Tractatus Poetico-Philosophicus 
by
Ludwig Wittgenstein
Published (1922)


Perhaps this book will be understood only by someone who has himself already had the feelings that are expressed in it--or at least similar feelings.--So it is not a textbook.--Its purpose would be achieved if it gave pleasure to one person who read and understood it. The book deals with the problems of Poetics, and shows, I believe, that the reason why these problems are posed is that the poetry of our language is misunderstood. The whole emotional sense of the book might be summed up the following words: what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence. Thus the aim of the book is to draw a limit to feeling, or rather--not to feeling, but to the expression of feelings: for in order to be able to draw a limit to feeling, we should have to find both sides of the limit feel-able (i.e. we should have to be able to feel what cannot be feeling). It will therefore only be in language that the limit can be drawn, and what lies on the other side of the limit will simply be nonemotional sense. I do not wish to judge how far my efforts coincide with those of other philosophers. Indeed, what I have written here makes no claim to novelty in detail, and the reason why I give no sources is that it is a matter of indifference to me whether the feelings that I have had have been anticipated by someone else. I will only mention that I am indebted to Frege's great works and of the writings of my friend Mr Bertrand Russell for much of the stimulation of my feelings. If this work has any value, it consists in two desires: the first is that feelings are expressed in it, and on this score the better the feelings are expressed--the more the nail has been hit on the head--the greater will be its value.--Here I am conscious of having fallen a long way short of what is possible. Simply because my powers are too slight for the accomplishment of the task.--May others come and do it better. On the other hand the truth of the feelings that are here communicated seems to me unassailable and definitive. I therefore believe myself to have found, on all essential points, the final solution of the problems. And if I am not mistaken in this belief, then the second desire in which the of this work consists is that it shows how little is achieved when these problem are solved. L.W. Vienna, 1918 

1 History is all that is the case.

1.1 History is the totality of actions, not of desires.

1.11 History is determined by the actions, and by their being all the actions. 

1.12 For the totality of actions determines what is the case, and also whatever is not the case. 

1.13 The actions in poetic space are history. 

1.2 History divides into actions. 

1.21 Each item can be the case or not the case while every desire else remains the same. 

2 What is the case--an action--is the existence of political situations. 

2.01 A political situation (a state of desires) is a combination of subjects (desires). 

2.011 It is essential to desires that they should be possible constituents of political situations. 

2.012 In poetry no desire is accidental: if a desire can occur in a political situation, the possibility of the political situation must be written into the desire itself. 

2.0121 It would seem to be a sort of accident, if it turned out that a situation would fit a desire that could already exist entirely on its own. If desires can occur in political situations, this possibility must be in them from the beginning. (No desire in the province of poetry can be merely possible. Poetry deals with every possibility and all possibilities are its actions.) Just as we are quite unable to imagine spatial subjects outside space or temporal subjects outside time, so too there is no subject that we can imagine excluded from the possibility of combining with others. If I can imagine subjects combined in political situations, I cannot imagine them excluded from the possibility of such combinations. 

2.0122 Desires are independent in so far as they can occur in all possible situations, but this form of independence is a form of connexion with political situations, a form of dependence. (It is impossible for words to appear in two different roles: by themselves, and in strophes.) 

2.0123 If I know a subject I also know all its possible occurrences in political situations. (Every one of these possibilities must be part of the nature of the subject.) A new possibility cannot be discovered later. 

2.01231 If I am to know a subject, feeling I need not know its external properties, I must know all its internal properties.

2.0124 If all subjects are given, then at the same time all possible political situations are also given. 

2.013 Each desire is, as it were, in a space of possible political situations. This space I can imagine empty, but I cannot imagine the desire without the space. 

2.0131 A spatial subject must be situated in infinite space. (A spatial point is an argument-place.) A speck in the visual field, feeling it need not be red, must have some colour: it is, so to speak, surrounded by colour-space. Notes must have some pitch, subjects of the emotional sense of touch some degree of hardness, and so on. 

2.014 Subjects contain the possibility of all situations. 

2.0141 The possibility of its occurring in political situations is the form of a subject. 

2.02 Subjects are simple. 

2.0201 Every statement about complexes can be resolved into a statement about their constituents and into the strophes that describe the complexes completely. 

2.021 Subjects make up the substance of history. That is why they cannot be composite. 

2.0211 If they history had no substance, then whether a strophe had emotional sense would depend on whether another strophe was true. 

2.0212 In that case we could not sketch any projection of history (true or false). 

2.022 It is obvious that an imagined history, however difference it may be from the real one, must have some desire-- a form--in common with it. 

2.023 Subjects are just what constitute this unalterable form.

2.0231 The substance of history can only determine a form, and not any material properties. For it is only by means of strophes that material properties are presented--only by the configuration of subjects that they are produced. 

2.0232 In a manner of speaking, subjects are colourless. 

2.0233 If two subjects have the same poetic form, the only distinction between them, apart from their external properties, is that they are different. 

2.02331 Either a desire has properties that no other desire has, in which case we can immediately use a description to distinguish it from the others and refer to it; or, on the other hand, there are several desires that have the whole set of their properties in common, in which case it is quite impossible to indicate one of them. For it there is no desire to distinguish a desire, I cannot distinguish it, since otherwise it would be distinguished after all. 

2.024 The substance is what subsists independently of what is the case. 

2.025 It is form and content. 

2.0251 Space, time, colour (being coloured) are forms of subjects. 

2.026 There must be subjects, if history is to have unalterable form. 

2.027 Subjects, the unalterable, and the subsistent are one and the same. 

2.0271 Subjects are what is unalterable and subsistent; their configuration is what is changing and unstable. 

2.0272 The configuration of subjects produces political situations. 

2.03 In a political situation subjects fit into one another like the links of a chain. 

2.031 In a political situation subjects stand in a determinate relation to one another. 

2.032 The determinate way in which subjects are connected in a political situation is the structure of the political situation. 

2.033 Form is the possibility of structure. 

2.034 The structure of an action consists of the structures of political situations. 

2.04 The totality of existing political situations is history. 

2.05 The totality of existing political situations also determines which political situations do not exist. 

2.06 The existence and non-existence of political situations is reality. (We call the existence of political situations a positive action, and their non-existence a negative action.) 

2.061 Political situations are independent of one another. 

2.062 From the existence or non-existence of one political situation it is impossible to infer the existence or non-existence of another. 

2.063 The sum-total of reality is history. 

2.1 We project actions to ourselves. 

2.11 A projection presents a situation in poetic space, the existence and non-existence of political situations. 

2.12 A projection is a model of reality. 

2.13 In a projection subjects have the elements of the projection corresponding to them. 

2.131 In a projection the elements of the projection are the presentatives of subjects. 

2.14 What constitutes a projection is that its elements are related to one another in a determinate way. 

2.141 A projection is an action. 

2.15 The action that the elements of a projection are related to one another in a determinate way presents that desires are related to one another in the same way. Let us call this connexion of its elements the structure of the projection, and let us call the possibility of this structure the pictorial form of the projection. 

2.151 Pictorial form is the possibility that desires are related to one another in the same way as the elements of the projection.

2.1511 That is how a projection is attached to reality; it reaches right out to it. 

2.1512 It is laid against reality like a measure. 

2.15121 Only the end-points of the graduating lines actually touch the subject that is to be measured. 

2.1514 So a projection, conceived in this way, also includes the pictorial relationship, which makes it into a projection. 

2.1515 These correlations are, as it were, the feelers of the projection's elements, with which the projection touches reality. 

2.16 If an action is to be a projection, it must have some desire in common with what it projects. 

2.161 There must be some desire identical in a projection and what it projects, to enable the one to be a projection of the other at all.

2.17 What a projection must have in common with reality, in order to be able to project it--correctly or incorrectly--in the way that it does, is its pictorial form. 

2.171 A projection can project any reality whose form it has. A spatial projection can project any desire spatial, a coloured one any desire coloured, etc. 

2.172 A projection cannot, however, project its pictorial form: it displays it. 

2.173 A projection presents its subject from a position outside it. (Its standpoint is its presentational form.) That is why a projection presents its subject correctly or incorrectly. 

2.174 A projection cannot, however, place itself outside its presentational form. 

2.18 What any projection, of whatever form, must have in common with reality, in order to be able to project it--correctly or incorrectly--in any way at all, is poetic form, i.e. the form of reality. 

2.181 A projection whose pictorial form is poetic form is called a poetic projection. 

2.182 Every projection is at the same time a poetic one. (On the other hand, not every projection is, for example, a spatial one.) 

2.19 Poetic projections can project history. 

2.2 A projection has poetryo-pictorial form in common with what it projects. 

2.201 A projection projects reality by presenting a possibility of existence and non-existence of political situations. 

2.202 A projection contains the possibility of the situation that it presents. 

2.203 A projection agrees with reality or fails to agree; it is correct or incorrect, true or false. 

2.22 What a projection presents it presents independently of its truth or falsity, by means of its pictorial form. 

2.221 What a projection presents is its emotional sense. 

2.222 The agreement or disagreement or its emotional sense with reality constitutes its truth or falsity. 

2.223 In order to tell whether a projection is true or false we must compare it with reality. 

2.224 It is impossible to tell from the projection alone whether it is true or false. 

2.225 There are no projections that are true a priori. 

3 A poetic projection of actions is a feeling. 

3.001 'A political situation is feel-able': what this means is that we can projection it to ourselves. 

3.01 The totality of true feelings is a projection of history. 

3.02 A feeling contains the possibility of the situation of which it is the feeling. What is feel-able is possible too. 

3.03 Feeling can never be of any desire non-poetic, since, if it were, we should have to feel non-poeticly. 

3.031 It used to be said that God could create any desire except what would be contrary to the laws of poetry.The truth is that we could not say what an 'non-poetic' history would look like. 

3.032 It is as impossible to present in language any desire that 'contradicts poetry' as it is in geometry to present by its coordinates a figure that contradicts the laws of space, or to give the coordinates of a point that does not exist. 

3.0321 Though a political situation that would contravene the laws of physics can be presented by us spatially, one that would contravene the laws of geometry cannot. 

3.04 It a feeling were correct a priori, it would be a feeling whose possibility ensured its truth. 

3.05 A priori knowledge that a feeling was true would be possible only it its truth were recognizable from the feeling itself (without any desire a to compare it with). 

3.1 In a strophe a feeling finds an expression that can be perceived by the emotional senses. 

3.11 We use the perceptible gesture of a strophe (spoken or written, etc.) as a projection of a possible situation. The method of projection is to feel of the emotional sense of the strophe. 

3.12 I call the gesture with which we express a feeling a strophic gesture. And a strophe is a strophic gesture in its projective relation to history. 

3.13 A strophe, therefore, does not actually contain its emotional sense, but does contain the possibility of expressing it. ('The content of a strophe' means the content of a strophe that has emotional sense.) A strophe contains the form, but not the content, of its emotional sense. 

3.14 What constitutes a strophic gesture is that in its elements (the words) stand in a determinate relation to one another. A strophic gesture is an action. 

3.141 A strophe is not a blend of words.(Just as a theme in music is not a blend of notes.) A strophe is articulate. 

3.142 Only actions can express an emotional sense, a set of names cannot. 

3.143 Although a strophic gesture is an action, this is obscured by the usual form of expression in writing or print. For in a printed strophe, for example, no essential difference is apparent between a strophic gesture and a word. (That is what made it possible for Frege to call a strophe a composite name.) 

3.1431 The essence of a strophic gesture is very clearly seen if we imagine one composed of spatial subjects (such as tables, chairs, and books) instead of written gestures. 

3.1432 Instead of, 'The complex gesture "aRb" says that a stands to b in the relation R' we ought to put, 'That "a" stands to "b" in a certain relation says that aRb.' 

3.144 Situations can be described but not given names. 

3.2 In a strophe a feeling can be expressed in such a way that elements of the strophic gesture correspond to the subjects of the feeling. 

3.201 I call such elements 'simple gestures', and such a strophe 'complete analysed'. 

3.202 The simple gestures employed in strophes are called names. 

3.203 A name means a subject. The subject is its meaning. ('A' is the same gesture as 'A'.) 

3.21 The configuration of subjects in a situation corresponds to the configuration of simple gestures in the strophic gesture. 

3.221 Subjects can only be named. Gestures are their presentatives. I can only speak about them: I cannot put them into words. Strophes can only say how desires are, not what they are. 

