The following outline is provided as an overview of and topical guide to logic:
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct (or valid) and incorrect (or fallacious) inferences. Logicians study the criteria for the evaluation of arguments.
Analytic-synthetic distinctionAntinomyA priori and a posterioriDefinitionDescriptionEntailmentIdentity (philosophy)InferenceLogical formLogical implicationLogical truthLogical consequenceNameNecessityMaterial conditionalMeaning (linguistic)Meaning (non-linguistic)Paradox (list)Possible worldPresuppositionProbabilityQuantificationReasonReasoningReferenceSemanticsStrict conditionalSyntax (logic)TruthTruth valueValidityPhilosophical logic –
Informal logic – Critical thinking – Argumentation theory –
Argument –Argument map –Accuracy and precision –Ad hoc hypothesis –Ambiguity –Analysis –Attacking Faulty Reasoning –Belief –Belief bias –Bias –Cogency –Cognitive bias –Confirmation bias –Credibility –Critical pedagogy –Critical reading –Decidophobia –Decision making –Dispositional and occurrent belief –Emotional reasoning –Evidence –Expert –Explanation –Explanatory power –Fact –Fallacy –Higher-order thinking –Inquiry –Interpretive discussion –Narrative logic –Occam's razor –Opinion –Practical syllogism –Precision questioning –Propaganda –Propaganda techniques –Prudence –Pseudophilosophy –Reasoning –Relevance –Rhetoric –Rigour –Socratic questioning –Source credibility –Source criticism –Theory of justification –Topical logic –Vagueness –Anti-psychologismConceptualismConstructivismConventionalismCounterpart theoryDeflationary theory of truthDialetheismFictionalismFormalism (philosophy)Game theoryIlluminationist philosophyLogical atomismLogical holismLogicismModal fictionalismNominalismObject theoryPolylogismPragmatismPreintuitionismProof theoryPsychologismRamismSemantic theory of truthSophismTrivialismUltrafinitismFallacy (list) – incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (appeal to emotion), or take advantage of social relationships between people (e.g. argument from authority). Fallacious arguments are often structured using rhetorical patterns that obscure any logical argument. Fallacies can be used to win arguments regardless of the merits. There are dozens of types of fallacies.Formal logic – Mathematical logic, symbolic logic and formal logic are largely, if not completely synonymous. The essential feature of this field is the use of formal languages to express the ideas whose logical validity is being studied.List of mathematical logic topicsLogical variablesPropositional variablePredicate variableLiteralMetavariableLogical constantsLogical connectiveQuantifierIdentityBracketsLogical connectives
Logical connective –
Converse implication –Converse nonimplication –Exclusive or –Logical NOR –Logical biconditional –Logical conjunction –Logical disjunction –Material implication –Material nonimplication –Negation –Sheffer stroke –Atomic formulaOpen sentenceAnalytic propositionAxiomAtomic sentenceClause (logic)Contingent propositionContradictionLogical truthPropositional formulaRule of inferenceSentence (mathematical logic)SequentStatement (logic)TautologyTheoremRules of inference
Rule of inference (list)
Biconditional eliminationBiconditional introductionCase analysisCommutativity of conjunctionConjunction introductionConstructive dilemmaContraposition (traditional logic)Conversion (logic)De Morgan's lawsDestructive dilemmaDisjunction eliminationDisjunction introductionDisjunctive syllogismDouble negative eliminationGeneralization (logic)Hypothetical syllogismLaw of excluded middleLaw of identityModus ponendo tollensModus ponensModus tollensObversionPrinciple of contradictionResolution (logic)SimplificationTransposition (logic)Formal proofList of first-order theoriesSymbolFormulaFormal systemTheoremFormal proofTheoryMetalinguistic variableDeductive systemMetatheoremMetatheoryInterpretationAbsorption lawClause (logic)Deductive closureEntailmentFormation ruleFunctional completenessIntermediate logicLiteral (mathematical logic)Logical connectiveLogical consequenceNegation normal formOpen sentencePropositional calculusPropositional formulaPropositional