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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Analytic philosophy | 3/18 | https://en.wikipedia.org/wiki/Analytic_philosophy | reference | science, encyclopedia | 2026-05-05T16:19:43.103246+00:00 | kb-cron |
=== Principia Mathematica === Russell's book written with Alfred North Whitehead, Principia Mathematica (1910–1913), was the seminal text of classical logic and of the logicist project, and encouraged many philosophers to renew their interest in symbolic logic. It used a notation from Peano, and a theory of types to avoid the pitfalls of Russell's paradox. Whitehead developed process metaphysics in Process and Reality (1929).
=== Ideal language === Russell claimed the problems of philosophy can be solved by showing the simple constituents of complex notions. Logical form would be made clear by syntax. For example, the English word is has three distinct meanings, which predicate logic can express as follows:
For the sentence 'the cat is asleep', the is of predication means that "x is P" (denoted as P(x)). For the sentence 'there is a cat', the is of existence means that "there is an x" (∃x). For the sentence 'three is half of six', the is of identity means that "x is the same as y" (x=y). From about 1910 to 1930, analytic philosophers emphasized creating an ideal language for philosophical analysis, which would be free from the ambiguities of ordinary language that, in their opinion, often led philosophers astray.
== Early Wittgenstein ==
Russell's student Ludwig Wittgenstein developed a comprehensive system of logical atomism, with a picture theory of meaning, in his Tractatus Logico-Philosophicus (German: Logisch-Philosophische Abhandlung, 1921), sometimes known as simply the Tractatus. Wittgenstein thought he had solved all the problems of philosophy with the Tractatus. The book starts "The world is all that is the case." Wittgenstein claims the universe is the totality of actual states of affairs and that these states of affairs can be expressed and mirrored by the language of first-order predicate logic. Thus, a picture of the universe can be constructed by expressing facts in the form of atomic propositions and linking them using logical operators. The Tractatus introduced philosophers to the terms tautology, truth conditions, and to the truth table method. Wittgenstein believed tautologies or logical truths say nothing, but show the logical structure of the world, and has been labeled a mystic who believed in the ineffable by some readers. The Tractatus further ultimately concludes that all of its propositions are meaningless, illustrated with a ladder one must toss away after climbing up it. The book ends, "Whereof one cannot speak, thereof one must be silent."
== Logical positivism ==
During the late 1920s to 1940s, two groups of philosophers known as the Vienna Circle and the Berlin Circle developed Russell and Wittgenstein's philosophy into a doctrine known as "logical positivism" (or logical empiricism). The Vienna Circle (previously the Ernst Mach Society) was led by Moritz Schlick and included Rudolf Carnap and Otto Neurath. The Berlin Circle was led by Hans Reichenbach and included Carl Hempel and mathematician David Hilbert. Logical positivists used formal logical methods to develop an empiricist account of knowledge. They adopted the verification principle, according to which every meaningful statement is either analytic or synthetic. The truths of logic and mathematics were tautologies, and those of science were verifiable empirical claims. These two constituted the entire universe of meaningful judgments; anything else was nonsense. Thus the principle rejected statements of metaphysics, theology, ethics, and aesthetics as cognitively meaningless. The logical positivists saw their verificationism as a recapitulation of a quote by David Hume, the closing lines from An Enquiry Concerning Human Understanding (1748):
If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion. This led the logical positivists to reject many traditional problems of philosophy. They typically considered philosophy to have a minimal function, concerning the clarification of thoughts, rather than having a distinct subject matter of its own. Epistemology was still discussed. Schlick was a foundationalist, believing knowledge was like a pyramid, built on prior layers of knowledge except for the first layer. Neurath was an anti-foundationalist, coherentist who famously gave the analogy of reconstructing a ship while on the open sea. Friedrich Waismann introduced the concept of open texture to describe the universal possibility of vagueness in empirical statements. Waismann never finished a book titled Logik, Sprache, Philosophie intended to present the ideas of logical positivism to a wider audience. Carnap and Reichenbach started the journal Erkenntnis. Carnap advocated solving problems by "semantic ascent", talking about language instead of its objects. Carnap also distinguished between trivial internal questions and meaningless external questions. He is best known for works like Der logische Aufbau der Welt (translated as The Logical Structure of the World, 1967) and The Elimination of Metaphysics Through Logical Analysis of Language (1959). Several logical positivists were Jewish, such as Neurath, Waismann, Hans Hahn, and Reichenbach. Others, like Carnap, were gentiles but socialists or pacifists. With the coming to power of Adolf Hitler and Nazism in 1933, many members of the Vienna and Berlin Circles fled to Britain and the United States, which helped to reinforce the dominance of logical positivism and analytic philosophy in anglophone countries. In 1936, Schlick was murdered in Vienna by his former student, Hans Nelböck. The same year, A. J. Ayer's work Language, Truth and Logic introduced the English speaking world to logical positivism.
== Ordinary language == After World War II, analytic philosophy became interested in ordinary language philosophy, in contrast to ideal language philosophy. Rather than rely on logical constructions, philosophers emphasized the use of natural language. There were two strains of ordinary language philosophy: the later Wittgenstein and Oxford philosophies.
=== Later Wittgenstein === Wittgenstein's later philosophy, from the posthumous Philosophical Investigations (1953), differed dramatically from his early work of the Tractatus. Philosophers refer to them like two different philosophers: "early Wittgenstein" and "later Wittgenstein".