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{{Short description|20th-century tradition of Western philosophy}}
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'''Analytic philosophy''' is a broad movement within [[Western philosophy]], especially [[English-speaking world|anglophone]] philosophy, focused on [[analysis]] as a philosophical method.{{efn|[[A.P. Martinich]] draws an analogy between analytic philosophy and analytic chemistry, which aims to determine chemical compositions.<ref name=":4">{{Cite book |editor1-last=Martinich |editor1-first=A. P. |editor1-link=Aloysius Martinich |editor2-last=Sosa |editor2-first=David |editor2-link=David Sosa |title=A Companion to Analytic Philosophy |date=2001 |series=Blackwell Companions to Philosophy |publisher=Blackwell Publishers Ltd |doi=10.1002/9780470998656 |isbn=978-0-631-21415-1}}</ref>}}{{efn|"Without exception, the best philosophy departments in the United States are dominated by analytic philosophy, and among the leading philosophers in the United States, all but a tiny handful would be classified as analytic philosophers. Practitioners of types of philosophizing that are not in the analytic tradition—such as phenomenology, classical pragmatism, existentialism, or Marxism—feel it necessary to define their position in relation to analytic philosophy."<ref name="Searle03P1">[[John Searle]] (2003), ''Contemporary Philosophy in the United States'' in N. Bunnin and E. P. Tsui-James (eds.), ''The Blackwell Companion to Philosophy'', 2nd ed., (Blackwell, 2003), p. 1.</ref>}} It is characterized by a clarity of [[prose]]; rigor in arguments; and making use of [[formal logic]] and mathematics, and, to a lesser degree, the [[natural sciences]].<ref>{{Cite journal |last1=Glock |first1=H.J. |year=2004 |title=Was Wittgenstein an Analytic Philosopher? |journal=Metaphilosophy |volume=35 |issue=4 |pages=419–444 |doi=10.1111/j.1467-9973.2004.00329.x}}</ref><ref name="PenguinDicP22">Mautner, Thomas (editor) (2005) ''The Penguin Dictionary of Philosophy'', entry for "Analytic philosophy", pp. 22–23</ref>{{efn|Quote on the definition: "'Analytic' philosophy today names a ''style'' of doing philosophy, not a philosophical program or a set of substantive views. Analytic philosophers, crudely speaking, aim for argumentative clarity and precision; draw freely on the tools of logic; and often identify, professionally and intellectually, more closely with the sciences and mathematics, than with the humanities."<ref name="LeiterWeb">[[Brian Leiter]] (2006) webpage [https://web.archive.org/web/20061115002425/https://www.philosophicalgourmet.com/analytic.asp ''"Analytic" and "Continental" Philosophy'']<!-- https://www.philosophicalgourmet.com/analytic-and-continental-philosophy/ --></ref>}}{{efn|"analytical philosophy [is] too narrow a label, since [it] is not generally a matter of taking a word or concept and analyzing it (whatever exactly that might be). [...] This tradition emphasizes clarity, rigor, argument, theory, truth. It is not a tradition that aims primarily for inspiration or consolation or ideology. Nor is it particularly concerned with 'philosophy of life', though parts of it are. This kind of philosophy is more like science than religion, more like mathematics than poetry—though it is neither science nor mathematics."<ref>Colin McGinn, ''The Making of a Philosopher: My Journey through Twentieth-Century Philosophy'' (HarperCollins, 2002), p. xi.</ref>}}{{efn|According to [[Scott Soames]], "an implicit commitment—albeit faltering and imperfect—to the ideals of clarity, rigor and argumentation" and it "aims at truth and knowledge, as opposed to moral or spiritual improvement [...] the goal in analytic philosophy is to discover what is true, not to provide a useful recipe for living one's life". Soames also states that analytic philosophy is characterized by "a more piecemeal approach. There is, I think, a widespread presumption within the tradition that it is often possible to make philosophical progress by intensively investigating a small, circumscribed range of philosophical issues while holding broader, systematic questions in abeyance".<ref name="Soames">{{cite book |last=Soames |first=Scott |title=The dawn of analysis |publisher=Princeton Univ. Press |year=2003 |isbn=978-0-691-11573-3 |edition=2nd print., 1st papers. print |location=Princeton, NJ |pages=xiii–xvii}}</ref>}} It is further characterized by an interest in [[language]], [[semantics]] and [[Meaning (philosophy)|meaning]], known as the [[linguistic turn]].<ref name=":5">{{Harvnb|Dummett|1993|page=4, 22}}</ref>{{efn|"[I]t is difficult to give a precise definition of 'analytic philosophy' since it is not so much a specific doctrine as a loose concatenation of approaches to problems."<ref>See, e.g., Avrum Stroll, ''Twentieth-Century Analytic Philosophy'' (Columbia University Press, 2000), p. 5</ref>}}{{efn|"I think [[Hans Sluga|Sluga]] is right in saying 'it may be hopeless to try to determine the essence of analytic philosophy.' Nearly every proposed definition has been challenged by some scholar. [...] [W]e are dealing with a family resemblance concept."<ref>see Stroll (2000), p. 7</ref>}}{{efn|"The answer to the title question, then, is that analytic philosophy is a tradition held together ''both'' by ties of mutual influence ''and'' by family resemblances."<ref>See [[Hans-Johann Glock]], ''What Is Analytic Philosophy?'' (Cambridge University Press, 2008), p. 205</ref>}} It has developed several new branches of philosophy and logic, notably [[philosophy of language]], [[philosophy of mathematics]],  [[philosophy of science]], modern [[predicate logic]] and [[mathematical logic]].<ref>{{cite web |last=Koopman |first=Colin |date= |title=Bernard Williams on Philosophy's Need for History |url=https://pages.uoregon.edu/koopman/pub/2010rev-metaP_williams_hist_phil-final.pdf |access-date=2022-03-01 |website=pages.uoregon.edu}}</ref>

The proliferation of analysis in philosophy began around the turn of the 20th century and has been dominant since the latter half of the 20th century.<ref name="Vienne 1997 p. 140">{{cite book |last=Vienne |first=J.M. |url=https://books.google.com/books?id=LVXgT6lo6cwC&pg=PA140 |title=Philosophie analytique et histoire de la philosophie: actes du colloque (Université de Nantes, 1991) |publisher=J. Vrin |year=1997 |isbn=978-2-7116-1312-0 |series=Problèmes et controverses |page=140 |language=fr |access-date=2023-08-28}}</ref><ref name="Luft 2019 p. 258">{{cite book |last=Luft |first=S. |url=https://books.google.com/books?id=mCu6DwAAQBAJ&pg=PT258 |title=Philosophie lehren: Ein Buch zur philosophischen Hochschuldidaktik |publisher=Felix Meiner Verlag |year=2019 |isbn=978-3-7873-3766-8 |page=258 |language=de |access-date=2023-08-28}}</ref><ref name="Glock 2008 p. 1">{{cite book |last=Glock |first=H.J. |url=https://books.google.com/books?id=WnvhtAEACAAJ |title=What is Analytic Philosophy? |publisher=Cambridge University Press |year=2008 |isbn=978-0-521-87267-6 |page=1 |access-date=2023-08-28}}</ref>{{efn|The 1950s saw challenges to much which had been taken for granted, and roughly by 1960 anglophone philosophy began to incorporate a wider range of interests, opinions, and methods.<ref name="autogenerated3">{{cite web |title=Analytic Philosophy Internet Encyclopedia of Philosophy |url=http://www.iep.utm.edu/a/analytic.htm |url-status=live |archive-url=https://web.archive.org/web/20090703212901/http://www.iep.utm.edu/a/analytic.htm |archive-date=3 July 2009 |access-date=13 April 2018 |publisher=Iep.utm.edu}}</ref> Despite this, most philosophers in Britain and America still consider themselves "analytic philosophers".<ref name="LeiterWeb" /> They have done so largely by expanding the notion of "analytic philosophy" from the specific programs that dominated anglophone philosophy before 1960 to a much more general notion of an "analytic" style,<ref name="LeiterWeb" /><ref name="autogenerated3" /> characterized by mathematical precision and thoroughness about a specific topic, and resistance to "imprecise or cavalier discussions of broad topics".<ref name="autogenerated3" />}} Central figures in its historical development are [[Gottlob Frege]], [[Bertrand Russell]], [[G. E. Moore]], and [[Ludwig Wittgenstein]]. Other important figures in its history include [[Franz Brentano]], the [[logical positivism|logical positivists]] (particularly [[Rudolf Carnap]]), the [[ordinary language philosophy|ordinary language philosophers]], [[Willard Van Orman Quine|W. V. O. Quine]], and [[Karl Popper]]. After the decline of logical positivism, [[Saul Kripke]], [[David Lewis (philosopher)|David Lewis]], and others led a revival in [[metaphysics]].