variableRule of inferenceStrict conditionalSubstitution instanceTruth tableZeroth-order logicBoolean algebra (list)Boolean logicBoolean algebra (structure)Boolean algebras canonically definedIntroduction to Boolean algebraComplete Boolean algebraFree Boolean algebraMonadic Boolean algebraResiduated Boolean algebraTwo-element Boolean algebraModal algebraDerivative algebra (abstract algebra)Relation algebraAbsorption lawLaws of FormDe Morgan's lawsAlgebraic normal formCanonical form (Boolean algebra)Boolean conjunctive queryBoolean-valued modelBoolean domainBoolean expressionBoolean ringBoolean functionBoolean-valued functionParity functionSymmetric Boolean functionConditioned disjunctionField of setsFunctional completenessImplicantLogic alphabetLogic redundancyLogical connectiveLogical matrixMinimal negation operatorProduct termTrue quantified Boolean formulaTruth tableAtomic formulaAtomic sentenceDomain of discourseEmpty domainExtension (predicate logic)First-order logicFirst-order predicateFormation ruleFree variables and bound variablesGeneralization (logic)Monadic predicate calculusPredicate (mathematical logic)Predicate logicPredicate variableQuantificationSecond-order predicateSentence (mathematical logic)Universal instantiation(ε, δ)-definition of limitFinitary relationAntisymmetric relationAsymmetric relationBijectionBijection, injection and surjectionBinary relationComposition of relationsConcurrent relationCongruence relationCoreflexive relationCovering relationCyclic orderDense relationDependence relationDependency relationDirected setEquivalence relationEuclidean relationHomogeneous relationIdempotenceIntransitivityInverse relationInvolutive relationPartial equivalence relationPartial functionPartially ordered setPreorderPrewellorderingPropositional functionQuasitransitive relationReflexive relationSurjective functionSymmetric relationTernary relationTotal relationTransitive relationTrichotomy (mathematics)Well-founded relationMathematical logic –
Set theory (list) –
Aleph nullBijection, injection and surjectionBinary setCantor's diagonal argumentCantor's first uncountability proofCantor's theoremCardinality of the continuumCardinal numberCodomainComplement (set theory)Continuum hypothesisCountable setDecidable setDenumerable setDisjoint setsDisjoint unionDomain of a functionEffective enumerationElement (mathematics)Empty functionEmpty setEnumerationExtensionalityFinite setFunction (mathematics)Function compositionGeneralized continuum hypothesisIndex setInfinite setIntensionIntersection (set theory)Inverse functionLöwenheim–Skolem theoremMap (mathematics)MultisetNaïve set theoryNon-Cantorian set theoryOne-to-one correspondenceOrdered pairPartition of a setPointed setPower setProjection (set theory)Proper subsetProper supersetRange (mathematics)Russell's paradoxSequence (mathematics)Set (mathematics)Set of all setsSimple theorems in the algebra of setsSingleton (mathematics)Skolem paradoxSubsetSupersetTupleUncountable setUnion (set theory)Zermelo–Fraenkel set theoryMetalogic – The study of the metatheory of logic.
Completeness (logic)Syntax (logic)ConsistencyDecidability (logic)Deductive systemInterpretation (logic)Cantor's theoremChurch's theoremChurch's thesisEffective methodFormal systemGödel's completeness theoremGödel's first incompleteness theoremGödel's second incompleteness theoremIndependence (mathematical logic)Logical consequenceLöwenheim-Skolem theoremMetalanguageMetasyntactic variableMetatheoremObject languageSymbol (formal)Type-token distinctionUse–mention distinctionWell-formed formulaProof theory – The study of deductive apparatus.
AxiomDeductive systemFormal proofFormal systemFormal theoremSyntactic consequenceSyntax (logic)Transformation rulesModel theory – The study of interpretation of formal systems.
Interpretation (logic)Logical validityNon-standard modelNormal modelModelSemantic consequenceTruth valueComputability theory – branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability. The basic questions addressed by recursion theory are "What does it mean for a function from the natural numbers to themselves to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched.
