Tractatus Logico-Philosophicus

The Tractatus Logico-Philosophicus (usually shortened to Tractatus, and cited as TLP) is the only philosophical book Ludwig Wittgenstein published during his lifetime. It is very short, fewer than eighty pages in most editions, but it is one of the most discussed works of twentieth-century philosophy.

The book asks how language and thought are connected to the world. How is it possible for a sentence to be about something, and to be true or false? Wittgenstein’s answer leads him to a striking conclusion: there are limits to what can be said meaningfully, and many traditional questions of philosophy, as well as ethics, aesthetics and religion, lie beyond those limits.

In the preface Wittgenstein says that the whole meaning of the book could be summed up like this: what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence. He also claims, boldly, that he has solved the problems of philosophy in their essentials, and then adds that this shows how little is achieved when those problems are solved.

The Latin title means “Logical-Philosophical Treatise”. It was suggested for the English edition by the Cambridge philosopher G. E. Moore, echoing the title of Spinoza’s Tractatus Theologico-Politicus. The original German title was simply Logisch-philosophische Abhandlung.

The Tractatus is made of short, numbered remarks. There are seven main propositions, numbered 1 to 7. Each of them except the last is followed by comments with decimal numbers: 2.1 comments on 2, 2.12 comments on 2.1, and so on. A footnote explains that the numbers show the logical importance of each remark and the emphasis placed on it.

The seven main propositions give the skeleton of the book. In simple translations: 1. The world is everything that is the case. 2. What is the case, a fact, is the existence of states of affairs. 3. A logical picture of facts is a thought. 4. A thought is a proposition with a sense. 5. A proposition is a truth-function of elementary propositions. 6. (A formula giving the general form of a proposition.) 7. What we cannot speak about we must pass over in silence.

The style is compressed and oracular, more like a set of aphorisms than an argument. When Bertrand Russell urged Wittgenstein to give arguments for his claims, Wittgenstein is reported to have replied that arguments would spoil the book’s beauty. As a result, readers must reconstruct the reasoning, and this is one reason why interpretations differ so widely.

Roughly speaking, the book moves from the world (propositions 1–2), to how thoughts and sentences picture the world (3–4), to logic (5–6), and finally to the limits of language: the self, ethics, the mystical, and silence (the end of 6 and 7).

Ludwig Wittgenstein was born in Vienna in 1889, the youngest of eight children of the steel industrialist Karl Wittgenstein, in one of the richest families in the Austro-Hungarian Empire. Their home was a centre of Viennese musical life. He studied engineering in Berlin and then aeronautics in Manchester, where his interest turned to the foundations of mathematics.

On the advice of the German logician Gottlob Frege, he went to Cambridge in 1911 to study with Bertrand Russell, who quickly came to regard him as a genius. Wittgenstein worked intensely on logic, and in 1913 withdrew to a hut in Norway to think in isolation. Notes he dictated in 1913 and 1914 already contain some of the Tractatus’s central ideas.

When the First World War broke out in 1914, Wittgenstein volunteered for the Austro-Hungarian army. He served on a river patrol boat, in an artillery workshop, and later at the front on the Eastern and Italian fronts, where he was decorated for bravery. All the while he kept notebooks, writing philosophy on one side of the page and private, often religious reflections in code on the other. From 1916 onward, under the pressure of combat, his notes turned increasingly to ethics, God, death and the meaning of life.

He completed the book in 1918 while on leave in Austria. In November 1918 he was captured by Italian troops and spent about nine months in prisoner-of-war camps, from where he managed to send the manuscript to Russell in England.

The Tractatus begins with an account of what the world is. The world is not a collection of things but of facts. Facts are made up of simpler “states of affairs” (Sachverhalte), which are combinations of simple objects. Objects are what is fixed and unchanging; their possible combinations make up “logical space”, and the actual combinations make up the world. Wittgenstein gives no examples of simple objects, which has become one of the book’s puzzles.

Against this background he develops what is called the picture theory of meaning. A proposition is a picture of a possible state of affairs. Its elements (names) stand for objects, and the way the names are arranged in the proposition represents a way the objects might be arranged in reality. If they are so arranged, the proposition is true; if not, it is false. Wittgenstein is said to have been inspired by a report of a Paris court case in which an accident was reconstructed with toy models.