Analytic philosophy is often contrasted with [[continental philosophy]],{{efn|"Most non-analytic philosophers of the twentieth century do not belong to continental philosophy."<ref>H.-J. Glock, ''What Is Analytic Philosophy?'' (Cambridge University Press, 2008), p. 86</ref>}} which was coined as a catch-all term for other methods that were prominent in [[continental Europe]],{{efn|The distinction rests upon a confusion of geographical and methodological terms, as if one were to classify cars into front-wheel drive and Japanese. [...] the distinction between analytic and Continental philosophy rests upon a confused comparison of methodological and geographical categories.<ref>{{Cite book |last=Critchley |first=Simon |url=http://worldcat.org/oclc/1200924441 |title=Continental philosophy a very short introduction |date=2001 |publisher=Oxford University Press |oclc=1200924441}}</ref>}} most notably [[existentialism]], [[phenomenology (philosophy)|phenomenology]], and [[Hegelianism]].{{efn|"Analytic philosophy is mainly associated with the contemporary English-speaking world, but it is by no means the only important philosophical tradition. In this volume two other immensely rich and important such traditions are introduced: Indian philosophy, and philosophical thought in Europe from the time of Hegel."<ref>[[A.C. Grayling]] (ed.), ''Philosophy 2: Further through the Subject'' (Oxford University Press, 1998), p. 2</ref>}}{{efn|"So, despite a few overlaps, analytical philosophy is not difficult to distinguish broadly [...] from other modern movements, like phenomenology, say, or existentialism, or from the large amount of philosophizing that has also gone on in the present century within frameworks deriving from other influential thinkers like Aquinas, Hegel, or Marx."<ref>L.J. Cohen, ''The Dialogue of Reason: An Analysis of Analytical Philosophy'' (Oxford University Press, 1986), p. 5:</ref>}}{{efn|Steven D. Hales described analytic philosophy as one of three types of philosophical method practiced in the West: "[i]n roughly reverse order by number of proponents, they are phenomenology, ideological philosophy, and analytic philosophy".<ref>{{cite book |last=Hales |first=Steven D. |title=Analytic philosophy : classic readings |publisher=Wadsworth/Thomson Learning |year=2002 |isbn=978-0-534-51277-4 |location=Belmont, CA |pages=1–10}}</ref>}} There is widespread influence and debate between the analytic and continental traditions; some philosophers see the differences between the two traditions as being based on institutions, relationships, and ideology, rather than anything of significant philosophical substance.<ref name="Rinofner-Kreidl Wiltsche 2016 p.">{{cite book |last1=Rinofner-Kreidl |first1=S. |url=https://books.google.com/books?id=8-XVDAAAQBAJ |title=Analytic and Continental Philosophy: Methods and Perspectives. Proceedings of the 37th International Wittgenstein Symposium |last2=Wiltsche |first2=H.A. |publisher=De Gruyter |year=2016 |isbn=978-3-11-044887-0 |series=Publications of the Austrian Ludwig Wittgenstein Society – New Series |page= |access-date=2023-08-28}}</ref><ref name="Glock 2008 p.">{{cite book |last=Glock |first=H.J. |url=https://books.google.com/books?id=WnvhtAEACAAJ |title=What is Analytic Philosophy? |publisher=Cambridge University Press |year=2008 |isbn=978-0-521-87267-6 |page= |access-date=2023-08-28}}</ref> The distinction has also been drawn between "analytic" being [[Academy|academic]] or technical philosophy and "continental" being [[Literary criticism|literary]] philosophy.{{efn|"The distinction which Russell sets up between 'technical' philosophy and 'literary' philosophy has had many incarnations, from Plato's 'ancient quarrel between poetry and philosophy'..."<ref>{{Cite book |last=Luchte |first=James |url=https://books.google.com/books?id=UFBS4Kpz9ooC |title=Nietzsche's Thus Spoke Zarathustra: Before Sunrise |date=2011-11-03 |publisher=Bloomsbury Publishing |isbn=978-1-4411-1845-5 |language=en}}</ref>}}{{efn|The tradition has also been criticized for excessive formalism, ahistoricism, and aloofness towards alternative disciplines and outsiders.<ref name="Glock 2008 p. 231">{{cite book |last=Glock |first=H.J. |url=https://books.google.com/books?id=WnvhtAEACAAJ |title=What is Analytic Philosophy? |publisher=Cambridge University Press |year=2008 |isbn=978-0-521-87267-6 |page=231 |access-date=2023-08-28}}</ref><ref>{{Cite journal |last=Akehurst |first=Thomas L. |date=2009-03-01 |title=Writing history for the ahistorical: Analytic philosophy and its past |url=https://doi.org/10.1016/j.histeuroideas.2008.09.002 |journal=History of European Ideas |volume=35 |issue=1 |pages=116–121 |doi=10.1016/j.histeuroideas.2008.09.002 |issn=0191-6599 |s2cid=143566283}}</ref><ref>{{cite web |last=Beaney |first=Michael |date=2013-06-20 |editor1-last=Beaney |editor1-first=Michael |title=The Historiography of Analytic Philosophy |url=https://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199238842.001.0001/oxfordhb-9780199238842-e-029 |access-date=2022-02-18 |website=The Oxford Handbook of The History of Analytic Philosophy |language=en |doi=10.1093/oxfordhb/9780199238842.001.0001 |isbn=978-0-19-923884-2}}</ref> Some have tried to develop a [[postanalytic philosophy]].}}

{{anchor|History of analytic philosophy|History of Analytic philosophy|History of analytical philosophy|History of Analytical philosophy}}
== Emergence in Germany and Austria ==
[[File:Franz Brentano in Vienna, 1890.png|thumb|upright=0.8|Franz Brentano introduced the problem of intentionality.]]
Analytic philosophy was deeply influenced by what is called [[Austrian realism]] in the former state of [[Austria-Hungary]], so much so that Michael Dummett has remarked that analytic philosophy is better characterized as Anglo-Austrian rather than the usual Anglo-American.<ref>{{Harvnb|Dummett|1993|page=2}}</ref>

[[University of Vienna]] philosopher and psychologist [[Franz Brentano]]—in ''[[Psychology from an Empirical Standpoint]]'' (1874) and through the subsequent influence of the [[School of Brentano]] and its members, such as [[Edmund Husserl]] and [[Alexius Meinong]]—gave to analytic philosophy the problem of [[intentionality]] or of aboutness.<ref>{{Harvnb|Dummett|1993|page=28}}</ref> For Brentano, all mental events have a real, non-mental intentional object, which the thinking is directed at or "about".

Meinong is known for his unique [[ontology]] of real [[nonexistent objects]] as a solution to the problem of [[empty name]]s.<ref>Everett, Anthony and Thomas Hofweber (eds.) (2000), ''Empty Names, Fiction and the Puzzles of Non-Existence.''</ref> The [[Graz School]] followed Meinong. The Polish [[Lwów–Warsaw school]], founded by [[Kazimierz Twardowski]] in 1895, grew as an offshoot of the Graz School. It was closely associated with the [[Warsaw School of Mathematics]].

=== Frege ===
[[File:Young frege.jpg|thumb|upright=0.8|Gottlob Frege, the father of analytic philosophy]]
[[Gottlob Frege]] (1848–1925) was a German [[geometry]] professor at the [[University of Jena]] who is understood as the father of analytic philosophy. Frege proved influential as a [[philosopher of mathematics]] in Germany at the beginning of the 20th century. He advocated [[logicism]], the project of reducing [[arithmetic]] to pure logic.

==== Logic ====
As a result of his logicist project, Frege developed [[predicate logic]] in his book ''[[Begriffsschrift]]'' (English: ''Concept-script'', 1879), which allowed for a much greater range of sentences to be parsed into logical form than was possible using the ancient [[Aristotelian logic]]. An example of this is the [[problem of multiple generality]].

==== Number ====
[[Neo-Kantianism]] dominated the late 19th century in German philosophy. Edmund Husserl's 1891 book ''[[Philosophy of Arithmetic|Philosophie der Arithmetik]]'' argued that the concept of the [[cardinal number]] derived from psychical acts of grouping objects and counting them.<ref>{{cite journal |last=Willard |first=Dallas |title=Husserl on a Logic that Failed |journal=Philosophical Review |pages=52–53 |volume=89 |issue=1 |jstor=2184863 |year=1980}}</ref>

In contrast to this "[[psychologism]]", Frege in ''[[The Foundations of Arithmetic]]'' (1884) and ''The Basic Laws of Arithmetic'' ({{langx|de|link=no|Grundgesetze der Arithmetik}}, 1893–1903), argued similarly to [[Mathematical platonism|Plato]] or [[Bernard Bolzano|Bolzano]] that mathematics and logic have their own public objects, independent of the private judgments or mental states of individual mathematicians and logicians. Following Frege, the logicists tended to advocate a kind of [[Philosophy of mathematics|mathematical Platonism]].

==== Language ====
Frege also proved influential in the [[philosophy of language]] and analytic philosophy's interest in [[Semantics|meaning]].<ref name="Speaks">Jeff Speaks, [https://www3.nd.edu/~jspeaks/courses/2011-12/83104/handouts/frege-reference.pdf "Frege's theory of reference"] (2011)</ref> [[Michael Dummett]] traces the [[linguistic turn]] to Frege's ''Foundations of Arithmetic'' and his [[context principle]].<ref>{{Harvnb|Dummett|1993|p=5}}</ref>

Frege's paper "[[On Sense and Reference]]" (1892) is seminal, containing [[Frege's puzzles]] and providing a [[mediated reference theory]]. His paper "[[The Thought]]: A Logical Inquiry" (1918) reflects both his anti-idealism or anti-psychologism and his interest in language. In the paper, he argues for a [[Platonist]] account of [[proposition]]s or thoughts.

== 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.

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>

== Ordinary language ==
{{Main|Ordinary language philosophy}}

After [[World War II]], from the late 1940s to the 1950s, analytic philosophy became involved with ordinary-language analysis. This resulted in two main trends.

=== Later Wittgenstein ===
One strain of language analysis continued Wittgenstein's later philosophy, from the ''[[Philosophical Investigations]]'' (1953), which differed dramatically from his early work of the ''Tractatus''. The criticisms of [[Frank P. Ramsey]] on color and logical form in the ''Tractatus'' led to some of Wittgenstein's first doubts with regard to his early philosophy. Philosophers refer to them like two different philosophers: "early Wittgenstein" and "later Wittgenstein". In his later philosophy, Wittgenstein develops the concept of a "[[language-game]]" and, rather than his prior picture theory of meaning, advocates a theory of [[meaning as use]]. It also contains the [[private language argument]] and the notion of [[family resemblance]].

=== Oxford philosophy ===
The other trend was known as "[[University of Oxford|Oxford]] philosophy", in contrast to earlier analytic Cambridge philosophers (including the early Wittgenstein) who thought philosophers should avoid the deceptive trappings of natural language by constructing ideal languages. Influenced by Moore's ''Common Sense'' and what they perceived as the later Wittgenstein's [[Quietism (philosophy)|quietism]], the Oxford philosophers claimed that ordinary language already represents many subtle distinctions not recognized in the formulation of traditional philosophical theories or problems.

[[File:Rex Whistler - Gilbert Ryle, Fellow.jpg|thumb|upright=0.8|Gilbert Ryle]]
While schools such as logical positivism emphasize logical terms, which are supposed to be universal and separate from contingent factors (such as culture, language, historical conditions), ordinary-language philosophy emphasizes the use of language by ordinary people. The most prominent ordinary-language philosophers during the 1950s were [[P. F. Strawson]], [[J. L. Austin]], and [[Gilbert Ryle]].<ref>{{Citation |last=Longworth |first=Guy |title=John Langshaw Austin |date=2017 |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/archives/spr2020/entries/austin-jl/ |access-date=21 July 2020 |edition=Spring 2020 |publisher=Metaphysics Research Lab, Stanford University |encyclopedia=The Stanford Encyclopedia of Philosophy}}</ref>

Ordinary-language philosophers often sought to resolve philosophical problems by showing them to be the result of misunderstanding ordinary language. Ryle, in ''[[The Concept of Mind]]'' (1949), criticized Cartesian [[Mind–body dualism|dualism]], arguing in favor of disposing of "[[Ghost in the machine|Descartes' myth]]" via recognizing "[[Category mistake|category errors]]".

