Tractatus Logico-Philosophicus by Ludwig Wittgenstein

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Perhaps the most important work of philosophy written in the twentieth century, Tractatus Logico-Philosophicus was the only philosophical work that Ludwig Wittgenstein published during his lifetime. Written in short, carefully numbered paragraphs of extreme brilliance, it captured the... read more

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The opening pages of the Tractatus (sections 1–2.063) deal with ontology—what the world is fundamentally made up of. The basic building blocks of reality are simple objects combined to form states of affairs. Any possible state of affairs can either be the case or not be the case, independent... read more (warning: may contain spoilers)

States of affairs are combinations of objects. Objects are utterly simple and unanalyzable, and they can exist only in the context of states of affairs. They have a logical form that determines the ways in which they can be combined into states of affairs, and they fit into these states of affairs "like links in a chain" (2.03). That is, they fit together by virtue of their logical form alone, and do not need something extra (like a relational object) to hold them together.

From 2.1 to 4.128, the discussion deals with the question of how language works so that it can describe the world accurately. According to Wittgenstein, language consists of propositions that are complexes built from simple, elementary propositions. Elementary propositions are unanalyzable and consist solely of names. Language mirrors reality by sharing its logical form. Thus, names mirror objects, elementary propositions mirror as states of affairs, and propositions mirror facts. The totality of true propositions is the totality of language just as the totality of facts is the world. A proposition is a logical picture of reality: the elements of a proposition are arranged in such a way that they resemble the reality they represent, just as the elements of a portrait are arranged in such a way that they resemble the person they represent.

Signs are given meaning through their use in propositions, so it follows that if a sign is used in two different ways we are actually dealing with two different signs. For instance, the "is" in "John is tall" is different from the "is" in "John is the captain of the guard."

While a picture can represent a fact by means of sharing its logical form, this logical form itself cannot be depicted. We cannot say what the logical form of a proposition or fact is, but this form shows itself in the way the proposition or fact is held together. Similarly, the logical connections between states of affairs and between elementary propositions show themselves, so that there is no need for logical objects (like "and" and "not") to hold them together. Wittgenstein calls the observation that logical objects do not represent anything his "fundamental idea" (4.0312).

Most of the problems of philosophy arise when people try to talk about things that can only be shown, such as the logical structure of the world or language. Wittgenstein distinguishes between formal concepts (e.g. "x is a number"), which cannot be spoken about, and concepts proper (e.g. "x is a horse"), which are the legitimate constituents of propositions. Philosophy, unlike science, is not a body of propositions. It should be thought of as the activity of clarifying the often obscure logical structure of language and thought.

Starting at 4.2, Wittgenstein discusses logic. At 4.31, he introduces truth tables, a notation that makes clear that we can represent propositions and their truth-conditions without making use of logical connectives. There are three kinds of propositions: tautologies, which are always true, contradictions, which are always false, and propositions with a sense, which can be true or false depending on what is or is not the case in the world. One proposition follows from another if that proposition is true whenever the other proposition is true. We do not need laws of inference to tell us what follows from what, as this is clear from the structure of the propositions themselves. Wittgenstein also shows how logical form can explain probability.

We can generate new propositions out of old ones by means of operations. The successive application of an operation produces a series of new propositions. Given the elementary propositions, we can generate all other propositions by successive application of the operation that negates all the propositions it is applied to.

The propositions of logic are all tautologies, and so are all equivalent. We do not need axioms or laws of inference to tell us how to proceed in logic, since this should make itself manifest. "Logic must look after itself" (5.473): we should not need external laws to tell us how proceed with logic since there is nothing external to logic. Wittgenstein also shows how signs for generality and identity are unnecessary to logic.

Propositions of the form "A believes that p" do not relate a proposition, p, to a person, A. Rather, they relate p to the verbal expression of p, so that what we are really saying is "'p' says that p."

That both language and the world share the same limits leads to the reflection that solipsism is correct in the claim that "the world is my world" (5.62). However, the thesis of solipsism cannot be put into language, but can only show itself. With regard to everything that can be said, there is no difference between solipsism and pure realism, so Wittgenstein suggests the distinction between the two is an artificial development of muddled philosophy.

Mathematics is a logical method derived from the repeated application of operations. The number 2, for instance, is the exponent given to an operation that is applied twice. Thus, the propositions of mathematics do not say anything about the world, but only reflect the method in which propositions are constructed.

The laws of science are not logical laws, nor are they empirical observations. Rather, they constitute an interpretive method, by means of which we can more accurately describe reality. Science is ultimately descriptive, not explanatory.

There is no perspective external to the world from which we can talk about the world or its contents generally. Thus, statements of value (as we find in ethics or aesthetics) are nonsense, since they evaluate the world as a whole. The feeling of life as a limited whole is what Wittgenstein calls "the mystical."

