Ludwig Wittgenstein

"The first time I remember having a "revelatory insight" reading Wittgenstein was late one night while working behind the counter at an all-night gas station. I read the remark "why can't I describe the aroma of coffee". I fully understood then what Ludwig Wittgenstein meant by his writings as a "kind of therapy", and further the metaphysical focus of his intellectual and moral quest. I had always been struck by his method of writing little numbered comments as a kind of Zen koan" On Ludwig Wittgenstein

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Selections from Tractatus Logico-Philosophicus

1		The world is all that is the case.
1.1		The world is the totality of facts, not of things.
1.11		The world is determined by the facts, and by their being all the facts.
1.12		For the totality of facts determines what is the case, and also whatever is not the case.
1.13		The facts in logical space are the world.
1.2		The world divides into facts.
1.21		Each item can be the case or not the case while everything else remains the same.
2		What is the case—a fact—is the existence of states of affairs.
2.01		A state of affairs (a state of things) is a combination of objects (things).
2.02		Objects are simple.
2.03		In a state of affairs objects fit into one another like the links of a chain.
2.04		The totality of existing states of affairs is the world.
2.05		The totality of existing states of affairs also determines which states of affairs do not exist.
2.06		The existence and non-existence of states of affairs is reality.
2.1		We picture facts to ourselves.
2.11		A picture presents a situation in logical space, the existence and non-existence of states of affairs.
2.12		A picture is a model of reality.
2.13		In a picture objects have the elements of the picture corresponding to them.
2.14		What constitutes a picture is that its elements are related to one another in a determinate way.
2.15		The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way.       Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture.
2.16		If a fact is to be a picture, it must have something in common with what it depicts.
2.17		What a picture must have in common with reality, in order to be able to be able to depict it—correctly or incorrectly—in the way it does, is its pictorial form.
2.18		What any picture, of whatever form, must have in common with reality, in order to be able to depict it—correctly or incorrectly—in any way at all, is logical form, i.e. the form of reality.
2.19		Logical pictures can depict the world.
2.2		A picture has logico-pictorial form in common with what it depicts.
2.21		A picture agrees with reality or fails to agree, it is correct or incorrect, true or false.
2.22		What a picture represents it represents independently of its truth or falsity, by means of its pictorial form.
3		A logical picture of facts is a thought.
3.01		The totality of true thoughts is a picture of the world.
3.02		A thought contains the possibility of the situation of which it is the thought. What is thinkable is possible too.
3.03		Thought can never be of anything illogical, since, if it were, we should have to think illogically.
3.04		If a thought were correct a priori, it would be a thought whose possibility ensured its truth.
3.05		A priori knowledge that a thought was true would be possible only if its truth were recognizable from thought itself (without anything to compare it with).
3.1		In a proposition a thought finds an expression that can be perceived by the senses.
3.11		We use the perceptible sign of a proposition (spoken or written, etc.) as a projection of a possible situation.
3.12		I call the sign with which we express a thought a propositional sign—And a proposition is a propositional sign in its projective relation to the world.
3.13		A proposition includes all that the projection includes, but not what is projected.       Therefore, though what is projected is not itself included, its possibility is.       A proposition, therefore, does not actually contain its sense, but does contain the possibility of expressing it.       (‘The content of proposition’ means the content of a proposition that has sense.)       A proposition contains the form, but not the content, of its sense.
3.14		What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to one another.
3.2		In a proposition a thought can be expressed in such a way that elements of the propositional sign correspond to the objects of the thought.
3.21		The configuration of objects in a situation corresponds to the configuration of simple signs in the propositional sign.
3.22		In a proposition a name is the representative of an object.
3.23		The requirement that simple signs be possible is the requirement that sense be determinate.
3.24		A proposition about a complex stands in an internal relation to a proposition about a constituent of the complex.       A complex can be given only by its description, which will be right or wrong. A proposition that mentions a complex will not be nonsensical, if the complex does not exist, but simply false.       When a propositional element signifies a complex, this can be seen from an indeterminateness in the propositions in which it occurs. In such cases we know that the proposition leaves something undetermined. (In fact 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 proposition has one and only one complete analysis.
3.26		A name cannot be dissected any further by means of a definition: it is a primitive sign.
3.3		Only propositions have sense; only in the nexus of a proposition does a name have meaning.
3.31		I call any part of propositions that characterizes its sense an expression (or a symbol).       (A proposition is itself an expression.)       Everything essential to their sense that propositions can have in common with one another is an expression.       An expression is the mark of a form and a content.
3.32		A sign is what can be perceived of a symbol.
3.33		In logical syntax the meaning of a sign should never play a role. It must be possible to establish logical syntax without mentioning the meaning of a sign: only the description of expressions may be presupposed.
