Definition
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship such objects have with physical reality consists.
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PeirceCharles Sanders PeirceCharles Sanders Peirce bibliographyCharvakaChinese philosophyChristian philosophyChristoph von SigwartChurch FathersChurch encodingChurch–Turing thesisClass (set theory)Classical RealismClassical liberalismClassical logicCodomainCognitionCognitive biasCognitive science of mathematicsCoherentismCollective intelligenceCollectivism and individualismCombinatoricsCommunications on Pure and Applied MathematicsCommunitarianismCommutative algebraCompactness theoremCompatibilismComplement (set theory)Complete theoryComplex analysisComplex geometryComplex numberComputability theoryComputable functionComputable numberComputable setComputably enumerable setComputational complexity theoryComputational geometryComputational mathematicsComputerComputer algebraComputer scienceConceptConceptualismConcrete categoryConeConfirmation holismConfucianismConic sectionConsequentConsequentialismConservatismConservative extensionConsilienceConsistencyConsistency proofConstructible universeConstruction of the real numbersConstructive analysisConstructive mathematicsConstructive set theoryConstructivism (philosophy of mathematics)Contemporary philosophyContext-free grammarContinental philosophyContinuous functionContinuum hypothesisContradictionControl theoryConventionalismConventionalistCountable setCountably infiniteCounterexampleCrispin WrightCritical rationalismCritical theoryCritical thinkingCynicism (philosophy)CyrenaicsCzech philosophyDanish philosophyDavid CorfieldDavid HilbertDecidability (logic)DecimalDecision problemDecision theoryDeconstructionDeductive closureDeductive reasoningDeductive systemDeductivismDefinitionDefinitions of mathematicsDennis Elliot ShashaDeontologyDescriptionDeterminismDiagram (mathematical logic)DichotomyDifferentiable functionDifferential equationDifferential geometryDifferential topologyDiophantine geometryDiscrete geometryDiscrete mathematicsDispositioDivine proportionDomain of a functionDouble negation eliminationDutch philosophyDvaita VedantaE.O. WilsonEarly modern philosophyEastern philosophyEdo neo-ConfucianismEdward N. ZaltaEinsteinEleaticsElectronElement (mathematics)Elementary algebraElementary diagramElementary equivalenceElementary function arithmeticEliminative materialismEllipseEmbodied mindEmergentismEmpirical evidenceEmpiricismEmpty setEngineering mathematicsEnumerationEpicureanismEpiphenomenalismEpistemicEpistemic communityEpistemological particularismEpistemologicallyEpistemologyEquiconsistencyEquivalence relationErdős numberEretrian schoolErrett BishopEthicsEthiopian philosophyEuclidEuclid's ElementsEuclidean geometryEugene WignerEuler's identityEvent (philosophy)EvolutionExistenceExistential quantificationExistentialismExperimental philosophyExperimentationExpression (mathematics)Extension by definitionsExtension by new constant and function namesExtensionalityFalsifiabilityFalsifiableFeminist philosophyFictionFictionalismFideismFinitary relationFinite-valued logicFinite geometryFinite model theoryFinite setFinitismFirst-order logicFixed-point logicForcing (mathematics)Formal grammarFormal languageFormal logicFormal proofFormal semantics (logic)Formal semantics (natural language)Formal systemFormalism (art)Formalism (mathematics)Formalism (philosophy of mathematics)Formation ruleFoundation of mathematicsFoundational crisis of mathematicsFoundationalismFoundations of geometryFoundations of mathematicsFrankfurt SchoolFree logicFree variables and bound variablesFree willFrege's theoremFrench philosophyFunction (mathematics)Functional analysisFunctional predicateFunctionalism (philosophy of mind)Fundamental theorem of arithmeticFuture of mathematicsFuzzy setG. H. HardyGameGame theoryGeneral relativityGeneral set theoryGeneral topologyGeomathematicsGeometric topologyGeometryGeorg CantorGeorge BerkeleyGeorge LakoffGerman idealismGerman philosophyGlossary of mathematical symbolsGolden ratioGottlob FregeGrammatical tenseGraph theoryGreek mathematicsGregory ChaitinGrothendieck universeGround expressionGround formulaGroup theoryGustave Le BonGödel's completeness theoremGödel's incompleteness theoremGödel's incompleteness theoremsGödel numberingH. M. WeberHallucinationHalting problemHard determinismHard incompatibilismHarmonic analysisHartry FieldHaskell CurryHegelianismHellenistic philosophyHenri PoincaréHereditary setHermeneuticsHexadecimalHigher-order logicHilary