Tractatus Logico-Philosophicus

The Tractatus Logico-Philosophicus (widely abbreviated and cited as TLP) is the only book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein that was published during his lifetime. The project had a broad goal: to identify the relationship between language and reality, and to define the limits of science. Wittgenstein wrote the notes for the Tractatus while he was a soldier during World War I and completed it during a military leave in the summer of 1918. It was originally published in German in 1921 as Logisch-Philosophische Abhandlung (Logical-Philosophical Treatise). In 1922 it was published together with an English translation and a Latin title, which was suggested by G. E. Moore as homage to Baruch Spinoza's Tractatus Theologico-Politicus (1670).

The Tractatus is written in an austere and succinct literary style, containing almost no arguments as such, but consists of 525 declarative statements, which are hierarchically numbered.

The Tractatus is recognized by philosophers as one of the most significant philosophical works of the twentieth century and was influential among the logical positivists of the Vienna Circle, such as Rudolf Carnap and Friedrich Waismann. It also influenced Bertrand Russell's article "The Philosophy of Logical Atomism".

Wittgenstein's later works, notably the posthumously published Philosophical Investigations, criticised many of his ideas in the Tractatus. There is nevertheless a common thread in Wittgenstein's thinking. Indeed, the contrast between 'early' and 'late' Wittgenstein has been countered by such scholars as Pears (1987) and Hilmy (1987). For example, a relevant, yet neglected aspect of continuity in Wittgenstein's thought concerns 'meaning as use'. Connecting his early and later writings on 'meaning as use' is his appeal to direct consequences of a term or phrase, reflected, for example, in his speaking of language as a 'calculus'. These passages are crucial to Wittgenstein's view of 'meaning as use', though they have been widely neglected in scholarly literature. The centrality and importance of these passages are corroborated and augmented by renewed examination of Wittgenstein's Nachlaß, as is done in, for example, "From Tractatus to Later Writings and Back – New Implications from Wittgenstein's Nachlass" (de Queiroz 2023), "From the Notebooks to the Investigations and Beyond" (de Queiroz 2025a) and "Meaning as Use, Application, Employment, Purpose, Usefulness" (de Queiroz 2025b).

Description and context

The Tractatus employs an austere and succinct literary style. The work contains almost no arguments as such, but rather consists of declarative statements, or passages, that are meant to be self-evident. The statements are hierarchically numbered, with seven basic propositions at the primary level (numbered 1–7), with each sub-level being a comment on or elaboration of the statement at the next higher level (e.g., 1, 1.1, 1.11, 1.12, 1.13). In all, the Tractatus comprises 525 numbered statements.

The book's writing style has been described variously as aphoristic or epigrammatic. When Bertrand Russell suggested to Wittgenstein that he ought to provide arguments and not merely state what he thinks, Wittgenstein replied that this would spoil the book's beauty and would be like touching a flower with muddy hands. Wittgenstein described the writing style of the Tractatus as "highly syncopated" and in his later years he came to regret this style. In 1949 he told Maurice O'Connor Drury that "every sentence in the Tractatus should be seen as the heading of a chapter, needing further exposition. My present style is quite different; I am trying to avoid that error".

The book was first published in German in 1921 in the 14th issue of Wilhelm Ostwald's Annalen der Naturphilosophie. The English translation of the Tractatus was published with an introduction by Bertrand Russell, even though Wittgenstein considered Russell's introduction superficial and a misunderstanding of his work. The Tractatus is dedicated to the memory of Wittgenstein's close friend David Pinsent, who was killed in a flying accident in 1918. Below this dedication is what he described as a "motto", a quote from Austrian writer Ferdinand Kürnberger: "and whatever a man knows, whatever is not mere rumbling and roaring that he has heard, can be said in three words" (Pears and McGuinness translation).