Strawson first became well known with his article "On Referring" (1950), a criticism of Russell's theory of descriptions explained in the latter's famous "On Denoting" article. In his book ''Individuals'' (1959), Strawson examines our conceptions of basic [[particular]]s. Austin, in the posthumously published ''[[How to Do Things with Words]]'' (1962), emphasized the theory of [[speech act]]s and the ability of words to [[Performative utterance|<em>do</em> things]] (e.g. "I promise") and not just say things. This influenced several fields to undertake what is called a [[performative turn]]. In ''[[Sense and Sensibilia (Austin book)|Sense and Sensibilia]]'' (1962), Austin criticized [[sense-data]] theories.

== Spread ==

=== Australia and New Zealand ===
The school known as [[Australian realism]] began when [[John Anderson (philosopher)|John Anderson]] accepted the Challis Chair of Philosophy at the [[University of Sydney]] in 1927. His elder brother was William Anderson, Professor of Philosophy at [[Auckland University College]] from 1921 to his death in 1955, who was described as "the most dominant figure in New Zealand philosophy."<ref>Weblin, Mark "[http://setis.library.usyd.edu.au/anderson/contributors/weblin/tnl/tnl03.pdf Idealism in Australia and New Zealand]" ''The Northern Line'' No. 3 May 2007, p 6. Retrieved 17 January 2011</ref> [[J. N. Findlay]] was a student of [[Ernst Mally]] of the Austrian realists and taught at the [[University of Otago]].

=== Finland ===
The Finnish [[Georg Henrik von Wright]] succeeded Wittgenstein at Cambridge in 1948.<ref>{{cite news |last=Hacker |first=P. M. S. |author-link=Peter Hacker |date=4 July 2003 |title=Obituary: Georg Henrik von Wright |work=[[The Guardian]] |url=https://www.theguardian.com/news/2003/jul/04/guardianobituaries.highereducation |access-date=5 July 2020}}</ref>

== Contemporary developments ==

=== Metaphysics ===

One difference with respect to early analytic philosophy was the revival of metaphysical theorizing during the second half of the 20th century, and metaphysics remains a fertile topic of research. Although many discussions are continuations of old ones from previous decades and centuries, the debates remains active.<ref name="inwagenetall1998">Van Inwagen, Peter, and Dean Zimmerman (eds.) (1998), ''Metaphysics: The Big Questions.''</ref>

==== Decline of logical positivism ====
The rise of metaphysics mirrored the decline of logical positivism, first challenged by the later Wittgenstein.

===== Sellars =====
[[Wilfrid Sellars|Wilfred Sellars]]'s criticism of the "Myth of the Given", in ''Empiricism and the Philosophy of Mind'' (1956), challenged logical positivism by arguing against sense-data theories. In his "Philosophy and the Scientific Image of Man" (1962), Sellars distinguishes between the "manifest image" and the "scientific image" of the world. Sellars's goal of a [[synoptic philosophy]] that unites the everyday and scientific views of reality is the foundation and archetype of what is sometimes called the Pittsburgh School, whose members include [[Robert Brandom]], [[John McDowell]], and [[John Haugeland]].

===== Quine =====
[[File:Willard Van Orman Quine on Bluenose II in Halifax NS harbor 1980.jpg|thumb|120px|W. V. O. Quine helped to undermine logical positivism.]]

Also among the developments that resulted in the decline of logical positivism and the revival of metaphysical theorizing was [[Harvard University|Harvard]] philosopher [[Willard Van Orman Quine|W. V. O. Quine]]'s attack on the [[analytic proposition|analytic–synthetic distinction]] in "[[Two Dogmas of Empiricism]]", published in 1951 in ''[[The Philosophical Review]]'' and republished in Quine's book ''From A Logical Point of View'' (1953), a paper "sometimes regarded as the most important in all of [[20th century philosophy|twentieth-century philosophy]]".<ref name=qui>{{cite journal |last=Quine |first=W. V. O. |year=1951 |title=Two Dogmas of Empiricism |url=https://courses.cs.sfu.ca/2015fa-phil-880-g1/pages/quine1/view |journal=[[The Philosophical Review]] |volume=60 |issue=1 |pages=20–43 |doi=10.2307/2181906 |jstor=2181906}} Reprinted in his 1953 ''From a Logical Point of View''. Harvard University Press.</ref><ref>S. Yablo and A. Gallois, ''Does Ontology Rest on a Mistake?'', Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 72, (1998), pp.&nbsp;229–261, 263–283 [https://www.mit.edu/%7Eyablo/om.pdf first part] {{webarchive|url=https://web.archive.org/web/20110912125408/http://www.mit.edu/%7Eyablo/om.pdf|date=12 September 2011}}</ref><ref>[[Peter Godfrey-Smith]], ''Theory and Reality'', 2003, [[University of Chicago]], {{ISBN|0-226-30062-5}}, pages 30–33 (section 2.4 "Problems and Changes")</ref>

''From a Logical Point of View'' also contains Quine's essay "[[wikisource:On What There Is|On What There Is]]" (1948), which elucidates Russell's theory of descriptions and contains Quine's famous dictum of [[ontological commitment]], "To be is to be the value of a [[Free variables and bound variables|variable]]". He also dubbed the problem of nonexistence [[Plato's beard]].

Quine sought to naturalize philosophy and saw philosophy as continuous with science, but instead of logical positivism advocated a kind of [[semantic holism]] and [[ontological relativity]], which explained that every term in any statement has its meaning contingent on a vast network of knowledge and belief, the speaker's conception of the entire world. In his magnum opus ''[[Word and Object]]'' (1960), Quine introduces the idea of [[radical translation]], an introduction to his theory of the [[indeterminacy of translation]], and specifically to prove the [[inscrutability of reference]].

===== Kripke =====
[[File:Kripke.JPG|thumb|160px|Saul Kripke helped to revive interest in metaphysics among analytic philosophers.]]

Important also for the revival of metaphysics was the further development of [[modal logic]], first introduced by pragmatist [[C. I. Lewis]], especially the work of [[Saul Kripke]] and his ''[[Naming and Necessity]]'' (1980).{{efn|Named in reference to Carnap's  ''[[Meaning and Necessity]]''.}}

According to one author, ''Naming and Necessity'' "played a large role in the implicit, but widespread, rejection of the view—so popular among ordinary language philosophers—that philosophy is nothing more than the analysis of language."<ref name=ageofm>Soames, Scott. 2005. ''Philosophical Analysis in the Twentieth Century: Volume 2: The Age of Meaning''. [[Princeton University Press]]. Cited in Byrne, Alex and Hall, Ned. 2004. 'Necessary Truths'. ''Boston Review'' October/November 2004.</ref>

Kripke was influential in arguing that flaws in common theories of descriptions and proper names are indicative of larger misunderstandings of the [[Modal metaphysics|metaphysics]] of necessity and [[Contingency (philosophy)|possibility]]. Kripke also argued that [[Metaphysical necessity|necessity]] is a metaphysical notion distinct from the [[Epistemology|epistemic]] notion of ''[[A priori and a posteriori|a priori]]'', and that there are [[Logical truth|necessary truths]] that are known ''[[A posteriori necessity|a posteriori]]'', such as that water is H<sub>2</sub>O.<ref name=":1">[[Dean Zimmerman (philosopher)|Zimmerman, Dean W.]], "Prologue" in ''Oxford Studies in Metaphysics, Volume 1'' (Oxford University Press, 2004), p. xix.</ref>

Kripke is widely regarded as having revived theories of [[essence]] and [[Identity (philosophy)|identity]] as respectable topics of philosophical discussion.<ref name=":1" /> Kripke and [[Hilary Putnam]] argued for realism about [[natural kind]]s. Kripke holds that it is [[Essentialism|essential]] that water is H<sub>2</sub>O, or for [[gold]] to be [[atomic number]] 79.  Putnam's [[Twin Earth thought experiment]] can be used to illustrate the same point with water.<ref>{{Citation |last1=Bird |first1=Alexander |title=Natural Kinds |date=2024 |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/archives/spr2024/entries/natural-kinds/ |access-date=2024-04-22 |edition=Spring 2024 |publisher=Metaphysics Research Lab, Stanford University |last2=Tobin |first2=Emma |editor2-last=Nodelman |editor2-first=Uri}}</ref>

===== David Lewis =====
American philosopher [[David Lewis (philosopher)|David Lewis]] defended a number of elaborate metaphysical theories. In works such as ''[[On the Plurality of Worlds]]'' (1986) and ''Counterfactuals'' (1973) he argued for [[modal realism]] and [[counterpart theory]]{{snd}}the belief in real, concrete [[possible world]]s. According to Lewis, "actual" is merely an indexical label we give a world when we are in it. Lewis also defended what he called Humean [[supervenience]], a [[Counterfactual conditional|counterfactual theory]] of [[Causality|causation]],<ref>{{Citation |last=Hitchcock |first=Christopher |title=Lewis on Causation |date=6 March 2015 |work=A Companion to David Lewis |pages=295–311 |place=Oxford, UK |publisher=John Wiley & Sons, Ltd |doi=10.1002/9781118398593.ch19 |isbn=978-1-118-39859-3}}</ref> and contributed to [[Abstract and concrete|abstract object]] theory.<ref name=":2">{{Cite journal |last=Lewis |first=David |date=March 1986 |title=Against structural universals |journal=Australasian Journal of Philosophy |volume=64 |issue=1 |pages=25–46 |doi=10.1080/00048408612342211 |issn=0004-8402}}</ref> He became closely associated with Australia, whose philosophical community he visited almost annually for more than 30 years.

