meaning of a sentence is determined as soon as the meaning of the component words is known. In order that a certain sentence should assert a certain fact, there must, however the language may be constructed, be something in common between the structure of the sentence and the structure of the fact. This is perhaps the most fundamental thesis of Mr. Wittgenstein's theory. That which has to be in common between the sentence and the fact cannot, he contends, be itself, in turn, said in language. It can, in his phraseology, only be shown, not said, for whatever we may say will still need to have the same structure. The first requisite of an ideal language would be that there should be one name for every simple, and never the same name for two different symbols. A name is a simple symbol in the sense that it has no parts which are themselves symbols. In a logically perfect language, nothing that is not simple will have a simple symbol. The symbol for the whole will be a quotes complex containing the symbols for the parts. In speaking of a quotes complex, we are, as will appear later, sinning against the rules of philosophical grammar, but this is unavoidable at the outset. Quote, Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language. They are of the same kind as the question whether the good is more or less identical than the beautiful. Bracket, What is complex in the world is a fact. Facts which are not compounded of other facts are what Mr. Wittgenstein calls soccer halt, whereas a fact which may consist of two or more facts is a tatsaka. Thus, for example, quote Socrates' wise, close quote, is a soccer halt, as well as a tatsaka, whereas quote Socrates' wise and Plato is his pupil, close quote, is a tatsaka, but not a soccer halt. He compares linguistic expression to projection in geometry. A geometrical figure may be projected in many ways, each of these ways corresponding to a different language, but the projective properties of the original figure remain unchanged, whichever of these ways may be adopted. These projective properties correspond to that which in his theory the proposition and the fact must have in common, if the proposition is to assert the fact. In certain elementary ways this is, of course, obvious. It is impossible, for example, to make a statement about two men, Bracket, assuming for the moment that the men may be treated as symbols, close Bracket, without employing two names. And if you are going to assert a relation between the two men, it will be necessary that the sentence in which you make the assertion shall establish a relation between the two names. If we say quote Plato loves Socrates, close quote, the word quotes loves, which occurs between the word quotes Plato and the word quotes Socrates, establishes a certain relation between these two words. And it is owing to this fact that our sentence is able to assert a relation between the persons named by the words quotes Plato and quotes Socrates. Quote, we must not say the complex sign quote A capital R B, close quote, says that quote A stands in a certain relation, capital R to B, close quote. But we must say that quotes A stands in a certain relation to quotes B says that A capital R B, close quote. Bracket 3.1432, close bracket. Mr. Wittgenstein begins his theory of symbolism with the statement, Bracket 2.1, close bracket. Quote, we make to ourselves pictures of facts, close quote. A picture, he says, is a model of the reality, and to the objects in the reality correspond the elements of the picture. The picture itself is a fact. The fact that things have a certain relation to each other is represented by the fact that in the picture, its elements have a certain relation to one another. Quote, in the picture and the pictured, there must be something identical in order that the one can be a picture of the other at all. What the picture must have in common with reality in order to be able to represent it after its manner, rightly or falsely, is its form of representation, close quote, Bracket 2.161, 2.17, close bracket. We speak of a logical picture of a reality when we wish to imply only so much resemblance as is essential to its being a picture in any sense. That is to say, when we wish to imply no more than identity of logical form. The logical picture of a fact, he says, is a gedonka. A picture can correspond or not correspond with the fact and be accordingly true or false, but in both cases it shares the logical form with the fact. The sense in which he speaks of pictures is illustrated by his statement. Quote, 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. Bracket 4.014, close bracket. The possibility of a proposition representing a fact rests upon the fact that in it objects are represented by signs, but are themselves present in the proposition as in the fact. The proposition and the fact must exhibit the same logical quotes manifold, and this cannot be itself represented since it has to be in common between the fact and the picture. Mr. Wittgenstein maintains that everything properly philosophical belongs to what can only be shown, or to what is common between a fact and its logical picture. It results from this view that nothing correct can be said in philosophy. Every philosophical proposition is bad grammar, and the best that we can hope to achieve by philosophical discussion is to lead people to see that philosophical discussion is a mistake. Quote, philosophy is not one of the natural sciences. Bracket. The word quotes philosophy must mean something which stands above or below, but not beside the natural sciences. Close bracket. The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory, but an activity. A philosophical work consists essentially of elucidations. The result of philosophy is not a number of quote philosophical propositions, close quote, but to make propositions clear. Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred, close quote. Bracket, 4.111 and 4.112 close bracket. In accordance with this principle, the things that have to be said in leading the reader to understand Mr. Wittgenstein's theory are all of them things which that theory itself condemns as meaningless. With this proviso, we will endeavor to convey the picture of the world which seems to underlie his system. The world consists of facts. Facts cannot strictly speaking be defined, but we can explain what we mean by saying that facts are what may propositions true or false. Facts may contain parts which are facts or may contain no such parts. For example, quote, Socrates was a wise Athenian, close quote, consists of the two facts, quote, Socrates was wise, close quote, and, quote, Socrates was an Athenian, close quote. A fact which has no parts that are facts is called by Mr. Wittgenstein a soccer health. This is the same thing that he calls an atomic fact. An atomic fact, although it contains no parts that are facts, nevertheless does contain parts. If we may regard, quote, Socrates is wise, close quote, as an atomic fact, we perceive that it contains the constituents, quotes Socrates and quotes wise. If an atomic fact is analyzed as fully as possible, bracket, theoretical, not practical possibility is meant, close bracket, the constituents finally reached maybe called quotes, symbols, or quotes objects. It is a logical necessity