Analytic philosophy
Analytic philosophy is a broad school of thought or style in contemporary Western philosophy, especially anglophone philosophy, with an emphasis on analysis, clear prose, rigorous arguments, formal logic, mathematics, and the natural sciences. It is further characterized by the linguistic turn, or a concern with language and meaning.
Analytic philosophy is often contrasted with continental philosophy, a catch-all term for other methods prominent in continental Europe, most notably existentialism, phenomenology, and Hegelianism. The distinction has also been drawn between "analytic" being academic or technical philosophy and "continental" being literary philosophy.
The proliferation of analytic philosophy began around the turn of the twentieth century and has been dominant since the second half of the century. Central figures in its history include Gottlob Frege, Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Other important figures include Franz Brentano, the logical positivists, and the ordinary language philosophers.
Wilfrid Sellars, W. V. O. Quine, Saul Kripke, David Lewis, and others, led a decline of logical positivism and a subsequent revival in metaphysics. Analytic philosophy has also developed several new branches of philosophy and logic, notably philosophy of language, mathematics, and science, and modern predicate and mathematical logic.
Austrian realism
Analytic philosophy was deeply influenced by Austrian realism in the former state of Austria-Hungary, so much so that Michael Dummett has remarked it is better characterized as Anglo-Austrian rather than the usual Anglo-American.Brentano
In Psychology from an Empirical Standpoint, University of Vienna philosopher and psychologist Franz Brentano gave to philosophy the problem of intentionality, or aboutness. For Brentano, all mental events or acts of consciousness had a real, non-mental intentional object, which the thinking is directed at or "about". Intentionality is "the mark of the mental." Intentionality is to be distinguished from intention or intension.The School of Brentano included Edmund Husserl and Alexius Meinong. Meinong founded the Graz School, and is known for his unique ontology of real, nonexistent objects; a solution to the problem of empty names. This view is known as Meinongianism, or pejoratively as Meinong's jungle. According to Meinong, objects like flying pigs or golden mountains are real and have being, even though they do not exist. The Polish Lwów–Warsaw school, founded by Kazimierz Twardowski, was also influenced by Brentano. Twardowski emphasized "small philosophy", or the detailed, systematic analysis of specific problems. Twardowski was further influenced by the Bohemian logical realist Bernard Bolzano.
Frege
Gottlob Frege was a German geometry professor at the University of Jena, logician, and philosopher who is understood as the father of analytic philosophy. He advocated logicism, the project of reducing arithmetic to pure logic; supporting Leibniz and opposing Kant in the philosophy of mathematics.Logic
Frege developed modern, mathematical and predicate logic with quantifiers in his book Begriffsschrift. Frege unified the two strains of ancient logic: Aristotelian and Stoic; allowing for a much greater range of sentences to be parsed into logical form. An example of this is the problem of multiple generality.Number
dominated the late nineteenth century in German philosophy. Husserl's book Philosophie der Arithmetik argued the concept of a cardinal number derived from mental acts of grouping objects and counting them. In contrast to this "psychologism", Frege, in The Foundations of Arithmetic and The Basic Laws of Arithmetic, argued that mathematics and logic have their own public objects, independent of one's private judgments or mental states. Following Frege, the logicists tended to advocate a kind of mathematical Platonism.The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor. Italian mathematician Giuseppe Peano simplified Dedekind's work to systematize mathematics with Peano arithmetic. Frege extended this work in an attempt to reduce arithmetic to logic, developing naive set theory and a set-theoretic definition of natural numbers.
