impredicative definitions
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impredicative definition — Term coined by Poincaré ; for a kind of definition in which a member of a set is defined in a way that presupposes the set taken as a whole. Poincaré believed that paradoxes like those of Russell and the barber were due to such definitions, and… … Philosophy dictionary
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
Impredicativity — In mathematics and logic, impredicativity is the property of a self referencing definition. More precisely, a definition is said to be impredicative if it invokes another set which contains the thing being defined.Russell s paradox is a famous… … Wikipedia
Morse–Kelley set theory — In the foundation of mathematics, Morse–Kelley set theory (MK) or Kelley–Morse set theory (KM) is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory … Wikipedia
Definition — Eine Definition (lateinisch definitio = Abgrenzung aus de = ab/weg und finis = Grenze) ist je nach der Definitionslehre, der hierbei gefolgt wird, entweder 1. eine Bestimmung des Wesens einer zu erklärenden Sache oder 2. eines Begriffs oder… … Deutsch Wikipedia
Henri Poincaré — Infobox Scientist box width = 300px name = Henri Poincaré image size = 250px caption = Jules Henri Poincaré (1854 1912). Photograph from the frontispiece of the 1913 edition of Last Thoughts. birth date = birth date|df=yes|1854|4|29 birth place … Wikipedia
Brouwer-Hilbert controversy — A foundational controversy in twentieth century history of mathematics opposed L. E. J. Brouwer, a supporter of intuitionism, and David Hilbert, the founder of formalism.BackgroundThe background for the controversy was set with David Hilbert s… … Wikipedia
Théorie des ensembles de Morse-Kelley — La théorie des ensembles de Morse Kelley (parfois abrégée en MK) est une théorie axiomatique exprimée en premier ordre dont les objets sont des classes, c est à dire des ensembles en un sens proche de celui de la théorie des ensembles de Zermelo… … Wikipédia en Français
ЗИХ — (Zieh), Отакар (р. 26 мая 1908). – чеш. логик, д р филос. наук (с 1960), профессор (с 1958) филос. ф та Карлова ун та. Науч. труды З. посвящены методологии естеств. и точных наук ( Логические и методологические аспекты эксперимента , 1957, рус.… … Философская энциклопедия
Russell's paradox — The most famous of the paradoxes in the foundations of set theory, discovered by Russell in 1901. Some classes have themselves as members: the class of all abstract objects, for example, is an abstract object. Others do not: the class of donkeys… … Philosophy dictionary
