Impredicative Definitions

Some articles on impredicative, impredicative definitions, definition:

Impredicativity - History
... Sets which do not meet the requirement are called impredicative ... Poincaré and Weyl argued that impredicative definitions are problematic only when one or more underlying sets are infinite ... Objection concerning nonpredicative definition" where he argued against "Poincaré (1906, p ...
Axiom Of Reducibility - Criticism of The Axiom of Reducibility - Stephen Kleene 1952
... discovery of the paradoxes, Russell excluded impredicative definitions by his ramified theory of types (1908, 1910)" ... Kleene observes that "to exclude impredicative definitions within a type, the types above type 0 are further separated into orders ... observes that "the logicistic definition of natural number now becomes predicative when the P in it is specified to range only over properties of a given order in case the property ...

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