- Outline of logic
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The following outline is provided as an overview of and topical guide to logic:
Logic – formal 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.
Foundations of logic
Main article: Philosophy of logic- Analytic-synthetic distinction
- Antinomy
- A priori and a posteriori
- Definition
- Description
- Entailment
- Identity (philosophy)
- Material conditional
- Meaning (linguistic)
- Meaning (non-linguistic)
- Paradox
- Possible world
- Presupposition
- Probability
Philosophical logic
Informal logic and critical thinking
- Argument –
- Argument map –
- Accuracy and precision –
- Ad hoc hypothesis –
- Ambiguity –
- Analysis –
- Attacking Faulty Reasoning –
- Belief –
- Belief bias –
- Bias –
- Cogency –
- Cognitive bias –
- Confirmation bias –
- Credibility –
- Critical pedagogy –
- Critical reading –
- Decidophobia –
- Decision making –
- Dispositional and occurrent belief –
- Emotional reasoning –
- Evidence –
- Expert –
- Explanation –
- Explanatory power –
- Fact –
- Fallacy –
- Higher-order thinking –
- Inquiry –
- Interpretive discussion –
- Narrative logic –
- Occam's razor –
- Opinion –
- Practical syllogism –
- Precision questioning –
- Propaganda –
- Propaganda techniques –
- Prudence –
- Pseudophilosophy –
- Reasoning –
- Relevance –
- Rhetoric –
- Rigour –
- Socratic questioning –
- Source credibility –
- Source criticism –
- Theory of justification –
- Topical logic –
- Vagueness –
- Weak mindedness –
Deductive reasoning
Theories of deduction
Fallacies
Main article: List of fallaciesFormal fallacies In propositional logic In quantificational logic Syllogistic fallacy Other types of formal fallacy · List of fallaciesInformal fallacies Absence paradox · Begging the question · Blind men and an elephant · Cherry picking · Complex question · False analogy · Fallacy of distribution (Composition · Division) · Furtive fallacy · Hasty generalization · I'm entitled to my opinion · Loaded question · McNamara fallacy · Name calling · Nirvana fallacy · Rationalization (making excuses) · Red herring fallacy · Special pleading · Slothful inductionCorrelative-based fallacies Deductive fallacies Inductive fallacies Vagueness and ambiguity Equivocation Questionable cause Animistic · Appeal to consequences · Argumentum ad baculum · Correlation does not imply causation (Cum hoc) · Gambler's fallacy and its inverse · Post hoc · Prescience · Regression · Single cause · Slippery slope · Texas sharpshooter · The Great Magnet · Unknown Root · Wrong directionList of fallacies · Other types of fallacyFormal 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.
Formal logic –
Symbols and strings of symbols
Logical symbols
Main articles: Table of logic symbols and Symbol (formal)- Logical constants
- Logical connective
- Quantifier
- Identity
- Brackets
Logical connectives
- Converse implication –
- Converse nonimplication –
- Exclusive or –
- Logical NOR –
- Logical biconditional –
- Logical conjunction –
- Logical disjunction –
- Material implication –
- Material nonimplication –
- Negation –
- Sheffer stroke –
Logical connectives Strings 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: Metalanguage- Metalinguistic variable
- Deductive system
- Metatheorem
- Metatheory
- Interpretation
Propositional and boolean logic
Propositional logic
Main article: Propositional logic- Absorption law
- Clause (logic)
- Deductive closure
- Entailment
- Formation rule
Boolean logic
- Boolean algebras canonically defined
- Introduction to Boolean algebra
- Complete Boolean algebra
- Free Boolean algebra
- Monadic Boolean algebra
- Residuated Boolean algebra
- Two-element Boolean algebra
- Boolean function
- Boolean-valued function
- Parity function
- Symmetric Boolean function
- Conditioned disjunction
- Field of sets
- Functional completeness
- Implicant
- Logic alphabet
- Logic redundancy
- Logical connective
- Logical matrix
- Minimal negation operator
- Product term
- True quantified Boolean formula
- Truth table
Predicate logic and relations
Predicate logic
Main article: Predicate logic- First-order predicate
- Formation rule
- Free variables and bound variables
- Generalization (logic)
- Monadic predicate calculus
- Predicate (mathematical logic)
- Predicate logic
Relations
Main article: Mathematical relationMathematical logic
Set theory
- Aleph null
- Bijection, injection and surjection
- Binary set
- Cantor's diagonal argument
- Cantor's first uncountability proof
- Cantor's theorem
- Cardinality of the continuum
- Cardinal number
- Codomain
- Complement (set theory)
- Continuum hypothesis
- Countable set
- Decidable set
- Denumerable set
- Disjoint sets
- Disjoint union
- Domain of a function
- Effective enumeration
- Element (mathematics)
- Empty function
- Empty set
- Enumeration
- Extensionality
- Finite set
- Function (mathematics)
- Function composition
- Generalized continuum hypothesis
- Index set
- Infinite set
- Intension
- Intersection (set theory)
- Inverse function
- Löwenheim–Skolem theorem
- Map (mathematics)
- Multiset
- Naïve set theory
- Non-Cantorian set theory
- One to one correspondence
- Ordered pair
- Partition of a set
- Pointed set
- Power set
- Projection (set theory)
- Proper subset
- Proper superset
- Range (mathematics)
- Russell's paradox
- Sequence (mathematics)
- Set (mathematics)
- Set of all sets
- Simple theorems in the algebra of sets
- Singleton (mathematics)
- Skolem paradox
- Subset
- Superset
- Tuple
- Uncountable set
- Union (set theory)
- Zermelo–Fraenkel set theory
Metalogic
Metalogic – The study of the metatheory of logic.
