Outline of logic

Foundations 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

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 –

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

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

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

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

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 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

Formal proof

List of first-order theories

Expressions in an object language

Symbol

Formula

Formal system

Theorem

Formal proof

Theory

Expressions in a metalanguage

Metalinguistic variable

Deductive system

Metatheorem

Metatheory

Interpretation

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

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

Minimal negation operator

Product term

True quantified Boolean formula

Truth table

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

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  (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)

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 (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

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

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 (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 –

Properties of classical logics:

Law of the excluded middle

Double negative 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

General concepts in classical logic

Baralipton

Baroco

Bivalence

Boolean logic

Boolean-valued function

Categorical proposition

Distribution of terms

End term

Enthymeme

Immediate inference

Law of contraries

Logical connective

Major term

Middle term

Minor term

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 –Quantification

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 –

Journals

Journal of Logic, Language and Information

Journal of Philosophical Logic

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

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

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

Logic organizations

Association for Symbolic Logic

Logicians

List of logicians

List of philosophers of language