Tractatus Logico-Philosophicus: the original authoritative edition

by Ludwig Wittgenstein

In the part of his theory which deals with Symbolism he is concerned with the conditions which would have to be fulfilled by a logically perfect language.

what relation must one fact (such as a sentence) have to another in order to be capable of being a symbol for that other?

A logically perfect language has rules of syntax which prevent nonsense, and has single symbols which always have a definite and unique meaning.

The essential business of language is to assert or deny facts. Given the syntax of a language, the meaning of a sentence is determinate as soon as the meaning of the component words is known. In order that a certain sentence should assert a certain fact there must, however the language may be constructed, be something in common between the structure of the sentence and the structure of the fact. This is perhaps the most fundamental thesis of Mr Wittgenstein’s theory. That which has to be in common between the sentence and the fact cannot, so he contends, be itself in turn said in language. It can, in his phraseology, only be shown, not said, for whatever we may say will still need to have the same structure.

fact. Facts which are not compounded of other facts are what Mr Wittgenstein calls Sachverhalte, whereas a fact which may consist of two or more facts is called a Tatsa-che: thus, for example, “Socrates is wise” is a Sachverhalt, as well as a Tatsache, whereas “Socrates is wise and Plato is his pupil” is a Tatsache but not a Sachverhalt.

“In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all. What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation” (2.161, 2.17).

The logical picture of a fact, he says, is a Gedanke.

The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory but an activity.

It is not necessarily assumed that the complexity of facts is finite; even if every fact consisted of an infinite number of atomic facts and if every atomic fact consisted of an infinite number of objects there would still be objects and atomic facts

The world is fully described if all atomic facts are known, together with the fact that these are all of them. The world is not described by merely naming all the objects in it; it is necessary also to know the atomic facts of which these objects are constituents.

A proposition (true or false) asserting an atomic fact is called an atomic proposition. All atomic propositions are logically independent of each other. No atomic proposition implies any other or is inconsistent with any other. Thus the whole business of logical inference is concerned with propositions which are not atomic.

The fact that nothing can be deduced from an atomic proposition has interesting applications, for example, to causality. There cannot, in Wittgenstein’s logic, be any such thing as a causal nexus. “The events of the future,” he says, “cannot be inferred from those of the present.

necessity. It has been sought to find such a property in self-identity, but the conception of identity is subjected by Wittgenstein to a destructive criticism from which there seems no escape. The definition of identity by means of the identity of indiscernibles is rejected, because the identity of indiscernibles appears to be not a logically necessary principle.

We here touch one instance of Wittgenstein’s fundamental thesis, that it is impossible to say anything about the world as a whole, and that whatever can be said has to be about bounded portions of the world. This view may have been originally suggested by notation, and if so, that is much

in its favour, for a good notation has a subtlety and suggestive-ness which at times make it seem almost like a live teacher. Notational irregularities are often the first sign of philosophical errors, and a perfect notation would be a substitute for thought. But although notation may have first suggested to Mr Wittgenstein the limitation of logic to things within the world as opposed to the world as a whole, yet the view, once suggested, is seen to have much else to recommend it.

There are some respects, in which, as it seems to me, Mr Wittgenstein’s theory stands in need of greater technical development. This applies in particular to his theory of number (6.02 ff.) which, as it stands, is only capable of dealing with finite numbers.

These difficulties suggest to my mind some such possibility as this: that every language has, as Mr Wittgenstein says, a structure concerning which, in the language, nothing can be said, but that there may be another language dealing with the structure of the first language, and having itself a new structure, and that to this hierarchy of languages there may be no limit. Mr Wittgenstein would of course reply that his whole theory is applicable unchanged to the totality of such languages.

wrong. But to have constructed a theory of logic which is not at any point obviously wrong is to have achieved a work of extraordinary difficulty and importance. This merit, in my opinion, belongs to Mr Wittgenstein’s book, and makes it one which no serious philosopher can afford to neglect.

1 The world is everything that is the case.∗ 1.1 The world is the totality of facts, not of things.

1.2 The world divides into facts.

What is the case, the fact, is the existence of atomic facts.

If I know an object, then I also know all the possibilities of its occurrence in atomic facts.

In order to know an object, I must know not its external but all its internal qualities.

If all objects are given, then thereby are all possible atomic facts also given.

Objects form the substance of the world. Therefore they cannot be compound.

If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.

It would then be impossible to form a picture of the world (true or false).

Roughly speaking: objects are colourless.

Two objects of the same logical form are—apart from their external properties—only differentiated from one another in that they are different.

The configuration of the objects forms the atomic fact.

2.033 The form is the possibility of the structure. 2.034 The structure of the fact consists of the structures of the atomic facts.

The totality of existent atomic facts also determines which atomic facts do not exist.

The existence and non-existence of atomic facts is the reality. (The existence of atomic facts we also call a positive fact, their non-existence a negative fact.)

We make to ourselves pictures of facts.

The picture is a model of reality.

The picture is a fact.

2.1511 Thus the picture is linked with reality; it reaches up to it. 2.1512 It is like a scale applied to reality. 2.15121 Only the outermost points of the dividing lines touch the object to be measured.

The representing relation consists of the co-ordinations of the elements of the picture and the things.

In order to be a picture a fact must have something in common with what it pictures.

In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.

What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation.

But the picture cannot place itself outside of its form of representation.

If the form of representation is the logical form, then the picture is called a logical picture.

Every picture is also a logical picture. (On the other hand, for example, not every picture is spatial.)

The picture depicts reality by representing a possibility of the existence and non-existence of atomic facts.

3 The logical picture of the facts is the thought.

3.01 The totality of true thoughts is a picture of the world.

It used to be said that God could create everything, except what was contrary to the laws of logic. The truth is, we could not say of an “unlogical” world how it would look.

We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

To the proposition belongs everything which belongs to the projection; but not what is projected.