- Completeness
- Syntax (logic)
- Consistency
- Decidability (logic)
- Deductive system
- Interpretation (logic)
- Cantor's theorem
- Church's theorem
- Church's thesis
- Effective method
- Formal system
- Gödel's completeness theorem
- Gödel's first incompleteness theorem
- Gödel's second incompleteness theorem
- Independence (mathematical logic)
- Logical consequence
- Löwenheim-Skolem theorem
- Metalanguage
- Metasyntactic variable
- Metatheorem
- Object language
- Symbol (formal)
- Type-token distinction
- Use–mention distinction
- Well-formed formula
Proof theory
Proof theory – The study of deductive apparatus.
- Axiom
- Deductive system
- Formal proof
- Formal system
- Formal theorem
- Syntactic consequence
- Syntax (logic)
- Transformation rules
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
Main article: Computability theoryClassical logic
- Baralipton
- Baroco
- Bivalence
- Boolean logic
- Boolean-valued function
- Categorical proposition
- Commutativity of conjunction
- De Morgan duality
- Distribution of terms
- Double negative elimination
- End term
- Enthymeme
- Immediate inference
- Idempotency of entailment
- Law of contraries
- Law of noncontradiction
- Law of the excluded middle
Non-classical logic
- Decision theory –
- Game theory –
- Probability theory –
- Affine logic –
- Bunched logic –
- Description logic –
- Free logic –
- Intensional logic –
- Intuitionistic logic –
- Many-valued logic –
- Minimal logic –
- Noncommutative logic –
- Non-monotonic logic –
- Paraconsistent logic –
- Quantum logic –
- Relevance logic –
- Strict logic –
- Substructural logic –
Modal logic
- Alethic logic –
- Axiological logic –
- Deontic logic –
- Doxastic logic –
- Epistemic logic –
- Temporal logic –
Concepts of logic
- Proof theory –
- Set theory –
- Formal system –
- Boolean algebra –
- Boolean logic –
- Truth value –
- Venn diagram –
- Pierce's law –
- Aristotelian logic –
- Non-Aristotelian logic –
- Informal logic –
- Fuzzy logic –
- Infinitary logic –
- Infinity –
- Categorical logic –
- College logic –
- Linear logic –
- Metalogic –
- Ordered logic –
- Temporal logic –
- Sequential logic –
- Provability logic –
- Quantum logic –
- Relevant logic –
- Theorem –
- Axiom –
- Axiomatic system –
- Axiomatization –
- Fallacy –
- Existential fallacy –
- Logical fallacy –
- Syllogistic fallacy –
- Rule of inference –
- Inference procedure –
- Inference rule –
- Introduction rule –
- Law of excluded middle –
- Law of non-contradiction –
- Logical constant –
- Logical connective –
- Quantifier –
- Logic gate –
- Tautology –
- Logical assertion –
- Logical conditional –
- Logical biconditional –
- Logical equivalence –
- Logical AND –
- Negation –
- Logical OR –
- Logical NAND –
- Logical NOR –
- Contradiction –
- Major premise –
- Minor premise –
- Term –
- Singular term –
- Major term –
- Middle term –
- Inverse (logic) –
- Non sequitur –
- Tolerance –
- Satisfiability –
- Logical language –
- Paradox –
- Polish notation –
- Principia Mathematica –
- Quod erat demonstrandum –
- Reductio ad absurdum –
- Rhetoric –
- Self-reference –
- Necessary and sufficient –
- Sufficient condition –
- Nonfirstorderizability –
- Occam's Razor –
- Socratic dialoge –
- Socratic method –
- Argument form –
- Logic programming –
- Unification –
History of logic
Main article: History of logicLogicians
Main article: List of logiciansLiterature
- A System of Logic
- Association for Symbolic Logic
- Attacking Faulty Reasoning
- Begriffsschrift
- Categories (Aristotle)
- Charles Sanders Peirce bibliography
- De Interpretatione
- Gödel, Escher, Bach
- Introduction to Mathematical Philosophy
- Journal of Logic, Language and Information