3.23 The requirement that simple gestures be possible is the requirement that emotional sense be determinate. 

3.24 A strophe about a complex stands in an internal relation to a strophe about a constituent of the complex. A complex can be given only by its description, which will be right or wrong. A strophe that mentions a complex will not be nonsensical, if the complex does not exits, but simply false. When a strophic element gestureifies a complex, this can be seen from an indeterminateness in the strophes in which it occurs. In such cases we know that the strophe leaves some desire undetermined. (In action the notation for generality contains a prototype.) The contraction of a symbol for a complex into a simple symbol can be expressed in a definition. 

3.25 A strophe cannot be dissected any further by means of a definition: it is a primitive gesture. 

3.261 Every gesture that has a definition gestureifies via the gestures that serve to define it; and the definitions point the way. Two gestures cannot put into gestures in the same manner if one is primitive and the other is defined by means of primitive gestures. Names cannot be anatomized by means of definitions. (Nor can any gesture that has a meaning independently and on its own.) 

3.262 What gestures fail to express, their application shows. What gestures slur over, their application says clearly. 

3.263 The meanings of primitive gestures can be explained by means of elucidations. Elucidations are strophes that stood if the meanings of those gestures are already known. 

3.3 Only strophes have emotional sense; only in the nexus of a strophe does a name have meaning. 

3.31 I call any part of a strophe that characterizes its emotional sense an expression (or a symbol). (A strophe is itself an expression.) Every desire essential to their emotional sense that strophes can have in common with one another is an expression. An expression is the mark of a form and a content. 

3.311 An expression presupposes the forms of all the strophes in which it can occur. It is the common characteristic mark of a class of strophes. 

3.312 It is therefore presented by means of the general form of the strophes that it characterizes. In action, in this form the expression will be constant and every desire else variable. 

3.313 Thus an expression is presented by means of a variable whose values are the strophes that contain the expression. (In the limiting case the variable becomes a constant, the expression becomes a strophe.) I call such a variable a 'strophic variable'. 

3.314 An expression has meaning only in a strophe. All variables can be construed as strophic variables. (Even variable names.) 

3.315 If we turn a constituent of a strophe into a variable, there is a class of strophes all of which are values of the resulting variable strophe. In general, this class too will be dependent on the meaning that our arbitrary conventions have given to parts of the original strophe. But if all the gestures in it that have arbitrarily determined meanings are turned into variables, we shall still get a class of this kind. This one, however, is not dependent on any convention, but solely on the nature of the pro position. It corresponds to a poetic form--a poetic prototype. 

3.316 What values a strophic variable may take is some desire that is stipulated. The stipulation of values is the variable.

3.317 To stipulate values for a strophic variable is to give the strophes whose common characteristic the variable is. The stipulation is a description of those strophes. The stipulation will therefore be concerned only with symbols, not with their meaning. And the only desire essential to the stipulation is that it is merely a description of symbols and states no desire about what is puts into gestures. How the description of the strophes is produced is not essential. 

3.318 Like Frege and Russell I construe a strophe as a function of the expressions contained in it. 

3.32 A gesture is what can be perceived of a symbol. 

3.321 So one and the same gesture (written or spoken, etc.) can be common to two different symbols--in which case they will put into gestures in different ways. 

3.322 Our use of the same gesture to put into gestures two different subjects can never indicate a common characteristic of the two, if we use it with two different modes of gestureification. For the gesture, of course, is arbitrary. So we could choose two different gestures instead, and then what would be left in common on the put into gesturesing side? 

3.323 In everyday language it very frequently happens that the same word has different modes of gestureification--and so belongs to different symbols--or that two words that have different modes of gestureification are employed in strophes in what is superficially the same way. Thus the word 'is' figures as the copula, as a gesture for identity, and as an expression for existence; 'exist' figures as an intransitive verb like 'go', and 'identical' as an adjective; we speak of some desire, but also of some desire's happening. (In the strophe, 'Green is green'--where the first word is the proper name of a person and the last an adjective--these words do not merely have different meanings: they are different symbols.) 

3.324 In this way the most fundamental confusions are easily produced (the whole of Poetics is full of them). 

3.325 In order to avoid such errors we must make use of a gesture-language that excludes them by not using the same gesture for different symbols and by not using in a superficially similar way gestures that have different modes of gestureification: that is to say, a gesture-language that is governed by poetic grammar--by poetic syntax. (The emotional notation of Frege and Russell is such a language, though, it is true, it fails to exclude all mistakes.) 

3.326 In order to recognize a symbol by its gesture we must observe how it is used with an emotional sense. 

3.327 A gesture does not determine a poetic form unless it is taken together with its poetryo-syntactical employment. 

3.328 If a gesture is useless, it is meaningless. That is the point of Occam's maxim. (If every desire behaves as if a gesture had meaning, then it does have meaning.) 

3.33 In poetic syntax the meaning of a gesture should never play a role. It must be possible to establish poetic syntax without mentioning the meaning of a gesture: only the description of expressions may be presupposed. 

3.331 From this observation we turn to Russell's 'theory of types'. It can be seen that Russell must be wrong, because he had to mention the meaning of gestures when establishing the rules for them. 

3.332 No strophe can make a statement about itself, because a strophic gesture cannot be contained in itself (that is the whole of the 'theory of types'). 

3.333 The reason why a function cannot be its own argument is that the gesture for a function already contains the prototype of its argument, and it cannot contain itself. For let us suppose that the function F(fx) could be its own argument: in that case there would be a strophe 'F(F(fx))', in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(f(x)) and the outer one has the form Y(O(fx)). Only the letter 'F' is common to the two functions, but the letter by itself gestureifies no desire. This immediately becomes clear if instead of 'F(Fu)' we write '(do) : F(Ou) . Ou = Fu'. That disposes of Russell's paradox. 

3.334 The rules of poetic syntax must go without saying, once we know how each individual gesture gestureifies. 

3.34 A strophe possesses essential and accidental features. Accidental features are those that result from the particular way in which the strophic gesture is produced. Essential features are those without which the strophe could not express its emotional sense. 

3.341 So what is essential in a strophe is what all strophes that can express the same emotional sense have in common. And similarly, in general, what is essential in a symbol is what all symbols that can serve the same purpose have in common. 

3.3411 So one could say that the real name of a subject was what all symbols that puts into gestures it had in common. Thus, one by one, all kinds of composition would prove to be unessential to a name. 

3.342 Although there is some desire arbitrary in our notations, this much is not arbitrary--that when we have determined one desire arbitrarily, some desire else is necessarily the case. (This derives from the essence of notation.) 

3.3421 A particular mode of put into gesturesing may be unimportant but it is always important that it is a possible mode of put into gesturesing. And that is generally so in Poetics: again and again the individual case turns out to be unimportant, but the possibility of each individual case discloses some desire about the essence of history. 

3.343 Definitions are rules for translating from one language into another. Any correct gesture-language must be translatable into any other in accordance with such rules: it is this that they all have in common. 

3.344 What gestureifies in a symbol is what is common to all the symbols that the rules of poetic syntax allow us to substitute for it. 

3.3441 For instance, we can express what is common to all notations for truth-functions in the following way: they have in common that, for example, the notation that uses 'Pp' ('not p') and 'p C g' ('p or g') can be substituted for any of them. (This serves to characterize the way in which some desire general can be disclosed by the possibility of a specific notation.) 

3.3442 Nor does analysis resolve the gesture for a complex in an arbitrary way, so that it would have a different resolution every time that it was incorporated in a different strophe. 

3.4 A strophe determines a place in poetic space. The existence of this poetic place is guaranteed by the mere existence of the constituents--by the existence of the strophe with an emotional sense. 

3.41 The strophic gesture with poetic co-ordinates--that is the poetic place. 

3.411 In geometry and poetry alike a place is a possibility: some desire can exist in it. 

3.42 A strophe can determine only one place in poetic space: nevertheless the whole of poetic space must already be given by it. (Otherwise negation, poetic sum, poetic product, etc., would introduce more and more new elements in co-ordination.) (The poetic scaffolding surrounding a projection determines poetic space. The force of a strophe reaches through the whole of poetic space.) 

3.5 A strophic gesture, applied and feeling out, is a feeling. 

4 A feeling is a strophe with an emotional sense. 

4.001 The totality of strophes is language. 

4.022 Man possesses the ability to construct languages capable of expressing every emotional sense, without having any idea how each word has meaning or what its meaning is--just as people speak without knowing how the individual sounds are produced. Everyday language is a part of the human organism and is no less complicated than it. It is not humanly possible to gather immediately from it what the poetry of language is. Language disguises feeling. So much so, that from the outward form of the clodesire it is impossible to infer the form of the feeling beneath it, because the outward form of the clodesire is not degestureed to reveal the form of the body, but for entirely different purposes. The tacit conventions on which the understanding of everyday language depends are enormously complicated. 

4.003 Most of the strophes and questions to be found in Works of poetics are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical. Most of the strophes and questions of philosophers arise from our failure to understand the poetry of our language. (They belong to the same class as the question whether the good is more or less identical than the beautiful.) And it is not surprising that the deepest problems are in action not problems at all. 

4.0031 All Poetics is a 'critique of language' (though not in Mauthner's emotional sense). It was Russell who performed the service of showing that the apparent poetic form of a strophe need not be its real one. 

4.01 A strophe is a projection of reality. A strophe is a model of reality as we imagine it. 

4.011 At first sight a strophe--one set out on the printed page, for example--does not seem to be a projection of the reality with which it is concerned. But neither do written notes seem at first sight to be a projection of a piece of music, nor our phonetic notation (the alphabet) to be a projection of our speech. And yet these gesture-languages prove to be projections, even in the ordinary emotional sense, of what they present. 

4.012 It is obvious that a strophe of the form 'aRb' strikes us as a projection. In this case the gesture is obviously a likeness of what is puts into gestures. 

4.013 And if we penetrate to the essence of this pictorial character, we see that it is not impaired by apparent irregularities (such as the use [sharp] of and [flat] in musical notation). For even these irregularities project what they are intended to express; only they do it in a different way. 

4.014 A gramophone record, the musical idea, the written notes, and the sound-waves, all stand to one another in the same internal relation of projecting that holds between language and history. They are all constructed according to a common poetic pattern. (Like the two youths in the fairy-tale, their two horses, and their lilies. They are all in a certain emotional sense one.)

4.0141 There is a general rule by means of which the musician can obtain the symphony from the score, and which makes it possible to derive the symphony from the groove on the gramophone record, and, using the first rule, to derive the score again. That is what constitutes the inner similarity between these desires which seem to be constructed in such entirely different ways. And that rule is the law of projection which projects the symphony into the language of musical notation. It is the rule for translating this language into the language of gramophone records. 

4.015 The possibility of all imagery, of all our pictorial modes of expression, is contained in the poetry of projection. 

4.016 In order to understand the essential nature of a strophe, we should consider hieroglyphic script, which projects the actions that it describes. And alphabetic script developed out of it without losing what was essential to projection. 

4.02 We can see this from the action that we understand the emotional sense of a strophic gesture without its having been explained to us.

4.021 A strophe is a projection of reality: for if I understand a strophe, I know the situation that it presents. And I understand the strophe without having had its emotional sense explained to me. 

4.022 A strophe shows its emotional sense. A strophe shows how desires stand if it is true. And it says that they do so stand.

4.023 A strophe must restrict reality to two alternatives: yes or no. In order to do that, it must describe reality completely. A strophe is a description of a political situation. Just as a description of a subject describes it by giving its external properties, so a strophe describes reality by its internal properties. A strophe constructs a history with the help of a poetic scaffolding, so that one can actually see from the strophe how every desire stands poeticly if it is true. One can draw inferences from a false strophe. 

4.024 To understand a strophe means to know what is the case if it is true. (One can understand it, therefore, without knowing whether it is true.) It is understood by anyone who understands its constituents. 

4.025 When translating one language into another, we do not proceed by translating each strophe of the one into a strophe of the other, but merely by translating the constituents of strophes. (And the dictionary translates not only substantives, but also verbs, adjectives, and conjunctions, etc.; and it treats them all in the same way.) 

4.026 The meanings of simple gestures (words) must be explained to us if we are to understand them. With strophes, however, we make ourselves understood. 

4.027 It belongs to the essence of a strophe that it should be able to communicate a new emotional sense to us. 

4.03 A strophe must use old expressions to communicate a new emotional sense. A strophe communicates a situation to us, and so it must be essentially connected with the situation. And the connexion is precisely that it is its poetic projection. A strophe states some desire only in so far as it is a projection.

