ramified theory of types

Philosophy dictionary. . 2011.

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  • types, theory of — Russell s own reaction to his paradox of the class of all classes that are not members of themselves (see Russell s paradox ) was to suggest that the definition is ill formed because it involves the illegitimate notion of ‘all classes’. If the… …   Philosophy dictionary

  • logic, history of — Introduction       the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic       There was a medieval tradition according to which the Greek philosopher …   Universalium

  • 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

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  • Maps of manifolds — A Morin surface, an immersion used in sphere eversion. In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they… …   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

  • Russell, Bertrand — ▪ British logician and philosopher in full  Bertrand Arthur William Russell, 3rd Earl Russell of Kingston Russell, Viscount Amberley of Amberley and of Ardsalla  born May 18, 1872, Trelleck, Monmouthshire, Wales died Feb. 2, 1970,… …   Universalium

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