Language
Frege also proved influential in the philosophy of language. Dummett traces the linguistic turn to Frege's Foundations of Arithmetic and his context principle. Frege writes "never... ask for the meaning of a word in isolation, but only in the context of a proposition." As Dummett explains, in order to answer a Kantian question, "How are numbers given to us, granted that we have no idea or intuition of them?", Frege finds the solution in defining "the sense of a proposition in which a number word occurs." Thus a problem, traditionally solved along idealist lines, is instead solved along linguistic ones.Sense and reference
Frege's paper "On Sense and Reference" is seminal, containing Frege's puzzles about identity and advancing a mediated reference theory. Frege points out the reference of "the Morning Star" and "the Evening Star" is the same: both refer to the planet Venus. Therefore, substituting one term for the other doesn't change the truth value. However, they differ in what Frege calls cognitive value or the mode of presentation. One has to distinguish between two notions of meaning: the reference of a term and the sense of a term. As Frege points out, "the Morning Star is the Morning Star" is uninformative, but "the Morning Star is the Evening Star" is informative; thus, the two expressions must differ in a way other than reference.A related puzzle is also known as Frege's puzzle, concerning intensional contexts and propositional attitude reports. Consider the statement "The ancients believed the morning star is the evening star." This statement might be false. However, the statement "The ancients believed the morning star is the morning star" is obviously true. Here again, the morning star and the evening star have different meanings, despite having the same reference.
In Frege's paper "On Concept and Object" he distinguishes between a concept which is the reference of a predicate, and an object which is the reference of a proper name.
Thought
The paper "The Thought: A Logical Inquiry" reflects Frege's anti-idealism. He argues for a Platonist account of propositions or thoughts. Frege claims propositions are intangible, like ideas; yet publicly available, like an object. In addition to the physical, public "first realm" of objects and the private, mental "second realm" of ideas, Frege posits a "third realm" of Platonic propositions, such as the Pythagorean theorem.Revolt against idealism
in the nineteenth century saw a revival of logic started by Richard Whately, in reaction to the anti-logical tradition of British empiricism. The major figure of this period is mathematician George Boole. Other figures include Scottish metaphysician William Hamilton, mathematician Augustus De Morgan, economist William Stanley Jevons, diagram namesake John Venn, Alice's Adventures in Wonderland author Lewis Carroll, Scottish mathematician Hugh MacColl, and American pragmatist Charles Sanders Peirce.However, British philosophy in the late nineteenth century was dominated by British idealism, a neo-Hegelian movement, as taught by philosophers such as F. H. Bradley and T. H. Green. Bradley's work Appearance and Reality exemplified the school.
Analytic philosophy in the narrower sense of twentieth-century anglophone philosophy is usually thought to begin with Cambridge philosophers Bertrand Russell and G. E. Moore's rejection of Hegelianism for being obscure; or the "revolt against idealism." Russell summed up Moore's common sense influence:
Russell and Moore contributed to the philosophy of perception with a naïve realism and sense-data theory. In America, the New Realists opposed idealism.
Logical atomism
An important aspect of Hegelianism and British idealism was logical holism—the belief that aspects of the world can be known only by knowing the whole world. This is closely related to the doctrine of internal relations, the belief that relations between items are internal relations, or essential properties the items have by nature. Russell and Moore in response promulgated logical atomism and the doctrine of external relations—the belief that the world consists of independent facts.Russell
In 1901, Russell famously discovered the paradox in Basic Law V, which undermined Frege's set theory. However, Russell was still a logicist, and in The Principles of Mathematics, he also argued for Meinongianism.Theory of descriptions
During his early career, Russell adopted Frege's predicate logic as his primary philosophical method, thinking it could expose the underlying structure of philosophical problems. This was done most famously in his theory of definite descriptions in "On Denoting", published in Mind in 1905. The essay has been called a "paradigm of philosophy."In this essay, Russell responds to both Meinong and Frege. Russell uses his analysis of descriptions to solve ascriptions of nonexistence, such as with "the present King of France". He argues all proper names are disguised definite descriptions; for example, "Walter Scott" can be replaced with "the author of Waverley". This position came to be called descriptivism.
Russell presents his own version of Frege's second puzzle.
"If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other without altering the truth or falsehood of that proposition. Now George IV wished to know whether Scott was the author of Waverley; and in fact Scott was the author of Waverley. Hence we may substitute “Scott” for “the author of Waverley” and thereby prove that George IV wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.”
The essay also illustrates the concept of scope ambiguity by showing how denying "The present King of France is bald" can mean either "There is no King of France" or "The present King of France is not bald". Russell quips "Hegelians, who love a synthesis, will probably conclude that he wears a wig." For Russell, there was knowledge by description and, from sense-data theory, knowledge by acquaintance.