demanded by theory, like an electron. His ground for maintaining that there must be symbols is that every complex presupposes a fact. It is not necessarily assumed that the complexity of facts is finite. Even if every fact consists of an infinite number of atomic facts, and if every atomic fact consisted of an infinite number of objects, there would still be objects and atomic facts. Bracket, 4.2211, close bracket. The assertion that there is a certain complex reduces to the assertion that its constituents are related in a certain way, which is the assertion of a fact. Thus, if we give a name to the complex, the name only has meaning in virtue of the truth of a certain proposition, namely the proposition asserting the relatedness of the constituents of the complex. Thus, the naming of complexes presupposes propositions, while propositions presupposes the naming of symbols. In this way, the naming of symbols is shown to be what is logically first in logic. The world is fully described if all atomic facts are known, together with the fact that these are all of them. The world is not described by merely naming all the objects in it. It is necessary also to know the atomic facts of which these objects are constituents. Given this total of atomic facts, every true proposition, however complex, can theoretically be inferred. A proposition, bracket, true or false, close bracket, asserting an atomic fact, is called an atomic proposition. All atomic propositions are logically independent of each other. No atomic proposition implies any other, or is inconsistent with any other. Thus, the whole business of logical inference is concerned with propositions which are not atomic. Such propositions may be called molecular. Fickenstein's theory of molecular propositions turns upon his theory of the construction of truth functions. A truth function of a proposition p is a proposition containing p, and such that its truth or falsehood depends only upon the truth or falsehood of p. And similarly, a truth function of several propositions, p, q, r, dot, dot, dot, is one containing p, q, r, dot, dot, dot, and such that its truth or falsehood depends only upon the truth or falsehood of p, q, r, dot, dot. It might seem at first sight, as though there were other functions of propositions besides truth functions, such, for example, would be quote, capital A believes p, close quote. For in general, capital A will believe some true propositions and some false ones, unless he is an exceptionally gifted individual. We cannot infer that p is true from the fact that he believes it, or that p is false from the fact that he does not believe it. Other apparent exceptions would be such as quote, p is a very complex proposition, close quote, or quote, p is a proposition about Socrates, close quote. Mr. Wittgenstein maintains, however, for reasons which will appear presently, that such exceptions are only apparent, and that every function of a proposition is really a truth function. It follows that if we can define truth functions generally, we can obtain a general definition of all propositions in terms of the original set of atomic propositions. This Wittgenstein proceeds to do. It has been shown by Dr. Scheffer, Bracket, Trans, Am, Math, Sock, following 14 pages 481 to 488, close bracket, that all truth functions of a given set of propositions can be constructed out of either of the two functions, quote, not p, or not q, close quote, or quote, not p, and not q, close quote. Wittgenstein makes use of the latter, assuming a knowledge of Dr. Scheffer's work, the manner in which other truth functions are constructed out of, quote, not p, and not q, close quote, is easy to see. Quote, not p, and not p, close quote, is equivalent to quote, not p, close quote. Hence, we obtain a definition of negation in terms of our primitive function. Hence, we can define quote, p, or q, close quote, since this is the negation of quote, not p, and not q, close quote, i.e., of our primitive function. The development of other truth functions out of, quote, not p, close quote, and quote, p, or q, close quote, is given in detail at the beginning of Principia Mathematica. This gives all that is wanted when the propositions, which are arguments to our truth function, are given by enumeration. Wittgenstein, however, by a very interesting analysis, succeeds in extending the process to general propositions, i.e., to cases where the propositions, which are arguments to our truth function, are not given by enumeration, but are given as all those satisfying some condition. For example, let fx be a propositional function, bracket i.e., a function whose values are propositions, close bracket, such as quote, x is human, close quote. Then, the various values of fx form a set of propositions. We may extend the idea, quote, not p, and not q, close quote, so as to apply two simultaneous denial of all the propositions, which are values of fx. In this way, we arrive at the proposition, which is ordinarily represented in Mathematica logic by the words, quote, fx is false for all values of x, close quote. The negation of this would be the proposition, quote, there is at least one x for which fx is true, close quote, which is represented by, quote, bracket, there exists symbol x, close bracket, and symbol fx, close quote. If we had started with not fx, instead of fx, we should have arrived at the proposition, quote, fx is true for all values of x, close quote, which is represented by, quote, bracket, x, close bracket, and symbol fx, close quote. Wittgenstein's method of dealing with general propositions, square bracket, in essence, quote, bracket, x, close bracket, and symbol fx, close quote, and quote, bracket, there exists symbol x, close bracket, and symbol fx, close quote, close square bracket, differs from previous methods by the fact that the generality comes only in specifying the set of propositions concerned, and when this has been done, the building up of truth functions proceeds exactly as it would in the case of a finite number of enumerated arguments, p, q, r, dot, dot, dot. Mr. Wittgenstein's explanation of his symbolism at this point is not quite fully given in the text. The symbol he uses is, square bracket, line over p, comma, line over xi, comma, capital N, bracket, line over xi, close bracket, close square bracket. The following is the explanation of this symbol. Line over p stands for all atomic propositions. Line over xi stands for any set of propositions. Capital N, bracket, line over xi, close bracket, stands for the negation of all the propositions making up xi. The whole symbol, square bracket, line over p, comma, line over xi, comma, capital N, bracket, line over xi, close bracket, close square bracket means whatever can be obtained by taking any selection of atomic propositions, negating them all, then taking any selection of the set of propositions now obtained, together with any of the originals, and so on indefinitely. This is, he says, the general truth function, and also the general form of proposition. What is meant is somewhat less complicated than it sounds. The symbol is intended to describe a process by the help of which, given the atomic propositions, all others can be manufactured. The process depends upon, a, Sheffer's proof that all truth functions can be