Outline of logic  

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

Logicformal science of using reason, 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.

Contents

Foundations of logic

Philosophical logic

Philosophical logic

Informal logic and critical thinking

Informal logicCritical thinkingArgumentation theory

Deductive reasoning

Theories of deduction

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

  • 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

Logical connectives

Logical connective

Strings of symbols

Types of propositions

Rules of inference

Formal theories

Expressions in an object language

Expressions in a metalanguage

Propositional and boolean logic

Propositional logic

Boolean logic

Boolean algebra Boolean logic Boolean algebra (structure)

Predicate logic and relations

Predicate logic

Relations

Mathematical logic

Mathematical logic

Set theory

Set theory

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

Non-classical logic

Non-classical logicDeviant logic

Modal logic

Modal logic

Concepts of logic

Mathematical logic

History of logic

Logicians

Literature

Lists

See also





Unless indicated otherwise, the text in this article is either based on Wikipedia article "Outline of logic" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on original research by Jahsonic and friends. See Art and Popular Culture's copyright notice.

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