Outline of logic

The following outline is provided as an overview of and topical guide to logic:

Logic – formal science of using reason, 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.

Foundations of logic

Main article: 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
• Possible world
• Presupposition
• Probability

• Quantification
• Reason
• Reasoning
• Reference
• Semantics
• Syntax (logic)
• Truth
• Truth value
• Validity

Philosophical 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 –
• 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 –
• Weak mindedness –

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 Object theory Polylogism

Pragmatism Preintuitionism Proof theory Psychologism Ramism Semantic theory of truth Sophism Trivialism Ultrafinitism

Fallacies

Main article: List 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.

Formal logic –

Symbols and strings of symbols

Logical symbols

Main articles: Table of logic symbols and Symbol (formal)

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

Main article: Well-formed formula

• Atomic formula
• Open sentence

Types of propositions

Main article: Proposition

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

Rules of inference

Main article: Rule of inference

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 negative 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

Main article: Theory (mathematical logic)

• Formal proof
• List of first-order theories

Expressions in an object language

Main article: Object language

• Symbol
• Formula
• Formal system
• Theorem
• Formal proof
• Theory

Expressions in a metalanguage

Main article: Metalanguage

• Metalinguistic variable
• Deductive system
• Metatheorem
• Metatheory
• Interpretation

Propositional and boolean logic

Propositional logic

Main article: Propositional logic

Absorption law Clause (logic) Deductive closure 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

Boolean logic

Boolean algebra

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
• Minimal negation operator
• Product term
• True quantified Boolean formula
• Truth table

Predicate logic and relations

Predicate logic

Main article: 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 (ε, δ)-definition of limit

Relations

Main article: Mathematical relation

Finitary relation Antisymmetric relation Asymmetric relation Bijection Bijection, injection and surjection Binary relation Composition of relations Concurrent relation Congruence relation Coreflexive relation

Covering relation Cyclic order Dense relation Dependence relation Dependency relation Directed set Equivalence relation Euclidean relation Homogeneous relation Idempotence

Intransitivity Inverse relation Involutive relation Partial equivalence relation Partial function Partially ordered set Preorder Prewellordering Propositional function Quasitransitive relation

Reflexive relation Surjective function Symmetric relation Ternary relation Total relation Transitive relation Trichotomy (mathematics) Well-founded relation

Mathematical logic

Mathematical logic –

Set theory

Set theory –

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) 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 Function (mathematics) Function composition Generalized continuum hypothesis Index set Infinite set

Intension Intersection (set theory) Inverse function Löwenheim–Skolem theorem Map (mathematics) Multiset Naïve set theory Non-Cantorian set theory One to one correspondence Ordered pair Partition of a set Pointed set Power set Projection (set theory) Proper subset Proper superset

Range (mathematics) 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) Zermelo–Fraenkel set theory

Metalogic

Metalogic – The study of the metatheory of logic.

• Completeness
• 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
• Symbol (formal)
• Type-token distinction
• Use–mention distinction
• Well-formed formula

Proof theory

Proof theory – The study of deductive apparatus.

• 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

Main article: Computability theory

Alpha recursion theory Arithmetical set Church–Turing thesis Computability logic Computable function Computation

Decision problem Effective method Entscheidungsproblem Enumeration Forcing (recursion theory) 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 languages and sets Recursive set Recursively enumerable language Recursively enumerable set Reduction (recursion theory) Turing machine

Classical logic

Classical logic –

Term logic –

Baralipton Baroco Bivalence Boolean logic Boolean-valued function Categorical proposition Commutativity of conjunction De Morgan duality

Distribution of terms Double negative elimination End term Enthymeme Immediate inference Idempotency of entailment Law of contraries Law of noncontradiction Law of the excluded middle

Logical connective Major term Middle term Minor term Monotonicity of entailment Organon Polysyllogism Port-Royal Logic Premise

Prior Analytics Relative term Sorites paradox Square of opposition Sum of Logic Syllogism Tetralemma Truth function

Non-classical logic

Non-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

Modal logic –

• Alethic logic –
• Axiological logic –
• Deontic logic –
• Doxastic logic –
• Epistemic logic –
• Temporal 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 –
  • 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 –
• Introduction 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 –

History of logic

Main article: History of logic

Logicians

Main article: List of logicians

Literature

A System of Logic Association for Symbolic Logic Attacking Faulty Reasoning Begriffsschrift Categories (Aristotle) Charles Sanders Peirce bibliography De Interpretatione Gödel, Escher, Bach Introduction to Mathematical Philosophy Journal of Logic, Language and Information Journal of Philosophical Logic Language, Truth, and Logic Laws of Form

Linguistics and Philosophy Logic Made Easy Metamagical Themas Minds, Machines and Gödel Novum Organum On Formally Undecidable Propositions of Principia Mathematica and Related Systems Organon Philosophical Investigations Philosophy of Arithmetic (book) 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 The Logic of Scientific Discovery Topics (Aristotle) Tractatus Logico-Philosophicus What the Tortoise Said to Achilles Where Mathematics Comes From

Lists

• List of Boolean algebra topics
• List of mathematical logic topics
• List of set theory topics
• Index of logic articles
• List of fallacies
• List of logicians
• List of paradoxes
• List of philosophers of language
• List of rules of inference

• For introductory set theory and other supporting material see the outline of discrete mathematics.

See also

Logic portal

• Mathematics
  • List of basic mathematics topics
  • List of mathematics articles
• Philosophy
  • List of basic philosophy topics
  • List of philosophy topics

External links

• LogicWiki, an external wiki
• An Introduction to Philosophical Logic, by Paul Newall, aimed at beginners
• forall x: an introduction to formal logic, by P.D. Magnus, covers sentential and quantified logic
• Translation Tips, by Peter Suber, for translating from English into logical notation
• Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas. In The Dictionary of the History of Ideas.
• [1] Test your logic skills
• Logic Self-Taught: A Workbook (originally prepared for on-line logic instruction)