obtained out of simultaneous negation, i.e., out of, quote, not p and not q, close quote. b. Mr. Wittgenstein's theory of the derivation of general propositions from conjunctions and disjunctions. c. The assertion that a proposition can only occur in another proposition as argument to a truth function. Given these three foundations, it follows that all propositions, which are not atomic, can be derived from such as are, by a uniform process, and it is this process which is indicated by Mr. Wittgenstein's symbol. From this uniform method of construction, we arrive at an amazing simplification of the theory of inference, as well as a definition of the sort of propositions that belong to logic. The method of generation, which has just been described, enables Wittgenstein to say that all propositions can be constructed in the above manner from atomic propositions, and in this way, the totality of propositions is defined. Bracket, the apparent exceptions which we mentioned above, are dealt with in a manner which we shall consider later, close bracket. Wittgenstein is enabled to assert that propositions are all that follows from the totality of atomic propositions, bracket, together with the fact that it is the totality of them, close bracket. That a proposition is always a truth function of atomic propositions, and that if P follows from Q, the meaning of P is contained in the meaning of Q, from which of course it results that nothing can be deduced from an atomic proposition. All the propositions of logic he maintains are tautologies, such for example as, quote, P or not P, close quote. The fact that nothing can be deduced from an atomic proposition has interesting applications, for example to causality. There cannot, in Wittgenstein's logic, be any such thing as a causal nexus. Quote, the events of the future, close quote, he says, quote, cannot be inferred from those of the present. Superstition is the belief in the causal nexus, close quote. That the sun will rise tomorrow is a hypothesis. We do not in fact know whether it will rise, since there is no compulsion according to which one thing must happen because another happens. Let us now take up another subject, that of names. In Wittgenstein's theoretical, logical language, names are only given to symbols. We do not give two names to one thing, or one name to two things. There is no way, whatever, according to him, by which we can describe the totality of things that can be names. In other words, the totality of what there is in the world. In order to be able to do this, we should have to know of some property which must belong to everything by a logical necessity. It has been sought to find such a property in self-identity. But the conception of identity is subjected by Wittgenstein to a destructive criticism from which there seems no escape. The definition of identity by means of the identity of indiscernible is rejected, because the identity of indiscernible appears to be not a logically necessary principle. According to this principle, x is identical with y, if every property of x is a property of y. But it would, after all, be logically possible for two things to have exactly the same properties. If this does not, in fact, happen, that is an accidental characteristic of the world, not a logically necessary characteristic, and accidental characteristics of the world must, of course, not be admitted into the structure of logic. Mr. Wittgenstein accordingly banishes identity and adopts the convention that different letters are to mean different things. In practice, identity is needed as between a name and a description or between two descriptions. It is needed for such propositions as, quote, Socrates is the philosopher who drank the hemlock, close quote, or quote, even prime is the next number after one, close quote. For such uses of identity, it is easy to provide on Wittgenstein's system. The rejection of identity removes one method of speaking of the totality of things, and it will be found that any other method that may be suggested is equally fallacious, so at least Wittgenstein contends, and I think rightly. This amounts to saying that quote's object is a pseudo-concept. To say quote x is an object, close quote, is to say nothing. It follows from this that we cannot make such statements as, quote, there are more than three objects in the world, close quote, or, quote, there are an infinite number of objects in the world, close quote. Objects can only be mentioned in connection with some definite property. We can say, quote, there are more than three objects which are human, close quote, or, quote, there are more than three objects which are red, close quote. For in these statements, the word object can be replaced by a variable in the language of logic. The variable being one which satisfies in the first case the function, quote, x is human, close quote. In the second the function, quote, x is red, close quote. But when we attempt to say, quote, there are more than three objects, close quote. This substitution of the variable for the word, quote, object becomes impossible, and the proposition is therefore seen to be meaningless. We hear touch one instance of Wittgenstein's fundamental thesis, that it is impossible to say anything about the world as a whole, and that whatever can be said has to be about bounded portions of the world. This view may have been originally suggested by a notation, and if so, that is much in its favor. For a good notation has a subtlety and suggestiveness, which at times make it seem almost like a live teacher. Notational irregularities are often the first sign of philosophical errors, and a perfect notation would be a substitute for thought. But although notation may have first suggested to Mr. Wittgenstein the limitation of logic to things within the world as opposed to the world as a whole, yet the view, once suggested, is seen to have much else to recommend it. Whether it is ultimately true, I do not, for my part, profess to know. In this introduction, I am concerned to expound it, not to pronounce upon it. According to this view, we could only say things about the world as a whole if we could get outside the world, if, that is to say, it seems to be for us the whole world. Our world may be bounded for some superior being who can survey it from above, but for us, however finite it may be, it cannot have a boundary, since it has nothing outside it. Wittgenstein uses, as an analogy, the field of vision. Our field of vision does not, for us, have a visual boundary, just because there is nothing outside it. And in like manner, our logical world has no logical boundary because our logic knows of nothing outside it. These considerations lead him to a somewhat curious discussion of solipsism. Logic, he says, fills the world. The boundaries of the world are also its boundaries. In logic, therefore, we cannot say there is this and this in the world, but not that. For to say so would apparently presuppose that we exclude certain possibilities, and this cannot be the case, since it would require that logic should go beyond the boundaries of the world as if it could contemplate these boundaries from the other side also. What we cannot think, we cannot think. Therefore, we also cannot say what we cannot think. This, he says, gives the key to