Outline of logic
The following outline is provided as an overview of and topical guide to logic:
Logic – 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.
Contents
 Foundations of logic 1

Philosophical logic 2
 Informal logic and critical thinking 2.1

Deductive reasoning 2.2
 Theories of deduction 2.2.1
 Fallacies 2.3

Formal logic 3

Symbols and strings of symbols 3.1

Logical symbols 3.1.1
 Logical connectives 3.1.1.1
 Strings of symbols 3.1.2

Types of propositions 3.1.3
 Rules of inference 3.1.3.1
 Formal theories 3.1.4
 Expressions in an object language 3.1.5
 Expressions in a metalanguage 3.1.6

Logical symbols 3.1.1

Propositional and boolean logic 3.2
 Propositional logic 3.2.1
 Boolean logic 3.2.2

Predicate logic and relations 3.3
 Predicate logic 3.3.1
 Relations 3.3.2

Symbols and strings of symbols 3.1

Mathematical logic 4
 Set theory 4.1

Metalogic 4.2
 Proof theory 4.2.1
 Model theory 4.2.2
 Computability theory 4.3
 Classical logic 5

Nonclassical logic 6
 Modal logic 6.1
 Concepts of logic 7
 History of logic 8

Literature about logic 9
 Journals 9.1
 Books 9.2
 Logic organizations 10
 Logicians 11
 See also 12
 External links 13
Foundations of logic
 Analyticsynthetic 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 (nonlinguistic)
 Paradox (list)
 Possible world
 Presupposition
 Probability
 Quantification
 Reason
 Reasoning
 Reference
 Semantics
 Strict conditional
 Syntax (logic)
 Truth
 Truth value
 Validity
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 –
 Higherorder 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
 Antipsychologism
 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.
Symbols and strings of symbols
Logical symbols
Logical connectives
 Converse implication –
 Converse nonimplication –
 Exclusive or –
 Logical NOR –
 Logical biconditional –
 Logical conjunction –
 Logical disjunction –
 Material implication –
 Material nonimplication –
 Negation –
 Sheffer stroke –
Strings of symbols
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
 Biconditional elimination
 Biconditional introduction
 Case analysis
 Commutativity of conjunction
 Conjunction introduction
 Constructive dilemma
 Contraposition (traditional logic)
 Conversion (logic)
 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
Expressions in an object language
Expressions in a metalanguage
Propositional and boolean logic
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
 Zerothorder 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
 Twoelement Boolean algebra
 Modal algebra
 Derivative algebra (abstract algebra)
 Relation algebra
 Absorption law
 Laws of Form
 Algebraic normal form
 Canonical form (Boolean algebra)
 Boolean conjunctive query
 Booleanvalued model
 Boolean domain
 Boolean expression
 Boolean ring
 Boolean function
 Booleanvalued 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
 Atomic formula
 Atomic sentence
 Domain of discourse
 Empty domain
 Extension (predicate logic)
 Firstorder logic
 Firstorder predicate
 Formation rule
 Free variables and bound variables
 Generalization (logic)
 Monadic predicate calculus
 Predicate (mathematical logic)
 Predicate logic
 Predicate variable
 Quantification
 Secondorder 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)
 Wellfounded relation
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
 NonCantorian 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
 LöwenheimSkolem theorem
 Metalanguage
 Metasyntactic variable
 Metatheorem
 Object language
 Symbol (formal)
 Typetoken distinction
 Use–mention distinction
 Wellformed 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
 Nonstandard 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
 Properties of classical logics:
 Term logic

General concepts in classical logic
 Baralipton
 Baroco
 Bivalence
 Boolean logic
 Booleanvalued function
 Categorical proposition
 Distribution of terms
 End term
 Enthymeme
 Immediate inference
 Law of contraries
 Logical connective
 Major term
 Middle term
 Minor term
 Organon
 Polysyllogism
 PortRoyal Logic
 Premise
 Prior Analytics
 Relative term
 Sorites paradox
 Square of opposition
 Sum of Logic
 Syllogism
 Tetralemma
 Truth function
Nonclassical logic
Nonclassical 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 –
 Manyvalued logic –
 Minimal logic –
 Noncommutative logic –
 Nonmonotonic 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 –
Concepts of logic
 Proof theory –
 Set theory –
 Formal system –
 Boolean algebra –
 Aristotelian logic –
 NonAristotelian logic –
 Informal logic –
 Fuzzy logic –

Infinitary logic –
 Infinity –
 Categorical logic –
 College logic –
 Linear logic –
 Metalogic –
 Ordered logic –
 Temporal logic –
 Sequential logic –
 Provability logic –
 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 –
 Fallacy –
 Type theory –
 Game theory –
 Game semantics –
 Rule of inference –
 Inference procedure –
 Inference rule –Quantification
 Introduction rule –
 Law of excluded middle –
 Law of noncontradiction –
 Logical constant –
 Logic gate –
 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 –
 Inverse (logic) –
 Non sequitur –
 Tolerance –
 Satisfiability –
 Logical language –
 Paradox –
 Polish notation –
 Principia Mathematica –
 Quod erat demonstrandum –
 Reductio ad absurdum –
 Rhetoric –
 Selfreference –
 Necessary and sufficient –
 Sufficient condition –
 Nonfirstorderizability –
 Occam's Razor –
 Socratic dialoge –
 Socratic method –
 Argument form –
 Logic programming –
 Unification –
History of logic
Literature about logic
Journals
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
 PortRoyal 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 LogicoPhilosophicus
 What the Tortoise Said to Achilles
 Where Mathematics Comes From
Logic organizations
Logicians
See also
 Index of logic articles
 Mathematics
 Philosophy
 Outline of discrete mathematics – for introductory set theory and other supporting material see this
External links
 Taxonomy of Logical Fallacies
 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.
 Logic test Test your logic skills
 Logic SelfTaught: A Workbook (originally prepared for online logic instruction)