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3.34		A proposition possesses essential and accidental features.       Accidental features are those that result from the particular way in which the propositional sign is produced. Essential features are those without which the proposition could not express its sense.
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3.4		A proposition determines a place in logical space. The existence of this logical place is guaranteed by the mere existence of the constituents—by the existence of the proposition with a sense.
3.41		The propositional sign with logical coordinates—that is the logical space.
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3.42		A proposition can determine only one place in logical space: nevertheless the whole of logical space must already be given by it.       (Otherwise negation, logical sum, logical product, etc., would introduce more and more new elements—in coordination.)       (The logical scaffolding surrounding a picture determines logical space. The force of a proposition reaches through the whole of logical space.)
3.5		A propositional sign, applied and thought out, is a thought.
4		A thought is a proposition with a sense.
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4.01		A proposition is a picture of reality.       A proposition is a model of reality as we imagine it.
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4.02		We can see this from the fact that we understand the sense of a propositional sign without its having been explained to us.
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4.03		A proposition must use old expressions to communicate a new sense.       A proposition communicates a situation to us, and so it must be essentially connected with the situation.       And the connexion is precisely that it is its logical picture.       A proposition states something only in so far as it is a picture.
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4.04		In a proposition there must be exactly as many distinguishable parts as in the situation that it represents.       The two must possess the same logical (mathematical) multiplicity. (Compare Hertz’s Mechanics on dynamical models.)
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4.05		Reality is compared with propositions.
4.06		A proposition can be true or false only in virtue of being a picture of reality.
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4.1		Propositions represent the existence and non-existence of states of affairs.
4.11		The totality of true propositions is the whole of natural science (or the whole corpus of the natural sciences).
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4.12		Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it—logical form.       In order to be able to represent logical form, we should have to be able to station ourselves with propositions somewhere outside logic, that is to say outside the world.
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4.2		The sense of a proposition is its agreement and disagreement with possibilities of existence and non-existence of states of affairs.
4.21		The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs.
4.211		It is a sign of a proposition’s being elementary that there can be no elementary proposition contradicting it.
4.22		An elementary proposition consists of names. It is a nexus, a concatenation, of names.
4.23		It is only in the nexus of an elementary proposition that a name occurs in a proposition.
4.24		Names are the simple symbols: I indicate them by single letters . I write elementary propositions as functions of names, so that they have the form , , etc.       Or I indicate them by the letters .
4.25		If an elementary proposition is true, the state of affairs exists: if an elementary proposition is false, the state of affairs does not exist.
4.26		If all true elementary propositions are given, the result is a complete description of the world. The world is completely described by giving all elementary propositions, and adding which of them are true and which false.
4.27		For states of affairs, there are possibilities of existence and non-existence.       Of these states of affairs 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 elementary propositions.
4.3		Truth-possibilities of elementary propositions mean possibilities of existence and non-existence of states of affairs.
4.31		We can represent truth-possibilities by schemata of the following kind (‘T’ means ‘true’, ‘F’ means ‘false’; the rows of ‘Ts’ and ‘Fs’ under the row of elementary propositions symbolize their truth-possibilities in a way that can easily be understood):
4.4		A proposition is an expression of agreement and disagreement with truth-possibilities of elementary propositions.
4.41		Truth-possibilities of elementary propositions are the conditions of the truth and falsity of propositions.
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4.42		For elementary propositions there are ways in which a proposition 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.
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4.44		The sign that results from correlating the mark ‘T’ with truth-possibilities is a propositional sign.
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4.45		For elementary propositions there are possible groups of truth-conditions.       The groups of truth-conditions that are obtainable from the truth-possibilities of a given number of elementary propositions 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 proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological.       In the second case the proposition is false for all the truth-possibilities: the truth-conditions are contradictory.       In the first case we call the proposition a tautology; in the second, a contradiction.
4.5		It now seems possible to give the most general propositional form: that is, to give a description of the proposition of any sign-language whatsoever in such a way that every possible sense can be expressed by a symbol satisfying the description, and every symbol satisfying the description can express a sense, provided that the meanings of the names are suitably chosen.       It is clear that only what is essential to the most general propositional form may be included in its description—for otherwise it would not be the most general form.       The existence of a general propositional form is proved by the fact that there cannot be a proposition whose form could not have been foreseen (i.e. constructed). The general form of a proposition is: This is how things stand.
4.51		Suppose that I am given all elementary propositions: then I can simply ask what propositions I can construct out of them. And there I have all propositions, and that fixes their limits.
4.52		Propositions comprise all that follows from the totality of all elementary propositions (and, of course, from its being the totality of them all). (Thus, in a certain sense, it could be said that all propositions were generalizations of elementary propositions.)
