Editing Analytic philosophy (section)

== Emergence in Great Britain ==
[[File:Russell1907-2.jpg|thumb|upright=0.8|Bertrand Russell in 1907]]
British philosophy in the 19th century had seen 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 English mathematician [[George Boole]]. Other figures include [[Sir William Hamilton, 9th Baronet|William Hamilton]], [[Augustus De Morgan]], [[William Stanley Jevons]], ''[[Alice's Adventures in Wonderland]]'' author [[Lewis Carroll]], [[Hugh MacColl]], and American pragmatist [[Charles Sanders Peirce]].<ref>"History of Logic", by Arthur Prior, ''Cambridge Encyclopedia of Philosophy'' (1961) p. 541</ref>

However, British philosophy in the late 19th century was dominated by [[British idealism]], a [[neo-Hegelian]] movement, as taught by philosophers such as [[F. H. Bradley]] (1846–1924) and [[T. H. Green]] (1836–1882).

=== Russell ===
Analytic philosophy in the narrower sense of 20th and 21st century anglophone philosophy is usually thought to begin with [[University of Cambridge|Cambridge]] philosophers Bertrand Russell and G. E. Moore's rejection of [[Hegelianism]] for being obscure; or the "revolt against idealism"—see for example Moore's "[[A Defence of Common Sense]]".<ref>Michael Beaney (ed.), ''The Oxford Handbook of The History of Analytic Philosophy'', Oxford University Press, 2013, p. 383.</ref>{{efn|"Analytic philosophy opposed right from its beginning English neo-Hegelianism of Bradley's sort and similar ones. It did not only criticize the latter's denial of the existence of an external world (anyway an unjust criticism), but also the bombastic, obscure style of Hegel's writings."<ref>{{cite journal |last=Jonkers |first=Peter |year=2003 |title=Perspectives on Twentieth Century Philosophy: A Reply to Tom Rockmore |journal=[[Ars Disputandi]] |volume=3 |doi=10.1080/15665399.2003.10819802 |s2cid=70060684 |issn=1566-5399 |doi-access=free}}</ref>}} Russell summed up Moore's influence:
{{blockquote| "G. E. Moore...took the lead in rebellion, and I followed, with a sense of emancipation. Bradley had argued that everything common sense believes in is mere appearance; we reverted to the opposite extreme, and that everything is real that common sense, uninfluenced by philosophy of theology, supposes real. With a sense of escaping from prison, we allowed ourselves to think that grass is green, that the sun and stars would exist if no one was aware of them, and also that there is a pluralistic timeless world of Platonic ideas."<ref>{{cite book |url=https://books.google.com/books?id=C4wrBgAAQBAJ |isbn=978-1-134-93573-4 |title=Philosophy of Meaning, Knowledge and Value in the Twentieth Century: Routledge History of Philosophy Volume 10 |date=12 October 2012 |publisher=Routledge}}</ref>}}

An important aspect of Hegelianism and British idealism was [[logical holism]]—the opinion that there are aspects of the world that can be known only by knowing the whole world. This is closely related to the [[doctrine of internal relations]], the opinion that [[Property (philosophy)#Relations|relations]] between items are ''internal relations'', that is, essential [[Property (philosophy)|properties]] of the nature of those items. Russell and Moore in response promulgated [[logical atomism]] and the doctrine of ''external relations''—the belief that the world consists of <em>independent</em> facts.<ref>Baillie, James, "Introduction to Bertrand Russell" in ''Contemporary Analytic Philosophy, Second Edition'' (Prentice Hall, 1997), p. 25.</ref>{{efn|Russell once explained, "Hegel had maintained that all separateness is illusory and that the universe is more like a pot of [[treacle]] than a heap of [[Shot (pellet)|shot]]. I therefore said, "The universe is exactly like a heap of shot."<ref>Ryan, Alan. Bertrand Russell: A Political Life. United States, Farrar, Straus and Giroux, 1981. p. 23</ref>}}

Inspired by developments in modern [[formal logic]], the early Russell claimed that the problems of philosophy can be solved by showing the simple constituents of complex notions.<ref name="PenguinDicP22" /> [[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 (philosophy)|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 like Frege, Russell, Moore, and Russell's student [[Ludwig Wittgenstein]] emphasized creating an [[Ideal language philosophy|ideal language]] for philosophical analysis, which would be free from the ambiguities of ordinary language that, in their opinion, often made philosophers incorrect.