PutnamHilbert's axiomsHilbert's programHilbert systemHindu philosophyHistoricismHistory and philosophy of scienceHistory of logicHistory of mathematical logicHistory of mathematicsHistory of philosophyHistory of philosophy in FinlandHistory of philosophy in PolandHolismHomological algebraHomotopy theoryHuayanHumanismHume's principleHusserlHypercomplex analysisIan Stewart (mathematician)IdealismIlluminationismIllusionImage (mathematics)Imaginary numberImmanent realismImre LakatosIn re structuralismInaccessible cardinalIncompatibilismIndependence (mathematical logic)Index of logic articlesIndian philosophyIndiana Philosophy Ontology ProjectIndigenous American philosophyIndispensability argumentIndividualismIndonesian philosophyInductive reasoningInferenceInference ruleInfinite-valued logicInfinite setInfinite setsInfinitesimalInformal logicInformal mathematicsInformation theoryInhabited setInjective functionInstitutional theory of artIntegersInternalism and externalismInternetInternet Encyclopedia of PhilosophyInterpretation (logic)Interpretation (model theory)Interpretation functionIntersection (set theory)Intrinsic and extrinsic properties (philosophy)Introduction to Mathematical PhilosophyIntuitionIntuition (knowledge)IntuitionismIntuitionistic logicIonian School (philosophy)Iranian philosophyIslamic philosophyIsomorphismItalian idealismItalian philosophyJain philosophyJames Franklin (philosopher)Japanese philosophyJerrold KatzJewish philosophyJohann Eduard ErdmannJohannes KeplerJohn Penn MayberryJohn RawlsJohn Stuart MillJudeo-Islamic philosophies (800–1400)KalamKantianismKarl PopperKeith DevlinKnot theoryKokugakuKolmogorov complexityKorean ConfucianismKorean philosophyKrausismKripke's theory of truthKripke–Platek set theoryKyoto SchoolL. E. J. BrouwerLambda calculusLarge cardinalLarge numbersLaw of excluded middleLaw of the excluded middleLegal positivismLegalism (Chinese philosophy)Lemma (mathematics)Leopold KroneckerLibertarianism (metaphysics)Lindström's theoremLine (geometry)Linear algebraLinguistic entailmentList of Boolean algebra topicsList of Hilbert systemsList of Slovene philosophersList of Turkish philosophersList of axiomsList of fallaciesList of films about mathematiciansList of first-order theoriesList of formal systemsList of logic symbolsList of logiciansList of mathematical logic topicsList of mathematical theoriesList of mathematiciansList of paradoxesList of rules of inferenceList of set identities and relationsList of set theory topicsList of statements independent of ZFCLists of mathematics topicsLiteratureLogicLogic in computer scienceLogical Investigations (Husserl)Logical biconditionalLogical conjunctionLogical connectiveLogical consequenceLogical constantLogical disjunctionLogical equalityLogical equivalenceLogical formLogical positivismLogical theoryLogical truthLogicismLudwig WittgensteinLuitzen Egbertus Jan BrouwerLöwenheim–Skolem theoremMachine-readable mediumMadhyamakaManifoldMany-valued logicMap (mathematics)Marxist philosophyMary LengMary TilesMassimo PigliucciMaterial conditionalMaterialismMathematicalMathematical PlatonismMathematical analysisMathematical and theoretical biologyMathematical beautyMathematical chemistryMathematical constructivismMathematical economicsMathematical empiricismMathematical entityMathematical financeMathematical folkloreMathematical geologyMathematical intuitionismMathematical linguisticsMathematical logicMathematical modelMathematical objectMathematical optimizationMathematical philosophyMathematical physicsMathematical practiceMathematical proofMathematical psychologyMathematical rigorMathematical sociologyMathematical statisticsMathematical structuralismMathematical theoryMathematical universe hypothesisMathematicianMathematiciansMathematicismMathematicsMathematics and artMathematics educationMaurice Merleau-PontyMax TegmarkMazdakismMeasure (mathematics)Medieval philosophyMegarian schoolMeta-ethicsMetalanguageMetalogicMetamathematicsMetaphilosophyMetaphysical naturalismMetaphysicsMiddle Eastern philosophyMiddle PlatonismMind–body dualismMinimal axioms for Boolean algebraMithraismModel complete theoryModel theoryModern philosophyModernismMohismMonadic predicate calculusMonadic second-order logicMonismMoral absolutismMoral nihilismMoral particularismMoral realismMoral skepticismMoral universalismMorse–Kelley set theoryMultilinear algebraMīmāṃsāNP (complexity)Naive set theoryNameNatural deductionNatural lawNatural numberNaturalism (philosophy)Naturalized epistemologyNavya-NyāyaNecessity and