class paradox

Philosophy dictionary. . 2011.

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  • Class (set theory) — In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) which can be unambiguously defined by a property that all its members share. The precise definition of class… …   Wikipedia

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  • class, logical — Sometimes used as a synonym for set . But a class is contrasted with a set in classical set theory. A class of things may answer to a condition but not form a set, if various restrictions designed to avoid the logical paradoxes are not met.… …   Philosophy dictionary

  • Cantor's paradox — In set theory, Cantor s paradox is the theorem that there is no greatest cardinal number, so that the collection of infinite sizes is itself infinite. Furthermore, it follows from this fact that this collection is not a set but a proper class; in …   Wikipedia

  • Russell's paradox — Part of the foundations of mathematics, Russell s paradox (also known as Russell s antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction.It might be assumed that, for any formal… …   Wikipedia

  • Raven paradox — The Raven paradox, also known as Hempel s paradox or Hempel s ravens is a paradox proposed by the German logician Carl Gustav Hempel in the 1940s to illustrate a problem where inductive logic violates intuition. It reveals the problem of… …   Wikipedia

  • Banach–Tarski paradox — The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3 dimensional space can be split into several non overlapping pieces, which can then be put back together in a different way to yield two identical …   Wikipedia

  • Epimenides paradox — Epimenides from Promptuarii Iconum Insigniorum The Epimenides paradox is a problem in logic. It is named after the Cretan philosopher Epimenides of Knossos (alive circa 600 BC), There is no single statement of the problem; a typical variation is… …   Wikipedia

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