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- Logicism abstract "Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory, created by mathematicians Richard Dedekind and Gottlob Frege.Dedekind's path to logicism had a turning point when he was able to reduce the theory of real numbers to the rational number system by means of set theory. This and related ideas convinced him that arithmetic, algebra and analysis were reducible to the natural numbers plus a \"logic\" of sets; furthermore by 1872 he had concluded that the naturals themselves were reducible to sets and mappings. It is likely that other logicists, most importantly Frege, were also guided by the new theories of the real numbers published in the year 1872. This started a period of expansion of logicism, with Dedekind and Frege as its main exponents, which however was brought to a deep crisis with the discovery of the classical paradoxes of set theory (Cantor 1896, Zermelo and Russell 1900–1901). Frege gave up on the project after Russell recognized and communicated his paradox exposing an inconsistency in naive set theory. On the other hand, Russell wrote The Principles of Mathematics in 1903 using the paradox and developments of Giuseppe Peano's school of geometry. Since he treated the subject of primitive notions in geometry and set theory, this text is a watershed in the development of logicism. Evidence of the assertion of logicism was collected by Russell and Whitehead in their Principia Mathematica.Today, the bulk of modern mathematics is believed to be reducible to a logical foundation using the axioms of Zermelo-Fraenkel set theory (or one of its extensions, such as ZFC), which has no known inconsistencies (although it remains possible that inconsistencies in it may still be discovered). Thus to some extent Dedekind's project was proved viable, but in the process the theory of sets and mappings came to be regarded as transcending pure logic.Kurt Gödel's incompleteness theorem undermines logicism because it shows that no particular axiomatization of mathematics can decide all statements. Some believe that the basic spirit of logicism remains valid because that theorem is proved with logic just like other theorems. However, that conclusion fails to acknowledge any distinction between theorems of mathematical logic and theorems of higher-order logic. The former can be proven using the fundamental theorem of arithmetic (see Gödel numbering), while the latter must rely on human-provided models. Tarski's undefinability theorem shows that Gödel numbering can be used to prove syntactical constructs, but not semantic assertions. Therefore, any claim that logicism remains a valid concept must strictly rely on the dubious notion that a system of proof based on man-made models is precisely as powerful and authoritative as one based on the existence and properties of the natural numbers.Logicism was key in the development of analytic philosophy in the twentieth century.".
- Logicism wikiPageExternalLink Logicism.
- Logicism wikiPageExternalLink faq001.htm.
- Logicism wikiPageID "350672".
- Logicism wikiPageLength "77903".
- Logicism wikiPageOutDegree "71".
- Logicism wikiPageRevisionID "687725482".
- Logicism wikiPageWikiLink %5Bd.
- Logicism wikiPageWikiLink Alfred_North_Whitehead.
- Logicism wikiPageWikiLink Algebraic_logic.
- Logicism wikiPageWikiLink Analytic_philosophy.
- Logicism wikiPageWikiLink Axiom_of_pairing.
- Logicism wikiPageWikiLink Axiom_of_reducibility.
- Logicism wikiPageWikiLink Axiomatic_system.
- Logicism wikiPageWikiLink Bertrand_Russell.
- Logicism wikiPageWikiLink Bob_Hale_(philosopher).
- Logicism wikiPageWikiLink Boolean_algebra.
- Logicism wikiPageWikiLink Cardinal_number.
- Logicism wikiPageWikiLink Category:Theories_of_deduction.
- Logicism wikiPageWikiLink Crispin_Wright.
- Logicism wikiPageWikiLink D.
- Logicism wikiPageWikiLink Dedekind_cut.
- Logicism wikiPageWikiLink Empiricism.
- Logicism wikiPageWikiLink Function_(mathematics).
- Logicism wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Logicism wikiPageWikiLink Geometric_Shapes.
- Logicism wikiPageWikiLink Giuseppe_Peano.
