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Outline of logic

Summary

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

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

Modal logic edit

Modal logic

Non-classical logic edit

Non-classical logic

Concepts of logic edit

Mathematical logic

History of logic edit

History of logic

Literature about logic edit

Journals edit

Books edit

Logic organizations edit

Logicians edit

See also edit

External links edit

  • Taxonomy of Logical Fallacies
  • 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)

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