impredicative

In the following we shall make use of the convention according to which the adjective “intuitionistic” refers to those set theories, such as IZF, which are impredicative, while

Set Theory: Constructive and Intuitionistic ZF Crosilla, Laura 2009

(For instance, ˜the tallest boy in the class™ appears unproblematic despite being impredicative.)

Platonism in the Philosophy of Mathematics Linnebo, Øystein 2009

According to one notion, a definition is impredicative if it defines an object by reference to a totality which includes the object to be defined.

Set Theory: Constructive and Intuitionistic ZF Crosilla, Laura 2009

One such argument is suggested by Gödel, who claims that the legitimacy of impredicative definitions is best explained by the truth of some form of platonism, including something like our claim Independence

Platonism in the Philosophy of Mathematics Linnebo, Øystein 2009

It is said to be a provably consistent type-free extension of second-order logic, admitting impredicative definitions.

Tropes Bacon, John 2008

The description is of course impredicative, since it implicitly refers to all descriptions, including itself.

Self-Reference Bolander, Thomas 2008

Berry's paradox is another paradox based on an impredicative definition, or rather, an impredicative description.

Self-Reference Bolander, Thomas 2008

Very roughly, C is a higher order impredicative type theory, extending Girard's system F, a powerful second-order typed lambda calculus with abstraction on types which is suitable for representing proofs of impredicative intuitionistic second order logic.

Paradoxes and Contemporary Logic Cantini, Andrea 2007

Quantification over arbitrary types is legitimate and hence types are closed under impredicative comprehension, which is considered necessary for mathematics.

Paradoxes and Contemporary Logic Cantini, Andrea 2007

After the first forty years, the by-products of the paradoxes included axiomatizations of set theory, a systematic development of type theory, the foundations of semantics, a theory of formal systems (at least in nuce), besides the introduction of the dichotomy predicative/impredicative which was important for conceptual reasons, but also for the future of proof theoretical methods.

Paradoxes and Contemporary Logic Cantini, Andrea 2007