Home›Philosophers›Branch of Philosophy›Philosophy of MathematicsBranches of PhilosophyPhilosophy of MathematicsLogicReference and ClassificationVerifiedThe branch of philosophy that studies the nature of mathematical entities such as numbers and sets, and how, if at all, we can have knowledge of them. The Stanford Encyclopedia of Philosophy frames its central task as determining what the nature of mathematical entities consists in and how we can have knowledge of mathematical entities, a question that sets mathematics apart from the empirical sciences because mathematical truths seem to be established by proof rather than observation. The field is closely related to, but distinct from, the foundations of mathematics, the more technical project of grounding mathematical practice in a formal system.FactsPhilosophy of MathematicsConnectionsSourcesComments (0)Reader Challenges (0)FactsCentral QuestionWell-attestedWhat is the nature of mathematical entities such as numbers and sets, and how, if at all, can we have knowledge of them? 1Key DebateWell-attestedMathematical platonism against nominalism and fictionalism: whether numbers, sets and other mathematical objects exist independently of the mind and of any physical instantiation, as platonists hold, or whether mathematical language is a useful fiction with no such independent objects behind it. A further, more recent debate concerns mathematical pluralism, the view that any consistent mathematical theory describes a free-standing mathematical universe and that no such theory is more true than any other, which unsettles the very idea of a single fact of the matter about which axioms are correct. 1DisputedKey DebateScholarly debateWhether a proof by exhaustive computer calculation, as in Appel and Haken's 1976 proof of the four color theorem, counts as genuine mathematical proof given that no human being can survey it, or marks a break from the traditional requirement that a proof be humanly checkable. 2Kenneth Appel and Wolfgang Haken's 1976 proof of the four color theorem, verified by computer case-checking no mathematician could survey by hand, forced this question onto philosophers of mathematics.Philosophy of MathematicsFilter Results18 entriesMovementAllAfrican Epistemology (1)Analytic Logic (4)Analytic Philosophy Of Language (2)Analytic Philosophy Of Mind (1)Analytic Philosophy Of Science (1)Contemporary Continental Philosophy (2)Continental And Phenomenological Philosophy Of Language (1)Other Logic Traditions (2)Other Philosophy Of Science Traditions (1)Pragmatist Philosophy Of Mind (1)Pragmatist Philosophy Of Science (2)EraAll1859 (1)1885 (1)1908 (1)1909 (1)1922 (1)1925 (1)1926 (1)1930 (2)1942 (2)1947 (1)1954 (1)1955 (1)1959 (1)TraditionAllAnalytic philosophy (3)Analytic philosophy, naturalized epistemology (1)Analytic philosophy, pragmatism (1)Continental philosophy (1)Pittsburgh School (analytic Hegelianism) (1)Pragmatic realism (1)NationalityAllAustralia (1)Canada (1)Chile (1)France (2)Hungary (1)Israel (1)Japan (1)South Africa (1)United Kingdom (5)United States (2)Influenced ByAllNishida Kitaro (1)In GroupAllAfrican Epistemology (1)Analytic Logic (4)Analytic Philosophy Of Language (2)Analytic Philosophy Of Mind (1)Analytic Philosophy Of Science (1)Contemporary Continental Philosophy (2)Continental And Phenomenological Philosophy Of Language (1)Other Logic Traditions (2)Other Philosophy Of Science Traditions (1)Pragmatist Philosophy Of Mind (1)Pragmatist Philosophy Of Science (2)Birthplace / RegionAllAustralia (1)Canada (1)Chile (1)France (3)Hungary (1)Israel (1)Japan (1)South Africa (1)Spain (1)United Kingdom (5)United States (2)Show ResultsBrowseCompareSelect all 18Carl PosyPhilosophy of MathematicsCrispin WrightPhilosophy of MathematicsDanielle MacbethPhilosophy of MathematicsHenri BergsonPhilosophy of MathematicsHilary PutnamPhilosophy of MathematicsImre LakatosPhilosophy of MathematicsJesús Padilla GálvezPhilosophy of MathematicsJohn McDowellPhilosophy of MathematicsMark ColyvanPhilosophy of MathematicsMary LengPhilosophy of MathematicsMax BlackPhilosophy of MathematicsMichael DummettPhilosophy of MathematicsPaul BenacerrafPhilosophy of MathematicsPhilip KitcherPhilosophy of MathematicsRoberto