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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**List of philosophy topics (R-Z)**— RRaRabad Rabbinic law Rabbinic theology Francois Rabelais François Rabelais race racetrack paradox racism Gustav Radbruch Janet Radcliffe Richards Sarvepalli Radhakrishnan radical Aristotelianism radical behaviourism radical feminism radical… … Wikipedia**Europe, history of**— Introduction history of European peoples and cultures from prehistoric times to the present. Europe is a more ambiguous term than most geographic expressions. Its etymology is doubtful, as is the physical extent of the area it designates.… … Universalium**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**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