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Logicism

Definition

In philosophy of mathematics, logicism is a school of thought comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano.

Related concepts

A priori and a posteriori Abraham Fraenkel Absorption (logic)Abstract logic Abstract object theory Abstract structuralism Ackermann set theory Aleph number Alfred North Whitehead Alfred Tarski Algebra Algebraic logic Alphabet (formal languages)Ambiguity Analysis Analytic philosophy Antithesis Argument Aristotelian realist philosophy of mathematics Arithmetic Arity Associative property Asymmetric relation Atomic formula Atomic model (mathematical logic)Atomic sentence Augustus De Morgan Automata theory Automated theorem proving Axiom Axiom of choice Axiom of infinity Axiom of pairing Axiom of reducibility Axiom schema Axiom schema of replacement Axiom schema of unrestricted comprehension Axiomatic metaphysics Axiomatic set theory Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Basic Law V Begriffsschrift Belief Bernard Bolzano Bertrand Russell Bias Biconditional elimination Biconditional introduction Bijection Binary operation Bob Hale (philosopher)Boolean algebra Boolean algebras canonically defined Boolean function Boolean logic Calculus of relations Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinal number Cardinality Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Charles Sanders Peirce Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Commutativity of conjunction Compactness theorem Complement (set theory)Complete theory Computability theory Computable function Computable set Computably enumerable set Concrete category Conjunction elimination Conjunction introduction Connected relation Conservative extension Consistency Constructible universe Construction of the real numbers Constructive dilemma Constructive set theory Constructivism (philosophy of mathematics)Continuity (mathematics)Continuum hypothesis Contradiction Countable set Credibility Crispin Wright Critical thinking David Hilbert De Morgan's laws Decidability (logic)Decision problem Dedekind Dedekind cut Deductive reasoning Deductive system Destructive dilemma Diagram (mathematical logic)Dialectic Dialetheism Diogenes Laërtius Disjunction elimination Disjunction introduction Disjunctive syllogism Distributive property Domain of a function Double negation elimination Double negation introduction Edward N. Zalta Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Empiricism Empty set Enumeration Epistemic Epistemology Equiconsistency Equivalence relation Ernst Schröder (mathematician)Euclid's Elements Euclidean geometry Evidence Existential generalization Existential instantiation Existential quantification Existential quantifier Explanation Explanatory power Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Fact Fallacy Felix Hausdorff Fictionalism Finitary relation Finite-valued logic Finite model theory Finite set Finitism First-order logic Fixed-point logic Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formalism (mathematics)Formalism (philosophy of mathematics)Formation rule Foundationalism Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Frege Function (mathematics)Function and Concept Functional predicate Fuzzy set General set theory Geometry Georg Cantor George Boole Giuseppe Peano God Gottlob Frege Grattan-Guinness Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Henri Poincaré Henry M. Sheffer Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Hugh MacColl Hume's principle Hypothesis Hypothetical syllogism Idealism If and only if Image (mathematics)Impredicative Impredicativity Inaccessible cardinal Inconsistency Independence (mathematical logic)Inference Infinite-valued logic Infinite regress Infinite set Infinity Informal logic Information theory Inhabited set Injective function Inquiry Integer Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Intuitionism Irrational number Isomorphism Ivor Grattan-Guinness J. Barkley Rosser Jan Łukasiewicz Kant Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Kuratowski Kuratowski ordered pair Kurt Gödel Lambda calculus Large cardinal Law of excluded middle Law of noncontradiction Leibniz Lemma (mathematics)Leopold Kronecker Lindström's theorem List of Hilbert systems List of axioms List of fallacies List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logical atomism Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Louis Couturat Ludwig Wittgenstein Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Material conditional Material implication (rule of inference)Mathematical induction Mathematical logic Mathematical object Mathematical proof Mathematics Metalanguage Minimal axioms for Boolean algebra Modal logic Model complete theory Model theory Modus ponendo tollens Modus ponens Modus tollens Monadic predicate calculus Monadic second-order logic Monotonicity of entailment Morse–Kelley set theory NP (complexity)Naive set theory Natural deduction Natural number Negation Negation introduction New Foundations Nominalism Nominalistic Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Norbert Wiener Number theory Occam's razor Ontology Open formula Operation (mathematics)Opinion Ordered pair Ordinal analysis Ordinal number P (complexity)P versus NP problem Paradoxes of set theory Partition of a set Peano's axioms Peano axioms Philosophical analysis Philosophical logic Philosophical razor Philosophical realism Philosophy Philosophy of mathematics Philosophy of science Plato Platonic realism Platonism Power set Pragmatism Predicate (mathematical logic)Predicate logic Predicate variable Premise Prime model Primitive notion Primitive recursive arithmetic Primitive recursive function Principia Mathematica Principle of bivalence Principle of explosion Problem of multiple generality Proof of impossibility Proof theory Propaganda Proposition Propositional calculus Propositional formula Propositional variable Prudence Pure mathematics Quantifier (logic)Quantifier rank Rational number Rationalism Real number Reason Recursion Recursive set Reductio ad absurdum Reduction (philosophy)Relation (mathematics)Relevance Reverse mathematics Rhetoric Richard Dedekind Rigour Robinson arithmetic Ronald Jensen Rudolf Carnap Rule of inference Russell's paradox Russell paradox Satisfiability Saturated model Schröder–Bernstein theorem Science Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics Semantics of logic Sentence (logic)Sentence (mathematical logic)Sequent calculus Set (mathematics)Set theory Sheffer's stroke Signature (logic)Singleton (mathematics)Skolem arithmetic Socratic method Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Stanford Encyclopedia of Philosophy Stanford School Stephen Cole Kleene Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Subset Substitution (logic)Substructure (mathematics)Supertask Surjective function Syllogism Symbol (formal)Symbolic logic Syntax Syntax (logic)T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic The Foundations of Arithmetic The Principles of Mathematics Theorem Theories of truth Theory Theory (mathematical logic)Thing-in-itself Three-valued logic Timeline of mathematical logic Tractatus Logico-Philosophicus Transfer principle Transitive relation Transitive set Transposition (logic)True arithmetic Truth function Truth predicate Truth table Truth value Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Unity of opposites Universal generalization Universal instantiation Universal quantification Universal quantifier Universal set Universe (mathematics)Urelement Vagueness Validity (logic)Variable (mathematics)Venn diagram Von Neumann ordinal Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Willard Van Orman Quine Wittgenstein World Congress of Philosophy ZFC Zermelo–Fraenkel set theory

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