For a picture to represent reality at all, it must share something with it: its logical form. But this shared form cannot itself be pictured. A proposition cannot step outside itself to describe how it represents; the logical form “shows itself” in the proposition. This distinction between what can be said and what can only be shown runs through the whole book.

The picture theory explains why a sentence can have meaning even when it is false, and why we can understand a sentence we have never heard before: we understand its parts and how they are combined. These were real problems for the logic of Frege and Russell, and the Tractatus offered a new solution.

Wittgenstein held that all meaningful propositions are built out of elementary propositions by truth-functional combination: “not”, “and”, “or”, “if … then”. Whether a complex proposition is true depends only on the truth or falsity of its elementary parts. The Tractatus helped make popular the method of truth tables for showing this, a technique that the American logician Emil Post developed independently at about the same time.

He called the idea that the “logical constants” (words like “not” and “or”) do not stand for any objects his “fundamental thought”. Logic is not a science of special logical objects or the most general facts about the world; it reflects the structure that any language capable of picturing the world must have.

The propositions of logic are tautologies, true whatever the facts are, like “it is raining or it is not raining”. Contradictions are false whatever the facts are. Both, Wittgenstein says, “say nothing” about the world, but they show its logical structure. Mathematics, similarly, consists of equations that show rather than state facts. This view deeply influenced later ideas that logic and mathematics are true by virtue of form or meaning rather than by describing reality.

Proposition 6 gives a single formula for the general form of every proposition, based on one operation of joint negation (“neither … nor …”) applied repeatedly to elementary propositions. Whether this formula can really generate all of logic, including statements about “all” and “some”, has been much debated by logicians.

If meaningful propositions are pictures of possible facts, then many sentences that look meaningful are not. Philosophical statements about the essence of the world, about logical form, or about value do not picture any possible state of affairs. Wittgenstein concludes that philosophy is not a body of doctrine but an activity: the clarification of thoughts. Most philosophical problems arise because we misunderstand the logic of our language.

In the 5.6s he writes that the limits of my language mean the limits of my world, and that the subject, the “I”, is not in the world but is a limit of the world, as the eye is not part of the visual field it sees. These remarks on solipsism are among the most discussed and puzzling passages in the book.

In the 6.4s and 6.5s the book turns to ethics, aesthetics, death and the meaning of life. The sense of the world must lie outside the world; there can be no propositions of ethics; ethics and aesthetics are one. “It is not how things are in the world that is mystical, but that it exists.” Even if all possible scientific questions were answered, he says, the problems of life would not have been touched at all.

Finally, Wittgenstein says that his own propositions are nonsensical: anyone who understands him will recognize them as such, having used them as steps to climb beyond them, and must throw away the ladder after climbing it. Only then will they see the world rightly. Then comes proposition 7, and silence. In a 1919 letter to a possible publisher, Ludwig von Ficker, he explained that the book’s point was ethical, and that it consisted of two parts, the one written and everything he had not written, and that the second was the important one.

Finding a publisher was difficult. Several publishers turned the book down. Wittgenstein met Russell in The Hague in December 1919 to go through it line by line, and Russell agreed to write an introduction to help it get published. When Wittgenstein read the introduction, he thought it misunderstood his work, and he withdrew his support for publication with it, leaving the matter in Russell’s hands.

The German text finally appeared in 1921 in volume 14 of Annalen der Naturphilosophie, a journal edited by the chemist Wilhelm Ostwald, with Russell’s introduction in German. The printing contained many errors, and Wittgenstein was unhappy with it.

In 1922 the book was published in London by Kegan Paul in a series edited by C. K. Ogden, with the German and English on facing pages and Russell’s introduction. The translation was largely prepared by the young Cambridge mathematician Frank Ramsey and was checked by Wittgenstein, who sent back detailed corrections. A second English translation, by David Pears and Brian McGuinness, appeared in 1961 and is now often preferred; several new translations have been published since 2020.

An earlier manuscript version of the book was discovered in Vienna in 1965 by the philosopher Georg Henrik von Wright and published in 1971 as the Prototractatus. Wittgenstein’s wartime notebooks were published in 1961 as Notebooks 1914–1916. These documents allow scholars to follow how the book’s ideas and its numbering system developed.

Believing he had finished with philosophy, Wittgenstein gave away his share of the family fortune and worked as an elementary schoolteacher in villages in Lower Austria from 1920 to 1926. He then worked as a gardener in a monastery and helped design a modernist house in Vienna for his sister Margarete.

