Outline of logic

Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and 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.

Foundations of logic Philosophy of logic

Analytic-synthetic distinction Antinomy A priori and a posteriori Definition Description Entailment Identity (philosophy) Inference Logical form Logical implication Logical truth Logical consequence Name Necessity Material conditional Meaning (linguistic) Meaning (non-linguistic) Paradox (list) Possible world Presupposition Probability Quantification Reason Reasoning Reference Semantics Strict conditional Syntax (logic) Truth Truth value Validity

Branches of logic Affine logic Alethic logic Aristotelian logic Boolean logic Buddhist logic Bunched logic Categorical logic Classical logic Computability logic Deontic logic Dependence logic Description logic Deviant logic Doxastic logic Epistemic logic First-order logic Formal logic Free logic Fuzzy logic Higher-order logic Infinitary logic Informal logic Intensional logic Intermediate logic Interpretability logic Intuitionistic logic Linear logic Many-valued logic Mathematical logic Metalogic Minimal logic Modal logic Non-Aristotelian logic Non-classical logic Noncommutative logic Non-monotonic logic Ordered logic Paraconsistent logic Philosophical logic Predicate logic Propositional logic Provability logic Quantum logic Relevance logic Sequential logic Spatial logic Strict logic Substructural logic Syllogistic logic Symbolic logic Temporal logic Term logic Topical logic Traditional logic Zeroth-order logic

Philosophical logic

Informal logic and critical thinking Informal logic Critical thinking Argumentation theory

Argument Argument map Accuracy and precision Ad hoc hypothesis Ambiguity Analysis Attacking Faulty Reasoning Belief Belief bias Bias Cognitive bias Confirmation bias Credibility Critical reading Critical thinking Decidophobia Decision making Dispositional and occurrent belief Emotional reasoning Evidence Expert Explanation Explanatory power Fact Fallacy Higher-order thinking Inquiry Interpretive discussion Occam's razor Opinion Practical syllogism Precision questioning Propaganda Propaganda techniques Problem Solving Prudence Pseudophilosophy Reasoning Relevance Rhetoric Rigour Socratic questioning Source credibility Source criticism Theory of justification Topical logic Vagueness

Deductive reasoning

Theories of deduction Anti-psychologism Conceptualism Constructivism Conventionalism Counterpart theory Deflationary theory of truth Dialetheism Fictionalism Formalism (philosophy) Game theory Illuminationist philosophy Logical atomism Logical holism Logicism Modal fictionalism Nominalism Polylogism Pragmatism Preintuitionism Proof theory Psychologism Ramism Semantic theory of truth Sophism Trivialism Ultrafinitism

Fallacies Fallacy (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 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 topics

Symbols and strings of symbols

Logical symbols

Logical variables Propositional variable Predicate variable Literal Metavariable Logical constants Logical connective Quantifier Identity Brackets

Logical connectives Logical connective

Converse implication Converse nonimplication Exclusive or Logical NOR Logical biconditional Logical conjunction Logical disjunction Material implication Material nonimplication Negation Sheffer stroke

Strings of symbols

Atomic formula Open sentence

Types of propositions Proposition

Analytic proposition Axiom Atomic sentence Clause (logic) Contingent proposition Contradiction Logical truth Propositional formula Rule of inference Sentence (mathematical logic) Sequent Statement (logic) Subalternation Tautology Theorem

Rules of inference Rule of inference (list)

Biconditional elimination Biconditional introduction Case analysis Commutativity of conjunction Conjunction introduction Constructive dilemma Contraposition (traditional logic) Conversion (logic) De Morgan's laws Destructive dilemma Disjunction elimination Disjunction introduction Disjunctive syllogism Double negation elimination Generalization (logic) Hypothetical syllogism Law of excluded middle Law of identity Modus ponendo tollens Modus ponens Modus tollens Obversion Principle of contradiction Resolution (logic) Simplification Transposition (logic)