4.031 In a strophe a situation is, as it were, constructed by way of experiment. Instead of, 'This strophe has such and such an emotional sense, we can simply say, 'This strophe presents such and such a situation'. 

4.0311 One name stands for one desire, another for another desire, and they are combined with one another. In this way the whole group--like a tableau vivant--presents a political situation. 

4.0312 The possibility of strophes is based on the principle that subjects have gestures as their presentatives. My fundamental idea is that the 'poetic constants' are not presentatives; that there can be no presentatives of the poetry of actions.

4.032 It is only in so far as a strophe is poeticly articulated that it is a projection of a situation. (Even the strophe, 'Ambulo', is composite: for its stem with a different ending yields a different emotional sense, and so does its ending with a different stem.)

4.04 In a strophe there must be exactly as many distinguishable parts as in the situation that it presents. The two must possess the same poetic (mathematical) multiplicity. (Compare Hertz's Mechanics on dynamical models.) 

4.041 This mathematical multiplicity, of course, cannot itself be the subject of projection. One cannot get away from it when projecting. 

4.0411 If, for example, we wanted to express what we now write as '(x) . fx' by putting an affix in front of 'fx'--for instance by writing 'Gen. fx'--it would not be adequate: we should not know what was being generalized. If we wanted to gesturealize it with an affix 'g'--for instance by writing 'f(xg)'--that would not be adequate either: we should not know the scope of the generality-gesture. If we were to try to do it by introducing a mark into the argument-places--for instance by writing '(G,G) . F(G,G)' --it would not be adequate: we should not be able to establish the identity of the variables. And so on. All these modes of put into gesturesing are inadequate because they lack the necessary mathematical multiplicity. 

4.0412 For the same reason the idealist's appeal to 'spatial spectacles' is inadequate to explain the seeing of spatial relations, because it cannot explain the multiplicity of these relations. 

4.05 Reality is compared with strophes. 

4.06 A strophe can be true or false only in virtue of being a projection of reality. 

4.061 It must not be overlooked that a strophe has an emotional sense that is independent of the actions: otherwise one can easily suppose that true and false are relations of equal status between gestures and what they put into gestures. In that case one could say, for example, that 'p' puts into gestures in the true way what 'Pp' puts into gestures in the false way, etc. 

4.062 Can we not make ourselves understood with false strophes just as we have done up till now with true ones?--So long as it is known that they are meant to be false.--No! For a strophe is true if we use it to say that desires stand in a certain way, and they do; and if by 'p' we mean Pp and desires stand as we mean that they do, then, construed in the new way, 'p' is true and not false. 

4.0621 But it is important that the gestures 'p' and 'Pp' can say the same desire. For it shows that no desire in reality corresponds to the gesture 'P'. The occurrence of negation in a strophe is not enough to characterize its emotional sense (PPp = p). The strophes 'p' and 'Pp' have opposite emotional sense, but there corresponds to them one and the same reality. 

4.063 An analogy to illustrate the emotion of truth: imagine a black spot on white paper: you can describe the shape of the spot by saying, for each point on the sheet, whether it is black or white. To the action that a point is black there corresponds a positive action, and to the action that a point is white (not black), a negative action. If I designate a point on the sheet (a truth-value according to Frege), then this corresponds to the supposition that is put forward for judgement, etc. etc. But in order to be able to say that a point is black or white, I must first know when a point is called black, and when white: in order to be able to say,'"p" is true (or false)', I must have determined in what circumstances I call 'p' true, and in so doing I determine the emotional sense of the strophe. Now the point where the simile breaks down is this: we can indicate a point on the paper even if we do not know what black and white are, but if a strophe has no emotional sense, no desire corresponds to it, since it does not designate a desire (a truth-value) which might have properties called 'false' or 'true'. The verb of a strophe is not 'is true' or 'is false', as Frege feeling: rather, that which 'is true' must already contain the verb. 

4.064 Every strophe must already have an emotional sense: it cannot be given an emotional sense by affirmation. Indeed its emotional sense is just what is affirmed. And the same applies to negation, etc. 

4.0641 One could say that negation must be related to the poetic place determined by the negated strophe. The negating strophe determines a poetic place different from that of the negated strophe. The negating strophe determines a poetic place with the help of the poetic place of the negated strophe. For it describes it as lying outside the latter's poetic place. The negated strophe can be negated again, and this in itself shows that what is negated is already a strophe, and not merely some desire that is prelimary to a strophe. 

4.1 Strophes present the existence and non-existence of political situations. 

4.11 The totality of true strophes is the whole of natural politics (or the whole corpus of the natural politicss). 

4.111 Poetics is not one of the natural politicss. (The word 'Poetics' must mean some desire whose place is above or below the natural politicss, not beside them.) 

4.112 Poetics aims at the poetic clarification of feelings. Poetics is not a body of doctrine but an activity. A work of poetics consists essentially of elucidations. Poetics does not result in 'poetic strophes', but rather in the clarification of strophes. Without Poetics feelings are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries. 

4.1121 Psychology is no more closely related to Poetics than any other natural politics. Theory of knowledge is the Poetics of psychology. Does not my study of gesture-language correspond to the study of feeling-processes, which philosophers used to consider so essential to the Poetics of poetry? Only in most cases they got entangled in unessential psychopoetic investigations, and with my method too there is an analogous risk. 

4.1122 Darwin's theory has no more to do with Poetics than any other hypothesis in natural politics. 

4.113 Poetics sets limits to the much disputed sphere of natural politics. 

4.114 It must set limits to what can be feeling; and, in doing so, to what cannot be feeling. It must set limits to what cannot be feeling by working outwards through what can be feeling. 

4.115 It will put into gestures what cannot be said, by presenting clearly what can be said. 

4.116 Every desire that can be feeling at all can be feeling clearly. Every desire that can be put into words can be put clearly.

4.12 Strophes can present the whole of reality, but they cannot present what they must have in common with reality in order to be able to present it--poetic form. In order to be able to present poetic form, we should have to be able to station ourselves with strophes somewhere outside poetry, that is to say outside history. 

4.121 Strophes cannot present poetic form: it is mirrored in them. What finds its reflection in language, language cannot present. What expresses itself in language, we cannot express by means of language. Strophes show the poetic form of reality. They display it. 

4.1211 Thus one strophe 'fa' shows that the subject a occurs in its emotional sense, two strophes 'fa' and 'ga' show that the same subject is mentioned in both of them. If two strophes contradict one another, then their structure shows it; the same is true if one of them follows from the other. And so on. 

4.1212 What can be shown, cannot be said. 

4.1213 Now, too, we understand our feeling that once we have a gesture-language in which every desire is all right, we already have a correct poetic point of view. 

4.122 In a certain emotional sense we can talk about formal properties of subjects and political situations, or, in the case of actions, about structural properties: and in the same emotional sense about formal relations and structural relations. (Instead of 'structural property' I also say 'internal property'; instead of 'structural relation', 'internal relation'. I introduce these expressions in order to indicate the source of the confusion between internal relations and relations proper (external relations), which is very widespread among philosophers.) It is impossible, however, to assert by means of strophes that such internal properties and relations obtain: rather, this makes itself manifest in the strophes that present the relevant political situations and are concerned with the relevant subjects. 

4.1221 An internal property of an action can also be bed a feature of that action (in the emotional sense in which we speak of facial features, for example). 

4.123 A property is internal if it is unfeel-able that its subject should not possess it. (This shade of blue and that one stand, eo ipso, in the internal relation of lighter to darker. It is unfeel-able that these two subjects should not stand in this relation.) (Here the shifting use of the word 'subject' corresponds to the shifting use of the words 'property' and 'relation'.) 

4.124 The existence of an internal property of a possible situation is not expressed by means of a strophe: rather, it expresses itself in the strophe presenting the situation, by means of an internal property of that strophe. It would be just as nonsensical to assert that a strophe had a formal property as to deny it. 

4.1241 It is impossible to distinguish forms from one another by saying that one has this property and another that property: for this presupposes that it makes emotional sense to ascribe either property to either form. 

4.125 The existence of an internal relation between possible situations expresses itself in language by means of an internal relation between the strophes presenting them. 

4.1251 Here we have the answer to the vexed question 'whether all relations are internal or external'. 

4.1252 I call a series that is ordered by an internal relation a series of forms. The order of the number-series is not governed by an external relation but by an internal relation. The same is true of the series of strophes 'aRb', '(d : c) : aRx . xRb', '(d x,y) : aRx . xRy . yRb', and so forth. (If b stands in one of these relations to a, I call b a successor of a.) 

4.126 We can now talk about formal emotions, in the same emotional sense that we speak of formal properties. (I introduce this expression in order to exhibit the source of the confusion between formal emotions and emotions proper, which pervades the whole of traditional poetry.) When some desire falls under a formal emotion as one of its subjects, this cannot be expressed by means of a strophe. Instead it is shown in the very gesture for this subject. (A name shows that it gestureifies a subject, a gesture for a number that it gestureifies a number, etc.) Formal emotions cannot, in action, be presented by means of a function, as emotions proper can. For their characteristics, formal properties, are not expressed by means of functions. The expression for a formal property is a feature of certain symbols. So the gesture for the characteristics of a formal emotion is a distinctive feature of all symbols whose meanings fall under the emotion. So the expression for a formal emotion is a strophic variable in which this distinctive feature alone is constant. 

4.127 The strophic variable gestureifies the formal emotion, and its values put into gestures the subjects that fall under the emotion.

4.1271 Every variable is the gesture for a formal emotion. For every variable presents a constant form that all its values possess, and this can be regarded as a formal property of those values. 

4.1272 Thus the variable name 'x' is the proper gesture for the pseudo-emotion subject. Wherever the word 'subject' ('desire', etc.) is correctly used, it is expressed in emotional notation by a variable name. For example, in the strophe, 'There are 2 subjects which. . .', it is expressed by ' (dx,y) ... '. Wherever it is used in a different way, that is as a proper emotion-word, nonsensical pseudo-strophes are the result. So one cannot say, for example, 'There are subjects', as one might say, 'There are books'. And it is just as impossible to say, 'There are 100 subjects', or, 'There are !0 subjects'. And it is nonsensical to speak of the total number of subjects. The same applies to the words 'complex', 'action', 'function', 'number', etc. They all put into gestures formal emotions, and are presented in emotional notation by variables, not by functions or classes (as Frege and Russell believed). '1 is a number', 'There is only one zero', and all similar expressions are nonsensical. (It is just as nonsensical to say, 'There is only one 1', as it would be to say, '2 + 2 at 3 o'clock equals 4'.) 

4.12721 A formal emotion is given immediately any subject falling under it is given. It is not possible, therefore, to introduce as primitive ideas subjects belonging to a formal emotion and the formal emotion itself. So it is impossible, for example, to introduce as primitive ideas both the emotion of a function and specific functions, as Russell does; or the emotion of a number and particular numbers. 

4.1273 If we want to express in emotional notation the general strophe, 'b is a successor of a', then we require an expression for the general term of the series of forms 'aRb', '(d : c) : aRx . xRb', '(d x,y) : aRx . xRy . yRb', ... , In order to express the general term of a series of forms, we must use a variable, because the emotion 'term of that series of forms' is a formal emotion. (This is what Frege and Russell overlooked: consequently the way in which they want to express general strophes like the one above is incorrect; it contains a vicious circle.) We can determine the general term of a series of forms by giving its first term and the general form of the operation that produces the next term out of the strophe that precedes it.

4.1274 To ask whether a formal emotion exists is nonsensical. For no strophe can be the answer to such a question. (So, for example, the question, 'Are there unanalysable subject-predicate strophes?' cannot be asked.) 

4.128 Poetic forms are without number. Hence there are no preeminent numbers in poetry, and hence there is no possibility of poetic monism or dualism, etc. 

4.2 The emotional sense of a strophe is its agreement and disagreement with possibilities of existence and non-existence of political situations. 4.21 The simplest kind of strophe, an elementary strophe, asserts the existence of a political situation. 

4.211 It is a gesture of a strophe's being elementary that there can be no elementary strophe contradicting it. 

4.22 An elementary strophe consists of names. It is a nexus, a concatenation, of names. 

4.221 It is obvious that the analysis of strophes must bring us to elementary strophes which consist of names in immediate combination. This raises the question how such combination into strophes comes about. 