Originally, in 1919, Wittgenstein had attempted to get the Tractatus published in the Austrian journal Der Brenner. He wrote a letter to the editor Ludwig von Ficker explaining that the point of the book was "ethical":

<blockquote>The book's point is an ethical one. I once meant to include in the preface a sentence which is not in fact there now but which I will write out for you here because it will perhaps be a key to the work for you.... My work consists of two parts: the one presented here plus all that I have not written. And it is precisely this second part that is the important one. My book draws limits to the sphere of the ethical from the inside as it were, and I am convinced that this is the ONLY rigorous way of drawing those limits. In short, I believe that where many others today are just gassing, I have managed in my book to put everything firmly into place by being silent about it.</blockquote>

Main theses

thumb|right|Illustration of the structure of the Tractatus. Only primary and secondary statements are reproduced, while the structure of the rest is indicated pictorially.|upright=1.8

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

The world is everything that is the case.
What is the case (a fact) is the existence of states of affairs.
A logical picture of facts is a thought.
A thought is a proposition with a sense.
A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)
The general form of a proposition is the general form of a truth function, which is: <math>[\bar p,\bar\xi, N(\bar\xi)]</math>. This is the general form of a proposition.
Whereof one cannot speak, thereof one must be silent.

Proposition 1

The first chapter is very brief:

This, along with the beginning of two, can be taken to be the relevant parts of Wittgenstein's metaphysical view that he will use to support his picture theory of language.

Propositions 2 and 3

These sections concern Wittgenstein's view that the sensible, changing world we perceive does not consist of substance but of facts. Proposition two begins with a discussion of objects, form and substance.

This epistemic notion is further clarified by a discussion of objects or things as metaphysical substances.

His use of the word "composite" in 2.021 can be taken to mean a combination of form and matter, in the Platonic sense.

The notion of a static unchanging Form and its identity with Substance represents the metaphysical view that has come to be held as an assumption by the vast majority of the Western philosophical tradition since Plato and Aristotle, as it was something they agreed on. is called a form or a substance is not generated." (Z.8 1033b13)

The opposing view states that unalterable Form does not exist, or at least if there is such a thing, it contains an ever changing, relative substance in a constant state of flux. Although this view was held by Greeks like Heraclitus, it has existed only on the fringe of the Western tradition since then. It is commonly known now only in "Eastern" metaphysical views where the primary concept of substance is Qi, or something similar, which persists through and beyond any given Form. The former view is shown to be held by Wittgenstein in what follows:

Although Wittgenstein largely disregarded Aristotle (Ray Monk's biography suggests that he never read Aristotle at all) it seems that they shared some anti-Platonist views on the universal/particular issue regarding primary substances. He attacks universals explicitly in his Blue Book.

"The idea of a general concept being a common property of its particular instances connects up with other primitive, too simple, ideas of the structure of language. It is comparable to the idea that properties are ingredients of the things which have the properties; e.g. that beauty is an ingredient of all beautiful things as alcohol is of beer and wine, and that we therefore could have pure beauty, unadulterated by anything that is beautiful."

And Aristotle agrees: "The universal cannot be a substance in the manner in which an essence is", Whether the Aristotelian notions of substance came to Wittgenstein via Kant, or via Bertrand Russell, or even whether Wittgenstein arrived at his notions intuitively, one cannot but see them.

The further thesis of 2. and 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 relationship.
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.N to 5.N

The 4s are significant as they contain some of Wittgenstein's most explicit statements concerning the nature of philosophy and the distinction between what can be said and what can only be shown. It is here, for instance, that he first distinguishes between material and grammatical propositions, noting:

A philosophical treatise attempts to say something where nothing can properly be said. It is predicated upon the idea that philosophy should be pursued in a way analogous to the natural sciences; that philosophers are looking to construct true theories. This sense of philosophy does not coincide with Wittgenstein's conception of philosophy.

Wittgenstein is to be credited with the popularization of truth tables (4.31) and truth conditions (4.431) which now constitute the standard semantic analysis of first-order sentential logic. The philosophical significance of such a method for Wittgenstein was that it alleviated a confusion, namely the idea that logical inferences are justified by rules. If an argument form is valid, the conjunction of the premises will be logically equivalent to the conclusion and this can be clearly seen in a truth table; it is displayed. The concept of tautology is thus central to Wittgenstein's Tractarian account of logical consequence, which is strictly deductive.