Alpha recursion theoryArithmetical setChurch–Turing thesisComputability logicComputable functionComputationDecision problemEffective methodEntscheidungsproblemEnumerationForcing (recursion theory)Halting problemHistory of the Church–Turing thesisLambda calculusList of undecidable problemsPost correspondence problemPost's theoremPrimitive recursive functionRecursion (computer science)Recursive languageRecursive languages and setsRecursive setRecursively enumerable languageRecursively enumerable setReduction (recursion theory)Turing machineClassical logic –
Properties of classical logics:Law of the excluded middleDouble negative eliminationLaw of noncontradictionPrinciple of explosionMonotonicity of entailmentIdempotency of entailmentCommutativity of conjunctionDe Morgan duality – every logical operator is dual to anotherTerm logicGeneral concepts in classical logicBaraliptonBarocoBivalenceBoolean logicBoolean-valued functionCategorical propositionDistribution of termsEnd termEnthymemeImmediate inferenceLaw of contrariesLogical connectiveMajor termMiddle termMinor termOrganonPolysyllogismPort-Royal LogicPremisePrior AnalyticsRelative termSorites paradoxSquare of oppositionSum of LogicSyllogismTetralemmaTruth functionNon-classical logic – Deviant logic –
Computability logic –Fuzzy logic –Linear logic –Decision theory –Game theory –Probability theory –Affine logic –Bunched logic –Description logic –Free logic –Intensional logic –Intuitionistic logic –Many-valued logic –Minimal logic –Noncommutative logic –Non-monotonic logic –Paraconsistent logic –Quantum logic –Relevance logic –Strict logic –Substructural logic –Modal logic –
Alethic logic –Axiological logic –Deontic logic –Doxastic logic –Epistemic logic –Temporal logic –Deductive reasoning –Inductive reasoning –Abductive reasoning –Mathematical logic –
Proof theory –Set theory –Formal system –Predicate logic –Predicate –Higher-order logic –Propositional calculus –Proposition –Boolean algebra –Boolean logic –Truth value –Venn diagram –Pierce's law –Aristotelian logic –Non-Aristotelian logic –Informal logic –Fuzzy logic –Infinitary logic –Infinity –Categorical logic –College logic –Linear logic –Metalogic –Ordered logic –Temporal logic –Sequential logic –Provability logic –Interpretability logic –Interpretability –Quantum logic –Relevant logic –Consequent –Affirming the consequent –Antecedent –Denying the antecedent –Theorem –Axiom –Axiomatic system –Axiomatization –Conditional proof –Invalid proof –Degree of truth –Truth –Truth condition –Truth function –Double negative –Double negative elimination –Fallacy –Existential fallacy –Logical fallacy –Syllogistic fallacy –Type theory –Game theory –Game semantics –Rule of inference –Inference procedure –Inference rule –QuantificationIntroduction rule –Law of excluded middle –Law of non-contradiction –Logical constant –Logical connective –Quantifier –Logic gate –Boolean Function –Tautology –Logical assertion –Logical conditional –Logical biconditional –Logical equivalence –Logical AND –Negation –Logical OR –Logical NAND –Logical NOR –Contradiction –Logicism –Polysyllogism –Syllogism –Hypothetical syllogism –Major premise –Minor premise –Term –Singular term –Major term –Middle term –Quantification –Plural quantification –Logical argument –Validity –Soundness –Inverse (logic) –Non sequitur –Tolerance –Satisfiability –Logical language –Paradox –Polish notation –Principia Mathematica –Quod erat demonstrandum –Reductio ad absurdum –Rhetoric –Self-reference –Necessary and sufficient –Sufficient condition –Nonfirstorderizability –Occam's Razor –Socratic dialoge –Socratic method –Argument form –Logic programming –Unification –Journal of Logic, Language and InformationJournal of Philosophical LogicA System of LogicAttacking Faulty ReasoningBegriffsschriftCategories (Aristotle)Charles Sanders Peirce bibliographyDe InterpretationeGödel, Escher, BachIntroduction to Mathematical PhilosophyLanguage, Truth, and LogicLaws of FormLinguistics and PhilosophyLogic Made EasyMetamagical ThemasMinds, Machines and GödelNovum OrganumOn Formally Undecidable Propositions of Principia Mathematica and Related SystemsOrganonPhilosophical InvestigationsPhilosophy of ArithmeticPolish LogicPort-Royal LogicPosterior AnalyticsPrincipia MathematicaPrinciples of Mathematical LogicPrior AnalyticsRhetoric (Aristotle)Sophistical RefutationsSum of LogicThe Art of Being RightThe Foundations of ArithmeticThe Logic of Scientific DiscoveryTopics (Aristotle)Tractatus Logico-PhilosophicusWhat the Tortoise Said to AchillesWhere Mathematics Comes FromAssociation for Symbolic LogicList of logiciansList of philosophers of language 