4.53		The general propositional form is a variable.
5		A proposition is a truth-function of elementary propostions.       (An elementary proposition is a truth-function of itself.)
5.01		Elementary propositions are the truth-arguments of propostions.
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 signs containing them       For example, when Russell writes '+c', the 'c' is an affix which indicates that the sign as a whole is the addition-sign for cardinal numbers. But the use of this sign is the result of arbitrary convention and it would be quite possible to choose a simple sign instead of '+c'; in '~p', however, 'p' is not an affix but an argument: the sense of '~p' cannot be understood unless the 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 object 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 propostions and functions is based on the confusion between an argument and an affix. Frege regarded the proposition of logic as names, and their arguments as the affixes of those names.
5.1		Truth-functions can be arranged in series.       That is the foundations of the theory of probability.
5.101		The truth-functions of every number of elementary propostions can be written in a schema of the following kind:       Those truth-functions of its truth-arguments, which verify the propostion, I shall call its truth-grounds.
5.11		If all the truth-grounds that are common to a number of propostions are at the same time truth-grounds of a certain propostion, then we say that the truth of that proposition follows from the truth of the others.
5.12		In particular, the truth of a propostion 'p' follows from the truth of another propostion 'q' if all the truth-grounds of the latter are truth-grounds of the former.
5.121		The truth-grounds of 'q' are contained in those of 'p'; 'p' follows from 'q'.
5.122		If 'p' follows from 'q', the sense of 'p' is contained in that of 'q'.
5.123		If a god creates a world in which certain propostions are true, he creates thereby also a world in which all propositions consequent on them are true. And similarly he could not create a world in which the propostion 'p' is true without creating all its objects.
5.124		A proposition asserts every propostion which follows from it.
5.13		When the truth of one proposition follows from the truth of others, we can see this from the structure of the propositions.
5.133		All inference takes place a priori.
5.134		From an elementary proposition no other can be inferred.
5.135		In no way can an inference be made from the existence of another entirely different from it.
5.136		There is no causal nexus which justifies such an inference.
5.14		If one proposition follows from another, then the latter says more than the former, and the former less than the latter.
5.15		If Tr is the number of the truth-grounds of a proposition 'r', and if Trs is the number of the truth-grounds of a proposition 's' that are at the same time truth-grounds of 'r', then we call the ratio Trs : Tr the degree of probability that the proposition 'r' gives to the proposition 's'.
5.2		The structures of propositions 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 represent a proposition as the result of an operation that produces it out of other propositions (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 proposition in order to make the other out of it.
5.24		An operation manifests itself in a variable; it shows how we can get from one form of proposition 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.)
5.25		The occurrence of an operation does not characterize the sense of a proposition.       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.)
5.3		All propositions are results of truth-operations on elementary propositions.       A truth-operation is the way in which a truth-function is produced out of elementary propositions.       It is the essence of truth-operations that, just as elementary propositions 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 propositions, it always generates another truth-function of elementary propositions, another proposition. When a truth-operation is applied to the result of truth-operations on elementary propositions, there is always a single operation on elementary propositions that has the same result.       Every proposition is the result of truth-operations on elementary propositions.
5.31		The schemata in 4.31 have a meaning even when 'p', 'q', 'r', etc. are not elementary propositions.       And it is easy to see that the propositional sign in 4.42 expresses a single truth-function of elementary propositions even when 'p' and 'q' are truth-functions of elementary propositions.
5.32		All truth-functions are results of successive applications to elementary propositions of a finite number of truth-operations.
5.4		At this point it becomes manifest that there are no 'logical objects' or 'logical constants' (in Frege's and Russell's sense).
5.41		The reason is that the result of truth-operations on truth-functions are always identical whenever they are one and the same truth-function of elementary propositions.
5.42		It is self-evident that that v, , etc. are not relations in the sense in which right and left etc. are relations.       The interdefinability of Frege's and Russell's 'primitive signs' of logic is enough to show that they are not primitive signs, still less signs for relations.       And it is obvious that the '' defined by means of '~' and 'v' is identical with the one that figures with '~' in the definition of 'v': and that the second 'v' 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 fact p infinitely many others, namely ~~p, ~~~~p, etc. And it is no less remarkable that the infinite number of propositions of logic (mathematics) follow from half a dozen 'primitive propostions'.       But in fact all propositions of logic say the same thing, to wit nothing.
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 sense negation is contained in affirmation? Does '~~p' negate ~p, or does it affirm p--or both?       The proposition '~~p' is not about negation, as if negation were an object: on the other hand, the possibility of negation is already written into affirmation.       And if there were an object called '~', it would follow that '~~p' said something different from what 'p' said, just because the one proposition would then be about ~ and the other would not.
