Outline of Logic Information
Logic is the formal science of using reason. It is considered a branch of both philosophy and mathematics. 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. 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.
Foundations of logic
Main articles: Philosophy of logic and Philosophical logicTraditional logic
Main articles: Term logic and Classical logicInformal logic and critical thinking
Main articles: Informal logic and Critical thinkingFallacies
Main article: List of fallacies
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Formal and mathematical logic
Main articles: Formal logic and Mathematical logicMathematical 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
Main article: Logical connectiveStrings of symbols
Main article: Well-formed formulaTypes of propositions
Main article: 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
Main article: Rule of inferenceFormal theories
Main article: Theory (mathematical logic)Expressions in an object language
Main article: Object languageExpressions in a metalanguage
Main article: MetalanguagePropositional and boolean logic
Propositional logic
Main article: Propositional logicBoolean logic
Main article: Boolean logicPredicate logic and relations
Predicate logic
Main article: Predicate logicRelations
Main article: Mathematical relationSet theory
Main article: Outline of set theoryMetalogic
Main article: MetalogicProof theory
Main article: Proof theory- Axiom
- Deductive system
- Formal proof
- Formal system
- Formal theorem
- Syntactic consequence
- Syntax (logic)
- Transformation rules
Model theory
Main article: Model theory- Interpretation (logic)
- Logical validity
- Non-standard model
- Normal model
- Model
- Semantic consequence
- Truth value
Recursion theory
Main article: Recursion theoryNon-classical and deviant logics
Main articles: Non-classical logic and Deviant logicModal logic
Main article: Modal logic- Alethic logic
- Axiological logic
- Deontic logic
- Doxastic logic
- Epistemic logic
- Temporal logic
History of logic
Main article: History of logicGeneral logic concepts
- Abduction – Affirming the consequent – Antecedent – Argument form – Aristotelian logic – Axiom – Axiomatic system – Axiomatization – Boolean algebra (logic) – Boolean logic – Categorical logic – College logic – Conditional proof – Consequent – Contradiction – Deductive reasoning – Degree of truth – Denying the antecedent – Double negative – Double negative elimination – Existential fallacy – Fallacy – Fuzzy logic – Game theory – Game semantics – Higher-order predicate – Hypothetical syllogism – Inductive logic – Inductive reasoning – Inference procedure – Inference rule – Infinitary logic – Infinity – Informal logic – Interpretability – Interpretability logic – Introduction rule – Invalid proof – Inverse (logic) – Law of excluded middle – Law of non-contradiction – Laws of Form – Linear logic – Logic – Logic gate – Logical argument – Logical assertion – Logical biconditional – Logical conditional – Logical conjunction – Logical disjunction – Logical equivalence – Logical fallacy – Logical language – Logical nand – Logical nor – Logical operator – Logicism – Logic programming – Major premise – Major term – Mathematical logic – Metalogic – Middle term – Minor premise – Necessary and sufficient – Negation – Non-Aristotelian logic – Nonfirstorderizability – Non sequitur – Occam's Razor – Ordered logic – Paradox – Pierce's law – Plural quantification – Polish notation – Polysyllogism – Predicate – Principia Mathematica – Proof theory – Proposition – Propositional calculus – Propositional logic – Provability logic – Quantification – Quantum logic – Quod erat demonstrandum – Reductio ad absurdum – Relevant logic – Rhetoric – Rule of inference – Satisfiability – Self-reference – Sequential logic – Set theory – Singular term – Socratic dialog – Socratic method – Soundness – Sufficient condition – Syllogism – Syllogistic fallacy – Tautology – Temporal logic – Term – Theorem – Tolerance – Truth – Truth condition – Truth function – Truth value – Type theory – Unification – Validity – Venn diagram
Famous logicians
Main article: List of logicians- George Boole – Abraham Robinson – Gerhard Gentzen – Luitzen Egbertus Jan Brouwer – Haskell Curry – Gottlob Frege – Alonzo Church – Jacques Herbrand – Dana Scott – John Barkley Rosser – Jean-Yves Girard – David Hilbert – Kurt Gödel – William Lawvere – William Stanley Jevons – Stephen Cole Kleene – Alfred Tarski – Thoralf Skolem – Saharon Shelah – Jan Łukasiewicz – Giuseppe Peano – Charles Sanders Peirce – W.V. Quine – Frank P. Ramsey – Bertrand Russell – Alfred North Whitehead
Theories of deduction
Logic literature
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Logic lists
- List of boolean algebra topics
- List of fallacies
- List of logicians
- List of mathematical logic topics
- List of paradoxes
- List of philosophers of language
- List of rules of inference
- List of set theory topics
- List of topics in logic
- For introductory set theory and other supporting material see the outline of discrete mathematics.
See also
| Logic portal |
External links
- LogicWiki, an external wiki
- An Introduction to Philosophical Logic, by Paul Newall, aimed at beginners
- 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.
- [1] Test your logic skills
- Logic Self-Taught: A Workbook (originally prepared for on-line logic instruction)
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Categories: Outlines | Logic | Mathematical logic | Mathematics-related lists | Philosophy-related lists
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