Formal theories

Formal proof List of first-order theories

Expressions in a metalanguage Metalanguage

Metalinguistic variable Deductive system Metatheorem Metatheory Interpretation

Propositional and Boolean logic

Propositional logic

Absorption law Clause (logic) Deductive closure Distributive property Entailment Formation rule Functional completeness Intermediate logic Literal (mathematical logic) Logical connective Logical consequence Negation normal form Open sentence Propositional calculus Propositional formula Propositional variable Rule of inference Strict conditional Substitution instance Truth table Zeroth-order logic

Boolean logic Boolean algebra (list) Boolean logic Boolean algebra (structure) Boolean algebras canonically defined Introduction to Boolean algebra Complete Boolean algebra Free Boolean algebra Monadic Boolean algebra Residuated Boolean algebra Two-element Boolean algebra Modal algebra Derivative algebra (abstract algebra) Relation algebra Absorption law Laws of Form De Morgan's laws Algebraic normal form Canonical form (Boolean algebra) Boolean conjunctive query Boolean-valued model Boolean domain Boolean expression Boolean ring Boolean function Boolean-valued function Parity function Symmetric Boolean function Conditioned disjunction Field of sets Functional completeness Implicant Logic alphabet Logic redundancy Logical connective Logical matrix Product term True quantified Boolean formula Truth table

Predicate logic and relations

Predicate logic

Atomic formula Atomic sentence Domain of discourse Empty domain Extension (predicate logic) First-order logic First-order predicate Formation rule Free variables and bound variables Generalization (logic) Monadic predicate calculus Predicate (mathematical logic) Predicate logic Predicate variable Quantification Second-order predicate Sentence (mathematical logic) Universal instantiation

Relations Mathematical relation

Finitary relation Antisymmetric relation Asymmetric relation Bijection Bijection, injection and surjection Binary relation Composition of relations Congruence relation Connected relation Converse relation Coreflexive relation Covering relation Cyclic order Dense relation Dependence relation Dependency relation Directed set Equivalence relation Euclidean relation Homogeneous relation Idempotence Intransitivity Involutive relation Partial equivalence relation Partial function Partially ordered set Preorder Prewellordering Propositional function Quasitransitive relation Reflexive relation Serial relation Surjective function Symmetric relation Ternary relation Transitive relation Trichotomy (mathematics) Well-founded relation

Mathematical logic Mathematical logic

Set theory Set theory list Aleph null Bijection, injection and surjection Binary set Cantor's diagonal argument Cantor's first uncountability proof Cantor's theorem Cardinality of the continuum Cardinal number Codomain Complement (set theory) Constructible universe Continuum hypothesis Countable set Decidable set Denumerable set Disjoint sets Disjoint union Domain of a function Effective enumeration Element (mathematics) Empty function Empty set Enumeration Extensionality Finite set Forcing (mathematics) Function (set theory) Function composition Generalized continuum hypothesis Index set Infinite set Intension Intersection (set theory) Inverse function Large cardinal Löwenheim–Skolem theorem Map (mathematics) Multiset Morse–Kelley set theory Naïve set theory One-to-one correspondence Ordered pair Partition of a set Pointed set Power set Projection (set theory) Proper subset Proper superset Range of a function Russell's paradox Sequence (mathematics) Set (mathematics) Set of all sets Simple theorems in the algebra of sets Singleton (mathematics) Skolem paradox Subset Superset Tuple Uncountable set Union (set theory) Von Neumann–Bernays–Gödel set theory Zermelo set theory Zermelo–Fraenkel set theory

Metalogic Metalogic – The study of the metatheory of logic.

Completeness (logic) Syntax (logic) Consistency Decidability (logic) Deductive system Interpretation (logic) Cantor's theorem Church's theorem Church's thesis Effective method Formal system Gödel's completeness theorem Gödel's first incompleteness theorem Gödel's second incompleteness theorem Independence (mathematical logic) Logical consequence Löwenheim–Skolem theorem Metalanguage Metasyntactic variable Metatheorem Object language – see metalanguage Symbol (formal) Type–token distinction Use–mention distinction Well-formed formula

Proof theory Proof theory – The study of deductive systems.