- Journal of Philosophical Logic
- Language, Truth, and Logic
- Laws of Form
- Linguistics and Philosophy
- Logic Made Easy
- Metamagical Themas
- Minds, Machines and Gödel
- Novum Organum
- On Formally Undecidable Propositions of Principia Mathematica and Related Systems
- Organon
- Philosophical Investigations
- Philosophy of Arithmetic (book)
- Polish Logic
- Port-Royal Logic
- Posterior Analytics
- Principia Mathematica
- Principles of Mathematical Logic
- Prior Analytics
- Rhetoric (Aristotle)
- Sophistical Refutations
- Sum of Logic
- The Art of Being Right
- The Foundations of Arithmetic
- The Logic of Scientific Discovery
- Topics (Aristotle)
- Tractatus Logico-Philosophicus
- What the Tortoise Said to Achilles
- Where Mathematics Comes From
Lists
- List of Boolean algebra topics
- List of mathematical logic topics
- List of set theory topics
- Index of logic articles
- List of fallacies
- List of logicians
- List of paradoxes
- List of philosophers of language
- List of rules of inference
- For introductory set theory and other supporting material see the outline of discrete mathematics.
See also
- Mathematics
- Philosophy
- List of basic philosophy topics
- List of philosophy topics
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)
Logic Overview Academic
areas- Argumentation theory
- Axiology
- Critical thinking
- Computability theory
- Formal semantics
- History of logic
- Informal logic
- Logic in computer science
- Mathematical logic
- Mathematics
- Metalogic
- Metamathematics
- Model theory
- Philosophical logic
- Philosophy
- Philosophy of logic
- Philosophy of mathematics
- Proof theory
- Set theory
Foundational
concepts- Abduction
- Analytic truth
- Antinomy
- A priori
- Deduction
- Definition
- Description
- Entailment
- Induction
- Inference
- Logical consequence
- Logical form
- Logical implication
- Logical truth
- Name
- Necessity
- Meaning
- Paradox
- Possible world
- Presupposition
- Probability
- Reason
- Reasoning
- Reference
- Semantics
- Statement
- Substitution
- Syntax
- Truth
- Truth value
- Validity
Philosophical logic Critical thinking
and
Informal logicTheories of deduction Metalogic and metamathematics - Cantor's theorem
- Church's theorem
- Church's thesis
- Consistency
- Effective method
- Foundations of mathematics
- Gödel's completeness theorem
- Gödel's incompleteness theorems
- Soundness
- Completeness
- Decidability
- Interpretation
- Löwenheim–Skolem theorem
- Metatheorem
- Satisfiability
- Independence
- Type–token distinction
- Use–mention distinction
Mathematical logic General- Formal language
- Formation rule
- Formal system
- Deductive system
- Formal proof
- Formal semantics
- Well-formed formula
- Set
- Element
- Class
- Classical logic
- Axiom
- Natural deduction
- Rule of inference
- Relation
- Theorem
- Logical consequence
- Axiomatic system
- Type theory
- Symbol
- Syntax
- Theory
Non-classical logic - Degree of truth
- Fuzzy rule
- Fuzzy set
- Fuzzy finite element
- Fuzzy set operations
Logicians - Anderson
- Aristotle
- Averroes
- Avicenna
- Bain
- Barwise
- Bernays
- Boole
- Boolos
- Cantor
- Carnap
- Church
- Chrysippus
- Curry
- De Morgan
- Frege
- Geach
- Gentzen
- Gödel
- Hilbert
- Kleene
- Kripke
- Leibniz
- Löwenheim
- Peano
- Peirce
- Putnam
- Quine
- Russell
- Schröder
- Scotus
- Skolem
- Smullyan
- Tarski
- Turing
- Whitehead
- William of Ockham
- Wittgenstein
- Zermelo
Lists Topics - Outline of logic
- Index of logic articles
- Mathematical logic
- Boolean algebra
- Set theory
Other - Logicians
- Rules of inference
- Paradoxes
- Fallacies
- Logic symbols
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