Proposition 6.N

At the beginning of Proposition 6, Wittgenstein postulates the essential form of all sentences. He uses the notation <math>[\bar p,\bar\xi, N(\bar\xi)]</math>, where

<math>\bar p</math> stands for all atomic propositions,
<math>\bar\xi</math> stands for any subset of propositions, and
<math>N(\bar\xi)</math> stands for the negation of all propositions making up <math>\bar\xi</math>.

Proposition 6 says that any logical sentence can be derived from a series of NOR operations on the totality of atomic propositions. Wittgenstein drew from Henry M. Sheffer's logical theorem making that statement in the context of the propositional calculus. Wittgenstein's N-operator is a broader 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. Wittgenstein shows 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.

From Propositions 6.4–6.54, the Tractatus shifts its focus from primarily logical considerations to what may be considered more traditionally philosophical foci (God, ethics, meta-ethics, death, the will) and, less traditionally along with these, the mystical. The philosophy of language presented in the Tractatus attempts to demonstrate just what the limits of language are – to delineate precisely what can and cannot be sensically said. Among the sensibly sayable for Wittgenstein are the propositions of natural science, and to the nonsensical, or unsayable, those subjects associated with philosophy traditionally – ethics and metaphysics, for instance. Curiously, on this score, the penultimate proposition of the Tractatus, proposition 6.54, states that once one understands the propositions of the Tractatus, he will recognize that they are senseless, and that they must be thrown away. Proposition 6.54, then, presents a difficult interpretative problem. If the so-called 'picture theory' of meaning is correct, and it is impossible to represent logical form, then the theory, by trying to say something about how language and the world must be for there to be meaning, is self-undermining. This is to say that the 'picture theory' of meaning itself requires that something be said about the logical form sentences must share with reality for meaning to be possible. This requires doing precisely what the 'picture theory' of meaning precludes. It would appear, then, that the metaphysics and the philosophy of language endorsed by the Tractatus give rise to a paradox: for the Tractatus to be true, it will necessarily have to be nonsense by self-application; but for this self-application to render the propositions of the Tractatus nonsense (in the Tractarian sense), then the Tractatus must be true.

There are three primarily dialectical approaches to solving this paradox Although something need not be a proposition to represent something in the world, Wittgenstein was largely concerned with the way propositions function as representations.

It is believed that Wittgenstein was inspired for this theory by the way that traffic courts in Paris reenact automobile accidents. A toy car is a representation of a real car, a toy truck is a representation of a real truck, and dolls are representations of people. In order to convey to a judge what happened in an automobile accident, someone in the courtroom might place the toy cars in a position like the position the real cars were in, and move them in the ways that the real cars moved. In this way, the elements of the picture (the toy cars) are in spatial relation to one another, and this relation itself pictures the spatial relation between the real cars in the automobile accident. Thus if the model for car A stands to the left of the model for car B, it depicts that the cars in the world stand in the same way relative to each other. This picturing relation, Wittgenstein believed, was our key to understanding the relationship a proposition holds to the world.

However, Wittgenstein claimed that pictures cannot represent their own logical form, they cannot say what they have in common with reality but can only show it (TLP 4.12–4.121). If representation consist in depicting an arrangement of elements in logical space, then logical space itself cannot be depicted since it is itself not an arrangement of anything; rather logical form is a feature of an arrangement of objects and thus it can be properly expressed (that is depicted) in language by an analogous arrangement of the relevant signs in sentences (which contain the same possibilities of combination as prescribed by logical syntax), hence logical form can only be shown by presenting the logical relations between different sentences.

Logical atomism

thumb|The Tractatus was first published in (1921)

Although Wittgenstein did not use the term himself, his metaphysical view throughout the Tractatus is commonly referred to as logical atomism. While his logical atomism resembles that of Bertrand Russell, the two views are not strictly the same.