- Logicism wikiPageWikiLink Gottlob_Frege.
- Logicism wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Logicism wikiPageWikiLink Gödel_numbering.
- Logicism wikiPageWikiLink Higher-order_logic.
- Logicism wikiPageWikiLink Humes_principle.
- Logicism wikiPageWikiLink Idealism.
- Logicism wikiPageWikiLink Impredicativity.
- Logicism wikiPageWikiLink Intuitionism.
- Logicism wikiPageWikiLink Kurt_Gödel.
- Logicism wikiPageWikiLink Leopold_Kronecker.
- Logicism wikiPageWikiLink Logic.
- Logicism wikiPageWikiLink Mathematical_logic.
- Logicism wikiPageWikiLink Mathematics.
- Logicism wikiPageWikiLink Modus_ponens.
- Logicism wikiPageWikiLink Naive_set_theory.
- Logicism wikiPageWikiLink Nominalism.
- Logicism wikiPageWikiLink Philosophical_realism.
- Logicism wikiPageWikiLink Philosophy_of_mathematics.
- Logicism wikiPageWikiLink Platonism.
- Logicism wikiPageWikiLink Primitive_notion.
- Logicism wikiPageWikiLink Principia_Mathematica.
- Logicism wikiPageWikiLink Rationalism.
- Logicism wikiPageWikiLink Real_number.
- Logicism wikiPageWikiLink Reductionism.
- Logicism wikiPageWikiLink Richard_Dedekind.
- Logicism wikiPageWikiLink Russells_paradox.
- Logicism wikiPageWikiLink S.
- Logicism wikiPageWikiLink Second-order_logic.
- Logicism wikiPageWikiLink Set_theory.
- Logicism wikiPageWikiLink Tarskis_undefinability_theorem.
- Logicism wikiPageWikiLink The_Principles_of_Mathematics.
- Logicism wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Logicism wikiPageWikiLinkText "Logicism".
- Logicism wikiPageWikiLinkText "Logicism#Neo-logicism".
- Logicism wikiPageWikiLinkText "logicism".
- Logicism wikiPageWikiLinkText "logicist".
- Logicism wikiPageWikiLinkText "neo-logicism".
- Logicism wikiPageUsesTemplate Template:Philosophical_logic.
- Logicism wikiPageUsesTemplate Template:Reflist.
- Logicism subject Category:Theories_of_deduction.
- Logicism hypernym Schools.
- Logicism type School.
- Logicism type Theory.
- Logicism comment "Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory, created by mathematicians Richard Dedekind and Gottlob Frege.Dedekind's path to logicism had a turning point when he was able to reduce the theory of real numbers to the rational number system by means of set theory.".
- Logicism label "Logicism".
- Logicism sameAs Q845691.
- Logicism sameAs منطقانية.
- Logicism sameAs Logicisme.
- Logicism sameAs Logizismus.
- Logicism sameAs Λογικισμός.
- Logicism sameAs Logicismo.
- Logicism sameAs Logitsism.
- Logicism sameAs Logisismi.
- Logicism sameAs Logicisme.
- Logicism sameAs Logicismo.
- Logicism sameAs 論理主義_(数学).
- Logicism sameAs Логицизм.
- Logicism sameAs 논리주의.
- Logicism sameAs Логицизим.
- Logicism sameAs Logicisme.
- Logicism sameAs Logicyzm.
- Logicism sameAs Logicism.
- Logicism sameAs Logicismo.
- Logicism sameAs m.01z72m.
- Logicism sameAs Логицизм.
- Logicism sameAs Logicizmus_(filozofia).
- Logicism sameAs Логицизам.
- Logicism sameAs Logicism.
- Logicism sameAs Logitsizm.
- Logicism sameAs Q845691.
- Logicism sameAs 邏輯主義.
- Logicism wasDerivedFrom Logicism?oldid=687725482.
- Logicism isPrimaryTopicOf Logicism.