Meanwhile the Tractatus found enthusiastic readers. In Vienna, a group of philosophers and scientists around Moritz Schlick, later known as the Vienna Circle, studied it line by line in the mid-1920s. They read it as support for their logical empiricism: meaningful statements are either tautologies of logic or claims that can be verified by experience, and metaphysics is meaningless. Wittgenstein met Schlick, Friedrich Waismann and Rudolf Carnap, but he disagreed with them about the importance of what cannot be said, and sometimes read them poetry by Rabindranath Tagore instead of discussing philosophy.

In 1929 Wittgenstein returned to Cambridge. He submitted the Tractatus as his doctoral thesis, examined by Russell and Moore. Over the following years he developed a new philosophy, centred on language as a set of activities or “language-games”, that became the Philosophical Investigations, published after his death in 1951. In its preface he wrote that he had been forced to recognize grave mistakes in his first book.

The Tractatus shaped analytic philosophy in many ways: through logical positivism, through its treatment of logic as tautology, through its picture of the relationship between language and reality, and through its idea of philosophy as clarification. It has also influenced artists, composers and writers fascinated by its final silence.

The central interpretive problem is the book’s ending. If its own propositions are nonsense, how can it teach anything? Traditional or “metaphysical” readings, associated with G. E. M. Anscombe’s An Introduction to Wittgenstein’s Tractatus (1959) and later with P. M. S. Hacker, hold that the book tries to convey real insights about logic, the world and value that cannot be stated but can be shown. On this view the Tractatus contains ineffable truths, and its nonsense is illuminating nonsense.

Since the late 1980s the “resolute” or “New Wittgenstein” reading, developed especially by Cora Diamond and James Conant, has argued that this is incoherent: nonsense is simply nonsense, and there are no ineffable truths. The book’s aim is therapeutic. By leading readers into the illusion that they understand its metaphysical sentences, and then revealing that they do not, it frees them from the temptation to philosophize in this way. The frame (preface and ending) tells the reader how to take the body of the book.

Critics of the resolute reading argue that it ignores Wittgenstein’s own statements, in letters and conversations, that he was trying to convey something important, and that it makes the detailed logical doctrines of the book pointless. Many scholars now take intermediate positions. The debate also affects how one sees the relation between the “early” and “later” Wittgenstein: resolute readers see more continuity, traditional readers a sharper break.

Other debates concern the nature of the simple objects (whether they are sense-data, spatial points, or something else, or whether Wittgenstein deliberately left this open), the relation of the Tractatus to Frege and Russell, the influence of Schopenhauer and of Tolstoy’s religious writings on its ethical remarks, and how far the book belongs to Viennese culture, including the critique of language by Karl Kraus and the architecture of Adolf Loos.

Scholars of the Tractatus work with several layers of evidence: the 1913 “Notes on Logic” and the notes dictated to Moore in Norway in 1914; the surviving wartime notebooks (three of several are known); the Prototractatus manuscript; typescripts and the corrected printings; and Wittgenstein’s letters to Russell, Ogden, Ficker and the architect Paul Engelmann, his friend from the war years. Study of the Prototractatus has shown that the decimal numbering was built up gradually, and some scholars argue that the book should be read as a tree, following each number’s comments, rather than page by page.

Translation is itself an interpretive problem. Key terms such as Sachverhalt (translated “atomic fact” by Ogden, “state of affairs” by Pears and McGuinness), Bild (“picture”), Sinn (“sense”) and unsinnig (“nonsensical”) carry philosophical commitments in the choice of English words. The Ogden–Ramsey version is more literal and sometimes awkward; the Pears–McGuinness version is smoother but, some argue, less faithful. Wittgenstein’s own corrections to the Ogden translation are an important source for his intentions.

Biographical context has also shaped interpretation. Ray Monk’s biography Ludwig Wittgenstein: The Duty of Genius (1990) emphasized how the ethical and religious crisis of the war years is bound up with the book’s last pages. Some philosophers object that biography should not settle questions of logical content; others reply that Wittgenstein himself insisted that the point of the book was ethical.

A century after its publication, the Tractatus remains unusual in being both a technical work in the philosophy of logic and a meditation on what lies beyond words. Its reception history, from the Vienna Circle to the resolute readers, is a case study in how a short, difficult text can generate opposing traditions of reading.