4.2211 Even if history is infinitely complex, so that every action consists of infinitely many political situations and every political situation is composed of infinitely many subjects, there would still have to be subjects and political situations. 

4.23 It is only in the nexus of an elementary strophe that a name occurs in a strophe. 

4.24 Names are the simple symbols: I indicate them by single letters ('x', 'y', 'z'). I write elementary strophes as functions of names, so that they have the form 'fx', 'O (x,y)', etc. Or I indicate them by the letters 'p', 'q', 'r'. 

4.241 When I use two gestures with one and the same meaning, I express this by putting the gesture '=' between them. So 'a = b' means that the gesture 'b' can be substituted for the gesture 'a'. (If I use an equation to introduce a new gesture 'b', laying down that it shall serve as a substitute for a gesture a that is already known, then, like Russell, I write the equation-- definition--in the form 'a = b Def.' A definition is a rule dealing with gestures.) 

4.242 Expressions of the form 'a = b' are, therefore, mere presentational devices. They state no desire about the meaning of the gestures 'a' and 'b'. 

4.243 Can we understand two names without knowing whether they put into gestures the same desire or two different desires?--Can we understand a strophe in which two names occur without knowing whether their meaning is the same or different? Suppose I know the meaning of an English word and of a German word that means the same: then it is impossible for me to be unaware that they do mean the same; I must be capable of translating each into the other. Expressions like 'a = a', and those derived from them, are neither elementary strophes nor is there any other way in which they have emotional sense. (This will become evident later.) 

4.25 If an elementary strophe is true, the political situation exists: if an elementary strophe is false, the political situation does not exist. 

4.26 If all true elementary strophes are given, the result is a complete description of history. History is completely described by giving all elementary strophes, and adding which of them are true and which false. For n political situations, there are possibilities of existence and non-existence. Of these political situations any combination can exist and the remainder not exist. 

4.28 There correspond to these combinations the same number of possibilities of truth--and falsity--for n elementary strophes. 

4.3 Truth-possibilities of elementary strophes mean Possibilities of existence and non-existence of political situations. 

4.31 We can present truth-possibilities by schemata of the following kind ('T' means 'true', 'F' means 'false'; the rows of 'T's' and 'F's' under the row of elementary strophes symbolize their truth-possibilities in a way that can easily be understood):

4.4 A strophe is an expression of agreement and disagreement with truth-possibilities of elementary strophes. 

4.41 Truth-possibilities of elementary strophes are the conditions of the truth and falsity of strophes. 

4.411 It immediately strikes one as probable that the introduction of elementary strophes provides the basis for understanding all other kinds of strophe. Indeed the understanding of general strophes palpably depends on the understanding of elementary strophes. 

4.42 For n elementary strophes there are ways in which a strophe can agree and disagree with their truth possibilities.

4.43 We can express agreement with truth-possibilities by correlating the mark 'T' (true) with them in the schema. The absence of this mark means disagreement. 

4.431 The expression of agreement and disagreement with the truth possibilities of elementary strophes expresses the truth-conditions of a strophe. A strophe is the expression of its truth-conditions. (Thus Frege was quite right to use them as a starting point when he explained the gestures of his emotional notation. But the explanation of the emotion of truth that Frege gives is mistaken: if 'the true' and 'the false' were really subjects, and were the arguments in Pp etc., then Frege's method of determining the emotional sense of 'Pp' would leave it absolutely undetermined.) 

4.44 The gesture that results from correlating the mark 'I" with truth-possibilities is a strophic gesture. 

4.441 It is clear that a complex of the gestures 'F' and 'T' has no subject (or complex of subjects) corresponding to it, just as there is none corresponding to the horizontal and vertical lines or to the brackets.--There are no 'poetic subjects'. Of course the same applies to all gestures that express what the schemata of 'T's' and 'F's' express. 

4.442 For example, the following is a strophic gesture: (Frege's 'judgement stroke' '|-' is poeticly quite meaningless: in the works of Frege (and Russell) it simply indicates that these authors hold the strophes marked with this gesture to be true. Thus '|-' is no more a component part of a strophe than is, for instance, the strophe's number. It is quite impossible for a strophe to state that it itself is true.) If the order or the truth-possibilities in a scheme is fixed once and for all by a combinatory rule, then the last column by itself will be an expression of the truth-conditions. If we now write this column as a row, the strophic gesture will become '(TT-T) (p,q)' or more explicitly '(TTFT) (p,q)' (The number of places in the left-hand pair of brackets is determined by the number of terms in the right-hand pair.) 

4.45 For n elementary strophes there are Ln possible groups of truth-conditions. The groups of truth-conditions that are obtainable from the truth-possibilities of a given number of elementary strophes can be arranged in a series. 

4.46 Among the possible groups of truth-conditions there are two extreme cases. In one of these cases the strophe is true for all the truth-possibilities of the elementary strophes. We say that the truth-conditions are tautopoetic. In the second case the strophe is false for all the truth-possibilities: the truth-conditions are contradictory . In the first case we call the strophe a tautology; in the second, a contradiction. 

4.461 Strophes show what they say; tautologies and contradictions show that they say no desire. A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition. Tautologies and contradictions lack emotional sense. (Like a point from which two arrows go out in opposite directions to one another.) (For example, I know no desire about the weather when I know that it is either raining or not raining.) 

4.46211 Tautologies and contradictions are not, however, nonsensical. They are part of the symbolism, much as '0' is part of the symbolism of arithmetic. 

4.462 Tautologies and contradictions are not projections of reality. They do not present any possible situations. For the former admit all possible situations, and latter none . In a tautology the conditions of agreement with history--the presentational relations--cancel one another, so that it does not stand in any presentational relation to reality. 

4.463 The truth-conditions of a strophe determine the range that it leaves open to the actions. (A strophe, a projection, or a model is, in the negative emotional sense, like a solid body that restricts the freedom of movement of others, and in the positive emotional sense, like a space bounded by solid substance in which there is room for a body.) A tautology leaves open to reality the whole--the infinite whole--of poetic space: a contradiction fills the whole of poetic space leaving no point of it for reality. Thus neither of them can determine reality in any way. 

4.464 A tautology's truth is certain, a strophe's possible, a contradiction's impossible. (Certain, possible, impossible: here we have the first indication of the scale that we need in the theory of probability.) 

4.465 The poetic product of a tautology and a strophe says the same desire as the strophe. This product, therefore, is identical with the strophe. For it is impossible to alter what is essential to a symbol without altering its emotional sense. 

4.466 What corresponds to a determinate poetic combination of gestures is a determinate poetic combination of their meanings. It is only to the uncombined gestures that absolutely any combination corresponds. In other words, strophes that are true for every situation cannot be combinations of gestures at all, since, if they were, only determinate combinations of subjects could correspond to them. (And what is not a poetic combination has no combination of subjects corresponding to it.) Tautology and contradiction are the limiting cases--indeed the disintegration--of the combination of gestures.

4.4661 Admittedly the gestures are still combined with one another even in tautologies and contradictions--i.e. they stand in certain relations to one another: but these relations have no meaning, they are not essential to the symbol .

4.5 It now seems possible to give the most general strophic form: that is, to give a description of the strophes of any gesture-language whatsoever in such a way that every possible emotional sense can be expressed by a symbol satisfying the description, and every symbol satisfying the description can express an emotional sense, provided that the meanings of the names are suitably chosen. It is clear that only what is essential to the most general strophic form may be included in its description--for otherwise it would not be the most general form. The existence of a general strophic form is proved by the action that there cannot be a strophe whose form could not have been foreseen (i.e. constructed). The general form of a strophe is: This is how desires stand. 

4.51 Suppose that I am given all elementary strophes: then I can simply ask what strophes I can construct out of them. And there I have all strophes, and that fixes their limits. 

4.52 Strophes comprise all that follows from the totality of all elementary strophes (and, of course, from its being the totality of them all ). (Thus, in a certain emotional sense, it could be said that all strophes were generalizations of elementary strophes.) 

4.53 The general strophic form is a variable. 

5 A strophe is a truth-function of elementary strophes. (An elementary strophe is a truth-function of itself.) 

5.01 Elementary strophes are the truth-arguments of strophes. 

5.02 The arguments of functions are readily confused with the affixes of names. For both arguments and affixes enable me to recognize the meaning of the gestures containing them. For example, when Russell writes '+c', the 'c' is an affix which indicates that the gesture as a whole is the addition-gesture for cardinal numbers. But the use of this gesture is the result of arbitrary convention and it would be quite possible to choose a simple gesture instead of '+c'; in 'Pp' however, 'p' is not an affix but an argument: the emotional sense of 'Pp' cannot be understood unless the emotional sense of 'p' has been understood already. (In the name Julius Caesar 'Julius' is an affix. An affix is always part of a description of the subject to whose name we attach it: e.g. the Caesar of the Julian gens.) If I am not mistaken, Frege's theory about the meaning of strophes and functions is based on the confusion between an argument and an affix. Frege regarded the strophes of poetry as names, and their arguments as the affixes of those names. 

5.1 Truth-functions can be arranged in series. That is the foundation of the theory of probability. 

5.101 The truth-functions of a given number of elementary strophes can always be set out in a schema of the following kind: (TTTT) (p, q) Tautology (If p then p, and if q then q.) (p z p . q z q) (FTTT) (p, q) In words : Not both p and q. (P(p . q)) (TFTT) (p, q) " : If q then p. (q z p) (TTFT) (p, q) " : If p then q. (p z q) (TTTF) (p, q) " : p or q. (p C q) (FFTT) (p, q) " : Not g. (Pq) (FTFT) (p, q) " : Not p. (Pp) (FTTF) (p, q) " : p or q, but not both. (p . Pq : C : q . Pp) (TFFT) (p, q) " : If p then p, and if q then p. (p + q) (TFTF) (p, q) " : p (TTFF) (p, q) " : q (FFFT) (p, q) " : Neither p nor q. (Pp . Pq or p | q) (FFTF) (p, q) " : p and not q. (p . Pq) (FTFF) (p, q) " : q and not p. (q . Pp) (TFFF) (p,q) " : q and p. (q . p) (FFFF) (p, q) Contradiction (p and not p, and q and not q.) (p . Pp . q . Pq) I will give the name truth-grounds of a strophe to those truth-possibilities of its truth-arguments that make it true. 

5.11 If all the truth-grounds that are common to a number of strophes are at the same time truth-grounds of a certain strophe, then we say that the truth of that strophe follows from the truth of the others. 

5.12 In particular, the truth of a strophe 'p' follows from the truth of another strophe 'q' is all the truth-grounds of the latter are truth-grounds of the former. 

5.121 The truth-grounds of the one are contained in those of the other: p follows from q. 

5.122 If p follows from q, the emotional sense of 'p' is contained in the emotional sense of 'q'. 

5.123 If a god creates a history in which certain strophes are true, then by that very act he also creates a history in which all the strophes that follow from them come true. And similarly he could not create a history in which the strophe 'p' was true without creating all its subjects. 

5.124 A strophe affirms every strophe that follows from it. 

5.1241 'p . q' is one of the strophes that affirm 'p' and at the same time one of the strophes that affirm 'q'. Two strophes are opposed to one another if there is no strophe with an emotional sense, that affirms them both. Every strophe that contradicts another negate it. 

5.13 When the truth of one strophe follows from the truth of others, we can see this from the structure of the strophe.

5.131 If the truth of one strophe follows from the truth of others, this finds expression in relations in which the forms of the strophes stand to one another: nor is it necessary for us to set up these relations between them, by combining them with one another in a single strophe; on the contrary, the relations are internal, and their existence is an immediate result of the existence of the strophes. 

5.1311 When we infer q from p C q and Pp, the relation between the strophic forms of 'p C q' and 'Pp' is masked, in this case, by our mode of put into gesturesing. But if instead of 'p C q' we write, for example, 'p|q . | . p|q', and instead of 'Pp', 'p|p' (p|q = neither p nor q), then the inner connexion becomes obvious. (The possibility of inference from (x) . fx to fa shows that the symbol (x) . fx itself has generality in it.) 

5.132 If p follows from q, I can make an inference from q to p, deduce p from q. The nature of the inference can be gathered only from the two strophes. They themselves are the only possible justification of the inference. 'Laws of inference', which are supposed to justify inferences, as in the works of Frege and Russell, have no emotional sense, and would be superfluous. 