solipsism. What solipsism intends is quite correct, but this cannot be said. It can only be shown that the world is my world appears in the fact that the boundaries of language, bracket, the only language I understand, close bracket, indicate the boundaries of my world. The metaphysical subject does not belong to the world, but is a boundary of the world. We must take up next the question of molecular propositions, which are at first sight not truth functions of the propositions that they contain, such for example as, quote, capital A believes P, close quote. Wittgenstein introduces this subject in the statement of his position, namely that all molecular functions are truth functions. He says, bracket, 5.54, close bracket, quote, in the general propositional form, propositions occur in a proposition only as basis of truth operations, close quote. At first sight, he goes on to explain it seems as if a proposition could also occur in other ways. For example, quote, capital A believes P, close quote. Here it seems superficially as if the proposition P stood in a sort of relation to the object, capital A. Quote, but it is clear that, quote, capital A believes that P, close quote. Quote, capital A thinks P, close quote. Quote, capital A says P, close quote. R of the form enumerated arguments, P, Q, R, dot, dot, dot. Quote, P says P, close quote. And here we have no coordination of a fact in an object, but a coordination of facts by means of a coordination of their objects, close quote. Bracket, 5.542, close bracket. What Mr. Wittgenstein says here is said so shortly that its point is not likely to be clear to those who have not in mind the controversies with which he is concerned. The theory with which he is disagreeing will be found in my articles on the nature of truth and falsehood in philosophical essays and proceedings of the Aristotelian Society, 1906 to 1907. The problem at issue is the problem of the logical form of belief, i.e., what is the scheme of representing what occurs when a man believes? Of course, the problem applies not only to belief, but also to a host of other mental phenomena which may be called propositional attitudes, doubting, considering, desiring, etc. In all these cases, it seems natural to express the phenomena in the form, quote, capital A doubts P, close quote. Quote, capital A desires P, close quote, etc., which makes it appear as though we are dealing with a relation between a person and a proposition. This cannot, of course, be the ultimate analysis, since persons are fictions and so are propositions, except in the sense in which they are facts on their own account. A proposition, considered as a fact on its own account, may be a set of words which a man says over to himself or a complex image or train of images passing through his mind or a set of incipient bodily movements. It may be any one of innumerable different things. The proposition as a fact on its own account, for example, the actual set of words the man pronounces to himself, is not relevant to logic. What is relevant to logic is that common element among all these facts, which enables him, as we say, to mean the fact which the proposition asserts. To psychology, of course, more is relevant. For a symbol does not mean what it symbolizes in virtue of a logical relation alone, but in virtue also of a psychological relation of intention or association or whatnot. The psychological part of meaning, however, does not concern the logician. What does concern him in this problem of belief is the logical schema. It is clear that when a person believes a proposition, the person, considered as a metaphysical subject, should have to be assumed in order to explain what is happening. What has to be explained is the relation between the set of words, which is the proposition considered as a fact on its own account, and the quote's objective fact, which makes the proposition true or false. This reduces ultimately to the question of the meaning of propositions, that is to say, the meaning of propositions is the only non-psychological portion of the problem involved in the analysis of belief. The problem is simply one of a relation of two facts, namely, the relation between the series of words used by the believer and the fact which makes these words true or false. The series of words is a fact just as much as what makes it true or false is a fact. The relation between these two facts is not unanalyzable, since the meaning of a proposition results from the meaning of its constituent words. The meaning of the series of words, which is a proposition, is a function of the meaning of the separate words. Accordingly, the proposition as a whole does not really enter into what has to be explained in explaining the meaning of a proposition. It would perhaps help to suggest the point of view which I am trying to indicate. To say that in the cases which have been considered, the proposition occurs as a fact, not as a proposition. Such a statement, however, must not be taken too literally. The real point is that in believing, desiring, etc., what is logically fundamental is the relation of a proposition considered as a fact to the fact which makes it true or false, and that this relation of two facts is reducible to a relation of their constituents. Thus, the proposition does not occur at all in the same sense in which it occurs in a truth function. There are some respects in which, as it seems to me, Mr. Wittgenstein's theory stands in need of greater technical development. This applies in particular to his theory of number, bracket 6.02 ff, close bracket, which, as it stands, is only capable of dealing with finite numbers. No logic can be considered adequate until it has been shown to be capable of dealing with transfinite numbers. I do not think there is anything in Mr. Wittgenstein's system impossible for him to fill this lacuna. More interesting than such questions of comparative detail is Mr. Wittgenstein's attitude towards the mystical. His attitude upon this grows naturally out of his doctrine in pure logic, according to which the logical proposition is a picture, bracket, true or false, close bracket, of the fact, and has in common with the fact a certain structure. It is this common structure which makes it capable of being a picture of the fact, but the structure cannot itself be put into words, since it is a structure of words, as well as of the facts to which they refer. Everything, therefore, which is involved in the very idea of expressiveness of language must remain incapable of being expressed in language, and is, therefore, inexpressible in a perfectly precise sense. This inexpressible contains, according to Mr. Wittgenstein, the whole of logic and philosophy. The right method of teaching philosophy, he says, would be to confine oneself to propositions of the sciences, stated with all possible clearness and exactness, leaving philosophical assertions to the learner, and proving to him, whenever he made them, that they are meaningless. It is true that the fate of Socrates might be fallaman who attempted this method of teaching, but we are not to be deterred by that fear, if it is the only right method. It is not this that causes some hesitation in accepting Mr. Wittgenstein's position, in spite of the very powerful arguments which he brings to its support. What causes hesitation is the fact that, after all, Mr. Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the skeptical reader that, possibly, there may be some loophole through a hierarchy of languages or by some other exit. The whole subject of ethics, for example, is placed by Mr. Wittgenstein in the mystical, inexpressible region. Nevertheless, he is capable of conveying his ethical opinions. His defense would be that what he calls the mystical can be shown, although it cannot be said. It may be that this defense is adequate, but, for my part, I confess that it leaves me with a certain sense of intellectual discomfort. There is one purely logical problem in regard to which these difficulties are peculiarly acute. I mean the problem of generality. In the theory of generality, it is necessary to consider all propositions of the form fx, where fx is a given propositional function. This belongs to the part of logic which can be expressed, according to Mr. Wittgenstein's system. But the totality of possible values of x, which might seem to be involved in the totality of propositions of the form fx, is not admitted by Mr. Wittgenstein among the things that can be spoken of. For this is no other than the totality of things in the world, and thus involves the attempt to conceive the world as a whole. Quote, the feeling of the world as a bounded whole is the mystical. Hence, the totality of the values of x is mystical. This is expressly argued when Mr. Wittgenstein denies that we can make propositions as to how many things there are in the world, as, for example, that there are more than three. These difficulties suggest to my mind some such possibility as this, that every language has, as Mr. Wittgenstein says, a structure concerning which in the language nothing can be said, but that there may be another language dealing with the structure of the first language and having itself a new structure, and that to this hierarchy of languages there may be no limit. Mr. Wittgenstein would, of course, reply that his whole theory is applicable unchanged to the totality of such languages. The only retort would be to deny that there is any such totality. The totality is concerning which Mr. Wittgenstein holds that it is impossible to speak logically are nevertheless not by him to exist, and are the subject matter of his mysticism. The totality resulting from our hierarchy would be not merely logically inexpressible, but a fiction, a mere delusion, and, in this way, the supposed sphere of the mystical would be abolished. Such a hypothesis is very difficult, and I can see objections to it, which at the moment I do not know how to answer. Yet, I do not see how any easier hypothesis can escape from Mr. Wittgenstein's conclusions. Even if this very difficult hypothesis should prove tenable, it would leave untouched a very large part of Mr. Wittgenstein's theory, though possibly not the part upon which he himself would wish to lay most stress. As one with a long experience of the difficulties of logic and of the deceptiveness of theories which seem irrefutable, I find myself unable to be sure of the rightness of a theory merely on the ground that I cannot see any point but to have constructed a theory of logic, which is not at any point obviously wrong, is to have achieved a work of extraordinary difficulty and importance. This merit, in my opinion, belongs to Mr. Wittgenstein's book and makes it one which no serious philosopher can afford to neglect. Bertrand Russell May 1922 End of Section Zero Recording by Jeffrey Edwards Section One of Tractatus Logico Philosophicus This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org Recording by Jeffrey Edwards Tractatus Logico Philosophicus by Ludwig Wittgenstein translated by C.K. Ogden Section One Preface This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it or similar thoughts. It is therefore not a textbook. Its object would be attained if it afforded pleasure to one who read it with understanding. The book deals with the problems of philosophy as I believe that the method of formulating these problems rests on the misunderstanding of the logic of our language. Its whole meaning could be summed up somewhat as follows. What can be said at all can be said clearly and whereof one cannot speak thereof one must be silent. The book will, therefore, draw a limit to thinking or rather, not to thinking but to the expression of thoughts for, in order to draw a limit to thinking we should have to be able to think both sides of this limit. Bracket, we should therefore have to be able to think what cannot be thought. Close bracket. The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense. How far my efforts agree with those of other philosophers I will not decide. Indeed, what I have here written has no sources because it is indifferent to me whether what I have thought has already been thought before me by another. I will only mention that to the great works of Frigga and the writings of my friend Bertrand Russell I owe in large measure the stimulation of my thoughts. If this work has a value it consists in two things. First, that in it thoughts are expressed and that has been hit on the head. Here I am conscious that I have fallen far short of the possible simply because my powers are insufficient to cope with the task. May others come and do it better. On the other hand the truth of the thoughts communicated here seems to me unassailable and definitive. I am therefore of the opinion that the problems have in essentials being finally solved and that this work secondly consists in the fact that it shows how little has been done when these problems have been solved. LW Vienna 1918 1 The world is everything that is the case. 1.1 The world is the totality of facts not of things. 1.11 The world is determined by the facts and by these being all the facts. 1.12 For the totality of facts determines both what is the case and also all that is not the case. 1.13 The facts in logical space are the world. 1.2 The world divides into facts. 1.21 Anyone can either be the case or not be the case and everything else remain the same. 2. What is the case? The fact is the existence of atomic facts. 2.01 An atomic fact is a combination of objects bracket entities things close bracket 2.01 It is essential to a thing that it can be a constituent part of an atomic fact. In logic, nothing is accidental. If a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing. 2.0121 It would, so to speak, appear as an accident when to a thing that could exist alone on its own account subsequently a state of affairs could be made to fit. If things can occur in atomic facts this possibility must already lie in them. Bracket A logical entity cannot be merely possible. Logic treats of every possibility and all possibilities are its facts. Close bracket Just as we cannot think of spatial objects at all apart from space or temporal objects apart from time so we cannot think of any object apart from the possibility of its connection with other things. If I can think of an object in the context of an atomic fact I cannot think of it apart from the possibility of this context. 