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

Philosophy of logic

  • Analytic-synthetic distinction
  • Antinomy
  • A priori and a posteriori
  • Definition
  • Description
  • Entailment
  • Identity (philosophy)
  • Inference
  • Logical form
  • Logical implication
  • Logical truth
  • Logical consequence
  • Name
  • Necessity
  • Material conditional
  • Meaning (linguistic)
  • Meaning (non-linguistic)
  • Paradox (list)
  • Possible world
  • Presupposition
  • Probability
  • Quantification
  • Reason
  • Reasoning
  • Reference
  • Semantics
  • Strict conditional
  • Syntax (logic)
  • Truth
  • Truth value
  • Validity

Branches of logic

Philosophical logic

Informal logic and critical thinking

Informal logic Critical thinking Argumentation theory

  • Argument
  • Argument map
  • Accuracy and precision
  • Ad hoc hypothesis
  • Ambiguity
  • Analysis
  • Attacking Faulty Reasoning
  • Belief
  • Belief bias
  • Bias
  • Cognitive bias
  • Confirmation bias
  • Credibility
  • Critical reading
  • Critical thinking
  • Decidophobia
  • Decision making
  • Dispositional and occurrent belief
  • Emotional reasoning
  • Evidence
  • Expert
  • Explanation
  • Explanatory power
  • Fact
  • Fallacy
  • Higher-order thinking
  • Inquiry
  • Interpretive discussion
  • Occam's razor
  • Opinion
  • Practical syllogism
  • Precision questioning
  • Propaganda
  • Propaganda techniques
  • Problem Solving
  • Prudence
  • Pseudophilosophy
  • Reasoning
  • Relevance
  • Rhetoric
  • Rigour
  • Socratic questioning
  • Source credibility
  • Source criticism
  • Theory of justification
  • Topical logic
  • Vagueness

Deductive reasoning

Theories of deduction

  • Anti-psychologism
  • Conceptualism
  • Constructivism
  • Conventionalism
  • Counterpart theory
  • Deflationary theory of truth
  • Dialetheism
  • Fictionalism
  • Formalism (philosophy)
  • Game theory
  • Illuminationist philosophy
  • Logical atomism
  • Logical holism
  • Logicism
  • Modal fictionalism
  • Nominalism
  • Polylogism
  • Pragmatism
  • Preintuitionism
  • Proof theory
  • Psychologism
  • Ramism
  • Semantic theory of truth
  • Sophism
  • Trivialism
  • Ultrafinitism

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

Symbols and strings of symbols

Logical symbols

Main articles: Table of logic symbols and Symbol (formal)
Logical connectives

Logical connective

Strings of symbols

Main article: Well-formed formula

Types of propositions

Proposition

Rules of inference

Rule of inference (list)

Formal theories

Main article: Theory (mathematical logic)

Expressions in a metalanguage

Metalanguage

Propositional and boolean logic

Propositional logic

Boolean logic

Predicate logic and relations

Predicate logic

Main article: Predicate logic

Relations

Mathematical relation

Mathematical logic

Mathematical logic

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.

Semantics of natural language

Formal semantics (natural language)

  • Formal systems
    • Alternative semantics
    • Categorial grammar
    • Combinatory categorial grammar
    • Discourse representation theory
    • Dynamic semantics
    • Inquisitive semantics
    • Montague grammar
    • Situation semantics
  • Concepts

Classical logic

Classical logic

Modal logic

  • Alethic logic
  • Deontic logic
  • Doxastic logic
  • Epistemic logic
  • Temporal logic

Non-classical logic

Non-classical logic

Concepts of logic

  • Deductive reasoning
  • Inductive reasoning
  • Abductive reasoning

Mathematical logic

History of logic

History of logic

Literature about logic

Journals

  • Journal of Logic, Language and Information
  • Journal of Philosophical Logic
  • Linguistics and Philosophy

Books

Logic organizations

Logicians

  • List of logicians
  • List of philosophers of language

See also

References

  1. ^ Marco Aiello; Ian Pratt-Hartmann; Johan van Benthem, eds. (2007). Handbook of Spatial Logics. p. 1. doi:10.1007/978-1-4020-5587-4. ISBN 978-1-4020-5586-7. any formal language interpreted over a class of structures featuring geometrical entities and relations, broadly construed
  2. ^ "octagon of prophecies - Google Search". www.google.com. Retrieved 2024-10-29.
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