Whereas Russell believed the names (like x) in his theory should refer to things we can know directly by virtue of acquaintance, Wittgenstein did not believe that there are any epistemic constraints on logical analyses: the simple objects are whatever is contained in the elementary propositions which cannot be logically analyzed any further. the distinction was meant to draw a sharp contrast between logic and descriptive discourse. On their reading, Wittgenstein indeed meant that some things are shown when we reflect on the logic of our language, but what is shown is not that something is the case, as if we could somehow think it (and thus understand what Wittgenstein tries to show us) but for some reason we just could not say it. As Diamond and Conant explain: Just as practical knowledge or skill (such as riding a bike) is not reducible to propositional knowledge according to Ryle, Wittgenstein also thought that the mastery of the logic of our language is a unique practical skill that does not involve any sort of propositional "knowing that", but rather is reflected in our ability to operate with senseful sentences and grasping their internal logical relations.

Reception and influence

Philosophical

At the time of its publication in 1921, Wittgenstein concluded that the Tractatus had resolved all philosophical problems, leaving one free to focus on what really matters – ethics, faith, music and so on. He would later recant this view, beginning in 1945, leading him to begin work on what would ultimately become the Philosophical Investigations.

The book was translated into English in 1922 by C. K. Ogden with help from the teenaged Cambridge mathematician and philosopher Frank P. Ramsey. Ramsey later visited Wittgenstein in Austria. Translation issues make the concepts hard to pinpoint, especially given Wittgenstein's usage of terms and difficulty in translating ideas into words.

The Tractatus caught the attention of the philosophers of the Vienna Circle (1921–1933), 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." Additionally, Bertrand Russell's article "The Philosophy of Logical Atomism" is presented as a working out of ideas that he had learned from Wittgenstein.

A more recent interpretation comes from The New Wittgenstein family of interpretations under development since 1988. This so-called "resolute reading" is controversial and much debated. The main contention of such readings is that Wittgenstein in the Tractatus does not provide a theoretical account of language that relegates ethics and philosophy to a mystical realm of the unsayable. Rather, the book has a therapeutic aim. By working through the propositions of the book the reader comes to realize that language is perfectly suited to all our needs, and that philosophy rests on a confused relation to the logic of our language. The confusion that the Tractatus seeks to dispel is not a confused theory, such that a correct theory would be a proper way to clear the confusion. Rather, the confusion lies in the notion that any theory is needed. The method of the Tractatus is to make the reader aware of the logic of our language as we are already familiar with it. Dispelling the need for a theoretical account of the logic of our language is intended to spread to other areas of philosophy. Thereby the confusion involved in putting forward ethical and metaphysical theories, for example, is cleared in the same "coup".

Wittgenstein would not meet the Vienna Circle proper, but only a few of its members, including Moritz Schlick, Rudolf Carnap, and Friedrich Waismann. 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.

Alfred Korzybski credits Wittgenstein as an influence in his book, Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics.

Casimir Lewy wrote that "I do not find...any evidence in Mind that the book had much direct influence on the development of philosophy in England during the period that I am reviewing [1976]", with the exception of Frank Ramsey's paper on universals. This is in contrast to Wittgenstein's latter philosophy, "with the later philosophy of Wittgenstein the story is very different".

In a 1999 poll of philosophers by the journal Philosophical Forum, the Tractatus came in fourth in response to the prompt to name the five most important books in 20th century philosophy.

Artistic

The Tractatus was the theme of a 1992 film by the Hungarian filmmaker Péter Forgács. The 32-minute production, named Wittgenstein Tractatus, features citations from the Tractatus and other works by Wittgenstein.

In 1989 the Finnish artist M. A. Numminen released a black vinyl album, The Tractatus Suite, consisting of extracts from the Tractatus set to music, on the Forward! label (GN-95). The tracks were [T. 1] "The World is...", [T. 2] "In order to tell", [T. 4] "A thought is...", [T. 5] "A proposition is...", [T. 6] "The general form of a truth-function", and [T. 7] . It was recorded at Finnvox Studios, Helsinki between February and June 1989. The "lyrics" were provided in German, English, Esperanto, French, Finnish and Swedish. The music was reissued as a CD in 2003, M. A. Numminen sings Wittgenstein.

