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.

1 Foundations of logic
2 Philosophical logic
3 Formal logic
4 Mathematical logic
5 Classical logic
6 Non-classical logic
- 6.1 Modal logic
7 Concepts of logic
8 History of logic
9 Logicians
10 Literature
11 Lists
12 See also
13 External links

Foundations of logic

Main article: Philosophy of logic

Philosophical logic

Philosophical logic –

Informal logic and critical thinking

Informal logic – Critical thinking – Argumentation theory –

Deductive reasoning

Theories of deduction

Fallacies

Main article: List of fallacies

Fallacy – In logic and rhetoric, this is usually an 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

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

Logical connectives

Logical connective –

v t e Logical connectives

Tautology $\top$

NAND $\uparrow$ · Converse implication $\leftarrow$ · Implication $\rightarrow$ · OR $\or$

Negation $\neg$ · XOR $\oplus$ · Biconditional $\leftrightarrow$ · Statement

NOR $\downarrow$ · Nonimplication $\nrightarrow$ · Converse nonimplication $\nleftarrow$ · AND $\and$

Contradiction $\bot$

Strings of symbols

Main article: Well-formed formula

Types of propositions

Main article: Proposition

Expressions in a metalanguage

Main article: Metalanguage

Propositional and boolean logic

Propositional logic

Main article: Propositional logic

Boolean logic

Boolean algebra Boolean logic Boolean algebra (structure)

Predicate logic and relations

Predicate logic

Main article: Predicate logic

Relations

Main article: Mathematical relation

Mathematical logic

Mathematical logic –

Set theory

Set theory –

Metalogic

Metalogic – The study of the metatheory of logic.

Proof theory

Proof theory – The study of deductive apparatus.

Model theory

Model theory – The study of interpretation of formal systems.

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.

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

Non-classical logic

Non-classical logic – Deviant logic –

Modal logic

Modal logic –

Concepts of logic

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

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.

External links

Find more about Logic on Wikipedia's sister projects:
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	Learning resources from Wikiversity
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Taxonomy of Logical Fallacies
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.
Logic test Test your logic skills
Logic Self-Taught: A Workbook (originally prepared for on-line logic instruction)

Logic

Overview

Academic areas	Argumentation theory Axiology Critical thinking Computability theory Formal semantics History of logic Informal logic Logic in computer science Mathematical logic Mathematics Metalogic Metamathematics Model theory Philosophical logic Philosophy Philosophy of logic Philosophy of mathematics Proof theory Set theory

Foundational concepts	Abduction Analytic truth Antinomy A priori Deduction Definition Description Entailment Induction Inference Logical consequence Logical form Logical implication Logical truth Name Necessity Meaning Paradox Possible world Presupposition Probability Reason Reasoning Reference Semantics Statement Strict implication Substitution Syntax Truth Truth value Validity

Philosophical logic

Critical thinking and Informal logic	Analysis Ambiguity Argument Belief Bias Credibility Evidence Explanation Explanatory power Fact Fallacy Inquiry Opinion Parsimony Premise Propaganda Prudence Reasoning Relevance Rhetoric Rigor Vagueness

Theories of deduction	Constructivism Dialetheism Fictionalism Finitism Formalism Intuitionism Logical atomism Logicism Nominalism Platonic realism Pragmatism Realism

Metalogic and metamathematics

Cantor's theorem Church's theorem Church's thesis Consistency Effective method Foundations of mathematics Gödel's completeness theorem Gödel's incompleteness theorems Soundness Completeness Decidability Interpretation Löwenheim–Skolem theorem Metatheorem Satisfiability Independence Type–token distinction Use–mention distinction

Mathematical logic

General	Formal language Formation rule Formal system Deductive system Formal proof Formal semantics Well-formed formula Set Element Class Classical logic Axiom Natural deduction Rule of inference Relation Theorem Logical consequence Axiomatic system Type theory Symbol Syntax Theory

Traditional logic	Proposition Inference Argument Validity Cogency Syllogism Square of opposition Venn diagram

Propositional calculus and Boolean logic	Boolean functions Propositional calculus Propositional formula Logical connectives Truth tables

Predicate	First-order Quantifiers Predicate Second-order Monadic predicate calculus

Set theory	Set Empty set Enumeration Extensionality Finite set Function Subset Power set Countable set Recursive set Domain Range Ordered pair Uncountable set

Model theory	Model Interpretation Non-standard model Finite model theory Truth value Validity

Proof theory	Formal proof Deductive system Formal system Theorem Logical consequence Rule of inference Syntax

Computability theory	Recursion Recursive set Recursively enumerable set Decision problem Church–Turing thesis Computable function Primitive recursive function

Non-classical logic

Modal logic	Alethic Axiologic Deontic Doxastic Epistemic Temporal

Intuitionism	Intuitionistic logic Constructive analysis Heyting arithmetic Intuitionistic type theory Constructive set theory

Fuzzy logic	Degree of truth Fuzzy rule Fuzzy set Fuzzy finite element Fuzzy set operations

Substructural logic	Structural rule Relevance logic Linear logic

Paraconsistent logic	Dialetheism

Description logic	Ontology Ontology language

Logicians

Anderson Aristotle Averroes Avicenna Bain Barwise Bernays Boole Boolos Cantor Carnap Church Chrysippus Curry De Morgan Frege Geach Gentzen Gödel Hilbert Kleene Kripke Leibniz Löwenheim Peano Peirce Putnam Quine Russell Schröder Scotus Skolem Smullyan Tarski Turing Whitehead William of Ockham Wittgenstein Zermelo

Lists

Topics	Outline of logic Index of logic articles Mathematical logic Boolean algebra Set theory

Other	Logicians Rules of inference Paradoxes Fallacies Logic symbols

v t e Outlines

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Hypertext

Outline of logic

Contents

Foundations of logic

Philosophical logic

Informal logic and critical thinking

Deductive reasoning

Theories of deduction

Fallacies

Formal logic

Symbols and strings of symbols

Logical symbols

Logical connectives

Strings of symbols

Types of propositions

Rules of inference

Formal theories

Expressions in an object language

Expressions in a metalanguage

Propositional and boolean logic

Propositional logic

Boolean logic

Predicate logic and relations

Predicate logic

Relations

Mathematical logic

Set theory

Metalogic

Proof theory

Model theory

Computability theory

Classical logic

Non-classical logic

Modal logic

Concepts of logic

History of logic

Logicians

Literature

Lists

See also

External links