5.45		If there are primitive logical signs, then any logic that fails to show clearly how they are placed relatively to one another and to justify their existence will be incorrect. The construction of logic out of its primitive signs must be made clear.
5.46		If we introduced logical signs properly, then we should also have introduced at the same time the sense of all combinations of them; i.e. not only 'p v q' but '~(p v ~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 signs are not 'p v q', '(x).fx', etc. but the most general form of their combinations.
5.47		It is clear that whatever we can say in advance about the form of all propositions we must be able to say all at once.       An elementary proposition really contains all logical operations in itself. For 'fa' says the same as '(x).fx.x = a'.       Wherever there is compositeness, argument and function are present, and where these are present, we already have all the logical constants.       One could say that the sole logical constant was what all propositions, by their very nature, had in common with one another.       But that is the general propositional form.
5.5		Every truth-function is a result of successive applications to elementary propositions of the operation '(-----T)(,....)'.       This operation negates all the propositions in the right-hand pair of brackets, and I call it the negation of those propositions.
5.51		If has only one value, then N() = ~p (not p); if it has two values, then N( = ~p.~q (neither p nor q).
5.52		If has as its values all that values of a function fx for all values of x, then N()=~( x).fx.
5.53		Identity of the object I express by identity of sign, and not by using a sign for identity. Difference of objects I express by difference of signs.
5.54		In the general propositional form propostions occur in other propositions only as bases of truth-operations.
5.55		We now have to answer a priori the question about all the possible forms of elementary propositions.       Elementary propositions 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 propostions.
5.6		The limits of my language mean the limits of my world.
5.61		Logic pervades the world; the limits of the world are also its limits.       So we cannot say in logic, 'The world 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 logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well.       We cannot think what we cannot think; so what we cannot think 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.       The world is my world: this is manifest in the fact that the limits of language (of that language which alone I understand) mean the limits of my world.
5.63		I am my world. (The microcosm.)
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.
6		The general form of a truth-function is [, , N, ()]. This is the general form of a proposition.
6.1		The propositions of logic are are tautologies.
6.11		Therefore the propositions of logic say nothing. (They are the analytic propositions.)
6.12		The fact that the propositions of logic are tautologies shows the formal--logical--properties of language and the world.       The fact that a tautology is yielded by this particular way of connecting its constituents.       If propositions 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 way shows that they possess these structural properties.
6.13		Logic is not a body of doctrine, but a mirror-image of the world.       Logic is transcendental.
6.2		Mathematics is a logical method.       The propositions of mathematics are equations, and therefore pseudo-propositions.
6.21		A proposition of mathematics does not express a thought.
6.22		The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics.
6.23		If two expressions are combined by means of the sign 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 logical form.
6.24		The method by which mathematics arrives at its equations is the method of substitution.       For equations 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.
6.3		The exploration of logic means the exploration of everything that is subject to law. And outside logic everything is accidental.
6.31		The so-called law of induction cannot possibly be a law of logic, since it is obviously a proposition with 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.
6.33		We do not have an a priori belief in a law of conservation, but rather a priori knowledge of the possibility of a logical form.
6.34		All such propositions, including the principle of sufficient reason, the 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 propositions of science can be cast.
6.35		Although the spots in our picture are geometrical figures, nevertheless geometry can obviously say nothing at all about their actaul 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.
6.37		There is no compulsion making one thing happen because another has happened. The only necessity that exists is logical necessity.
6.4		All propositions are of equal value.
6.41		The sense of the world must lie outside the world. In the world everything is as it is, and everything 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 the world, since if it did it would itself be accidental.       It must lie outside the world.
6.42		So too it is impossible for there to be propositions of ethics.       Propositions can express nothing that is higher.
6.43		If the good or bad exercise of the will does alter the world, it can alter only the limits of the world, not the facts--not what can be expressed by means of language.       In short the effect must be that it becomes an altogether different world. It must, so to speak, was and wane as a whole.       The world of the man is a different one from that of the unhappy man.
6.44		It is not know things are in the world that is mystical, but that it exists.
6.45		To view the world sub specie aeterni1 is to view it as a whole--a limited whole.       Feeling the world 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 doubt where no question can be asked.       For doubt can exist only where a question exists, a question only where an answer exists, and an answer only where something can be said.
6.52		We feel that even when all possible scientific 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.
6.53		The correct method in philosophy would really be the following: to say nothing except what can be said, i.e. propositions of natural science--i.e. something that has nothing to do with philosophy--and then, whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions. Although it would not be satisfying to the other person--he would not have the feeling that we were teaching him philosophy--this method would be the only strictly correct one.
6.54		My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them--as steps--to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)       He must transcend these propositions, and then he will see the world aright.
7		What we cannot speak about we must pass over in silence.

 

 

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