Outline of logic

Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and 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[edit]

Philosophy of logic

Branches of logic[edit]

Philosophical logic[edit]

Informal logic and critical thinking[edit]

Informal logic Critical thinking Argumentation theory

Deductive reasoning[edit]

Theories of deduction[edit]

Fallacies[edit]

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[edit]

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[edit]

Logical symbols[edit]

Logical connectives[edit]

Logical connective

Strings of symbols[edit]

Types of propositions[edit]

Proposition

Rules of inference[edit]

Rule of inference (list)

Formal theories[edit]

Expressions in a metalanguage[edit]

Metalanguage

Propositional and boolean logic[edit]

Propositional logic[edit]

Propositional logic

Boolean logic[edit]

Predicate logic and relations[edit]

Predicate logic[edit]

Predicate logic

Relations[edit]

Mathematical relation

Mathematical logic[edit]

Mathematical logic

Set theory[edit]

Set theory (list)

Metalogic[edit]

Metalogic – The study of the metatheory of logic.

Proof theory[edit]

Proof theory – The study of deductive apparatus.

Model theory[edit]

Model theory – The study of interpretation of formal systems.

Computability theory[edit]

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.

Semantics of natural language[edit]

Formal semantics (natural language)

Classical logic[edit]

Classical logic

Properties of classical logics:
- Law of the excluded middle
- Double negation 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

Modal logic[edit]

Modal logic

Non-classical logic[edit]

Non-classical logic

Concepts of logic[edit]