2.0122 The thing is independent insofar as it can occur in all possible circumstances but this form of independence is a form of connection with the atomic fact a form of dependence Bracket it is impossible for words Close bracket 2.0123 If I know an object then I also know all the possibilities of its occurrence in atomic facts Bracket Every such possibility must lie in the nature of the object Close bracket A new possibility cannot subsequently be found 2.01231 In order to know an object I must know not its external but all its internal qualities 2.0124 If all objects are given then thereby are all possible atomic facts also given 2.013 Everything is, as it were in a space of possible atomic facts I can think of this space as empty but not of the thing without the space 2.0131 A spatial object must lie in infinite space Bracket A point in space is an argument place Close bracket The visual field need not be red but it must have a color it has, so to speak a color space around it a tone must have a pitch the object of the sense of touch a hardness, etc 2.014 Objects contain the possibility of all states of affairs 2.0141 The possibility of its occurrence in atomic facts is the form of the object 2.02 The object is simple 2.0201 Every statement about complexes can be analyzed into a statement about their constituent parts and into those propositions which completely describe the complexes 2.021 Objects form the substance of the world therefore they cannot be compound 2.0211 If the world had no substance then whether a proposition would depend on whether another proposition was true 2.0212 It would then be impossible to form a picture of the world Bracket, true or false Close bracket 2.022 It is clear that however different from the real one an imagined world may be it must have something a form in common with the real world 2.023 This fixed form consists of the objects 2.0231 The substance of the world can only determine a form and not any material properties for these are first presented by the propositions first formed by the configuration of the objects 2.0232 Roughly speaking objects are colorless 2.0233 Two objects of the same logical form are apart from their external properties only differentiated from one another in that they are different 2.02331 Either a thing has properties which no other has and then one can distinguish it straight away from the others by a description and refer to it or on the other hand there are several things which have the totality of their properties in common and then it is quite impossible to point to any one of them for if a thing is not distinguished by anything I cannot distinguish it for otherwise it would be distinguished 2.024 Substance is what exists independently of what is the case 2.025 It is form and content 2.0251 Space Time and color are forms of objects 2.026 Only if there are objects can there be a fixed form of the world 2.027 The fixed, the existent and the object are one 2.0271 The object is the fixed the existent The configuration is the changing the variable 2.0272 The configuration of the objects forms the atomic fact 2.03 In the atomic fact objects hang one in another like the links of a chain 2.031 In the atomic fact the objects are combined in a definite way 2.032 The way in which objects hang together in the atomic fact is the structure of the atomic fact 2.033 The form is the possibility of the structure 2.034 The structure of the fact consists of the structures of the atomic facts 2.04 The totality of existent atomic facts is the world 2.05 The totality of existent atomic facts also determines which atomic facts do not exist 2.06 The existence and non-existence of atomic facts is the reality Bracket The existence of atomic facts we also call a positive fact their non-existence a negative fact Close Bracket 2.061 Atomic facts are independent of one another 2.062 From the existence or non-existence of an atomic fact we cannot infer the existence or non-existence of another 2.063 The total reality is the world 2.1 We make to ourselves pictures of facts 2.11 The picture presents the facts in logical space the existence and non-existence of atomic facts 2.12 The picture is a model of reality 2.13 To the objects correspond in the picture the elements of the picture 2.131 The elements of the picture stand in the picture for the objects 2.14 The picture consists in the fact that its elements are combined with one another in a definite way 2.141 The picture is a fact 2.15 that the elements of the picture are combined with one another in a definite way represents that the things are so combined with one another This connection of the elements of the picture is called its structure and the possibility of this structure is called the form of representation of the picture 2.151 The form of representation is the possibility that the things are combined with one another as are the elements of the picture 2.1511 Thus the picture is linked with reality It reaches up to it 2.1512 It is like a scale applied to reality 2.15121 Only the outermost points of the dividing lines touch the object to be measured 2.1513 According to this view the representing relation which makes it a picture also belongs to the picture 2.1514 The representing relation consists of the coordinations of the elements of the picture and the things 2.1515 These coordinations are, as it were the feelers of its elements with which the picture touches reality 2.16 In order to be a picture a fact must have something in common with what it pictures 2.161 There must be something identical in order that the one can be a picture of the other at all 2.17 What the picture must have in common with reality in order to be able to represent it after its manner rightly or falsely is its form of representation 2.171 The picture can represent every reality whose form it has the spatial picture everything spatial the colored 2.172 The picture, however, cannot represent its form of representation it shows it forth 2.173 The picture represents its object from without bracket its standpoint is its form of representation close bracket therefore the picture represents its object rightly or falsely 2.174 But the picture cannot place itself on the side of its form of representation 2.18 Whatever picture of whatever form must have in common with reality in order to be able to represent it at all rightly or falsely is the logical form that is the form of reality 2.181 If the form of representation is the logical form then the picture is called a logical picture 2.182 Every picture is also a logical picture bracket on the other hand for example not every picture is spatial close bracket 2.19 The logical picture can depict the world 2.2 The picture has the logical form of representation in common with what it pictures 2.201 The picture depicts reality of existence and non-existence of atomic facts 2.202 The picture represents a possible state of affairs in logical space 2.203 The picture contains the possibility of the state of affairs which it represents 2.21 The picture agrees with reality or not it is right or wrong true or false 2.22 The picture represents what it represents independently of its truth or falsehood through the form of representation 2.221 What the picture represents is its sense 2.222 In the agreement or disagreement of its sense with reality its truth or falsity consists 2.223 In order to discover whether the picture is true or false we must compare