On the permissibility of impredicative comprehension

Øystein Linnebo, University of Oslo. Part of the logic seminar series.

Which comprehension axioms of higher-order logic are acceptable? It is well known that unrestricted higher-order comprehension is incompatible with unrestricted reification of higher-order entities. In search of a response to this conflict, an argument against all forms of impredicative comprehension is formulated. Although the argument is ultimately rejected, a careful analysis of it points the way to some milder logical restrictions, which suffice to resolve the conflict.

Øystein Linnebo, University of Oslo