==== Universals ====
In response to the [[Problem of universals|problem]] of [[Universal (metaphysics)|universals]], Australian [[David Malet Armstrong]] defended a kind of [[moderate realism]].<ref>{{Citation |last=Jackson |first=Frank |title=Armstrong, David Malet (1926–2014) |date=2016 |url=https://www.rep.routledge.com/articles/biographical/armstrong-david-malet-1926-2014/v-1 |access-date=21 July 2020 |edition=1 |place=London |publisher=Routledge |doi=10.4324/9780415249126-v035-1 |isbn=978-0-415-25069-6 |encyclopedia=Routledge Encyclopedia of Philosophy}}</ref><ref>{{Cite book |last=Armstrong |first=David Malet |title=Universals and scientific realism |date=1995 |publisher=Cambridge Univ. Press |isbn=0-521-28033-8 |oclc=174240749}}</ref> Quine and Lewis defended [[nominalism]].<ref name=":2" />

==== Mereology ====
Polish philosopher [[Stanisław Leśniewski]] coined the term [[mereology]], which is the formal study of parts and wholes, a subject that arguably goes back to the time of the [[Pre-Socratic philosophy|pre-Socratics]].<ref>Cotnoir, A. J., and Varzi, Achille C.. Mereology. United Kingdom, OUP Oxford, 2021. p. 2</ref> David Lewis believed in [[perdurantism]] and introduced the term '[[Gunk (mereology)|gunk]]'. [[Peter Van Inwagen]] believes in [[mereological nihilism]], except for living beings, a view called [[organicism]].

==== Free will and determinism ====
Peter van Inwagen's 1983 [[monograph]] ''An Essay on Free Will''{{sfn|van Inwagen|1983}} played an important role in rehabilitating [[Libertarianism (metaphysics)|libertarianism]] with respect to [[free will]], in mainstream analytical philosophy.{{sfn|Kane|2005|p=23}} In the book, he introduces the [[consequence argument]] and the term [[incompatibilism]] about free will and [[determinism]], to stand in contrast to [[compatibilism]]—the view that free will is compatible with determinism. [[C. D. Broad|Charlie Broad]] had previously made similar arguments.

==== Personal identity ====
Since [[John Locke]], philosophers have been concerned with the problem of [[personal identity]]. [[Derek Parfit]] in ''[[Reasons and Persons]]'' (1984) defends a kind of [[bundle theory]], while David Lewis again defends perdurantism. [[Bernard Williams]] in ''The Self and the Future'' (1970) argues that personal identity is bodily identity rather than mental continuity.<ref>{{Cite book |url=https://books.google.com/books?id=54nvGHWVfqY |title=Identity, Personal Identity, and the Self |pages=103}}</ref>

==== Principle of sufficient reason ====
Since [[Gottfried Wilhelm Leibniz|Leibniz]] philosophers have discussed the [[principle of sufficient reason]] or PSR. Van Inwagen criticizes the PSR.{{sfn|van Inwagen|1983}} [[Alexander Pruss]] defends it.<ref>Pruss, "Leibnizian Cosmological Arguments"</ref>

==== Philosophy of time ====
Analytic [[Philosophy of space and time|philosophy of time]] traces its roots to the British idealist [[J. M. E. McTaggart]]'s article "[[The Unreality of Time]]"  (1908). In it, McTaggart distinguishes between the dynamic, [[A series and B series|A-, or tensed, theory]] of time (past, present, future), in which [[flow of time|time flows]]; and the static or tenseless [[B-theory of time]] (earlier than, simultaneous with, later than). [[Eternalism (philosophy of time)|Eternalism]] holds that past, present, and future are equally real. In contrast, [[Presentism (philosophy of time)|Presentism]] holds that only entities in the present exist.<ref>{{harvnb|Loux|Crisp|2017|pp=206, 214–215}}</ref>

The theory of special relativity seems to advocate a B-theory of time. David Lewis's perdurantism, or [[four-dimensionalism]], requires a B-theory of time.<ref>[https://books.google.com/books?id=-9MYDQAAQBAJ Personal Identity and Resurrection]</ref> [[A. N. Prior]], who invented [[tense logic]], advocated the A-theory of time.

==== Logical pluralism ====
[[Many-valued logic|Many-valued]] and [[Non-classical logic|non-classical]] logics have been popular since the Polish logician [[Jan Łukasiewicz|Jan Lukasiewicz]]. [[Graham Priest]] is a [[Dialetheism|dialetheist]], seeing it as the most natural solution to problems such as the [[liar paradox]]. [[JC Beall]], together with [[Greg Restall]], is a pioneer of a widely-discussed version of [[logical pluralism]].<ref>{{Cite web |title=Logical Pluralism |url=https://global.oup.com/academic/product/logical-pluralism-9780199288410?cc=us&lang=en& |accessdate=February 5, 2017 |publisher=global.oup.com}}</ref>

=== Epistemology ===
{{Main|Epistemology}}

==== Justification ====

===== Gettier =====
[[File:Edmund L Gettier III ca 1960s umass.jpg|thumb|140px|Edmund Gettier helped to revitalize analytic epistemology.]]

Owing largely to [[Edmund Gettier]]'s 1963 paper "Is Justified True Belief Knowledge?",<ref>{{Citation |last=Gettier |first=Edmund |title=Is Justified True Belief Knowledge? |date=15 July 2020 |url=https://halshs.archives-ouvertes.fr/halshs-01439314/file/2013%20Gettier%20Conocimiento.pdf |work=Arguing About Knowledge |pages=14–15 |publisher=Routledge |doi=10.4324/9781003061038-5 |isbn=978-1-003-06103-8 |s2cid=243290967}}</ref> and the so-called [[Gettier problem]], epistemology has enjoyed a resurgence as a topic of analytic philosophy during the last 50 years. A large portion of current epistemological research is intended to resolve the problems that Gettier's examples presented to the traditional "justified true belief" model of knowledge, found as early as Plato's dialogue ''[[Theaetetus (dialogue)|Theaetetus]]''. These include developing [[Theory of justification|theories of justification]] to deal with Gettier's examples, or giving alternatives to the justified-true-belief model.

===== Theories =====
Chisholm defended [[foundationalism]]. Quine defended [[coherentism]], a "web of belief".<ref>The Web of Belief</ref> Quine proposed [[naturalized epistemology]].

====== Internalism and externalism ======
The debate between [[internalism and externalism]] still exists in analytic philosophy.<ref>Bonjour, Laurence, "Recent Work on the Internalism–Externalism Controversy" in Dancy, Sosa, and Steup (eds.), ''A Companion to Epistemology, Second Edition'' (Wiley-Blackwell, 2010), p. 33.</ref> [[Alvin Goldman]] is an externalist known for developing a popular form of externalism called [[reliabilism]]. Most externalists reject the [[KK thesis]], which has been disputed since the introduction of the epistemic logic by [[Jaakko Hintikka]] in 1962.<ref name=":3">{{Cite book |last1=Rahman |first1=Shahid |title=Logic, Epistemology, and the Unity of Science |last2=Symons |first2=John |last3=Gabbay |first3=Dov M. |last4=bendegem |first4=jean paul van |publisher=Springer Science & Business Media |year=2009 |isbn=978-1-4020-2807-6 |location=Dordrecht |pages=92 |language=en}}</ref>

==== Problem of the Criterion ====
While a problem since antiquity, American philosopher [[Roderick Chisholm]], in his ''Theory of Knowledge'', details the [[problem of the criterion]] with two sets of questions:

# What do we know? or What is the extent of our knowledge?
# How do we know? or What is the criterion for deciding whether we have knowledge in any particular case?

An answer to either set of questions will allow us to devise a means of answering the other. Answering the former question-set first is called ''[[Epistemological particularism|particularism]]'', whereas answering the latter set first is called ''[[Methodism (philosophy)|methodism]]''. A third solution is ''[[philosophical skepticism|skepticism]]'', or doubting there is such a thing as knowledge.

==== Truth ====
[[File:AlfredTarski1968.jpeg|thumb|150px|Alfred Tarski has an influential theory of truth.]]

Frege questioned standard theories of [[truth]], and sometimes advocated a [[redundancy theory of truth]]. Frank Ramsey also advocated a redundancy theory.  [[Alfred Tarski]] put forward a [[semantic theory of truth]].<ref name="Vaught">{{cite journal |last=Vaught |first=Robert L. |date=Dec 1986 |title=Alfred Tarski's Work in Model Theory |journal=[[Journal of Symbolic Logic]] |publisher=ASL |volume=51 |issue=4 |pages=869–882 |doi=10.2307/2273900 |jstor=2273900}}</ref><ref name="FF">[[Lwów–Warsaw school#F-F|Feferman & Feferman]], p. 1</ref>

In ''Truth-Makers'' (1984), [[Kevin Mulligan]], [[Peter Simons (academic)|Peter Simons]], and [[Barry Smith (academic)|Barry Smith]] introduced the [[Truthmaker theory|truth-maker]] idea as a contribution to the [[correspondence theory of truth]].<ref>{{cite journal |last1=Mulligan |first1=Kevin |last2=Simons |first2=Peter |last3=Smith |first3=Barry |date=1984 |title=Truth-Makers |url=https://philpapers.org/rec/MULT |journal=Philosophy and Phenomenological Research |volume=44 |issue=3 |pages=287–321 |doi=10.2307/2107686 |jstor=2107686}}</ref> A truth-maker is contrasted with a [[truth-bearer]].

==== Closure ====
[[File:3349839-left-hand-outstretched.jpg|thumb|140px|"Here is one hand"]]

[[Epistemic closure]] is the claim that knowledge is closed under [[Logical consequence|entailment]]; in other words epistemic closure is a [[Property (philosophy)|property]] or the [[Concept|principle]] that if a subject <math>S</math> knows <math>p</math>, and <math>S</math> knows that <math>p</math> [[Logical consequence|entails]] <math>q</math>, then <math>S</math> can thereby come to know <math>q</math>.<ref name="stanford">{{cite encyclopedia |title=The Epistemic Closure Principle |encyclopedia=[[Stanford Encyclopedia of Philosophy]] |publisher=Metaphysics Research Lab, Stanford University |date=31 December 2001 |author=Luper, Steven |chapter-url=http://plato.stanford.edu/entries/closure-epistemic/#CloPri |chapter=Epistemic Closure}}</ref> Most [[Epistemology|epistemological]] theories involve a closure principle, and many skeptical arguments assume a closure principle. In ''Proof of An External World'', G. E. Moore uses closure in his famous anti-skeptical "[[here is one hand]]" argument. Shortly before his death, Wittgenstein wrote ''[[On Certainty]]'' in response to Moore.