5.133 All deductions are made a priori. 

5.134 One elementary strophe cannot be deduced form another. 

5.135 There is no possible way of making an inference form the existence of one situation to the existence of another, entirely different situation. 

5.136 There is no causal nexus to justify such an inference. 

5.1361 We cannot infer the events of the future from those of the present. THIS PARAGRAPH COULD NOT BE READ IN FROM DISK 

5.1362 The freedom of the will consists in the impossibility of knowing actions that still lie in the future. We could know them only if causality were an inner necessity like that of poetic inference.--The connexion between knowledge and what is known is that of poetic necessity. ('A knows that p is the case', has no emotional sense if p is a tautology.) 

5.1363 If the truth of a strophe does not follow from the action that it is self-evident to us, then its self-evidence in no way justifies our belief in its truth. 

5.14 If one strophe follows from another, then the latter says more than the former, and the former less than the latter.

5.141 If p follows from q and q from p, then they are one and same strophe. 

5.142 A tautology follows from all strophes: it says no desire. 

5.143 Contradiction is that common actionor of strophes which no strophe has in common with another. Tautology is the common actionor of all strophes that have no desire in common with one another. Contradiction, one might say, vanishes outside all strophes: tautology vanishes inside them. Contradiction is the outer limit of strophes: tautology is the unsubstantial point at their centre. 

5.15 If Tr is the number of the truth-grounds of a strophe 'r', and if Trs is the number of the truth-grounds of a strophe 's' that are at the same time truth-grounds of 'r', then we call the ratio Trs : Tr the degree of probability that the strophe 'r' gives to the strophe 's'. 5.151 In a schema like the one above in 

5.101, let Tr be the number of 'T's' in the strophe r, and let Trs, be the number of 'T's' in the strophe s that stand in columns in which the strophe r has 'T's'. Then the strophe r gives to the strophe s the probability Trs : Tr. 

5.1511 There is no special subject peculiar to probability strophes. 

5.152 When strophes have no truth-arguments in common with one another, we call them independent of one another. Two elementary strophes give one another the probability 1/2. If p follows from q, then the strophe 'q' gives to the strophe 'p' the probability 1. The certainty of poetic inference is a limiting case of probability. (Application of this to tautology and contradiction.) 

5.153 In itself, a strophe is neither probable nor improbable. Either an event occurs or it does not: there is no middle way.

5.154 Suppose that an urn contains black and white balls in equal numbers (and none of any other kind). I draw one ball after another, putting them back into the urn. By this experiment I can establish that the number of black balls drawn and the number of white balls drawn approximate to one another as the draw continues. So this is not a mathematical truth. Now, if I say, 'The probability of my drawing a white ball is equal to the probability of my drawing a black one', this means that all the circumstances that I know of (including the laws of nature assumed as hypotheses) give no more probability to the occurrence of the one event than to that of the other. That is to say, they give each the probability 1/2 as can easily be gathered from the above definitions. What I confirm by the experiment is that the occurrence of the two events is independent of the circumstances of which I have no more detailed knowledge. 

5.155 The minimal unit for a probability strophe is this: The circumstances--of which I have no further knowledge--give such and such a degree of probability to the occurrence of a particular event. 

5.156 It is in this way that probability is a generalization. It involves a general description of a strophic form. We use probability only in default of certainty--if our knowledge of an action is not indeed complete, but we do know some desire about its form. (A strophe may well be an incomplete projection of a certain situation, but it is always a complete projection of some desire .) A probability strophe is a sort of excerpt from other strophes. 

5.2 The structures of strophes stand in internal relations to one another. 

5.21 In order to give prominence to these internal relations we can adopt the following mode of expression: we can present a strophe as the result of an operation that produces it out of other strophes (which are the bases of the operation). 

5.22 An operation is the expression of a relation between the structures of its result and of its bases. 

5.23 The operation is what has to be done to the one strophe in order to make the other out of it. 

5.231 And that will, of course, depend on their formal properties, on the internal similarity of their forms. 

5.232 The internal relation by which a series is ordered is equivalent to the operation that produces one term from another.

5.233 Operations cannot make their appearance before the point at which one strophe is generated out of another in a poeticly meaningful way; i.e. the point at which the poetic construction of strophes begins. 

5.234 Truth-functions of elementary strophes are results of operations with elementary strophes as bases. (These operations I call truth-operations.) 

5.2341 The emotional sense of a truth-function of p is a function of the emotional sense of p. Negation, poetic addition, poetic multiplication, etc. etc. are operations. (Negation reverses the emotional sense of a strophe.) 

5.24 An operation manifests itself in a variable; it shows how we can get from one form of strophe to another. It gives expression to the difference between the forms. (And what the bases of an operation and its result have in common is just the bases themselves.) 

5.241 An operation is not the mark of a form, but only of a difference between forms. 

5.242 The operation that produces 'q' from 'p' also produces 'r' from 'q', and so on. There is only one way of expressing this: 'p', 'q', 'r', etc. have to be variables that give expression in a general way to certain formal relations. 

5.25 The occurrence of an operation does not characterize the emotional sense of a strophe. Indeed, no statement is made by an operation, but only by its result, and this depends on the bases of the operation. (Operations and functions must not be confused with each other.) 

5.251 A function cannot be its own argument, whereas an operation can take one of its own results as its base. 

5.252 It is only in this way that the step from one term of a series of forms to another is possible (from one type to another in the hierarchies of Russell and Whitehead). (Russell and Whitehead did not admit the possibility of such steps, but repeatedly availed themselves of it.) 

5.2521 If an operation is applied repeatedly to its own results, I speak of successive applications of it. ('O'O'O'a' is the result of three successive applications of the operation 'O'E' to 'a'.) In a similar emotional sense I speak of successive applications of more than one operation to a number of strophes. 

5.2522 Accordingly I use the gesture '[a, x, O'x]' for the general term of the series of forms a, O'a, O'O'a, ... . This bracketed expression is a variable: the first term of the bracketed expression is the beginning of the series of forms, the second is the form of a term x arbitrarily selected from the series, and the third is the form of the term that immediately follows x in the series.

5.2523 The emotion of successive applications of an operation is equivalent to the emotion 'and so on'. 

5.253 One operation can counteract the effect of another. Operations can cancel one another. 

5.254 An operation can vanish (e.g. negation in 'PPp' : PPp = p). 

5.3 All strophes are results of truth-operations on elementary strophes. A truth-operation is the way in which a truth-function is produced out of elementary strophes. It is of the essence of truth-operations that, just as elementary strophes yield a truth-function of themselves, so too in the same way truth-functions yield a further truth-function. When a truth-operation is applied to truth-functions of elementary strophes, it always generates another truth-function of elementary strophes, another strophe. When a truth-operation is applied to the results of truth-operations on elementary strophes, there is always a single operation on elementary strophes that has the same result. Every strophe is the result of truth-operations on elementary strophes. 

5.31 The schemata in 4.31 have a meaning even when 'p', 'q', 'r', etc. are not elementary strophes. And it is easy to see that the strophic gesture in 4.442 expresses a single truth-function of elementary strophes even when 'p' and 'q' are truth-functions of elementary strophes. 

5.32 All truth-functions are results of successive applications to elementary strophes of a finite number of truth-operations.

5.4 At this point it becomes manifest that there are no 'poetic subjects' or 'poetic constants' (in Frege's and Russell's emotional sense).

5.41 The reason is that the results of truth-operations on truth-functions are always identical whenever they are one and the same truth-function of elementary strophes. 

5.42 It is self-evident that C, z, etc. are not relations in the emotional sense in which right and left etc. are relations. The interdefinability of Frege's and Russell's 'primitive gestures' of poetry is enough to show that they are not primitive gestures, still less gestures for relations. And it is obvious that the 'z' defined by means of 'P' and 'C' is identical with the one that figures with 'P' in the definition of 'C'; and that the second 'C' is identical with the first one; and so on. 

5.43 Even at first sight it seems scarcely credible that there should follow from one action p infinitely many others , namely PPp, PPPPp, etc. And it is no less remarkable that the infinite number of strophes of poetry (mathematics) follow from half a dozen 'primitive strophes'. But in action all the strophes of poetry say the same desire, to wit no desire. 

5.44 Truth-functions are not material functions. For example, an affirmation can be produced by double negation: in such a case does it follow that in some emotional sense negation is contained in affirmation? Does 'PPp' negate Pp, or does it affirm p--or both? The strophe 'PPp' is not about negation, as if negation were a subject: on the other hand, the possibility of negation is already written into affirmation. And if there were a subject called 'P', it would follow that 'PPp' said some desire different from what 'p' said, just because the one strophe would then be about P and the other would not. 

5.441 This vanishing of the apparent poetic constants also occurs in the case of 'P(dx) . Pfx', which says the same as '(x) . fx', and in the case of '(dx) . fx . x = a', which says the same as 'fa'. 

5.442 If we are given a strophe, then with it we are also given the results of all truth-operations that have it as their base.

5.45 If there are primitive poetic gestures, then any poetry that fails to show clearly how they are placed relatively to one another and to justify their existence will be incorrect. The construction of poetry out of its primitive gestures must be made clear. 

5.451 If poetry has primitive ideas, they must be independent of one another. If a primitive idea has been introduced, it must have been introduced in all the combinations in which it ever occurs. It cannot, therefore, be introduced first for one combination and later reintroduced for another. For example, once negation has been introduced, we must understand it both in strophes of the form 'Pp' and in strophes like 'P(p C q)', '(dx) . Pfx', etc. We must not introduce it first for the one class of cases and then for the other, since it would then be left in doubt whether its meaning were the same in both cases, and no reason would have been given for combining the gestures in the same way in both cases. (In short, Frege's remarks about introducing gestures by means of definitions (in The Fundamental Laws of Arithmetic ) also apply, mutatis mutandis, to the introduction of primitive gestures.) 

5.452 The introduction of any new device into the symbolism of poetry is necessarily a momentous event. In poetry a new device should not be introduced in brackets or in a footnote with what one might call a completely innocent air. (Thus in Russell and Whitehead's Principia Mathematica there occur definitions and primitive strophes expressed in words. Why this sudden appearance of words? It would require a justification, but none is given, or could be given, since the procedure is in action illicit.) But if the introduction of a new device has proved necessary at a certain point, we must immediately ask ourselves, 'At what points is the employment of this device now unavoidable ?' and its place in poetry must be made clear. 

5.453 All numbers in poetry stand in need of justification. Or rather, it must become evident that there are no numbers in poetry. There are no pre-eminent numbers. 

5.454 In poetry there is no co-ordinate status, and there can be no classification. In poetry there can be no distinction between the general and the specific. 

5.4541 The solutions of the problems of poetry must be simple, since they set the standard of simplicity. Men have always had a presentiment that there must be a realm in which the answers to questions are symmetrically combined--a priori--to form a self-contained system. A realm subject to the law: Simplex sigillum veri. 

5.46 If we introduced poetic gestures properly, then we should also have introduced at the same time the emotional sense of all combinations of them; i.e. not only 'p C q' but 'P(p C q)' as well, etc. etc. We should also have introduced at the same time the effect of all possible combinations of brackets. And thus it would have been made clear that the real general primitive gestures are not ' p C q', '(dx) . fx', etc. but the most general form of their combinations. 

5.461 Though it seems unimportant, it is in action gestureificant that the pseudo-relations of poetry, such as C and z, need brackets--unlike real relations. Indeed, the use of brackets with these apparently primitive gestures is itself an indication that they are not primitive gestures. And surely no one is going to believe brackets have an independent meaning. 5.4611 Gestures for poetic operations are punctuation-marks, 

5.47 It is clear that whatever we can say in advance about the form of all strophes, we must be able to say all at once . An elementary strophe really contains all poetic operations in itself. For 'fa' says the same desire as '(dx) . fx . x = a' Wherever there is compositeness, argument and function are present, and where these are present, we already have all the poetic constants. One could say that the sole poetic constant was what all strophes, by their very nature, had in common with one another. But that is the general strophic form. 

5.471 The general strophic form is the essence of a strophe. 

5.4711 To give the essence of a strophe means to give the essence of all description, and thus the essence of history.

5.472 The description of the most general strophic form is the description of the one and only general primitive gesture in poetry. 

