axiom of reducibility

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• Axiom of reducibility — The axiom of reducibility was introduced by Bertrand Russell as part of his ramified theory of types, an attempt to ground mathematics in first order logic.The axiom of reducibility is introduced in number (chapter) *12 of Principia Mathematica… …   Wikipedia

• reducibility, axiom of — Axiom introduced by Russell and Whitehead in Principia Mathematica. In that system propositional functions are sorted into levels, as part of the ramified theory of types. The axiom says that for any function at any level there exists a formally… …   Philosophy dictionary

• reducibility — reducibility, axiom of …   Philosophy dictionary

• Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

• Logicism — is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.[1] Bertrand Russell and Alfred North Whitehead… …   Wikipedia

• Principia Mathematica — For Isaac Newton s book containing basic laws of physics, see Philosophiæ Naturalis Principia Mathematica. The title page of the shortened version of the Principia Mathematica to *56. The Principia Mathematica is a three volume work on the… …   Wikipedia

• List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …   Wikipedia

• Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… …   Wikipedia

• New Foundations — In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled New Foundations for …   Wikipedia

• List of philosophy topics (A-C) — 110th century philosophy 11th century philosophy 12th century philosophy 13th century philosophy 14th century philosophy 15th century philosophy 16th century philosophy 17th century philosophy 18th century philosophy 19th century philosophy220th… …   Wikipedia

• Philosophy of mathematics — The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of …   Wikipedia