The only correct method in philosophy is to remain silent about philosophical questions, and to point out to anyone who tries to talk philosophy that he or she is talking nonsense. The propositions of theTractatus themselves make general statements about the nature of the world, and so they too are nonsense. They should serve only as a ladder to be climbed and then discarded. "What we cannot speak about we must pass over in silence" (7).

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“"My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)"”
Wittgenstein
“"Logic must look after itself."”
Wittgenstein
“"Philosophy aims at the logical clarification of thoughts. Philosophy is not a body of doctrine but an activity."”
Wittgenstein
“"My fundamental idea is that the 'logical constants' are not representatives; that there can be no representatives of the logic of facts."”
Wittgenstein
“"We picture facts to ourselves."”
Wittgenstein

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what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence.
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Philosophy aims at the logical clarification of thoughts. Philosophy is not a body of doctrine but an activity. A philosophical work consists essentially of elucidations. Philosophy does not result in 'philosophical propositions', but rather in the clarification of propositions. Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries.
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In order that a certain sentence should assert a certain fact there must, however the language may be constructed, be something in common between the structure of the sentence and the structure of the fact. This is perhaps the most fundamental thesis of Mr Wittgenstein's theory. That which has to be in common between the sentence and the fact cannot, so he contends, be itself in turn said in language. It can, in his phraseology, only be shown, not said, for whatever we may say will still need to have the same structure.
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It is not how things are in the world that is mystical, but that it exists.
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what relation must one fact (such as a sentence) have to another in order to be capable of being a symbol for that other? This last is a logical question, and is the one with which Mr Wittgenstein is concerned. He is concerned with the conditions for accurate Symbolism, i.e. for Symbolism in which a sentence 'means' something quite definite.
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Everything that can be thought at all can be thought clearly. Everything that can be put into words can be put clearly.
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It is clear that ethics cannot be put into words. Ethics is transcendental. (Ethics and aesthetics are one and the same.)
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What we cannot speak about we must pass over in silence.
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Language disguises thought. So much so, that from the outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes. The tacit conventions on which the understanding of everyday language depends are enormously complicated.
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What we cannot think we cannot think, therefore we also cannot say what we cannot think.
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Perhaps this book will be understood only by someone who has himself already had the thoughts that are expressed in it-or at least similar thoughts.

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Contradiction: A proposition that is false no matter what is the case or is not the case. A contradiction lacks sense, but is not nonsensical.
Fact: A complex made up of states of affairs. The world is the totality of "positive facts," i.e. facts that are the case.
Logical space: The space in which objects and states of affairs exist. This is the most general kind of space there is, so everything that exists and everything that could exist exists in logical space.
Object: The simple items that constitute states of affairs. Objects can only exist within the context of states of affairs. They have a internal properties—their logical form—and external properties—whatever properties are ascribed to them in states of affairs.
Operation: The process by which one proposition is generated out of another. Operations are not themselves "things" in any sense of the word: they are simply the expression of a commonality (a common logical form) that exists between two propositions. All propositions can be generated by means of a single negating operation applied successively to elementary propositions.
Proposition: The means of transmitting thoughts. A proposition can take the form of written, spoken, or any other kind of communication. It is made up of simple names arranged in a particular logical form. A proposition thus serves as a picture of the facts it represents. Most propositions are complex; simple propositions are called "elementary propositions."
Solipsism: The philosophical position that nothing exists but outside of oneself. My world consists only of sensory stimuli, and so I cannot rightly say there are people or things in the world around me, only my own impressions of people and things. This is obviously a difficult position to maintain (why do I bother expressing this position if I don't believe there are other people out there who will consider it?), but it also notoriously difficult to disprove.
State of affairs: The simplest form of facts. States of affairs are utterly simple, unanalyzable, and mutually independent. The totality of states of affairs is the world.
Tautology: A proposition that is true regardless of what is and what is not the case. As such, tautologies lack sense (but are not nonsense) and say nothing. Wittgenstein asserts that the propositions of logic are tautologies, thus underscoring the idea that the propositions of logic can say anything about the world.
Thought: By "thought," Wittgenstein does not refer to a psychological entity, but to a logical one. We are able to think about facts and propositions because our thoughts share a logical form with facts and propositions. Thus, we are able to put our thoughts into the world in the form of propositions.
World: "The world is all that is the case." Wittgenstein generally uses "world" to refer to the totality of all facts. If we were to make an itemized list of every true proposition, this itemized list would be a full description of the world. Sometimes, however, Wittgenstein uses "world" to refer to the totality of both positive and negative facts, both to what is and what is not the case. He is referring then to everything that is logically possible.

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This is book 57 of 102 in National Review - 100 Best Non-fiction Books of the Century. (authoritative list)

This book is in William H. Gass’s Fifty Literary Pillars. (community list)

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Ludwig Wittgenstein (Author)

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Original Language: German
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Publication Date: 1921
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Page Count: 134

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Dewey: 192

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Books › Nonfiction › Philosophy › Logic & Language
Books › Nonfiction › Philosophy › Modern
Books › History › Europe › Germany

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