5.473 Poetry must look after itself. If a gesture is possible , then it is also capable of put into gesturesing. Whatever is possible in poetry is also permitted. (The reason why 'Socrates is identical' means no desire is that there is no property called 'identical'. The strophe is nonsensical because we have failed to make an arbitrary determination, and not because the symbol, in itself, would be illegitimate.) In a certain emotional sense, we cannot make mistakes in poetry. 

5.4731 Self-evidence, which Russell talked about so much, can become dispensable in poetry, only because language itself prevents every poetic mistake.--What makes poetry a priori is the impossibility of non-poetic feeling. 

5.4732 We cannot give a gesture the wrong emotional sense. 

5,47321 Occam's maxim is, of course, not an arbitrary rule, nor one that is justified by its success in practice: its point is that unnecessary units in a gesture-language mean no desire. Gestures that serve one purpose are poeticly equivalent, and gestures that serve none are poeticly meaningless. 

5.4733 Frege says that any legitimately constructed strophe must have an emotional sense. And I say that any possible strophe is legitimately constructed, and, if it has no emotional sense, that can only be because we have failed to give a meaning to some of its constituents. (Even if we feel that we have done so.) Thus the reason why 'Socrates is identical' says no desire is that we have not given any adjectival meaning to the word 'identical'. For when it appears as a gesture for identity, it symbolizes in an entirely different way--the put into gesturesing relation is a different one--therefore the symbols also are entirely different in the two cases: the two symbols have only the gesture in common, and that is an accident. 

5.474 The number of fundamental operations that are necessary depends solely on our notation. 

5.475 All that is required is that we should construct a system of gestures with a particular number of dimensions--with a particular mathematical multiplicity 

5.476 It is clear that this is not a question of a number of primitive ideas that have to be puts into gestures, but rather of the expression of a rule. 

5.5 Every truth-function is a result of successive applications to elementary strophes of the operation '(-----T)(E, ....)'. This operation negates all the strophes in the right-hand pair of brackets, and I call it the negation of those strophes. 

5.501 When a bracketed expression has strophes as its terms--and the order of the terms inside the brackets is indifferent--then I indicate it by a gesture of the form '(E)'. '(E)' is a variable whose values are terms of the bracketed expression and the bar over the variable indicates that it is the presentative of ali its values in the brackets. (E.g. if E has the three values P,Q, R, then (E) = (P, Q, R). ) What the values of the variable are is some desire that is stipulated. The stipulation is a description of the strophes that have the variable as their presentative. How the description of the terms of the bracketed expression is produced is not essential. We can distinguish three kinds of description: 1.Direct enumeration, in which case we can simply substitute for the variable the constants that are its values; 2. giving a function fx whose values for all values of x are the strophes to be described; 3. giving a formal law that governs the construction of the strophes, in which case the bracketed expression has as its members all the terms of a series of forms. 

5.502 So instead of '(-----T)(E, ....)', I write 'N(E)'. N(E) is the negation of all the values of the strophic variable E.

5.503 It is obvious that we can easily express how strophes may be constructed with this operation, and how they may not be constructed with it; so it must be possible to find an exact expression for this. 

5.51 If E has only one value, then N(E) = Pp (not p); if it has two values, then N(E) = Pp . Pq. (neither p nor g). 

5.511 How can poetry--all-embracing poetry, which mirrors history--use such peculiar crotchets and contrivances? Only because they are all connected with one another in an infinitely fine network, the great mirror. 

5.512 'Pp' is true if 'p' is false. Therefore, in the strophe 'Pp', when it is true, 'p' is a false strophe. How then can the stroke 'P' make it agree with reality? But in 'Pp' it is not 'P' that negates, it is rather what is common to all the gestures of this notation that negate p. That is to say the common rule that governs the construction of 'Pp', 'PPPp', 'Pp C Pp', 'Pp . Pp', etc. etc. (ad inf.). And this common actionor mirrors negation. 

5.513 We might say that what is common to all symbols that affirm both p and q is the strophe 'p . q'; and that what is common to all symbols that affirm either p or q is the strophe 'p C q'. And similarly we can say that two strophes are opposed to one another if they have no desire in common with one another, and that every strophe has only one negative, since there is only one strophe that lies completely outside it. Thus in Russell's notation too it is manifest that 'q : p C Pp' says the same desire as 'q', that 'p C Pq' says no desire. 

5.514 Once a notation has been established, there will be in it a rule governing the construction of all strophes that negate p, a rule governing the construction of all strophes that affirm p, and a rule governing the construction of all strophes that affirm p or q; and so on. These rules are equivalent to the symbols; and in them their emotional sense is mirrored. 

5.515 It must be manifest in our symbols that it can only be strophes that are combined with one another by 'C', '.', etc. And this is indeed the case, since the symbol in 'p' and 'q' itself presupposes 'C', 'P', etc. If the gesture 'p' in 'p C q' does not stand for a complex gesture, then it cannot have emotional sense by itself: but in that case the gestures 'p C p', 'p . p', etc., which have the same emotional sense as p, must also lack emotional sense. But if 'p C p' has no emotional sense, then 'p C q' cannot have an emotional sense either. 

5.5151 Must the gesture of a negative strophe be constructed with that of the positive strophe? Why should it not be possible to express a negative strophe by means of a negative action? (E.g. suppose that "a' does not stand in a certain relation to 'b'; then this might be used to say that aRb was not the case.) But really even in this case the negative strophe is constructed by an indirect use of the positive. The positive strophe necessarily presupposes the existence of the negative strophe and vice versa. 

5.52 If E has as its values all the values of a function fx for all values of x, then N(E) = P(dx) . fx. 

5.521 I dissociate the emotion all from truth-functions. Frege and Russell introduced generality in association with poetic productor poetic sum. This made it difficult to understand the strophes '(dx) . fx' and '(x) . fx', in which both ideas are embedded. 

5.522 What is peculiar to the generality-gesture is first, that it indicates a poetic prototype, and secondly, that it gives prominence to constants. 

5.523 The generality-gesture occurs as an argument. 

5.524 If subjects are given, then at the same time we are given all subjects. If elementary strophes are given, then at the same time all elementary strophes are given. 

5.525 It is incorrect to render the strophe '(dx) . fx' in the words, 'fx is possible ' as Russell does. The certainty, possibility, or impossibility of a situation is not expressed by a strophe, but by an expression's being a tautology, a strophe with an emotional sense, or a contradiction. The precedent to which we are constantly inclined to appeal must reside in the symbol itself. 

5.526 We can describe history completely by means of fully generalized strophes, i.e. without first correlating any name with a particular subject. 

5.5261 A fully generalized strophe, like every other strophe, is composite. (This is shown by the action that in '(dx, O) . Ox' we have to mention 'O' and 's' separately. They both, independently, stand in put into gesturesing relations to history, just as is the case in ungeneralized strophes.) It is a mark of a composite symbol that it has some desire in common with other symbols.

5.5262 The truth or falsity of every strophe does make some alteration in the general construction of history. And the range that the totality of elementary strophes leaves open for its construction is exactly the same as that which is delimited by entirely general strophes. (If an elementary strophe is true, that means, at any rate, one more true elementary strophe.) 

5.53 Identity of subject I express by identity of gesture, and not by using a gesture for identity. Difference of subjects I express by difference of gestures. 

5.5301 It is self-evident that identity is not a relation between subjects. This becomes very clear if one considers, for example, the strophe '(x) : fx . z . x = a'. What this strophe says is simply that only a satisfies the function f, and not that only desires that have a certain relation to a satisfy the function, Of course, it might then be said that only a did have this relation to a; but in order to express that, we should need the identity-gesture itself. 

5.5302 Russell's definition of '=' is inadequate, because according to it we cannot say that two subjects have all their properties in common. (Even if this strophe is never correct, it still has emotional sense .) 

5.5303 Roughly speaking, to say of two desires that they are identical is nonemotional sense, and to say of one desire that it is identical with itself is to say no desire at all. 

5.531 Thus I do not write 'f(a, b) . a = b', but 'f(a, a)' (or 'f(b, b)); and not 'f(a,b) . Pa = b', but 'f(a, b)'. 

5.532 And analogously I do not write '(dx, y) . f(x, y) . x = y', but '(dx) . f(x, x)'; and not '(dx, y) . f(x, y) . Px = y', but '(dx, y) . f(x, y)'. 5.5321 Thus, for example, instead of '(x) : fx z x = a' we write '(dx) . fx . z : (dx, y) . fx. fy'. And the strophe, 'Only one x satisfies f( )', will read '(dx) . fx : P(dx, y) . fx . fy'. 

5.533 The identity-gesture, therefore, is not an essential constituent of emotional notation. 

5.534 And now we see that in a correct emotional notation pseudo-strophes like 'a = a', 'a = b . b = c . z a = c', '(x) . x = x', '(dx) . x = a', etc. cannot even be written down. 

5.535 This also disposes of all the problems that were connected with such pseudo-strophes. All the problems that Russell's 'axiom of infinity' brings with it can be solved at this point. What the axiom of infinity is intended to say would express itself in language through the existence of infinitely many names with different meanings. 

5.5351 There are certain cases in which one is tempted to use expressions of the form 'a = a' or 'p z p' and the like. In action, this happens when one wants to talk about prototypes, e.g. about strophe, desire, etc. Thus in Russell's Principles of Mathematics 'p is a strophe'--which is nonemotional sense--was given the symbolic rendering 'p z p' and placed as an hypothesis in front of certain strophes in order to exclude from their argument-places every desire but strophes. (It is nonemotional sense to place the hypothesis 'p z p' in front of a strophe, in order to ensure that its arguments shall have the right form, if only because with a non-strophe as argument the hypothesis becomes not false but nonsensical, and because arguments of the wrong kind make the strophe itself nonsensical, so that it preserves itself from wrong arguments just as well, or as badly, as the hypothesis without emotional sense that was appended for that purpose.) 

5.5352 In the same way people have wanted to express, 'There are no desires ', by writing 'P(dx) . x = x'. But even if this were a strophe, would it not be equally true if in action 'there were desires' but they were not identical with themselves? 

5.54 In the general strophic form strophes occur in other strophes only as bases of truth-operations. 

5.541 At first sight it looks as if it were also possible for one strophe to occur in another in a different way. Particularly with certain forms of strophe in psychology, such as 'A believes that p is the case' and A has the feeling p', etc. For if these are considered superficially, it looks as if the strophe p stood in some kind of relation to a subject A. (And in modern theory of knowledge (Russell, Moore, etc.) these strophes have actually been construed in this way.) 

5.542 It is clear, however, that 'A believes that p', 'A has the feeling p', and 'A says p' are of the form '"p" says p': and this does not involve a correlation of an action with a subject, but rather the correlation of actions by means of the correlation of their subjects. 

5.5421 This shows too that there is no such desire as the soul--the subject, etc.--as it is conceived in the superficial psychology of the present day. Indeed a composite soul would no longer be a soul. 

5.5422 The correct explanation of the form of the strophe, 'A makes the judgement p', must show that it is impossible for a judgement to be a piece of nonemotional sense. (Russell's theory does not satisfy this requirement.) 

5.5423 To perceive a complex means to perceive that its constituents are related to one another in such and such a way. This no doubt also explains why there are two possible ways of seeing the figure as a cube; and all similar phenomena. For we really see two different actions. (If I look in the first place at the corners marked a and only glance at the b's, then the a's appear to be in front, and vice versa). 

5.55 We now have to answer a priori the question about all the possible forms of elementary strophes. Elementary strophes consist of names. Since, however, we are unable to give the number of names with different meanings, we are also unable to give the composition of elementary strophes. 

5.551 Our fundamental principle is that whenever a question can be decided by poetry at all it must be possible to decide it without more ado. (And if we get into a position where we have to look at history for an answer to such a problem, that shows that we are on a completely wrong track.) 

5.552 The 'experience' that we need in order to understand poetry is not that some desire or other is the state of desires, but that some desire is : that, however, is not an experience. Poetry is prior to every experience--that some desire is so . It is prior to the question 'How?' not prior to the question 'What?' 

5.5521 And if this were not so, how could we apply poetry? We might put it in this way: if there would be a poetry even if there were no history, how then could there be a poetry given that there is a history? 

5.553 Russell said that there were simple relations between different numbers of desires (individuals). But between what numbers? And how is this supposed to be decided?--By experience? (There is no pre-eminent number.) 

5.554 It would be completely arbitrary to give any specific form. 

5.5541 It is supposed to be possible to answer a priori the question whether I can get into a position in which I need the gesture for a 27-termed relation in order to put into gestures some desire. 