While the principle of epistemic closure is generally regarded as intuitive,<ref>{{cite journal |author1=Brady, Michael |author2=Pritchard, Duncan |year=2005 |title=Epistemological Contextualism: Problems and Prospects |journal=[[The Philosophical Quarterly]] |volume=55 |issue=219 |pages=161–171 |doi=10.1111/j.0031-8094.2005.00393.x}}</ref> philosophers, such as [[Fred Dretske]] with [[relevant alternatives theory]] and Robert Nozick in ''[[Philosophical Explanations]]'', have argued against it.

==== Induction ====
[[File:Зүмірет.jpg|thumb|150px|All emeralds are "grue".]]

In his book ''[[Fact, Fiction, and Forecast]]'', [[Nelson Goodman]] introduced the "[[new riddle of induction]]", so-called by analogy with [[David Hume|Hume]]'s classical [[problem of induction]].  Goodman's famous example was to introduce the predicates [[New riddle of induction|grue and bleen]]. "Grue" applies to all things before a certain time ''t'', just in case they are green, but also just in case they are blue after time ''t''; and "bleen" applies to all things before a certain time ''t'', just in the case they are blue, but also just in case they are green after time ''t''.

==== Other topics ====
Other, related topics of contemporary research include debates over basic knowledge, the nature of [[evidence]], the value of knowledge, [[epistemic luck]], [[virtue epistemology]], the role of [[intuition (philosophy)|intuitions]] in justification, and treating knowledge as a primitive concept.

=== Ethics ===
Due to the commitments to [[empiricism]] and [[Mathematical logic|symbolic logic]] in the early analytic period, early analytic philosophers often thought that inquiry in the ethical domain could not be made rigorous enough to merit any attention.<ref name=":0">{{Cite book|url=https://books.google.com/books?id=5lK6DTadnaQC&q=%22analytic+philosophy%22+ethics&pg=PT213|title=A Brief History of Analytic Philosophy: From Russell to Rawls|last=Schwartz|first=Stephen P.|year=2012|publisher=John Wiley & Sons|isbn=978-1-118-27172-8|language=en}}</ref> It was only with the emergence of ordinary-language philosophers that ethics started to become an acceptable area of inquiry for analytic philosophers.<ref name=":0" /> Philosophers working within the analytic tradition have gradually come to distinguish three major types of moral philosophy.

* [[Meta-ethics]], which investigates moral terms and concepts;<ref>{{Cite book|title=Key Terms in Ethics|last=Kuusela|first=Oskari|publisher=Continuum International Publishing Group|year=2011|isbn=978-1-4411-6610-4|location=London|page=61}}</ref>
* [[Normative ethics]], which examines and produces normative ethical judgments;
* [[Applied ethics]], which investigates how existing normative principles should be applied to difficult or borderline cases, often cases created by new technology or new scientific knowledge.

==== Meta-ethics ====
As well as Hume's famous [[Is–ought problem|is/ought distinction]], twentieth-century meta-ethics has two original strains.

===== ''Principia Ethica'' =====
[[File:1914 George Edward Moore (cropped).jpg|thumb|160px|G. E. Moore was an ethical non-naturalist.]]

The first is [[G. E. Moore]]'s investigation into the nature of ethical terms (e.g., good) in his ''Principia Ethica'' (1903), which  advances a kind of [[moral realism]] called [[ethical non-naturalism]] and is known for the [[Open-question argument|open question argument]] and identifying the [[naturalistic fallacy]], a major topic of investigation for analytical philosophers. According to Moore, "[[Goodness and value theory|Goodness]] is a simple, undefinable, non-natural [[Property (philosophy)|property]]."

Contemporary philosophers, such as [[Russ Shafer-Landau]] in ''[[Moral Realism: A Defence]]'', defend ethical non-naturalism.

===== Emotivism =====
The second is founded on logical positivism and its attitude that unverifiable statements are meaningless. As a result, they avoided normative ethics and instead began [[meta-ethics|meta-ethical]] investigations into the nature of moral terms, statements, and judgments.

The logical positivists opined that statements about [[Value (ethics)|value]]—including all ethical and aesthetic judgments—are [[non-cognitivism|non-cognitive]]; that is, they cannot be objectively verified or falsified. Instead, the logical positivists adopted an [[emotivism|emotivist]] theory, which was that value judgments expressed the attitude of the speaker. It is also known as the boo/hurrah theory. For example, in this view, saying, "Murder is wrong", is equivalent to saying, "Boo to murder", or saying the word "murder" with a particular tone of disapproval.

While analytic philosophers generally accepted non-cognitivism, emotivism had many deficiencies. It evolved into more sophisticated non-cognitivist theories, such as the [[expressivism]] of [[Charles Stevenson (philosopher)|Charles Stevenson]], and the [[universal prescriptivism]] of [[R. M. Hare]], which was based on J. L. Austin's philosophy of [[speech acts]].

===== Critics =====
As non-cognitivism, the is/ought distinction, and the naturalistic fallacy were questioned, analytic philosophers showed a renewed interest in the traditional questions of moral philosophy.

[[Philippa Foot]] defended [[Ethical naturalism|naturalist]] moral realism and contributed several essays attacking other theories.{{efn|Foot was the granddaughter of former US President [[Grover Cleveland]].}} Foot introduced the famous "[[trolley problem]]" into the ethical discourse.<ref name="Philippa Foot 1978">Philippa Foot, "[https://www2.econ.iastate.edu/classes/econ362/hallam/Readings/FootDoubleEffect.pdf The Problem of Abortion and the Doctrine of the Double Effect]" {{Webarchive|url=https://web.archive.org/web/20190824083120/http://www2.econ.iastate.edu/classes/econ362/hallam/Readings/FootDoubleEffect.pdf|date=24 August 2019}} in ''Virtues and Vices'' (Oxford: Basil Blackwell, 1978) (originally in the ''Oxford Review'', No. 5, 1967).</ref>

Perhaps the most influential critic was [[Elizabeth Anscombe]], whose monograph ''Intention'' was called by [[Donald Davidson (philosopher)|Donald Davidson]] "the most important treatment of [[Action theory (philosophy)|action]] since Aristotle".<ref>From the cover of the 2000 Harvard University Press edition of ''Intention''.</ref> A favorite student and friend of Ludwig Wittgenstein, her 1958 article "[[Modern Moral Philosophy]]" declared the "is-ought" impasse to be unproductive. [[J.O. Urmson]]'s article "On Grading" also called the is/ought distinction into question.

Australian [[J. L. Mackie]], in ''Ethics: Inventing Right And Wrong'', defended anti-realist [[error theory]]. [[Bernard Williams]] also influenced ethics by advocating a kind of [[moral relativism]] and rejecting all other theories.<ref>Ethics and the Limits of Philosophy</ref>

==== Normative ethics ====
The first half of the 20th century was marked by skepticism toward, and neglect of, normative ethics. However, contemporary normative ethics is dominated by three schools: [[consequentialism]], [[virtue ethics]], and [[deontology]].{{efn|Anscombe introduced the term "[[consequentialism]]" into the philosophical lexicon.}}

===== Consequentialism, or Utilitarianism =====

During the early 20th century, [[utilitarianism]] was the only non-skeptical type of ethics to remain popular among analytic philosophers. However, as the influence of logical positivism declined mid-century, analytic philosophers had a renewed interest in ethics. ''Utilitarianism: For and Against'' was written with [[J. J. C. Smart]] arguing for and Bernard Williams arguing against.

===== Virtue ethics =====
Anscombe, Foot, and [[Alasdair MacIntyre|Alasdair Macintyre]]'s ''After Virtue'' sparked a revival of [[Aristotle]]'s [[Virtue ethics|virtue ethical]] approach. This increased interest in virtue ethics has been dubbed the "[[Virtue ethics|aretaic turn]]" mimicking the linguistic turn.

===== Deontology =====
[[John Rawls]]'s 1971 ''[[A Theory of Justice]]'' restored interest in [[Kantian]] ethical philosophy.

==== Applied ethics ====
Since around 1970, a significant feature of analytic philosophy has been the emergence of [[applied ethics]]—an interest in the application of moral principles to specific practical issues. The philosophers following this orientation view ethics as involving humanistic values, which involve practical implications and applications in the way people interact and lead their lives socially.<ref>{{Cite book|title=Philosophical Perspectives on Communalism and Morality in African Traditions|last=Ikuenobe|first=Polycarp|publisher=Lexington Books|year=2006|isbn=978-0-7391-1131-4|location=Oxford|page=104}}</ref>

Topics of special interest for applied ethics include [[environmental ethics]], [[animal rights]], and the many challenges created by advancing [[bioethics|medical science]].<ref>Brennan, Andrew and Yeuk-Sze Lo (2002). "Environmental Ethics" [http://plato.stanford.edu/entries/ethics-environmental/#2 §2] {{webarchive|url=https://web.archive.org/web/20130801143528/http://plato.stanford.edu/entries/ethics-environmental/ |date=1 August 2013 }}, in ''The Stanford Encyclopedia of Philosophy''.</ref><ref>Gruen, Lori (2003). "[http://plato.stanford.edu/entries/moral-animal/ The Moral Status of Animals]," in ''The Stanford Encyclopedia of Philosophy''.</ref><ref>See Hursthouse, Rosalind (2003). "Virtue Ethics" [http://plato.stanford.edu/entries/ethics-virtue/#3 §3], in ''The Stanford Encyclopedia of Philosophy'' and Donchin, Anne (2004). "[http://plato.stanford.edu/entries/feminist-bioethics/ Feminist Bioethics]" in ''The Stanford Encyclopedia of Philosophy''.</ref> In education, applied ethics addressed themes such as punishment in schools, [[Equal opportunity|equality of educational opportunity]], and education for democracy.<ref>{{Cite book|title=Methods in Philosophy of Education|url=https://archive.org/details/methodsphilosoph00heyt|url-access=limited|last1=Heyting|first1=Frieda|last2=Lenzen|first2=Dieter|last3=White|first3=John|publisher=Routledge|year=2002|isbn=978-0-415-24260-8|location=New York|pages=[https://archive.org/details/methodsphilosoph00heyt/page/n30 18]}}</ref>

===Political philosophy===

====Liberalism====
[[File:John Rawls (1971 photo portrait).jpg|thumb|140px|John Rawls]]

[[Isaiah Berlin]] had a lasting influence on both analytic political philosophy and liberalism with his lecture "[[Two Concepts of Liberty]]".{{Citation needed|date=August 2022}} Berlin defined 'negative liberty' as absence of coercion or interference in private actions. 'Positive liberty' Berlin maintained, could be thought of as self-mastery, which asks not what we are free from, but what we are free to do.

