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Impredicativity - Wikipedia

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In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that contains the thing being defined. There is no generally accepted precise definition of what it means to be predicative or impredicative. Authors have given different but related definitions. The opposite of impredicativity is predicativity, which essentially entails building stratified (or ramified) theories where quantification over a type at one 'level' results in types at a new, higher, level. A prototypical example is intuitionistic type theory, which retains ramification (without the explicit levels) so as to discard impredicativity. The 'levels' here correspond to the number of layers of dependency in a term definition. Russell's paradox is a famous example of an impredicative construction—namely the set of all set

Impredicativity - Wikipedia Jump to content From Wikipedia, the free encyclopedia Notion of self-reference in mathematics and philosophy In mathematics , logic and philosophy of mathematics , something that is impredicative is a self-referencing definition . Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that contains the thing being defined. There is no generally accepted precise definition of what it means to be predicative or impredicative. Authors have given different but related definitions.

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