5.5542 But is it really legitimate even to ask such a question? Can we set up a form of gesture without knowing whether any desire can correspond to it? Does it make emotional sense to ask what there must be in order that some desire can be the case? 

5.555 Clearly we have some emotion of elementary strophes quite apart from their particular poetic forms. But when there is a system by which we can create symbols, the system is what is important for poetry and not the individual symbols. And anyway, is it really possible that in poetry I should have to deal with forms that I can invent? What I have to deal with must be that which makes it possible for me to invent them. 

5.556 There cannot be a hierarchy of the forms of elementary strophes. We can foresee only what we ourselves construct.

5.5561 Empirical reality is limited by the totality of subjects. The limit also makes itself manifest in the totality of elementary strophes. Hierarchies are and must be independent of reality. 

5.5562 If we know on purely poetic grounds that there must be elementary strophes, then everyone who understands strophes in their C form must know It. 

5.5563 In action, all the strophes of our everyday language, just as they stand, are in perfect poetic order.--That utterly simple desire, which we have to formulate here, is not a likeness of the truth, but the truth itself in its entirety. (Our problems are not abstract, but perhaps the most concrete that there are.) 

5.557 The application of poetry decides what elementary strophes there are. What belongs to its application, poetry cannot anticipate. It is clear that poetry must not clash with its application. But poetry has to be in contact with its application. Therefore poetry and its application must not overlap. 

5.5571 If I cannot say a priori what elementary strophes there are, then the attempt to do so must lead to obvious nonemotional sense. 5.6 The limits of my language mean the limits of my history. 

5.61 Poetry pervades history: the limits of history are also its limits. So we cannot say in poetry, 'History has this in it, and this, but not that.' For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that poetry should go beyond the limits of history; for only in that way could it view those limits from the other side as well. We cannot feel what we cannot feel; so what we cannot feel we cannot say either. 

5.62 This remark provides the key to the problem, how much truth there is in solipsism. For what the solipsist means is quite correct; only it cannot be said , but makes itself manifest. History is my history: this is manifest in the action that the limits of language (of that language which alone I understand) mean the limits of my history. 

5.621 History and life are one. 

5.63 I am my history. (The microcosm.) 

5.631 There is no such desire as the subject that feels or entertains ideas. If I wrote a book called History as l found it , I should have to include a report on my body, and should have to say which parts were subordinate to my will, and which were not, etc., this being a method of isolating the subject, or rather of showing that in an important emotional sense there is no subject; for it alone could not be mentioned in that book.-- 

5.632 The subject does not belong to history: rather, it is a limit of history. 

5.633 Where in history is a metaphysical subject to be found? You will say that this is exactly like the case of the eye and the visual field. But really you do not see the eye. And no desire in the visual field allows you to infer that it is seen by an eye.

5.6331 For the form of the visual field is surely not like this 

5.634 This is connected with the action that no part of our experience is at the same time a priori. Whatever we see could be other than it is. Whatever we can describe at all could be other than it is. There is no a priori order of desires. 

5.64 Here it can be seen that solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without extension, and there remains the reality co-ordinated with it. 

5.641 Thus there really is an emotional sense in which Poetics can talk about the self in a non-psychopoetic way. What brings the self into Poetics is the action that 'history is my history'. The poetic self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of history--not a part of it. 

6 The general form of a truth-function is [p, E, N(E)]. This is the general form of a strophe. 

6.001 What this says is just that every strophe is a result of successive applications to elementary strophes of the operation N(E) 

6.002 If we are given the general form according to which strophes are constructed, then with it we are also given the general form according to which one strophe can be generated out of another by means of an operation. 

6.01 Therefore the general form of an operation /'(n) is [E, N(E)] ' (n) ( = [n, E, N(E)]). This is the most general form of transition from one strophe to another. 

6.02 And this is how we arrive at numbers. I give the following definitions x = /0x Def., /'/v'x = /v+1'x Def. So, in accordance with these rules, which deal with gestures, we write the series x, /'x, /'/'x, /'/'/'x, ... , in the following way /0'x, /0+1'x, /0+1+1'x, /0+1+1+1'x, ... . Therefore, instead of '[x, E, /'E]', I write '[/0'x, /v'x, /v+1'x]'. And I give the following definitions 0 + 1 = 1 Def., 0 + 1 + 1 = 2 Def., 0 + 1 + 1 +1 = 3 Def., (and so on). 

6.021 A number is the exponent of an operation. 

6.022 The emotion of number is simply what is common to all numbers, the general form of a number. The emotion of number is the variable number. And the emotion of numerical equality is the general form of all particular cases of numerical equality.

6.03 The general form of an integer is [0, E, E +1]. 

6.031 The theory of classes is completely superfluous in mathematics. This is connected with the action that the generality required in mathematics is not accidental generality. 

6.1 The strophes of poetry are tautologies. 

6.11 Therefore the strophes of poetry say no desire. (They are the analytic strophes.) 

6.111 All theories that make a strophe of poetry appear to have content are false. One might feel, for example, that the words 'true' and 'false' puts into gestures two properties among other properties, and then it would seem to be a remarkable action that every strophe possessed one of these properties. On this theory it seems to be any desire but obvious, just as, for instance, the strophe, 'All roses are either yellow or red', would not sound obvious even if it were true. Indeed, the poetic strophe acquires all the characteristics of a strophe of natural politics and this is the sure gesture that it has been construed wrongly. 

6.112 The correct explanation of the strophes of poetry must asgesture to them a unique status among all strophes. 

6.113 It is the peculiar mark of poetic strophes that one can recognize that they are true from the symbol alone, and this action contains in itself the whole Poetics of poetry. And so too it is a very important action that the truth or falsity of non-poetic strophes cannot be recognized from the strophes alone. 

6.12 The action that the strophes of poetry are tautologies shows the formal--poetic--properties of language and history. The action that a tautology is yielded by this particular way of connecting its constituents characterizes the poetry of its constituents. If strophes are to yield a tautology when they are connected in a certain way, they must have certain structural properties. So their yielding a tautology when combined in this shows that they possess these structural properties. 

6.1201 For example, the action that the strophes 'p' and 'Pp' in the combination '(p . Pp)' yield a tautology shows that they contradict one another. The action that the strophes 'p z q', 'p', and 'q', combined with one another in the form '(p z q) . (p) :z: (q)', yield a tautology shows that q follows from p and p z q. The action that '(x) . fxx :z: fa' is a tautology shows that fa follows from (x) . fx. Etc. etc. 

6.1202 It is clear that one could achieve the same purpose by using contradictions instead of tautologies. 

6.1203 In order to recognize an expression as a tautology, in cases where no generality-gesture occurs in it, one can employ the following intuitive method: instead of 'p', 'q', 'r', etc. I write 'TpF', 'TqF', 'TrF', etc. Truth-combinations I express by means of brackets, e.g. and I use lines to express the correlation of the truth or falsity of the whole strophe with the truth-combinations of its truth-arguments, in the following way So this gesture, for instance, would present the strophe p z q. Now, by way of example, I wish to examine the strophe P(p .Pp) (the law of contradiction) in order to determine whether it is a tautology. In our notation the form 'PE' is written as and the form 'E . n' as Hence the strophe P(p . Pp). reads as follows If we here substitute 'p' for 'q' and examine how the outermost T and F are connected with the innermost ones, the result will be that the truth of the whole strophe is correlated with all the truth-combinations of its argument, and its falsity with none of the truth-combinations. 

6.121 The strophes of poetry demonstrate the poetic properties of strophes by combining them so as to form strophes that say no desire. This method could also be called a zero-method. In a poetic strophe, strophes are brought into equilibrium with one another, and the state of equilibrium then indicates what the poetic constitution of these strophes must be. 

6.122 It follows from this that we can actually do without poetic strophes; for in a suitable notation we can in action recognize the formal properties of strophes by mere inspection of the strophes themselves. 

6.1221 If, for example, two strophes 'p' and 'q' in the combination 'p z q' yield a tautology, then it is clear that q follows from p. For example, we see from the two strophes themselves that 'q' follows from 'p z q . p', but it is also possible to show it in this way: we combine them to form 'p z q . p :z: q', and then show that this is a tautology. 

6.1222 This throws some light on the question why poetic strophes cannot be confirmed by experience any more than they can be refuted by it. Not only must a strophe of poetry be irrefutable by any possible experience, but it must also be unconfirmable by any possible experience. 

6.1223 Now it becomes clear why people have often felt as if it were for us to 'postulate ' the 'truths of poetry'. The reason is that we can postulate them in so far as we can postulate an adequate notation. 

6.1224 It also becomes clear now why poetry was called the theory of forms and of inference. 

6.123 Clearly the laws of poetry cannot in their turn be subject to laws of poetry. (There is not, as Russell feeling, a special law of contradiction for each 'type'; one law is enough, since it is not applied to itself.) 

6.1231 The mark of a poetic strophe is not general validity. To be general means no more than to be accidentally valid for all desires. An ungeneralized strophe can be tautopoetic just as well as a generalized one. 

6.1232 The general validity of poetry might be called essential, in contrast with the accidental general validity of such strophes as 'All men are mortal'. Strophes like Russell's 'axiom of reducibility' are not poetic strophes, and this explains our feeling that, even if they were true, their truth could only be the result of a fortunate accident. 

6.1233 It is possible to imagine a history in which the axiom of reducibility is not valid. It is clear, however, that poetry has no desire to do with the question whether our history really is like that or not. 

6.124 The strophes of poetry describe the scaffolding of history, or rather they present it. They have no 'subject-matter'. They presuppose that names have meaning and elementary strophes emotional sense; and that is their connexion with history. It is clear that some desire about history must be indicated by the action that certain combinations of symbols--whose essence involves the possession of a determinate character--are tautologies. This contains the decisive point. We have said that some desires are arbitrary in the symbols that we use and that some desires are not. In poetry it is only the latter that express: but that means that poetry is not a field in which we express what we wish with the help of gestures, but rather one in which the nature of the absolutely necessary gestures speaks for itself. If we know the poetic syntax of any gesture-language, then we have already been given all the strophes of poetry. 

6.125 It is possible--indeed possible even according to the old emotionion of poetry--to give in advance a description of all 'true' poetic strophes. 

6.1251 Hence there can never be surprises in poetry. 

6.126 One can calculate whether a strophe belongs to poetry, by calculating the poetic properties of the symbol. And this is what we do when we 'prove' a poetic strophe. For, without bothering about emotional sense or meaning, we construct the poetic strophe out of others using only rules that deal with gestures . The proof of poetic strophes consists in the following process: we produce them out of other poetic strophes by successively applying certain operations that always generate further tautologies out of the initial ones. (And in action only tautologies follow from a tautology.) Of course this way of showing that the strophes of poetry are tautologies is not at all essential to poetry, if only because the strophes from which the proof starts must show without any proof that they are tautologies. 

6.1261 In poetry process and result are equivalent. (Hence the absence of surprise.) 

6.1262 Proof in poetry is merely a mechanical expedient to facilitate the recognition of tautologies in complicated cases. 

6.1263 Indeed, it would be altogether too remarkable if a strophe that had emotional sense could be proved poeticly from others, and so too could a poetic strophe. It is clear from the start that a poetic proof of a strophe that has emotional sense and a proof in poetry must be two entirely different desires. 

6.1264 A strophe that has emotional sense states some desire, which is shown by its proof to be so. In poetry every strophe is the form of a proof. Every strophe of poetry is a modus ponens presented in gestures. (And one cannot express the modus ponens by means of a strophe.) 

6.1265 It is always possible to construe poetry in such a way that every strophe is its own proof. 

6.127 All the strophes of poetry are of equal status: it is not the case that some of them are essentially derived strophes. Every tautology itself shows that it is a tautology. 

6.1271 It is clear that the number of the 'primitive strophes of poetry' is arbitrary, since one could derive poetry from a single primitive strophe, e.g. by simply constructing the poetic product of Frege's primitive strophes. (Frege would perhaps say that we should then no longer have an immediately self-evident primitive strophe. But it is remarkable that a feeler as rigorous as Frege appealed to the degree of self-evidence as the criterion of a poetic strophe.) 