==== Paradox ====
Russell famously discovered the [[Russell's paradox|paradox]] in [[Basic Law V]] which undermined Frege's logicist project. However, like Frege, Russell argued that mathematics is reducible to logical fundamentals, in ''[[The Principles of Mathematics]]'' (1903). He also argued for [[Existence#Meinongianism|Meinongianism]].<ref>p. 449</ref>

==== "On Denoting" ====
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 descriptions|theory]] of [[definite description]]s in "[[On Denoting]]", published in ''[[Mind (journal)|Mind]]'' in 1905.<ref>{{cite journal |last=Russell |first=Bertrand |year=1905 |title=On Denoting |url=http://www.fh-augsburg.de/~harsch/anglica/Chronology/20thC/Russell/rus_deno.html |url-status=live |journal=[[Mind (journal)|Mind]] |volume=14 |pages=473–493 |archive-url=https://web.archive.org/web/20060331212120/http://www.fh-augsburg.de/~harsch/anglica/Chronology/20thC/Russell/rus_deno.html |archive-date=31 March 2006}}</ref> Russell here argues against Meinongianism. He argues all [[name]]s (aside from demonstratives like ''this'' or ''that'') are disguised definite descriptions, using this to solve ascriptions of nonexistence. This position came to be called [[Descriptivist theory of names|descriptivism]].

==== ''Principia Mathematica'' ====
Later, his book written with [[Alfred North Whitehead]], ''[[Principia Mathematica]]'' (1910–1913), the seminal text of [[classical logic]] and of the logicist project, encouraged many philosophers to renew their interest in the development of [[Mathematical logic|symbolic logic]]. It used a [[Peano–Russell notation|notation]] from Italian logician [[Giuseppe Peano]], and it uses a [[theory of types]] to avoid the pitfalls of Russell's paradox. Whitehead developed [[process metaphysics]] in ''[[Process and Reality]]''.<ref>{{multiref|{{harvnb|Desmet|Irvine|2022|loc=§&nbsp;6. Metaphysics}}|{{harvnb|Palmer|1998|p=[https://books.google.com/books?id=ZT2pI9IMiYUC&pg=PA175 175]}}}}</ref>

=== Early Wittgenstein ===
[[File:Ludwig Wittgenstein 1929.jpg|thumb|upright=0.8|Ludwig Wittgenstein]]
[[Ludwig Wittgenstein]] developed a comprehensive system of logical atomism with a [[picture theory of meaning]] in his ''[[Tractatus Logico-Philosophicus]]'' ({{langx|de|Logisch-Philosophische Abhandlung}}, 1921) sometimes known as simply the ''Tractatus''. He claimed 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 <em>picture</em> of the universe can be constructed by expressing facts in the form of atomic propositions and linking them using [[logical operator]]s. The ''Tractatus'' introduced philosophers to the [[truth table]] method.

Wittgenstein thought he had solved all the problems of philosophy with the ''Tractatus''. The work further ultimately concludes that all of its propositions are meaningless, illustrated with a [[Wittgenstein's ladder|ladder]] one must toss away after climbing up it.

=== Logical positivism ===
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{{Main|Logical positivism}}

During the late 1920s to 1940s, a group of philosophers known as the [[Vienna Circle]], and another one known as the [[Berlin Circle]], developed Russell and Wittgenstein's philosophy into a doctrine known as "[[logical positivism]]" (or logical empiricism).  The Vienna Circle was led by [[Moritz Schlick]] and included [[Rudolf Carnap]] and [[Otto Neurath]].<ref>{{cite news |url=https://indystar.newspapers.com/article/the-baltimore-sun-logical-positivism-pag/134256383/ |title=Savants Move to Abandon Metaphysical Philosophy |date=December 31, 1935 |work=Baltimore Sun}}</ref> 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.<ref>{{cite book |last=Carnap |first=R. |title=The Logical Structure of the World |publisher=Felix Meiner Verlag |year=1928 |isbn=978-0-8126-9523-6 |lccn=66013604}}</ref> They adopted the [[verification principle]], according to which every meaningful statement is either [[Analytic proposition|analytic]] or synthetic. The truths of logic and mathematics were [[tautology (logic)|tautologies]], and those of science were verifiable empirical claims. These two constituted the entire universe of meaningful judgments; anything else was nonsense.

This led the logical positivists to reject many traditional problems of philosophy, especially those of [[metaphysics]], as meaningless. It had the additional effect of making (ethical and aesthetic) value judgments (as well as religious statements and beliefs) meaningless. Logical positivists therefore typically considered philosophy as having a [[Quietism (philosophy)|minimal function]]. For them, philosophy concerned the clarification of thoughts, rather than having a distinct subject matter of its own.

Several logical positivists were Jewish, such as Neurath, [[Hans Hahn (mathematician)|Hans Hahn]], [[Philipp Frank]], [[Friedrich Waismann|Friedrich Waissmann]], 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.{{efn| Named in reference to Waismann's ''Logik, Sprache, Philosophie''}}

The logical positivists saw their rejection of metaphysics in some ways as a recapitulation of a quote by [[David Hume]]:

<blockquote>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.<ref>An Enquiry Concerning Human Understanding (1748) sect. 12, pt. 3</ref></blockquote>