Current analytic political philosophy owes much to [[John Rawls]], who in a series of papers from the 1950s onward (most notably "Two Concepts of Rules" and "Justice as Fairness") and his 1971 book ''[[A Theory of Justice]]'', produced a sophisticated defense of a generally liberal [[Egalitarianism|egalitarian]] account of distributive justice. Rawls introduced the term the [[Original position|veil of ignorance]].

This was followed soon by Rawls's colleague [[Robert Nozick]]'s book ''[[Anarchy, State, and Utopia]]'', a defense of [[free-market]] [[libertarianism]].  [[Consequentialist libertarianism]] also derives from the analytic tradition {{Citation needed|date=August 2022}}.

During recent decades there have also been several critics of liberalism, including the [[feminism|feminist]] critiques by [[Catharine MacKinnon]] and [[Andrea Dworkin]], the [[multiculturalism|multiculturalist]] critiques by [[Amy Gutmann]] and [[Charles Taylor (philosopher)|Charles Taylor]], and the [[communitarianism|communitarian]] critiques by [[Michael Sandel]] and [[Alasdair MacIntyre]] (although neither of them endorses the term).

==== Analytical Marxism ====
Another development of political philosophy was the emergence of the school of [[analytical Marxism]]. Members of this school seek to apply techniques of analytic philosophy and modern social science to clarify the theories of [[Karl Marx]] and his successors. The best-known member of this school is [[G. A. Cohen]], whose 1978 book, ''[[Karl Marx's Theory of History: A Defence]]'', is generally considered to represent the genesis of this school. In that book, Cohen used logical and linguistic analysis to clarify and defend Marx's materialist conception of history. Other prominent analytical Marxists include the economist [[John Roemer]], the social scientist [[Jon Elster]], and the sociologist [[Erik Olin Wright]]. The work of these later philosophers has furthered Cohen's work by bringing to bear modern social science methods, such as [[rational choice theory]], to supplement Cohen's use of analytic philosophical techniques in the interpretation of Marxian theory.

Cohen himself would later engage directly with Rawlsian political philosophy to advance a [[socialist]] theory of justice that contrasts with both traditional Marxism and the theories advanced by Rawls and Nozick. In particular, he indicates Marx's principle of [[from each according to his ability, to each according to his need]].

Although not an analytic philosopher, [[Jürgen Habermas]] is another influential—if controversial—author in contemporary analytic political philosophy, whose social theory is a blend of social science, Marxism, [[neo-Kantianism]], and American [[pragmatism]].{{Citation needed|date=August 2022}}

==== Communitarianism ====
[[File:Alasdair MacIntyre.jpg|thumb|130px|Alasdair MacIntyre]]

[[Communitarian]]s such as [[Alasdair MacIntyre]], [[Charles Taylor (philosopher)|Charles Taylor]], [[Michael Walzer]], and [[Michael Sandel]] advance a critique of liberalism that uses analytic techniques to isolate the main assumptions of liberal individualists, such as Rawls, and then challenges these assumptions. In particular, communitarians challenge the liberal assumption that the individual can be considered as fully autonomous from the community in which he is brought up and lives. Instead, they argue for a conception of the individual that emphasizes the role that the community plays in forming his or her values, thought processes, and opinions. While in the analytic tradition, its major exponents often also engage at length with figures generally considered continental, notably [[G. W. F. Hegel]] and [[Friedrich Nietzsche]].

===Aesthetics===
{{Main|Aesthetics}}

As a result of logical positivism, as well as what seemed like rejections of the traditional aesthetic notions of beauty and sublimity from [[post-modern]] thinkers, analytic philosophers were slow to consider art and aesthetic judgment. [[Susanne Langer]]<ref>[[Susanne Langer]], ''Feeling and Form: A Theory of Art'' (1953)</ref> and [[Nelson Goodman]]<ref>[[Nelson Goodman]], ''Languages of Art: An Approach to a Theory of Symbols''. Indianapolis: Bobbs-Merrill, 1968. 2nd ed. Indianapolis: Hackett, 1976. Based on his 1960–61 John Locke lectures.</ref> addressed these problems in an analytic style during the 1950s and 1960s. Since Goodman, aesthetics as a discipline for analytic philosophers has flourished.<ref>Kivy, Peter, "Introduction: Aesthetics Today" in ''The Blackwell Guide to Aesthetics'' (Blackwell Publishing, 2004), p. 4.</ref>

[[Arthur Danto]] argued for a "institutional definition of art" in the 1964 essay "The Artworld" in which Danto coined the term "artworld" (as opposed to the existing "[[art world]]", though they mean the same), by which he meant cultural context or "an atmosphere of [[art theory]]".<ref>Adajian, Thomas. [http://plato.stanford.edu/entries/art-definition/ "The Definition of Art"], ''The Stanford Encyclopedia of Philosophy'', London, Oct 23, 2007. <!--accessed December 21, 2009--></ref>

Rigorous efforts to pursue analyses of traditional aesthetic concepts were performed by [[Guy Sircello]] in the 1970s and 1980s, resulting in new analytic theories of love,<ref>[[Guy Sircello]], ''Love and Beauty.'' Princeton, NJ: Princeton University Press, 1989.</ref> sublimity,<ref>[[Guy Sircello]] "How Is a Theory of the Sublime Possible?" ''The Journal of Aesthetics and Art Criticism'', Vol. 51, No. 4 (Autumn, 1993), pp.&nbsp;541–550</ref> and beauty.<ref>[[Guy Sircello]], ''A New Theory of Beauty.'' Princeton Essays on the Arts, 1. Princeton, NJ: Princeton University Press, 1975.</ref> In the opinion of [[Władysław Tatarkiewicz]], there are six conditions for the presentation of art: beauty, form, representation, reproduction of reality, artistic expression, and innovation. However, one may not be able to pin down these qualities in a work of art.<ref>{{cite book |last=Tatarkiewicz |first=Władysław |url=https://books.google.com/books?id=eD4qAQAAMAAJ |title=A History of Six Ideas: an essay in aesthetics |date=1980 |publisher=PWN/Polish Scientific Publishers |isbn=978-8301008246}}</ref>

[[George Dickie (philosopher)|George Dickie]] was an influential philosopher of art. Dickie's student [[Noël Carroll]] is a leading philosopher of art.

=== Philosophy of language ===
{{Main|Philosophy of language}}

Given the linguistic turn, it can be hard to separate logic, metaphysics, and the philosophy of language in analytic philosophy. Philosophy of language is a topic that has decreased in activity during the last four decades, as evidenced by the fact that few major philosophers today treat it as a primary research topic. While the debate remains fierce, it is still strongly influenced by those authors from the first half of the century, e.g. Frege, Russell, Wittgenstein, Austin, Tarski, and Quine.

==== Semantics ====
[[Saul Kripke]] provided a [[Kripke semantics|semantics]] for modal logic. In his book ''[[Naming and Necessity]]'' (1980), Kripke challenges the descriptivist theory with a [[causal theory of reference]]. In it he introduced the term [[rigid designator]]. According to one author, "In the philosophy of language, ''Naming and Necessity'' is among the most important works ever."<ref name=ageofm /> [[Ruth Barcan Marcus]] also challenged descriptivism. So did [[Keith Donnellan]].<ref>Keith Donnellan, "Reference and Definite Descriptions"</ref>

Hilary Putnam used the Twin Earth thought experiment to argue for [[semantic externalism]], or the view that the meanings of words are not psychological. [[Donald Davidson (philosopher)|Donald Davidson]] uses the thought experiment of Swampman to advocate for semantic externalism.

Kripke in ''[[Wittgenstein on Rules and Private Language]]'' provides a rule-following paradox that undermines the possibility of our ever following rules in our use of language and, so, calls into question the idea of meaning. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date". The [[portmanteau]] "Kripkenstein" has been coined as a term for a fictional person who holds the views expressed by Kripke's reading of Wittgenstein.

Another influential philosopher, [[Pavel Tichý]] initiated Transparent Intensional Logic, an original theory of the [[logical analysis]] of [[natural language]]s—the theory is devoted to the problem of saying exactly what it is that we learn, know, and can communicate when we come to understand what a sentence means.

==== Pragmatics ====
[[Paul Grice]] and his maxims and theory of [[implicature]] established the discipline of pragmatics.

=== Philosophy of mind and cognitive science ===
[[File:John searle2.jpg|thumb|130px|John Searle]]
[[John Searle]] suggests that the obsession with the philosophy of language during the 20th century has been superseded by an emphasis on the [[philosophy of mind]].<ref>Postrel and Feser, February 2000, ''Reality Principles: An Interview with John R. Searle'' at {{cite web |date=February 2000 |title=Reality Principles: An Interview with John R. Searle |url=http://www.reason.com/news/show/27599.html |url-status=dead |archive-url=https://web.archive.org/web/20080929023644/http://www.reason.com/news/show/27599.html |archive-date=29 September 2008 |access-date=23 September 2008}}</ref>

==== Physicalism ====
Motivated by the logical positivists' interest in verificationism, [[logical behaviorism]] was the most prominent [[philosophy of mind|theory of mind]] of analytic philosophy for the first half of the 20th century.<ref>Graham, George, "Behaviorism", ''The Stanford Encyclopedia of Philosophy'' (Fall 2010 Edition), Edward N. Zalta (ed.). [http://plato.stanford.edu/archives/fall2010/entries/behaviorism/]</ref> Behaviorism later became much less popular, in favor of either [[Identity theory of mind|type physicalism]] or [[Functionalism (philosophy of mind)|functionalism]]. During this period, topics of the philosophy of mind were often related strongly to topics of [[cognitive science]], such as [[modularity of mind|modularity]] or [[Psychological nativism|innateness]].

===== Behaviorism =====
Behaviorists such as [[B. F. Skinner]] tended to opine either that statements about the mind were equivalent to ''statements about'' behavior and dispositions to behave in particular ways or that mental states were directly equivalent to behavior and dispositions to behave.
 
[[File:Hilary Putnam.jpg|thumb|120px|Hilary Putnam]]

Hilary Putnam criticized behaviorism by arguing that it confuses the symptoms of mental states with the mental states themselves, positing "super Spartans" who never display signs of pain.<ref>Brains and Behavior, Hilary Putnam</ref>

See also: {{slink|Verbal_Behavior#Chomsky's_review_and_replies}}

===== Type Identity =====
Type physicalism or type identity theory identified mental states with brain states. Former students of Ryle at the [[University of Adelaide]]  [[J. J. C. Smart]] and [[Ullin Place]] argued for type physicalism.