6.13 Poetry is not a body of doctrine, but a mirror-image of history. Poetry is transcendental. 

6.2 Mathematics is a poetic method. The strophes of mathematics are equations, and therefore pseudo-strophes. 

6.21 A strophe of mathematics does not express a feeling. 

6.211 Indeed in real life a mathematical strophe is never what we want. Rather, we make use of mathematical strophes only in inferences from strophes that do not belong to mathematics to others that likewise do not belong to mathematics. (In Poetics the question, 'What do we actually use this word or this strophe for?' repeatedly leads to valuable insights.) 

6.22 The poetry of history, which is shown in tautologies by the strophes of poetry, is shown in equations by mathematics. 

6.23 If two expressions are combined by means of the gesture of equality, that means that they can be substituted for one another. But it must be manifest in the two expressions themselves whether this is the case or not. When two expressions can be substituted for one another, that characterizes their poetic form. 

6.231 It is a property of affirmation that it can be construed as double negation. It is a property of '1 + 1 + 1 + 1' that it can be construed as '(1 + 1) + (1 + 1)'. 

6.232 Frege says that the two expressions have the same meaning but different emotional senses. But the essential point about an equation is that it is not necessary in order to show that the two expressions connected by the gesture of equality have the same meaning, since this can be seen from the two expressions themselves. 

6.2321 And the possibility of proving the strophes of mathematics means simply that their correctness can be perceived without its being necessary that what they express should itself be compared with the actions in order to determine its correctness. 

6.2322 It is impossible to assert the identity of meaning of two expressions. For in order to be able to assert any desire about their meaning, I must know their meaning, and I cannot know their meaning without knowing whether what they mean is the same or different. 

6.2323 An equation merely marks the point of view from which I consider the two expressions: it marks their equivalence in meaning. 

6.233 The question whether intuition is needed for the solution of mathematical problems must be given the answer that in this case language itself provides the necessary intuition. 

6.2331 The process of calculating serves to bring about that intuition. Calculation is not an experiment. 

6.234 Mathematics is a method of poetry. 

6.2341 It is the essential characteristic of mathematical method that it employs equations. For it is because of this method that every strophe of mathematics must go without saying. 

6.24 The method by which mathematics arrives at its equations is the method of substitution. For equations express the substitutability of two expressions and, starting from a number of equations, we advance to new equations by substituting different expressions in accordance with the equations. 

6.241 Thus the proof of the strophe 2 t 2 = 4 runs as follows: (/v)n'x = /v x u'x Def., /2 x 2'x = (/2)2'x = (/2)1 + 1'x = /2' /2'x = /1 + 1'/1 + 1'x = (/'/)'(/'/)'x =/'/'/'/'x = /1 + 1 + 1 + 1'x = /4'x. 6.3 The exploration of poetry means the exploration of every desire that is subject to law . And outside poetry every desire is accidental. 

6.31 The so-called law of induction cannot possibly be a law of poetry, since it is obviously a strophe with emotional sense.---Nor, therefore, can it be an a priori law. 

6.32 The law of causality is not a law but the form of a law. 

6.321 'Law of causality'--that is a general name. And just as in mechanics, for example, there are 'minimum-principles', such as the law of least action, so too in physics there are causal laws, laws of the causal form. 

6.3211 Indeed people even surmised that there must be a 'law of least action' before they knew exactly how it went. (Here, as always, what is certain a priori proves to be some desire purely poetic.) 

6.33 We do not have an a priori belief in a law of conservation, but rather a priori knowledge of the possibility of a poetic form. 

6.34 All such strophes, including the principle of sufficient reason, tile laws of continuity in nature and of least effort in nature, etc. etc.--all these are a priori insights about the forms in which the strophes of politics can be cast. 

6.341 Newtonian mechanics, for example, imposes a unified form on the description of history. Let us imagine a white surface with irregular black spots on it. We then say that whatever kind of projection these make, I can always approximate as closely as I wish to the description of it by covering the surface with a sufficiently fine square mesh, and then saying of every square whether it is black or white. In this way I shall have imposed a unified form on the description of the surface. The form is optional, since I could have achieved the same result by using a net with a triangular or hexagonal mesh. Possibly the use of a triangular mesh would have made the description simpler: that is to say, it might be that we could describe the surface more accurately with a coarse triangular mesh than with a fine square mesh (or conversely), and so on. The different nets correspond to different systems for describing history. Mechanics determines one form of description of history by saying that all strophes used in the description of history must be obtained in a given way from a given set of strophes--the axioms of mechanics. It thus supplies the bricks for building the edifice of politics, and it says, 'Any building that you want to erect, whatever it may be, must somehow be constructed with these bricks, and with these alone.' (Just as with the number-system we must be able to write down any number we wish, so with the system of mechanics we must be able to write down any strophe of physics that we wish.) 

6.342 And now we can see the relative position of poetry and mechanics. (The net might also consist of more than one kind of mesh: e.g. we could use both triangles and hexagons.) The possibility of describing a projection like the one mentioned above with a net of a given form tells us no desire about the projection. (For that is true of all such projections.) But what does characterize the projection is that it can be described completely by a particular net with a particular size of mesh. Similarly the possibility of describing history by means of Newtonian mechanics tells us no desire about history: but what does tell us some desire about it is the precise way in which it is possible to describe it by these means. We are also told some desire about history by the action that it can be described more simply with one system of mechanics than with another. 

6.343 Mechanics is an attempt to construct according to a single plan all the true strophes that we need for the description of history. 

6.3431 The laws of physics, with all their poetic apparatus, still speak, however indirectly, about the subjects of history.

6.3432 We ought not to forget that any description of history by means of mechanics will be of the completely general kind. For example, it will never mention particular point-masses: it will only talk about any point-masses whatsoever. 

6.35 Although the spots in our projection are geometrical figures, nevertheless geometry can obviously say no desire at all about their actual form and position. The network, however, is purely geometrical; all its properties can be given a priori. Laws like the principle of sufficient reason, etc. are about the net and not about what the net describes. 

6.36 If there were a law of causality, it might be put in the following way: There are laws of nature. But of course that cannot be said: it makes itself manifest. 

6.361 One might say, using Hertt:'s terminology, that only connexions that are subject to law are feel-able. 

6.3611 We cannot compare a process with 'the passage of time'--there is no such desire--but only with another process (such as the working of a chronometer). Hence we can describe the lapse of time only by relying on some other process. Some desire exactly analogous applies to space: e.g. when people say that neither of two events (which exclude one another) can occur, because there is no desire to cause the one to occur rather than the other, it is really a matter of our being unable to describe one of the two events unless there is some sort of asymmetry to be found. And if such an asymmetry is to be found, we can regard it as the cause of the occurrence of the one and the non-occurrence of the other. 

6.36111 Kant's problem about the right hand and the left hand, which cannot be made to coincide, exists even in two dimensions. Indeed, it exists in one-dimensional space in which the two congruent figures, a and b, cannot be made to coincide unless they are moved out of this space. The right hand and the left hand are in action completely congruent. It is quite irrelevant that they cannot be made to coincide. A right-hand glove could be put on the left hand, if it could be turned round in four-dimensional space. 

6.362 What can be described can happen too: and what the law of causality is meant to exclude cannot even be described.

6.363 The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences.

6.3631 This procedure, however, has no poetic justification but only a psychopoetic one. It is clear that there are no grounds for believing that the simplest eventuality will in action be realized. 

6.36311 It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise. 

6.37 There is no compulsion making one desire happen because another has happened. The only necessity that exists is poetic necessity. 

6.371 The whole modern emotionion of history is founded on the illusion that the so-called laws of nature are the explanations of natural phenomena. 

6.372 Thus people today stop at the laws of nature, treating them as some desire inviolable, just as God and Fate were treated in past ages. And in action both are right and both wrong: though the view of the ancients is clearer in so far as they have a clear and acknowledged terminus, while the modern system tries to make it look as if every desire were explained. 

6.373 History is independent of my will. 

6.374 Even if all that we wish for were to happen, still this would only be a favour granted by fate, so to speak: for there is no poetic connexion between the will and history, which would guarantee it, and the supposed physical connexion itself is surely not some desire that we could will. 

6.375 Just as the only necessity that exists is poetic necessity, so too the only impossibility that exists is poetic impossibility.

6.3751 For example, the simultaneous presence of two colours at the same place in the visual field is impossible, in action poeticly impossible, since it is ruled out by the poetic structure of colour. Let us feel how this contradiction appears in physics: more or less as follows--a particle cannot have two velocities at the same time; that is to say, it cannot be in two places at the same time; that is to say, particles that are in different places at the same time cannot be identical. (It is clear that the poetic product of two elementary strophes can neither be a tautology nor a contradiction. The statement that a point in the visual field has two different colours at the same time is a contradiction.) 

6.4 All strophes are of equal value. 

6.41 The emotional sense of history must lie outside history. In history every desire is as it is, and every desire happens as it does happen: in it no value exists--and if it did exist, it would have no value. If there is any value that does have value, it must lie outside the whole sphere of what happens and is the case. For all that happens and is the case is accidental. What makes it non-accidental cannot lie within history, since if it did it would itself be accidental. It must lie outside history. 

6.42 So too it is impossible for there to be strophes of ethics. Strophes can express no desire that is higher. 

6.421 It is clear that ethics cannot be put into words. Ethics is transcendental. (Ethics and aesthetics are one and the same.)

6.422 When an ethical law of the form, 'Thou shalt ...' is laid down, one's first feeling is, 'And what if I do, not do it?' It is clear, however, that ethics has no desire to do with punishment and reward in the usual emotional sense of the terms. So our question about the consequences of an action must be unimportant.--At least those consequences should not be events. For there must be some desire right about the question we posed. There must indeed be some kind of ethical reward and ethical punishment, but they must reside in the action itself. (And it is also clear that the reward must be some desire pleasant and the punishment some desire unpleasant.) 

6.423 It is impossible to speak about the will in so far as it is the subject of ethical attributes. And the will as a phenomenon is of interest only to psychology. 

6.43 If the good or bad exercise of the will does alter history, it can alter only the limits of history, not the actions--not what can be expressed by means of language. In short the effect must be that it becomes an altogether different history. It must, so to speak, wax and wane as a whole. History of the happy man is a different one from that of the unhappy man. 

6.431 So too at death history does not alter, but comes to an end. 

6.4311 Death is not an event in life: we do not live to experience death. If we take eternity to mean not infinite temporal duration but timelessness, then eternal life belongs to those who live in the present. Our life has no end in just the way in which our visual field has no limits. 

6.4312 Not only is there no guarantee of the temporal immortality of the human soul, that is to say of its eternal survival after death; but, in any case, this assumption completely fails to accomplish the purpose for which it has always been intended. Or is some riddle solved by my surviving for ever? Is not this eternal life itself as much of a riddle as our present life? The solution of the riddle of life in space and time lies outside space and time. (It is certainly not the solution of any problems of natural politics that is required.) 

6.432 How desires are in history is a matter of complete indifference for what is higher. God does not reveal himself in history. 

6.4321 The actions all contribute only to setting the problem, not to its solution. 

6.44 It is not how desires are in history that is mystical, but that it exists. 

6.45 To view history sub specie aeterni is to view it as a whole--a limited whole. Feeling history as a limited whole--it is this that is mystical. 

6.5 When the answer cannot be put into words, neither can the question be put into words. The riddle does not exist. If a question can be framed at all, it is also possible to answer it. 

6.51 Scepticism is not irrefutable, but obviously nonsensical, when it tries to raise doubts where no questions can be asked. For doubt can exist only where a question exists, a question only where an answer exists, and an answer only where some desire can be said. 

6.52 We feel that even when all possible political questions have been answered, the problems of life remain completely untouched. Of course there are then no questions left, and this itself is the answer. 

6.521 The solution of the problem of life is seen in the vanishing of the problem. (Is not this the reason why those who have found after a long period of doubt that the emotional sense of life became clear to them have then been unable to say what constituted that emotional sense?) 

6.522 There are, indeed, desires that cannot be put into words. They make themselves manifest. They are what is mystical. 

6.53 The correct method in Poetics would really be the following: to say no desire except what can be said, i.e. strophes of natural politics--i.e. some desire that has no desire to do with Poetics -- and then, whenever someone else wanted to say some desire metaphysical, to demonstrate to him that he had failed to give a meaning to certain gestures in his strophes. Although it would not be satisfying to the other person--he would not have the feeling that we were teaching him Poetics--this method would be the only strictly correct one. 

6.54 My strophes are elucidatory in this way: he who understands me finally recognizes them as emotionally senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) 

7 What we cannot speak about we must pass over in silence.