Outline of logic explained
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
Philosophy of logic
Branches of logic
Informal logic and critical thinking
Informal logicCritical thinkingArgumentation 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.
Symbols and strings of symbols
Logical symbols
See main article: Table of logic symbols and Symbol (formal).
Logical connectives
Logical connective
Strings of symbols
See main article: Well-formed formula.
Types of propositions
Proposition
Rules of inference
Rule of inference (list)
Formal theories
See main article: Theory (mathematical logic).
Expressions in a metalanguage
Metalanguage
Propositional and boolean logic
Propositional logic
Propositional logic
Boolean logic
Predicate logic and relations
Predicate logic
Predicate logic
Relations
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.
Semantics of natural language
Formal semantics (natural language)
Classical logic
Classical logic
- Properties of classical logics:
- Term logic
- General concepts in classical logic
Modal logic
Modal logic
Non-classical logic
Non-classical logic
Concepts of logic
Mathematical logic
History of logic
History of logic
Literature about logic
Journals
Books
Logic organizations
Logicians
See also
External links