TorrettiPhilosophy of MathematicsSouleymane Bachir DiagnePhilosophy of MathematicsTanabe HajimePhilosophy of MathematicsWillard Van Orman QuinePhilosophy of MathematicsConnectionsAssociated WithBertrand Russell, Philosophers Well-attested Source Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)tier 1Gottlob Frege, Philosophers Well-attested Source Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)tier 1IncludesBenacerraf's Identification Problem, Arguments and Positions Well-attested Source Benacerraf's identification problem (Wikipedia)Carl Posy, Philosophers Well-attested Source Wikipedia: Carl Posytier 2Crispin Wright, Philosophers Well-attested Source Crispin Wright, WikipediaDanielle Macbeth, Philosophers Well-attested Source Danielle Macbeth, WikipediaHenri Bergson, Philosophers Well-attested Source Henri Bergson (Wikipedia)tier 2Hilary Putnam, Philosophers Well-attested Source Hilary Putnam (Wikipedia)tier 2Imre Lakatos, Philosophers Well-attested Source Imre Lakatos (Wikipedia)tier 3Jesús Padilla Gálvez, Philosophers Well-attested Source Jesús Padilla Gálvez, WikipediaJohn McDowell, Philosophers Well-attested Source John McDowell (Wikipedia)tier 3Mark Colyvan, Philosophers Well-attested Source Wikipedia: Mark Colyvantier 2Mary Leng, Philosophers Well-attested Source Wikipedia: Mary Lengtier 2Max Black, Philosophers Well-attested Source Max Black, WikipediaMichael Dummett, Philosophers Well-attested Source Michael Dummett (Wikipedia)Paul Benacerraf, Philosophers Well-attested Source Paul Benacerraf (Wikipedia)Philip Kitcher, Philosophers Well-attested Source Wikipedia: Philip KitcherPlatonism, Schools of Philosophy Well-attested Source Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)tier 1Quine-Putnam Indispensability Argument, Arguments and Positions Well-attested Source Quine-Putnam indispensability argument (Wikipedia)Roberto Torretti, Philosophers Well-attested Source Wikipedia: Roberto TorrettiSouleymane Bachir Diagne, Philosophers Well-attested Source Souleymane Bachir Diagne - WikipediaTanabe Hajime, Philosophers Well-attested Source Hajime Tanabe, WikipediaWillard Van Orman Quine, Philosophers Well-attested Source Willard Van Orman Quine (Wikipedia)tier 2Sources1. Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)tier 1Stanford Encyclopedia of PhilosophySection 1, opening paragraphwhat the nature of mathematical entities consists in and how we can have knowledge of mathematical entitiesSection 5.2any consistent mathematical theory describes a free-standing mathematical universe, and that no such theory is more true than any otherAssociated With: Gottlob FregeAssociated With: Bertrand RussellIncludes: Platonism, entry: Philosophy of Mathematics, Logic, and the Foundations of Mathematics, Section 3On the platonistic conception, the subject matter of mathematics consists of abstract entities.View the Source2. Stanford Encyclopedia of Philosophytier 1Stanford University, Center for the Study of Language and Informations.v. Philosophy of MathematicsQuote, s.v. Philosophy of MathematicsIf mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology.View the SourceWillard Van Orman Quine (Wikipedia)tier 2Wikimedia FoundationIncludes: Willard Van Orman Quine, Infobox: main_interestsQuote, Includes: Willard Van Orman Quine, Infobox: main_interestsLogic, ontology, epistemology, philosophy of language, philosophy of mind, philosophy of mathematics, philosophy of science, set theoryView the SourceHilary Putnam (Wikipedia)tier 2WikipediaIncludes: Hilary Putnam, Infobox: main_interestsQuote, Includes: Hilary Putnam, Infobox: main_interestsPhilosophy of mind, of language, of science, and of mathematics Metaphilosophy Epistemology Jewish philosophyView the SourceHenri Bergson (Wikipedia)tier 2WikipediaIncludes: Henri Bergson, Infobox: main_interestsQuote, Includes: Henri Bergson, Infobox: main_interestsMetaphysics, epistemology, philosophy of language, philosophy of mathematics, studies of immediate experienceView the SourceMichael Dummett (Wikipedia)WikipediaIncludes: Michael Dummett, Infobox: main_interestsQuote, Includes: Michael Dummett, Infobox: main_interestsPhilosophy of mathematics Philosophy of logic Mathematical logic