Tractatus Logico-Philosophicus

Tractatus Logico-Philosophicus is the only book-length work published by the philosopher Ludwig Wittgenstein in his lifetime. Originally published in German in 1921 as Logisch-Philosophische Abhandlung, when its author was just 32, it is now widely considered one of the most important philosophical works of the twentieth century. The Latin title was originally suggested by G. E. Moore, and is a homage to Tractatus Theologico-Politicus by Benedictus Spinoza. Wittgenstein´s 'notorious' literary style, his utterly sober and succinct manner of expressing himself, was moulded by the philosophical prose of the great German logician and philosopher Gottlob Frege.

Main theses

There are seven main propositions in the text. These are:

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• The world is everything that is the case.
• What is the case (a fact) is the existence of atomic states of affairs.
• A logical picture of facts is a thought.
• A thought is a proposition with sense.
• A proposition is a truth-function of elementary propositions.
• The general form of a proposition is the general form of a truth function, which is: $$. This is the general form of a proposition.
• What we cannot speak of we must pass over in silence.

Propositions 1.*-3.*

The central thesis of 1., 2., 3. and their subsidiary propositions is Wittgenstein?s picture theory of language. This can be summed up as follows:

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• The world consists of a totality of interconnected atomic facts, and propositions make "pictures" of the world.
• In order for a picture to represent a certain fact it must in some way possess the same logical structure as the fact. In this way, linguistic expression can be seen as a form of geometric projection, where language is the changing form of projection but the logical structure of the expression is the unchanging geometric relationships.
• We cannot say with language what is common in the structures, rather it must be shown, because any language we use will also rely on this relationship, and so we cannot step out of our language with language.

Propositions 4.*-5.*

Through 4., 5., and their subsidiaries, Wittgenstein explores the formal mechanisms required for a logically "ideal" language. He uses truth tables, which are now the standard method of explaining semantics for sentential logic, and gives a rigorous if rather opaque account of formal logic. In 5.101 Wittgenstein showed, possibly for the first time, that bit-patterns such as "TFTT" can be mapped directly to sentences such as "If C then A", much to the amusement of contemporary cyberneticists. Proposition 5.101 later turned out to be a special case of a Gödel code. He covers a fair amount of ground in a short space such as notation, Russell's paradox, the notions of tautology and contradiction, and truth-functions. He also covers questions of the connection between language, science, belief, and induction.

Related Topics:
Truth tables - Semantics - Formal logic - 5.101 - Gödel code - Notation - Russell's paradox - Tautology - Contradiction - Truth-functions - Induction

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• 5.2522 "The general term of the formal series a, O' a, O' O' a, ... I write thus: "". This expression in brackets is a variable. ...

Proposition 5.2522 expresses an inductive form, where a is a predicate, and O' a is an operation on a, etc.; this notation is used in proposition 6, below, and is meant to denote all possible truth functions of a.

Related Topics:
Inductive form - Predicate - Operation - Truth function

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Propositions 6.*

In the beginning of 6. Wittgenstein postulates the essential form of all sentences. The statement is not as mysterious as it appears on first reading, due partly to Wittgenstein?s peculiar notation: . Here is an explanation of the symbols:

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• stands for all atomic propositions.
• stands for any subset of propositions.
• stands for the negation of all propositions making up .

What proposition 6. really says is that any logical sentence can be derived from a series of nand operations on the totality of atomic propositions. This is in fact a well-known logical theorem produced by Henry M. Sheffer, of which Wittgenstein makes use.

Related Topics:
Nand - Theorem - Henry M. Sheffer

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Further on in the subsidiaries of 6. he moves on to more philosophical reflections on logic, which connect to ideas of knowledge, thought, and the a priori and transcendental. The final passages argue that logic and mathematics express only tautologies and are transcendental, i.e. they lie outside of the metaphysical subject?s world. In turn, a logically "ideal" language cannot supply meaning, it can only reflect the world, and so, sentences in a logical language cannot remain meaningful if they are not merely reflections of the facts.

Related Topics:
A priori - Transcendental

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In the final pages Wittgenstein veers towards what might be seen as religious considerations. This is founded on the gap between propositions 6.3 and 6.4. A logical positivist might accept the propositions of Tractatus before 6.4. But 6.41 and the succeeding propositions argue that ethics is also transcendental, and thus we cannot examine it with language, as it is a form of aesthetics and cannot be expressed. He begins talking of the will, life after death, and God. In his examination of these issues he argues that all discussion of them is a misuse of logic. Specifically, since logical language can only reflect the world, any discussion of the mystical, that which lies outside of the metaphysical subject's world, is meaningless. This suggests that many of the traditional domains of philosophy, e.g. ethics and metaphysics, cannot in fact be discussed meaningfully. Any attempt to discuss them immediately loses all sense. This also suggests that his own project of trying to explain language is impossible for exactly these reasons. He suggests that the project of philosophy must ultimately be abandoned for those logical practices which attempt to reflect the world, not what is outside of it. The natural sciences are just such a practice, he suggests.

Related Topics:
Ethics - Aesthetics - Mystical

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At the very end he borrows an analogy from Schopenhauer, and compares the book to a ladder that must be thrown away after one has climbed it. In doing so he suggests that through the philosophy of the book one must come to see the utter meaninglessness of philosophy.

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Proposition 7

As the last line in the book, proposition 7 has no supplementary propositions. It ends the book with a rather elegant and stirring proposition: "What we cannot speak of we must pass over in silence."

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