Editing Analytic philosophy (section)

=== 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>