Philosophy of language Metaphysics History of analytic philosophy Voting theory TheologyView the SourceImre Lakatos (Wikipedia)tier 3WikipediaIncludes: Imre Lakatos, Infobox: main_interestsQuote, Includes: Imre Lakatos, Infobox: main_interestsPhilosophy of mathematics, philosophy of science, history of science, epistemology, politicsView the SourceHajime Tanabe, WikipediaIncludes: Tanabe Hajime, Infobox: main_interestsQuote, Includes: Tanabe Hajime, Infobox: main_interestsPhilosophy of science, philosophy of mathematics, philosophy of physics, metaphysics, philosophy of religionView the SourceSouleymane Bachir Diagne - WikipediaIncludes: Souleymane Bachir Diagne, Infobox: main_interestsQuote, Includes: Souleymane Bachir Diagne, Infobox: main_interestsPhilosophy of mathematics, Epistemology, Logic, Linguistics, Mathematics, Islamic philosophyView the SourceCrispin Wright, WikipediaIncludes: Crispin Wright, Infobox: main_interestsQuote, Includes: Crispin Wright, Infobox: main_interestsPhilosophy of mind Philosophy of language Philosophy of mathematics Frege Wittgenstein EpistemologyView the SourceJohn McDowell (Wikipedia)tier 3WikipediaIncludes: John McDowell, Infobox: main_interestsQuote, Includes: John McDowell, Infobox: main_interestsMetaphysics, epistemology, logic, philosophy of language, philosophy of perception, philosophy of mathematics, philosophy of mind, ethics, meta-ethicsView the SourceMax Black, WikipediaIncludes: Max Black, Infobox: main_interestsQuote, Includes: Max Black, Infobox: main_interestsPhilosophy of language Philosophy of mathematics Philosophy of science Philosophy of artView the SourceDanielle Macbeth, WikipediaIncludes: Danielle Macbeth, LeadQuote, Includes: Danielle Macbeth, LeadDanielle Monique Macbeth (born 1954, Edmonton) is a Canadian philosopher whose work focuses on the philosophy of mathematics, the philosophy of language, metaphysics, and the philosophy of logic.View the SourceWikipedia: Philip KitcherIncludes: Philip Kitcher, Infobox: main_interestsQuote, Includes: Philip Kitcher, Infobox: main_interestsPhilosophy of science, philosophy of biology, bioethics, philosophy of mathematicsView the SourceWikipedia: Roberto TorrettiIncludes: Roberto Torretti, Infobox: main_interestsQuote, Includes: Roberto Torretti, Infobox: main_interestsHistory of philosophy, philosophy of physics, philosophy of mathematicsView the SourceJesús Padilla Gálvez, WikipediaIncludes: Jesús Padilla Gálvez, Infobox: main_interestsQuote, Includes: Jesús Padilla Gálvez, Infobox: main_interestsLogic, ontology, epistemology, philosophy of language, philosophy of mathematics, philosophy of science, ethics.View the SourceWikipedia: Mark Colyvantier 2WikipediaIncludes: Mark Colyvan, Infobox: main_interestsQuote, Includes: Mark Colyvan, Infobox: main_interestsPhilosophy of logic, philosophy of mathematics, conservation biologyView the SourceWikipedia: Mary Lengtier 2WikipediaIncludes: Mary Leng, LeadQuote, Includes: Mary Leng, LeadMary Leng is a British philosopher specialising in the philosophy of mathematics and philosophy of science.View the SourceBenacerraf's identification problem (Wikipedia)Includes: Benacerraf's Identification Problem, LeadQuote, Includes: Benacerraf's Identification Problem, LeadIn the philosophy of mathematics, Benacerraf's identification problem is a philosophical argument developed by Paul Benacerraf againstView the SourceQuine-Putnam indispensability argument (Wikipedia)Includes: Quine-Putnam Indispensability Argument, LeadQuote, Includes: Quine-Putnam Indispensability Argument, LeadThe Quine-Putnam indispensability argument is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical Platonism.View the SourcePaul Benacerraf (Wikipedia)Includes: Paul Benacerraf, Infobox: main_interestsQuote, Includes: Paul Benacerraf, Infobox: main_interestsPhilosophy of mathematicsView the SourceWikipedia: Carl Posytier 2WikipediaIncludes: Carl Posy, LeadQuote, Includes: Carl Posy, LeadPosy's areas of research interest include the philosophy of mathematics, philosophical logic, the history of philosophy (particularly Kant and his predecessors).View the SourceComments (0)No comments yet. 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