Outline of logic

From Wikipedia, the free encyclopedia

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

Philosophical logic[]

Informal logic and critical thinking[]

Informal logic Critical thinking Argumentation theory

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
  • Object theory
  • 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[]

  • 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[]

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

  • Analytic proposition
  • Axiom
  • Atomic sentence
  • Clause (logic)
  • Contingent proposition
  • Contradiction
  • Logical truth
  • Propositional formula
  • Rule of inference
  • Sentence (mathematical logic)
  • Sequent
  • Statement (logic)
  • Tautology
  • Theorem
Rules of inference[]

Rule of inference  (list)

Formal theories[]

Main article: Theory (mathematical logic)

Expressions in an object language[]

Object language

Expressions in a metalanguage[]

Metalanguage

  • Metalinguistic variable
  • Deductive system
  • Metatheorem
  • Metatheory
  • Interpretation

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.

  • Interpretation (logic)
  • Logical validity
  • Non-standard model
  • Normal model
  • Model
  • Semantic consequence
  • Truth value

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

Modal 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[]

Books[]

Logic organizations[]

  • Association for Symbolic Logic

Logicians[]

See also[]

External links[]

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