On the Permissibility of Impredicative Comprehension
Øystein Linnebo · Oxford University Press eBooks · 2018
Which comprehension axioms of higher-order logic are acceptable? That is, under what conditions does a formula define a concept or circumscribe some objects? 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; for example, when defining a concept, we may not quantify over a totality to which this concept belongs. Although this predicativist argument is ultimately rejected, a careful analysis of it points the way to some milder logical restrictions, which suffice to resolve the conflict.