it with reality 2.224 It cannot be discovered from the picture alone whether it is true or false 2.225 There is no picture which is a priori true 3. The logical picture of the facts is the thought 3.001 Quote an atomic fact is thinkable close quote means we can imagine it 3.01 The totality of true thoughts is a picture of the world 3.02 The thought contains the possibility of the state of affairs which it thinks thinkable is also possible 3.03 We cannot think anything unlogical for otherwise we should have to think unlogically 3.031 It used to be said that God could create everything except what was contrary to the laws of logic The truth is we could not say of an quotes unlogical world how it would look 3.032 To present in language anything which quotes contradicts logic is as impossible as in geometry to present by its coordinates a figure which contradicts the laws of space or to give the coordinates of a point which does not exist 3.0321 We could represent spatially an atomic fact which contradicted the laws of physics but not one which contradicted the laws of geometry 3.04 an a priori true thought would be one whose possibility 3.05 only we could know a priori that a thought is true if its truth was to be recognized from the thought itself bracket without an object of comparison close bracket 3.1 In the proposition the thought is expressed perceptibly through the senses 3.11 We use the sensibly perceptible sign bracket, sound or written sign etc. close bracket of the proposition as a projection of the possible state of affairs the method of projection is the thinking of the sense of the proposition 3.12 the sign through which we express the thought I call the proposition sign and the proposition is the proposition sign in its projective relation to the world 3.13 to the proposition belongs everything which belongs to the projection but not what is projected therefore the possibility of what is projected but not this itself in the proposition therefore its sense is not yet contained but the possibility of expressing it bracket the content of the proposition close quote means the content of the significant proposition close bracket in the proposition the form of its sense is contained but not its content 3.14 the propositional sign consists in the fact that its elements the words are combined in it in a definite way the propositional sign is a fact 3.141 the proposition is not a mixture of words bracket just as the musical theme is not a mixture of tones close bracket the proposition is articulate 3.142 only facts can express a sense a class of names cannot 3.143 that the propositional sign is a fact is concealed by the ordinary form of expression written or printed bracket for in the printed proposition for example the sign of a proposition does not appear essentially different from a word thus it was possible for Frigga to call the proposition a compounded name close bracket 3.1431 the essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects bracket such as tables, chairs, books close bracket instead of written signs the mutual spatial position of these things then expresses the sense of the proposition 3.1432 we must not say quote a complex sign quotes A capital R B says quote A stands in relation R to B close quote but we must say quote that quotes A stands in a certain relation to quotes B says that A capital R B 3.144 states of affairs can be described but not named bracket names resemble points propositions resemble arrows they have senses close bracket 3.2 in propositions thoughts can be so expressed that to the objects of the thoughts correspond the elements of the propositional sign 3.201 quotes simple signs and the proposition quotes completely analyzed 3.202 the simple signs employed in propositions are called names 3.203 the name means the object the object is its meaning bracket quotes A is the same sign as quotes A to the configuration of the simple signs in the propositional sign corresponds the configuration of the objects in the state of affairs 3.22 in the proposition the name represents the object 3.221 objects I can only name signs represent them I can only speak of them I cannot assert them a proposition can only say how a thing is not what it is 3.23 the postulate of the possibility of the simple signs is the postulate of the determinateness of the sense 3.24 a proposition about a complex stands in internal relation to the proposition about its constituent part a complex can only be given by its description and this will either be right or wrong the proposition in which there is mention of a complex if this does not exist it becomes not nonsense but simply false that a propositional element signifies a complex can be seen from an indeterminateness in the propositions in which it occurs we know that everything is not yet determined by this proposition bracket the notation for generality contains a prototype close bracket the combination of the symbols of a complex and a simple symbol can be expressed by a definition there is one and only one complete analysis of the proposition 3.251 the proposition expresses what it expresses in a definite and clearly specifiable way the proposition is articulate 3.26 the name cannot be analyzed further by any definition it is a primitive sign 3.261 every defined sign signifies via those signs by which it is defined and the definitions show the way two signs one a primitive sign and one defined by primitive signs cannot signify in the same way names cannot be taken to pieces by definition bracket nor any sign which alone and independently has a meaning close bracket 3.262 what does not get expressed in the sign is shown by its application what the signs conceal 3.263 the meanings of primitive signs can be explained by elucidations elucidations are propositions which contain the primitive signs they can therefore only be understood when the meanings of these signs are already known 3.3 only the proposition has sense only in the context of a proposition has a name meaning 3.31 every part of a proposition has an expression bracket a symbol bracket the proposition itself is an expression close bracket expressions are everything essential for the sense of the proposition that propositions can have in common with one another an expression characterizes a form and a content 3.311 an expression presupposes the forms of all propositions in which it can occur 3.312 it is therefore represented by the general form of the propositions which it characterizes and in this form the expression is constant and everything else variable 3.313 an expression is thus presented by a variable whose values are the propositions which contain the expression bracket in the limiting case the variable becomes constant the expression a proposition close bracket 3.313 quotes propositional variable 3.314 an expression has meaning only in a proposition every variable can be conceived as a propositional variable bracket including the variable name close bracket 3.315 if we change a constituent part of a proposition into a variable there is a class of propositions which are all the values of the resulting variable proposition this class in general still depends on what? by arbitrary agreement we mean by parts of that proposition but if we change all those signs whose meaning was arbitrarily