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 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, whose work he greatly admired.^[1]

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, intended to be such that 1.1 is a comment on or elaboration of 1, 1.11 and 1.12 comments on 1.1, and so forth. 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: .
7. Where (or of what) one cannot speak, one must remain silent.

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. The picture is a standard of reality. 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".

He covers a fair amount of ground in a short space, covering theories 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: . Here is an explanation of the symbols:

• 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. Sheffer's result was, however, restricted to the propositional calculus, and so, of limited significance. Wittgenstein's N-operator is however an infinitary analogue of the Sheffer stroke, which applied to a set of propositions produces a proposition that is equivalent to the denial of every member of that set. What Wittgenstein then goes on to show that this operator can cope with the whole of predicate logic with identity - defining the quantifiers at 5.52, and showing how identity would then be handled at 5.53-5.532.

The subsidiaries of 6. contain more philosophical reflections on logic, connecting 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.") The Ogden translation renders it: "Whereof one cannot speak, thereof one must be silent."

Both the first and the final proposition have acquired something of a proverbial quality in German, employed as aphorisms independently of discussion of Wittgenstein. [1][2]

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). Although the Vienna Circle's logical positivists appreciated the Tractatus, they argued that the last few passages, including Proposition 7, are confused. Carnap hailed the book as containing important insights, but encouraged people to ignore the concluding sentences. Wittgenstein responded to Schlick commenting, "...I cannot imagine that Carnap should have so completely misunderstood the last sentences of the book and hence the fundamental conception of the entire book."^[2] A more recent interpretation comes from the New Wittgenstein family of interpretations.^[3] This so-called "resolute reading" is controversial and much debated. It claims that Wittgenstein in the Tractatus does not relegate ethics and philosophy to a mystical realm of the unsayable, but rather has a purely therapeutical aim. By working through the propositions of the book the reader comes to realize that language is perfectly suited to all her needs, so the attempt to express philosophical and ethical insights is only the result of the confused relation we have to our ordinary forms of language. The Tractatus clears this confusion but does not put forward a theory. It only makes us aware of the logic of our language as we use it. James F. Conant argues that Wittgenstein's method in the Tractatus mirror the method of Kierkegaard's Climacus works.<ref name="Two" /> In the appendix of Concluding Unscientific Postscript, Kierkegaard writes:

[The reader] can understand that the understanding is a revocation--the understanding with him as the sole reader is indeed the revocation of the book. He can understand that to write a book and to revoke it is not the same as refraining from writing it, that to write a book that does not demand to be important for anyone is still not the same as letting it be unwritten.[3]

Wittgenstein would not meet the Vienna 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 the poetry of Rabindranath Tagore 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.^[4]

Carnap and a number of other members of the Vienna Circle seem according to modern research to have misinterpreted Wittgenstein's elementary statements as atomic reports of sensory experience, whence Carnap's attempt at a reduction of concepts to sense experience in his book The Logical Structure of the World. While this effort, in which the American philosopher Nelson Goodman participated in his own book The Structure of Appearance, strangely prefigures computer reconstruction of analogue experience (where Carnap's examples of color patches and tones prefigure pixels and sound files), Wittgenstein had arrived at the necessity for a formal language, which Wittgenstein describes only schematically, by way of theory, critically Wittgenstein's deduction of the necessity of ontological structure (if the world had no structure, then every proposition's meaning would depend on the truth of another proposition).

The Tractatus has been put to film in 1992 by the Hungarian filmmaker Peter Forgacs. It was named Wittgenstein Tractatus and features citations from the Tractatus and other works by Wittgenstein.

Wittgenstein’s return to philosophy

Conversations with Frank Ramsey in 1923 and with Schlick in the mid-twenties 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. C. K. Odgen (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: 1981 printing: ISBN 0-415-05186-X, 1999 Dover reprint: ISBN 0-486-40445-5
2. David Pears and Brian McGuinness (1961), Routledge, hardcover: ISBN 0-7100-3004-5, 1974 paperback: ISBN 0-415-02825-6, 2001 hardcover: ISBN 0-415-25562-7, 2001 paperback: ISBN 0-415-25408-6

Notes

See also

• Ludwig Wittgenstein
• Philosophical Investigations

External links

English versions online:

• http://www.kfs.org/~jonathan/witt/tlph.html (Ogden translation)
• http://www.gutenberg.org/etext/5740 (Pears & McGuinness translation)
• http://filepedia.org/node/15 (Full Text. PDF version)
• Graphical tabs-centered version of the Tractatus Logico-Philosophicus (based on the Project Gutenberg edition)

German version online:

• http://www.tractatus.hochholzer.info
• http://www.kfs.org/~jonathan/witt/tlph.html (Ogden translation)