Tractatus Logico-Philosophicus

Tractatus Logico-Philosophicus is the only book-length work published by the philosopher Ludwig Wittgenstein in his lifetime. It was written while he was a soldier on leave during World War I in 1918. First published in German in 1921 as Logisch-Philosophische Abhandlung, 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 an 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, whose work he greatly admired.

The slim volume (fewer than eighty pages) comprises a system of short, oracular utterances, numbered 1, 1.1, 1.11, 1.12, etc., through to 7, so that 1.1 is a  comment on or elaboration of 1, 1.11 and 1.12 comment on 1.1, and so forth, to demonstrate their nested interrelations. It sets forth on an ambitious project to identify the relationship between language and reality and to define the limits of philosophy by articulating “…the conditions for a logically perfect language.” (Russell, p. 8 in the C. K. Ogden Translation) The goal was a philosophical system that would complete Bertrand Russell's early philosophy of "logical atomism."

The ending of the book is a bit surprising, and comes to some rather drastic conclusions regarding philosophy. Specifically, it suggests that any discussion of metaphysics lies outside the realm of sense, and that it can only be shown, and not spoken of beyond the limits of language.

Tractatus Logico-Philosophicus was influential, chiefly amongst the logical positivists, but it has stimulated many other philosophers.

Main theses
There are seven main propositions in the text. These are:
 * 1) The world is everything that is the case.
 * 2) What is the case (a fact) is the existence of atomic states of affairs.
 * 3) A thought is a logical picture of a fact.
 * 4) A thought is a proposition with sense.
 * 5) A proposition is a truth-function of elementary propositions.
 * 6) The general form of a proposition is the general form of a truth function, which is: $$[\bar p,\bar\xi, N(\bar\xi)]$$.
 * 7) 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:
 * 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.


 * 5.2522 "The general term of the formal series a, O' a, O' O' a, ... I write thus: "[a, x, O' x]". 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.

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: $$[\bar p,\bar\xi, N(\bar\xi)]$$. Here is an explanation of the symbols:
 * $$\bar p$$ stands for all atomic propositions.
 * $$\bar\xi$$ stands for any subset of propositions.
 * $$N(\bar\xi)$$ stands for the negation of all propositions making up $$\bar\xi$$.

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.

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.

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.

At the very end of the text he borrows an analogy from Arthur 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.

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." (In German: "Wovon man nicht sprechen kann, darüber muß man schweigen.") A very popular alternative translation is "Whereof one cannot speak, thereof one must be silent."

Reception and effects of the work
Wittgenstein himself concluded that with the Tractatus he had resolved all philosophical problems, and upon its publication he retired to become a schoolteacher in Austria.

Meanwhile the book was translated into English by C. K. Ogden with help from the Cambridge mathematician and philosopher Frank P. Ramsey, then still in his teens. Ramsey later visited Wittgenstein in Austria. The Tractatus also caught the attention of the philosophers of the Vienna Circle, especially Rudolf Carnap and Moritz Schlick. The group spent many months working through the text out loud, line-by line. Schlick eventually convinced Wittgenstein to meet with members of the circle to discuss the Tractatus when he returned to Vienna (he was then working as an architect).

Wittgenstein would not meet the circle proper, but only a few of its members, including Schlick, Carnap, and Waissman. Often, though, he refused to discuss philosophy, and would insist on giving the meetings over to reciting poetry with his chair turned to the wall. He largely broke off formal relations even with these members of the circle after coming to believe Carnap had used some of his ideas without permission.

Wittgenstein’s return to philosophy
Conversations with Schlick during the period following the publication of Tractatus were largely responsible for drawing Wittgenstein back to philosophy. He began to doubt both the ideas and methods of the Tractatus, and in 1929 returned to Cambridge. He worked extensively but published nothing for the next twenty years. Shortly after his death in 1951 his second magnum opus, Philosophical Investigations was edited and published by his executors. Though it also dealt with the limits of philosophy imposed by the nature of language it radically departed from the picture theory of language he articulated in Tractatus.

Editions
The Tractatus is the English translation of
 * Logisch-Philosophische Abhandlung, Wilhelm Ostwald (ed.), Annalen der Naturphilosophie, 14 (1921)

Two notable English translations of the Tractatus have appeared in print, both include the introduction by Russell:


 * 1) The C. K. Odgen translation (1922), prepared with assistance from G. E. Moore, F. P. Ramsey, and Wittgenstein himself.  Routledge & Kegan Paul, parallel edition including the German text on the facing page to the English text: ISBN 041505186X (1981), Dover reprint (1999), ISBN 0486404455
 * 2) A new translation by David Pears and Brian McGuinness, Routledge, 1961 hardcover: ISBN 0710030045, 1974 paperback: ISBN 0415028256,  2001 hardcover: ISBN 0415255627,  2001 paperback: ISBN 0415254086