===== Functionalism =====
Functionalism remains the dominant theory. Type identity was criticized using [[multiple realizability]].

Searle's [[Chinese room]] argument criticized functionalism and holds that while a computer can understand syntax, it could never understand semantics.

===== Eliminativism =====
The view of [[eliminative materialism]] is most closely associated with [[Paul Churchland|Paul]] and [[Patricia Churchland]], who deny the existence of propositional attitudes, and with [[Daniel Dennett]], who is generally considered an eliminativist about [[qualia]] and phenomenal aspects of consciousness.

==== Dualism ====
[[File:David chalmers.jpg|thumb|140px|David Chalmers]]

Finally, analytic philosophy has featured a certain number of philosophers who were [[Dualism (philosophy of mind)|dualists]], and recently forms of [[property dualism]] have had a resurgence; the most prominent representative is [[David Chalmers]].<ref>{{cite SEP|url-id=dualism|title=Dualism}}</ref> Kripke also makes a notable argument for dualism.<ref>{{Cite web |title=Kripke on the distinctness of the mind from the body |url=https://www3.nd.edu/~jspeaks/courses/mcgill/415/kripke-mind-body.html |access-date=2024-04-22 |website=www3.nd.edu}}</ref>

[[Thomas Nagel]]'s "[[What Is It Like to Be a Bat?|What is it like to be a bat]]?" challenged the physicalist account of mind. So did [[Frank Jackson (philosopher)|Frank Jackson]]'s [[knowledge argument]], which argues for [[qualia]].

==== Theories of consciousness ====
In recent years, a central focus of research in the philosophy of mind has been [[consciousness]] and the [[philosophy of perception]]. While there is a general consensus for the global neuronal workspace model of consciousness,<ref>{{Cite journal |last1=Dennett |first1=D. |year=2001 |title=Are we explaining consciousness yet? |journal=Cognition |volume=79 |issue=1–2 |pages=221–237 |doi=10.1016/S0010-0277(00)00130-X |pmid=11164029 |s2cid=2235514}}</ref> there are many opinions as to the specifics. The best known theories are Searle's [[Naïve realism|naive realism]], [[Fred Dretske]] and [[Michael Tye (philosopher)|Michael Tye]]'s [[direct and indirect realism|representationalism]],  [[Daniel Dennett]]'s [[heterophenomenology]], and the [[Higher-order theories of consciousness|higher-order theories]] of either [[David M. Rosenthal (philosopher)|David M. Rosenthal]]—who advocates a higher-order thought (HOT) model—or [[David Malet Armstrong|David Armstrong]] and [[William Lycan]]—who advocate a higher-order perception (HOP) model. An alternative higher-order theory, the higher-order global states (HOGS) model, is offered by [[Robert van Gulick]].<ref>For summaries and some criticism of the different higher-order theories, see Van Gulick, Robert (2006) "Mirror Mirror – Is That All?" In Kriegel & Williford (eds.), ''Self-Representational Approaches to Consciousness''. Cambridge, MA: MIT Press. The final draft is also available here {{cite web |title=Mirror Mirror – Is That All? |url=http://web.syr.edu/~rnvangul/mirror-mirror.final.pdf |url-status=dead |archive-url=https://web.archive.org/web/20081002035247/http://web.syr.edu/~rnvangul/mirror-mirror.final.pdf |archive-date=2 October 2008 |access-date=23 September 2008}}. For Van Gulick's own view, see Van Gulick, Robert. "Higher-Order Global States HOGS: An Alternative Higher-Order Model of Consciousness." In Gennaro, R.J., (ed.) ''Higher-Order Theories of Consciousness: An Anthology.'' Amsterdam and Philadelphia: John Benjamins.</ref>

=== Philosophy of mathematics ===
[[File:Kurt gödel.jpg|thumb|130px|Kurt Gödel]]

Since the beginning, analytic philosophy has had an interest in the [[philosophy of mathematics]]. [[Kurt Gödel]], a student of Hans Hahn of the Vienna Circle, produced his [[Gödel's incompleteness theorems|incompleteness theorems]] showing that Russell and Whitehead's ''Principia Mathematica'' also failed to reduce arithmetic to logic. Gödel has been ranked as one  of the four greatest logicians of all time, along with [[Aristotle]], Frege, and Tarski.<ref name="Restall">{{cite web |last=Restall |first=Greg |date=2002–2006 |title=Great Moments in Logic |url=http://consequently.org/writing/logicians/ |url-status=live |archive-url=https://web.archive.org/web/20081206052240/http://consequently.org/writing/logicians/ |archive-date=6 December 2008 |access-date=2009-01-03}}</ref> [[Ernst Zermelo]] and [[Abraham Fraenkel]] established [[Zermelo–Fraenkel set theory|Zermelo Fraenkel Set Theory]]. Quine developed his own system, dubbed [[New Foundations]].

Physicist [[Eugene Wigner]]'s seminal paper "[[The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]" poses the question of why a formal pursuit like mathematics can have real utility.<ref>{{Cite journal|last1=Wigner|first1=E. P.|author-link=Eugene Wigner|year=1960|title=The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959|url=http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html|journal=Communications on Pure and Applied Mathematics|volume=13|issue=1|pages=1–14|bibcode=1960CPAM...13....1W|doi=10.1002/cpa.3160130102|s2cid=6112252|archive-url=https://web.archive.org/web/20210212111540/http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html|archive-date=2021-02-12}}</ref> [[José Benardete]] argued for the reality of [[infinity]].<ref>Infinity: An Essay In Metaphysics</ref>

Akin to the medieval debate on universals, between realists, idealists, and nominalists; the philosophy of mathematics has the debate between logicists or platonists, conceptualists or [[Intuitionism|intuitionists]], and [[Formalism (philosophy of mathematics)|formalists]].<ref>Quine, On What There Is</ref>

==== Platonism ====
Gödel was a platonist who postulated a special kind of mathematical intuition that lets us perceive mathematical objects directly. Quine and Putnam argued for platonism with the [[Quine–Putnam indispensability argument|indispensability argument]]. [[Crispin Wright]], along with [[Bob Hale (philosopher)|Bob Hale]], led a Neo-Fregean revival with his work ''Frege's Conception of Numbers as Objects''.<ref>The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics</ref>

===== Critics =====
[[Structuralism (philosophy of mathematics)|Structuralist]] [[Paul Benacerraf]] has an epistemological objection to mathematical platonism.

==== Intuitionism ====
The intuitionists, led by [[L. E. J. Brouwer]], are a [[Constructivism (philosophy of mathematics)|constructivist]] school of mathematics that argues that mathematics is a [[Cognition|cognitive]] [[Construct (philosophy)|construct]] rather than a type of [[objective truth]].

==== Formalism ====
The formalists, best exemplified by David Hilbert, considered mathematics to be merely the investigation of [[Formal system|formal axiom systems]]. [[Hartry Field]] defended [[mathematical fictionalism]].

=== Philosophy of religion ===
In ''Analytic Philosophy of Religion'', [[James Franklin Harris]] noted that:

{{blockquote|
...analytic philosophy has been a very heterogeneous 'movement'.... some forms of analytic philosophy have proven very sympathetic to the philosophy of religion and have provided a philosophical mechanism for responding to other more radical and hostile forms of analytic philosophy.<ref name=harris2001>{{cite book |last1=Harris |first1=James Franklin |title=Analytic philosophy of religion |date=2002 |publisher=Kluwer |location=Dordrecht |isbn=978-1-4020-0530-5 |url=https://books.google.com/books?id=Rx2Qf9ieFKYC}} (432 pages) (volume 3 of Handbook of Contemporary Philosophy of Religion, {{ISSN|1568-1556}})</ref>{{rp|3}}
}}

As with the study of ethics, early analytic philosophy tended to avoid the study of [[Philosophy of religion|religion]], largely dismissing (as per the logical positivists) the subject as a part of [[metaphysics]] and therefore meaningless.{{efn|A notable exception is the series of [[Michael Foster (philosopher)|Michael B. Foster]]'s 1934–36 ''[[Mind (journal)|Mind]]'' articles involving the Christian doctrine of creation and the rise of modern science.}} The demise of logical positivism led to a renewed interest in the philosophy of religion, prompting philosophers not only to introduce new problems, but to re-study classical topics such as the [[existence of God]], the nature of [[miracle]]s, the [[problem of evil]], the rationality of belief in God, concepts of the nature of God, and several others.<ref>Peterson, Michael et al. (2003). ''Reason and Religious Belief''</ref> The [[Society of Christian Philosophers]] was established in 1978.

==== Reformed epistemology ====
Analytic philosophy formed the basis for some sophisticated Christian arguments, such as those of the [[reformed epistemology|reformed epistemologists]] such as [[Alvin Plantinga]], [[William Alston]], and [[Nicholas Wolterstorff]].

[[File:AlvinPlantinga.JPG|thumb|160px|Alvin Plantinga]]

Plantinga was awarded the [[Templeton Prize]] in 2017 and was once described by ''[[Time (magazine)|Time]]'' magazine as "America's leading orthodox [[Protestantism|Protestant]] philosopher of God".<ref>{{Cite web |title=Emeritae and Emeriti // Department of Philosophy // University of Notre Dame |url=http://philosophy.nd.edu/people/alvin-plantinga/ |url-status=dead |archive-url=https://web.archive.org/web/20130831050623/http://philosophy.nd.edu/people/alvin-plantinga/ |archive-date=2013-08-31}}</ref> His seminal work ''[[God and Other Minds]]'' (1967) argues that belief in God is a properly basic belief akin to the belief in [[Problem of other minds|other minds]]. Plantinga also developed a modal [[Ontological argument#Alvin Plantinga|ontological argument]] in ''The Nature of Necessity'' (1974).

Plantinga, J. L. Mackie, and [[Antony Flew]] debated the use of the ''[[Alvin Plantinga's free-will defense|free will defense]]'' as a way to solve the problem of evil.<ref>Mackie, John L. (1982). ''The Miracle of Theism: Arguments For and Against the Existence of God''</ref> Plantinga's [[evolutionary argument against naturalism]] contends that there is a problem in asserting both evolution and naturalism. Plantinga further issued a trilogy on epistemology, and especially justification, ''[[Warrant: The Current Debate]]'', ''[[Warrant and Proper Function]]'', and ''[[Warranted Christian Belief]].''