determined into variables there always remains such a class but this is now no longer dependent on any agreement it depends only on the nature of the proposition it corresponds to a logical form to a logical prototype 3.316 what values the propositional variable can assume is determined the determination of the values is the variable 3.317 the determination of the values of the propositional variable is done by indicating the propositions whose common mark the variable is the determination is a description of these propositions the determination will therefore deal only with symbols not with their meanings only this is essential to the determination that is is only a description of symbols and asserts nothing about what is symbolized the way in which we describe the propositions is not essential 3.318 I conceive the proposition like Frigga and Russell as a function of the expressions contained in it 3.32 the sign is the part of the symbol perceptible by the senses 3.321 two different symbols can therefore have the sign bracket, the written sign or the sound sign close bracket in common they then signify in different ways 3.322 it can never indicate the common characteristic of two objects that we symbolize them with the same signs but by different methods of symbolizing for the sign is arbitrary we could therefore equally well choose two different signs one in the symbolization 3.323 in the language of everyday life it very often happens that the same word signifies in two different ways and therefore belongs to two different symbols or the two words which signify in different ways are apparently applied in the same way in the proposition thus the word quotes is appears as the copula as the sign of equality and as the expression of existence quotes to exist as an intransitive verb like quotes to go quotes identical as an adjective we speak of something but also of the fact of something happening bracket in the proposition quote green is green close quote where the first word is a proper name as the last an adjective these words have not merely different meanings but they are different symbols 3.324 thus there easily arise the most fundamental confusions bracket of which the whole of philosophy is full close bracket 3.325 in order to avoid these errors we must employ a symbolism which excludes them by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways a symbolism a grammar of logical syntax bracket the logical symbolism of free and wrestle is such a language which however does still not exclude all errors close bracket 3.326 in order to recognize the symbol in the sign we must consider the significant use 3.327 the sign determines a logical form only together with its logical syntactic application 3.328 if a sign is not necessary then it is meaningless that is the meaning of Occam's razor bracket if everything in the symbolism works as though a sign had meaning then it has meaning close bracket 3.33 in logical syntax the meaning of a sign ought never to play a role it must admit of being established without mention being thereby made it ought to presuppose only the description of the expressions 3.331 from this observation we get a further view into Russell's theory of types Russell's error is shown by the fact that in drawing up his symbolic rules he has to speak about the things his signs mean 3.332 no proposition can say anything about itself because the propositional sign cannot be contained in itself bracket that is the quote whole theory of types close quote close bracket 3.333 a function cannot be its own argument because the functional sign already contains the prototype of its own argument and it cannot contain itself if for example we suppose that the function capital F bracket could be its own argument then there would be a proposition quote capital F bracket capital F bracket close quote and in this the outer function capital F and the inner function capital F must have different meanings for the inner has the form psi bracket the outer the form psi bracket f x close bracket close bracket common to both functions is only the letter quotes capital F which by itself signifies nothing this is at once clear if instead of quote capital F bracket close bracket close quote we write bracket there exists symbol phi close bracket colon capital F bracket phi u close bracket and symbol phi 3.334 the rules of logical syntax must follow of themselves if we only know how every single sign signifies 3.34 a proposition possesses essential and accidental features accidental are the features which are due to a particular way of producing the propositional sign essential are those which alone enable the proposition to express its sense 3.341 is therefore that which is common to all propositions which can express the same sense and in the same way in general the essential in a symbol is that which all symbols which can fulfill the same purpose have in common 3.3411 one could therefore say the real name is that which all symbols which signify an object have in common it would then follow step by step that no sort of composition 3.342 in our notations there is indeed something arbitrary but this is not arbitrary namely that if we have determined anything arbitrarily then something else must be the case bracket this results from the essence of the notation close bracket 3.3421 a particular method of symbolizing may be unimportant but it is always important and this happens as a rule in philosophy the single thing proves over and over again to be unimportant but the possibility of every single thing reveals something about the nature of the world 3.343 definitions are rules for the translation of one language into another every correct symbolism must be translatable into every other according to such rules it is this which all have in common 3.344 what signifies in the symbol is what is common to all those symbols by which it can be replaced according to the rules of logical syntax 3.3441 we can, for example express what is common to all notations for the truth functions as follows it is common to them that they all, for example can be replaced by the notations of quotes not symbol p bracket quote not p close quote close bracket and quote p or symbol q close quote bracket quote p or q close quote close bracket bracket herewith is indicated 3.3442 the sign of the complex is not arbitrarily resolved in the analysis in such a way that its resolution would be different in every propositional structure 3.4 the proposition determines a place in logical space the existence of this logical place is guaranteed by the existence of the constituent parts alone by the existence of the significant proposition 3.41 the propositional sign and the logical coordinates that is the logical place 3.411 the geometrical and the logical place agree in that each is the possibility of an existence 3.42 although a proposition may only determine one place in logical space the whole logical space must already be given by it bracket otherwise denial the logical product would always introduce new elements in coordination close bracket bracket the logical scaffolding around the picture determines the logical space the proposition reaches through the whole logical space close bracket 3.5 the applied thought propositional sign is the thought end of section 1