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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 (with less emphasis on the humanities). 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 (especially Rudolf Carnap), 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 (1874), 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.

Every mental phenomenon is characterized by what the Scholastics of the Middle Ages called the intentional (or mental) inexistence of an object, and what we might call, though not wholly unambiguously, reference to a content, direction towards an object (which is not to be understood here as meaning a thing), or immanent objectivity. Every mental phenomenon includes something as object within itself, although they do not all do so in the same way. In presentation something is presented, in judgement something is affirmed or denied, in love loved, in hate hated, in desire desired and so on. This intentional in-existence is characteristic exclusively of mental phenomena. No physical phenomenon exhibits anything like it. We could, therefore, define mental phenomena by saying that they are those phenomena which contain an object intentionally within themselves.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 LwówWarsaw 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 (English: Concept-script, 1879). 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 === Neo-Kantianism dominated the late nineteenth century in German philosophy. Husserl's book Philosophie der Arithmetik (1891) 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 (1884) and The Basic Laws of Arithmetic (German: Grundgesetze der Arithmetik, 18931903), 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 ====