Outline of logic

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The following outline is provided as an overview of and topical guide to logic:

Logic is the 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[edit]

Main article: Philosophy of logic

Philosophical logic[edit]

Philosophical logic

Informal logic and critical thinking[edit]

Informal logicCritical thinkingArgumentation theory

Deductive reasoning[edit]

Theories of deduction[edit]


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[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.

Symbols and strings of symbols[edit]

Logical symbols[edit]

Logical connectives[edit]

Logical connective

Strings of symbols[edit]

Main article: Well-formed formula

Types of propositions[edit]

Main article: Proposition
Rules of inference[edit]
Main article: Rule of inference

Formal theories[edit]

Expressions in an object language[edit]

Main article: Object language

Expressions in a metalanguage[edit]

Main article: Metalanguage

Propositional and boolean logic[edit]

Propositional logic[edit]

Main article: Propositional logic

Boolean logic[edit]

Boolean algebra Boolean logic Boolean algebra (structure)

Predicate logic and relations[edit]

Predicate logic[edit]

Main article: Predicate logic


Main article: Mathematical relation

Mathematical logic[edit]

Mathematical logic

Set theory[edit]

Set theory


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.

Classical logic[edit]

Classical logic

Non-classical logic[edit]

Non-classical logicDeviant logic

Modal logic[edit]

Modal logic

Concepts of logic[edit]

Mathematical logic

History of logic[edit]

Main article: History of logic


Main article: List of logicians



See also[edit]

External links[edit]