sufficiencyNegationNeo-ConfucianismNeo-KantianismNeo-MarxismNeo-scholasticismNeoplatonismNeopythagoreanismNeuroscienceNew ConfucianismNew FoundationsNew historicismNewton's law of gravitationNewtonian mechanicsNewtonianismNihilismNimbarka SampradayaNominalismNon-Euclidean geometriesNon-Euclidean geometryNon-classical logicNon-logical symbolNon-standard analysisNon-standard modelNon-standard model of arithmeticNorm (philosophy)Normative ethicsNorwood Russell HansonNumberNumber lineNumber theoryNumeral systemNumerical analysisNyayaObjective idealismObjectivismObjectivity (philosophy)OccamismOmega baryonOn Computable Numbers, with an Application to the EntscheidungsproblemOn Formally Undecidable Propositions of Principia Mathematica and Related SystemsOntologicalOntologyOpen formulaOperation (mathematics)Operations researchOrder theoryOrdinal analysisOrdinal numberOrdinary language philosophyOutline of logicOutline of philosophyP (complexity)P versus NP problemPakistani philosophyParadoxParadoxes of set theoryParallel postulatePart of speechParticlePartition of a setPaul BenacerrafPaul ErdősPaul ErnestPeano axiomsPenelope MaddyPerceptionPerihelion precession of MercuryPeripatetic schoolPhenomenology (philosophy)PhilPapersPhilip J. 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NúñezRamified type theoryRationalismReal analysisRealism (philosophy)Realistic rationalismRealityReasonRecreational mathematicsRecursionRecursive setReductio ad absurdumReductionismReferenceReformed epistemologyRelation (mathematics)Relationship between mathematics and physicsRelativismRenaissance humanismRenaissance philosophyReuben HershReverse mathematicsRigorRobert AudiRobinson arithmeticRoman FriggRomanian philosophyRudolf CarnapRule of inferenceRussell's paradoxRussian cosmismRussian philosophySamkhyaSamuel EilenbergSarvastivadaSatisfiabilitySaturated modelSaunders Mac LaneSautrāntikaScholasticismSchool of NamesSchool of NaturalistsSchool of the SextiiSchröder–Bernstein theoremScienceScience Without NumbersScience studiesScientific methodScientific realismScientific skepticismScientismScotismScottish philosophySecond-order arithmeticSecond-order logicSecond SophisticSelf-verifying theoriesSemantic theory of truthSemantics of logicSentence (mathematical logic)Sequent calculusSet (mathematics)Set theorySherlock HolmesShuddhadvaitaSignature (logic)Singleton (mathematics)Sir Roger PenroseSkolem arithmeticSocial constructionismSocial constructivismSocial contractSocial philosophySocialismSolipsismSophistSoundnessSpacetimeSpanish philosophySpatiotemporalSpecial relativitySpectrum of a sentenceSpectrum of a theorySpinozismSquare of oppositionSquare root of 2Stanford Encyclopedia of PhilosophyStanislas DehaeneStatement (logic)StatisticsStephan HartmannStephan KörnerStephen Cole KleeneStephen YabloStewart ShapiroStoicismStrength (mathematical logic)String (formal languages)StructuralismStructuralism (philosophy of mathematics)Structure (mathematical logic)SubcultureSubjective idealismSubjectivismSubstitution (logic)Substructure (mathematics)Sufi philosophySupertaskSurjective functionSvatantrika–Prasaṅgika distinctionSyllogismSymbol (formal)Syntax (logic)SystemicsSystems scienceSyādvādaT-schemaTaoismTarski's axiomatization of the realsTarski's axiomsTarski's theory of truthTarski's undefinability theoremTarski–Grothendieck set theoryTautology (logic)Term (logic)Term logicThe AnalystThe Emperor's New MindThe Foundations of ArithmeticThe Math InstinctThe Unreasonable Effectiveness of Mathematics in the Natural SciencesThe artsTheoremTheoretical philosophyTheories of truthTheory (mathematical logic)Theory of computationTheory of relativityThomas TymoczkoThomismThree-valued logicTiantaiTibetan BuddhismTimeline of mathematical logicTimeline of mathematicsTopologyTrajectoriesTransactionalismTranscendental idealismTranscendentalismTransfer principleTransitive setTrue arithmeticTruthTruth predicateTruth tableTruth valueTuring machineType (mathematics)Type (model theory)Type theoryUbuntu philosophyUltrafilter (set theory)UltrafinitismUltraproductUncountable setUndecidable problemUnifying conjectureUninterpreted functionUnion (set theory)Uniqueness quantificationUniversal algebraUniversal quantificationUniversal setUniverse (mathematics)UrelementUseful fictionUtilitarianismVaisheshikaValidity (logic)Value theoryVariable (mathematics)Vector fieldVedantaVenn diagramVienna CircleVietnamese philosophyVirtue ethicsVishishtadvaitaVon Neumann universeVon Neumann–Bernays–Gödel set theoryW. 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