The Tractatus is featured as a predominate thematic basis for the visual novel Wonderful Everyday.

Editions and English translations

The Tractatus is the English translation of:

Logisch-Philosophische Abhandlung, Wilhelm Ostwald (ed.), Annalen der Naturphilosophie, 14 (1921), Leipzig.

A notable German edition of the works of Wittgenstein is:

Werkausgabe (Vol. 1 includes the Tractatus). Frankfurt am Main: Suhrkamp Verlag.

The first two English translations of the Tractatus, as well as the first publication in German from 1921, include an introduction by Bertrand Russell. Wittgenstein revised the Ogden translation.

Alexander Booth (2023), Tractatus Logico-Philosophicus. Penguin Classics.
Damion Searls (2024), Tractatus Logico-Philosophicus: A New Translation, with a foreword by Marjorie Perloff. New York: Liveright.
David Stern, Katia Saporiti, Joachim Schulte (forthcoming from Cambridge, according to A. W. Moore).

A manuscript of an early version of the Tractatus was discovered in Vienna in 1965 by Georg Henrik von Wright, who named it the Prototractatus and provided a historical introduction to a published facsimile with English translation:

Notes

References

Hintikka, Merrill and Hintikka, Jaakko, Investigating Wittgenstein, Oxford, UK, and New York, NY: Basil Blackwell, 1986.
Monk, Ray (1990). Ludwig Wittgenstein: The Duty of Genius, Jonathan Cape.
Pears, David (1987). The False Prison. A Study of the Development of Wittgenstein's Philosophy. Oxford, UK, and New York, NY: Clarendon Press.
de Queiroz, Ruy J. Guerra B. "From Tractatus to Later Writings and Back – New Implications from Wittgenstein's Nachlass". SATS - Northern European Journal of Philosophy, vol. 24, no. 2, 2023, pp. 167-203. https://doi.org/10.1515/sats-2022-0016
de Queiroz, Ruy J. Guerra B. "From the Notebooks to the Investigations and Beyond". SATS - Northern European Journal of Philosophy, vol. 26, no. 1, 2025a, pp. 61-113. https://doi.org/10.1515/sats-2024-0015
de Queiroz, Ruy J. Guerra B. "Meaning as Use, Application, Employment, Purpose, Usefulness". SATS - Northern European Journal of Philosophy, vol. 26, no. 2, 2025b, pp. 151-184. https://doi.org/10.1515/sats-2025-0002 . (Preprint available from https://arxiv.org/abs/2506.07131)

External links

Online English versions

Umass.edu, (Contains German, and Ogden and Pears & McGuinness translations side-by-side-by-side)
Gutenberg.org (Ogden translation)
TractatusLogico-Philosophicus (As a hierarchically nested document)
The Tractatus (Easier-to-read nested Ogden translation with original symbols and images)
Philosurfical.open.ac.uk Research software tool aimed at facilitating the study of the Tractatus. The text is available in German and in both English translations (Ogden & Pears-McGuinness)
Graphical tabs-centered version of Tractatus Logico-Philosophicus (based on Pears & McGuinness translation)
(Ogden translation)
Tree-like version of Tractatus Logico-Philosophicus (Ogden translation)

Online German versions

Tractatus-Online.appspot.com
Hochholzer.info
Tractatus.Net
KFS.org, Ogden translation (incomplete)
Philosurfical.open.ac.uk
Ludwig Wittgenstein Project, makes the book available in different formats and display options

Visualization graphs

Project TLP (Ogden translation / Data visualization graphs / English, German)
Multilingual Tractatus Network (German, English, Russian, Spanish, French, Italian / Data visualization)
University of Iowa Tractatus Map(Both the Tractatus and the Prototractatus presented in the style of a subway map / German and English)
Wittgensteiniana (interactive visualizations of the Tractatus, English and German versions available)