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Classical logic

Definition

Classical logic or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy.

Related concepts

A. N. WhiteheadAbsorption (logic)Abstract logicAckermann set theoryAleph numberAlfred TarskiAlgebraic logicAlphabet (formal languages)Analytic philosophyArgumentAristotleArithmeticArityAssociative propertyAtomic formulaAtomic model (mathematical logic)Atomic sentenceAugustus De MorganAutomata theoryAutomated theorem provingAxiomAxiom of choiceAxiom schemaAxiomatic systemAxiomatization of Boolean algebrasBanach–Tarski paradoxBegriffsschriftBernard BolzanoBertrand RussellBiconditional eliminationBiconditional introductionBijectionBinary operationBoolean-valued semanticsBoolean algebraBoolean algebra (structure)Boolean algebras canonically definedBoolean functionBoolean logicCalculus ratiocinatorCantor's diagonal argumentCantor's paradoxCantor's theoremCardinalityCartesian productCategorical theoryCategory (mathematics)Category of setsCategory theoryCharles Sanders PeirceChurch encodingChurch–Turing thesisClass (set theory)Classical antiquityCodomainCommutativity of conjunctionCompactness theoremComplement (set theory)Complete theoryComputability theoryComputable functionComputable setComputably enumerable setConcrete categoryConjunction eliminationConjunction introductionConservative extensionConsistencyConstructible universeConstruction of the real numbersConstructive dilemmaConstructive set theoryContinuum hypothesisCountable setDavid HilbertDe Morgan's lawsDe Morgan dualityDecidability (logic)Decision problemDeductive reasoningDeductive systemDestructive dilemmaDiagram (mathematical logic)Disjunction eliminationDisjunction introductionDisjunctive syllogismDistributive propertyDomain of a functionDouble negation eliminationDouble negation introductionDov GabbayElement (mathematics)Elementary diagramElementary equivalenceElementary function arithmeticEmpty setEnumerationEquiconsistencyEquivalence relationErnst Schröder (mathematician)Euclid's ElementsEuclidean geometryExistential generalizationExistential importExistential instantiationExistential quantificationExpression (mathematics)Extension by definitionsExtension by new constant and function namesExtensionalityFinitary relationFinite-valued logicFinite model theoryFinite setFirst-order logicFixed-point logicForcing (mathematics)Formal grammarFormal languageFormal proofFormal semantics (logic)Formal systemFormation ruleFoundations of geometryFoundations of mathematicsFree logicFree variables and bound variablesFunction (mathematics)Function and ConceptFunctional predicateFuzzy setGeneral set theoryGeometryGeorg CantorGeorge BooleGiuseppe PeanoGottlob FregeGrothendieck universeGround expressionGround formulaGödel's completeness theoremGödel's incompleteness theoremsGödel numberingHalting problemHenry M. ShefferHereditary setHigher-order logicHilbert's axiomsHilbert systemHistory of logicHistory of mathematical logicHugh MacCollHypothetical syllogismIdempotency of entailmentImage (mathematics)Inaccessible cardinalIndependence (mathematical logic)InferenceInfinite-valued logicInfinite setInformation theoryInhabited setInjective functionInterpretation (logic)Interpretation (model theory)Interpretation functionIntersection (set theory)IsomorphismJan ŁukasiewiczJohn VennKolmogorov complexityKripke's theory of truthKripke–Platek set theoryKurt GödelL. T. F. GamutLambda calculusLarge cardinalLaw of excluded middleLaw of noncontradictionLeibnizLemma (mathematics)Lindström's theoremList of Hilbert systemsList of axiomsList of first-order theoriesList of formal systemsList of mathematical theoriesList of set identities and relationsList of statements independent of ZFCLogicLogical biconditionalLogical conjunctionLogical connectiveLogical consequenceLogical constantLogical disjunctionLogical equalityLogical equivalenceLogical operatorLogical truthLogicismLudwig WittgensteinLöwenheim–Skolem theoremMany-valued logicMap (mathematics)Material conditionalMaterial implication (rule of inference)Mathematical logicMathematical objectMetalanguageMinimal axioms for Boolean algebraModel complete theoryModel theoryModus ponendo tollensModus ponensModus tollensMonadic predicate calculusMonadic second-order logicMonotonicity of entailmentMorse–Kelley set theoryNP (complexity)Naive set theoryNatural deductionNegationNegation introductionNew FoundationsNon-Euclidean geometryNon-classical logicNon-logical symbolNon-standard modelNon-standard model of arithmeticOpen formulaOperation (mathematics)Ordinal analysisOrdinal numberP (complexity)P versus NP problemParadoxes of set theoryPartition of a setPeano axiomsPhilosophy of mathematicsPower setPredicate (mathematical logic)Predicate logicPredicate variablePrime modelPrimitive recursive arithmeticPrimitive recursive functionPrincipia MathematicaPrinciple of bivalencePrinciple of explosionProblem of multiple generalityProof of impossibilityProof theoryPropositionPropositional calculusPropositional formulaPropositional logicPropositional variableQuantifier (logic)Quantifier rankRecursionRecursive setReductio ad absurdumRelation (mathematics)Reverse mathematicsRichard DedekindRobinson arithmeticRule of inferenceRussell's paradoxSatisfiabilitySaturated modelSchröder–Bernstein theoremSecond-order arithmeticSecond-order logicSelf-verifying theoriesSemantic theory of truthSemanticsSemantics of logicSentence (mathematical logic)Sequent calculusSet (mathematics)Set theorySignature (logic)Singleton (mathematics)Skolem arithmeticSoundnessSpectrum of a sentenceSpectrum of a theorySquare of oppositionStewart ShapiroStoic logicStrength (mathematical logic)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)SupertaskSurjective functionSusan HaackSyllogismSymbol (formal)Syntax (logic)T-schemaTarski's axiomatization of the realsTarski's axiomsTarski's theory of truthTarski's undefinability theoremTarski–Grothendieck set theoryTautology (logic)Term (logic)Term logicThe Principles of MathematicsTheoremTheories of truthTheory (mathematical logic)Three-valued logicTimeline of mathematical logicTractatus Logico-PhilosophicusTractatus Logico PhilosophicusTransfer principleTransitive setTransposition (logic)True arithmeticTruth functionTruth predicateTruth tableTruth valueTuring machineTwo-element Boolean algebraType (model theory)Type theoryUltrafilter (set theory)UltraproductUncountable setUndecidable problemUninterpreted functionUnion (set theory)Uniqueness quantificationUniversal generalizationUniversal instantiationUniversal quantificationUniversal setUniverse (mathematics)UrelementValidity (logic)Variable (mathematics)Venn diagramVon Neumann universeVon Neumann–Bernays–Gödel set theoryWell-formed formulaWillard Van Orman QuineWilliam Stanley JevonsZermelo–Fraenkel set theory

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