Alston defended [[divine command theory]] and applied the analytic philosophy of language to religious language. [[Robert Merrihew Adams]] also defended divine command theory, and worked on the relationship between faith and morality.<ref>Adams, Robert M. (1987). ''The Virtue of Faith And Other Essays in Philosophical Theology''</ref> [[William Lane Craig]] defends the [[Kalam cosmological argument]] in the [[The Kalām Cosmological Argument|book]] of the same name.

==== Analytic Thomism ====
Catholic philosophers in the analytic tradition—such as Elizabeth Anscombe, [[Peter Geach]], [[Anthony Kenny]], Alasdair MacIntyre, [[John Haldane (philosopher)|John Haldane]], [[Eleonore Stump]], and others—developed an [[Analytical Thomism|analytic approach]] to [[Thomism]].

==== Orthodox ====
[[Richard Swinburne]] wrote a trilogy of books, arguing for God, consisting of ''The Coherence of Theism'', ''[[The Existence of God (book)|The Existence of God]]'', and ''Faith and Reason''.

==== Wittgenstein and religion ====
The analytic philosophy of religion has been preoccupied with Wittgenstein, as well as his interpretation of [[Søren Kierkegaard]]'s philosophy of religion.<ref>Creegan, Charles. (1989). ''Wittgenstein and Kierkegaard: Religion, Individuality and Philosophical Method''</ref> Wittgenstein fought for the Austrian army in the [[First World War]] and came upon a copy of [[Leo Tolstoy]]'s ''Gospel in Brief''. At that time, he underwent some kind of religious conversion.<ref>{{Cite web |title=Wittgenstein Tolstoy and the Gospel in Brief (2001) |url=http://www.the-philosopher.co.uk/2001/04/wittgenstein-tolstoy-and-the-gospel-in.html |access-date=2024-04-11}}</ref>

Using first-hand remarks (which were later published in ''Philosophical Investigations'', ''Culture and Value'', and other works), philosophers such as [[Peter Winch]] and [[Norman Malcolm]] developed what has come to be known as "contemplative philosophy", a Wittgensteinian school of thought rooted in the "[[Swansea University|Swansea]] school", and which includes Wittgensteinians such as [[Rush Rhees]], Peter Winch, and [[D.Z. Phillips]], among others.

The name "contemplative philosophy" was coined by D. Z. Phillips in ''Philosophy's Cool Place'', which rests on an interpretation of a passage from Wittgenstein's ''Culture and Value''.<ref>Phillips, D.Z. (1999). ''Philosophy's Cool Place''. Cornell University Press. The quote is from Wittgenstein's ''Culture and Value'' (2e): "My ideal is a certain coolness. A temple providing a setting for the passions without meddling with them."</ref> This interpretation was first labeled "Wittgensteinian [[Fideism]]" by [[Kai Nielsen (philosopher)|Kai Nielsen]], but those who consider themselves members of the Swansea school have relentlessly and repeatedly rejected this construal as a caricature of Wittgenstein's position; this is especially true of Phillips.<ref>{{cite SEP|url-id=fideism|title=Fideism}}</ref> Responding to this interpretation, Nielsen and Phillips became two of the most prominent interpreters of Wittgenstein's philosophy of religion.<ref>Nielsen, Kai and D.Z. Phillips. (2005). ''Wittgensteinian Fideism?''</ref>

=== Philosophy of science ===
{{Main|Philosophy of science}}

Science and the [[philosophy of science]] have also had increasingly significant roles in analytic metaphysics. The theory of special relativity has had a profound effect on the philosophy of time, and quantum physics is routinely discussed in the free will debate.<ref name="inwagenetall1998" /> The weight given to scientific evidence is largely due to commitments of philosophers to [[scientific realism]] and [[Naturalism (philosophy)|naturalism]]. Others will see a commitment to using science in philosophy as [[scientism]].

==== Confirmation theory ====
Carl Hempel advocated confirmation theory or [[Bayesian epistemology]]. He introduced the famous [[Raven paradox|raven's paradox]].<ref name="Fitelson">{{cite book |last1=Fitelson |first1=Branden |title=The Place of Probability in Science |last2=Hawthorne |first2=James |date=2010 |publisher=Springer |isbn=978-90-481-3614-8 |series=Boston Studies in the Philosophy of Science |volume=284 |pages=247–275 |chapter=How Bayesian Confirmation Theory Handles the Paradox of the Ravens |doi=10.1007/978-90-481-3615-5_11 |chapter-url=https://philpapers.org/rec/HAWHBC}}</ref>

==== Falsification ====
[[File:Karl Popper.jpg|thumb|130px|Karl Popper]]

In reaction to what he considered excesses of logical positivism, [[Karl Popper]], in ''[[The Logic of Scientific Discovery]]'', insisted on the role of [[falsifiability|falsification]] in the philosophy of science, using it to solve the [[demarcation problem]].<ref>{{cite book |author=Popper, Karl R. |title=The Logic of Scientific Discovery |publisher=Routledge |year=2002 |isbn=978-0-415-27844-7}}</ref>

==== Confirmation holism ====
The [[Duhem–Quine thesis]], or problem of [[underdetermination]], posits that no [[Hypothesis|scientific hypothesis]] can be understood in isolation, a viewpoint called [[confirmation holism]].<ref name=qui/>

==== Constructivism ====
In reaction to both the logical positivists and Popper, discussions of the philosophy of science during the last 40 years were dominated by [[social constructivism|social constructivist]] and [[cognitive relativism|cognitive relativist]] theories of science. Following Quine and Duhem, subsequent theories emphasized [[theory-ladenness]]. [[Thomas Samuel Kuhn]], with his formulation of [[paradigm shift]]s, and [[Paul Feyerabend]], with his [[epistemological anarchism]], are significant for these discussions.<ref>Glock 2008, p. 47.</ref>

==== Biology ====
The [[philosophy of biology]] has also undergone considerable growth, particularly due to the considerable debate in recent years over the nature of [[evolution]], particularly [[natural selection]].<ref>Hull, David L. and [[Michael Ruse|Ruse, Michael]], "Preface" in ''The Cambridge Companion to the Philosophy of Biology'' (Cambridge University Press, 2007), pp. xix, xx.</ref> Daniel Dennett and his 1995 book ''[[Darwin's Dangerous Idea]]'', which defends [[Neo-Darwinism]], stand at the forefront of this debate.<ref>Lennox, James G., "Darwinism and Neo-Darwinism" in Sakar and Plutynski (eds.), ''A Companion to the Philosophy of Biology'' (Blackwell Publishing, 2008), p. 89.</ref> [[Jerry Fodor]] criticizes natural selection.

== Notes ==
{{notelist}}

== References ==
{{reflist|colwidth=30em}}

==Sources==
* Aristotle, ''[[Metaphysics (Aristotle)|Metaphysics]]''
* {{cite web |last1=Desmet |first1=Ronald |last2=Irvine |first2=Andrew David |title=Alfred North Whitehead |url=https://plato.stanford.edu/entries/whitehead/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=1 April 2024 |date=2022 }}
* {{cite book|url=https://archive.org/details/originsofanalyti0000dumm/|last=Dummett|first=Michael|title=The Origins of Analytical Philosophy|location= Cambridge, MA|publisher= Harvard University Press|year= 1993|isbn=978-0-674-64473-1 }}
* Geach, P., ''Mental Acts'', London 1957
* {{cite book |last1=Kane |first1=Robert |title=A Contemporary Introduction to Free Will |date=2005 |publisher=Oxford University Press |isbn=978-0-19-514970-8 |url=https://books.google.com/books?id=9BRiQgAACAAJ |access-date=April 13, 2020 }}
* Kenny, A.J.P., ''Wittgenstein'', London 1973.
* {{cite book |last1=Loux |first1=Michael J. |last2=Crisp |first2=Thomas M. |title=Metaphysics: A Contemporary Introduction |date=2017 |publisher=Routledge |isbn=978-1-138-63933-1 |edition=4}}
* {{cite book |last1=Palmer |first1=Clare |title=Environmental Ethics and Process Thinking |publisher=Clarendon Press |isbn=978-0-19-826952-6 |url=https://books.google.com/books?id=ZT2pI9IMiYUC&pg=PA175 |language=en |date=1998 |access-date=4 April 2024 |archive-date=2 April 2024 |archive-url=https://web.archive.org/web/20240402175535/https://books.google.com/books?id=ZT2pI9IMiYUC&pg=PA175 |url-status=live }}
* {{iep|/a/analytic.htm|Analytic philosophy|Aaron Preston}}
* Soames, Scott. ''Philosophical Analysis in the Twentieth Century: Volume 1, The Dawn of Analysis''. Princeton: Princeton University Press, 2003.
* {{cite book|first=Peter |last= van Inwagen|title=An Essay on Free Will|url=https://books.google.com/books?id=of1sJaUSdcYC|access-date=27 December 2012|year=1983|publisher=Clarendon Press|isbn=978-0-19-824924-5}}
* Wittgenstein, ''[[Tractatus Logico-Philosophicus]]''

==Further reading==
* The [http://www.ucl.ac.uk/philosophy/LPSG/ London Philosophy Study Guide] {{Webarchive|url=https://web.archive.org/web/20090923081848/http://www.ucl.ac.uk/philosophy/LPSG/Language.htm |date=23 September 2009 }} offers many suggestions on what to read, depending on the student's familiarity with the subject: [http://www.ucl.ac.uk/philosophy/LPSG/FRW.htm Frege, Russell, and Wittgenstein]
* Hirschberger, Johannes. ''A Short History of Western Philosophy'', ed. Clare Hay. [https://web.archive.org/web/20090413090205/http://www.lutterworth.com/lp/titles/shwphil.htm Short History of Western Philosophy, A]. {{ISBN|978-0-7188-3092-2}}
* Hylton, Peter. ''Russell, Idealism, and the Emergence of Analytic Philosophy''. Oxford: Oxford University Press, 1990.
* Passmore, John. ''A Hundred Years of Philosophy'', revised ed. New York: Basic Books, 1966.
* Weitz, Morris, ed. ''Twentieth Century Philosophy: The Analytic Tradition''. New York: Free Press, 1966.

==External links==
* {{IEP|analytic}}
* {{cite SEP |url-id=analysis/s6 |title=Conceptions of Analysis in Analytic Philosophy}}

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