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.

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

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

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

Logical connectives

Logical connective –

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

Predicate logic and relations

Predicate logic

Main article: Predicate logic

Relations

Main article: Mathematical relation

Mathematical logic

Mathematical logic –

Set theory

Set theory (list) –

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 –

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

History of logic

Main article: 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
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

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 Self-Taught: A Workbook (originally prepared for on-line logic instruction)

Logic

Fields

Foundations

Lists

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other	Logicians Rules of inference Paradoxes Fallacies Logic symbols

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