Axiom Deductive system Formal proof Formal system Formal theorem Syntactic consequence Syntax (logic) Transformation rules

Model theory Model theory – The study of interpretation of formal systems.

Interpretation (logic) Logical validity Non-standard model Normal model Model Semantic consequence Truth value

Computability theory Computability 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 theory Arithmetical set Church–Turing thesis Computability logic Computable function Computation Decision problem Effective method Entscheidungsproblem Enumeration Forcing (computability) Halting problem History of the Church–Turing thesis Lambda calculus List of undecidable problems Post correspondence problem Post's theorem Primitive recursive function Recursion (computer science) Recursive language Recursive set Recursively enumerable language Recursively enumerable set Reduction (recursion theory) Turing machine

Semantics of natural language Formal semantics (natural language)

Formal systems Alternative semantics Categorial grammar Combinatory categorial grammar Discourse representation theory Dynamic semantics Inquisitive semantics Montague grammar Situation semantics Concepts Compositionality Counterfactuals Generalized quantifier Logic translation Mereology Modality (natural language) Opaque context Presupposition Propositional attitudes Scope (formal semantics) Type shifter Vagueness

Classical logic Classical logic

Properties of classical logics: Law of the excluded middle Double negation elimination Law of noncontradiction Principle of explosion Monotonicity of entailment Idempotency of entailment Commutativity of conjunction De Morgan duality – every logical operator is dual to another Term logic Outline of logic Baralipton Baroco Bivalence Boolean logic Boolean-valued function Categorical proposition Distribution of terms End term Enthymeme Immediate inference Law of contraries Logical connective Logical cube Logical hexagon Major term Middle term Minor term Octagon of Prophecies Organon Polysyllogism Port-Royal Logic Premise Prior Analytics Absolute and relative terms Sorites paradox Square of opposition Triangle of opposition Sum of Logic Syllogism Tetralemma Truth function

Modal logic Modal logic

Alethic logic Deontic logic Doxastic logic Epistemic logic Temporal logic

Non-classical logic Non-classical logic

Affine logic Bunched logic Computability logic Decision theory Description logic Deviant logic Free logic Fuzzy logic Game theory Intensional logic Intuitionistic logic Linear logic Many-valued logic Minimal logic Non-monotonic logic Noncommutative logic Paraconsistent logic Probability theory Quantum logic Relevance logic Strict conditional Substructural logic

Concepts of 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 Peirce's law Aristotelian logic Non-Aristotelian logic Informal logic Fuzzy logic Infinitary logic Infinity Categorical logic Linear logic Metalogic Order Ordered logic Temporal logic Linear temporal logic Linear temporal logic to Büchi automaton 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 negation Double negation elimination Fallacy Existential fallacy Logical fallacy Syllogistic fallacy Type theory Game theory Game semantics Rule of inference Inference procedure Inference rule Introduction rule Law of excluded middle Law of non-contradiction Logical constant Logical connective Quantifier Logic gate Boolean Function Quantum logic gate Tautology Logical assertion Logical conditional Logical biconditional Logical equivalence Logical AND Negation Logical OR Logical NAND Logical NOR Contradiction Subalternation 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 dialogue Socratic method Argument form Logic programming Unification

History of logic History of logic

Literature about logic

Journals Journal of Logic, Language and Information Journal of Philosophical Logic Linguistics and Philosophy

Books A System of Logic Attacking Faulty Reasoning Begriffsschrift Categories (Aristotle) Charles Sanders Peirce bibliography De Interpretatione Gödel, Escher, Bach Introduction to Mathematical Philosophy Language, Truth, and Logic Laws of Form Novum Organum On Formally Undecidable Propositions of Principia Mathematica and Related Systems Organon Philosophy of Arithmetic Polish Logic Port-Royal Logic Posterior Analytics Principia Mathematica Principles of Mathematical Logic Prior Analytics Rhetoric (Aristotle) Sophistical Refutations Sum of Logic The Art of Being Right The Foundations of Arithmetic Topics (Aristotle) Tractatus Logico-Philosophicus

Logic organizations Association for Symbolic Logic

Logicians List of logicians List of philosophers of language

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