Australasian Journal of Logic

TitleA note on identity and higher-order quantification.
Publication TypeJournal Article
Year of Publication2009
AuthorsUrbaniak, R
JournalAustralasian Journal of Logic

It is a commonplace remark that the identity relation, even though not expressible in a first-order language without identity with classical set-theoretic semantics, can be dened in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higher-order languages with set-theoretic semantics (where the variables range over all subsets of the domain) in which the identity relation is not denable. The point is that the denability of identity in higher-order languages not only depends on what variables range over, but also is sensitive to how predication is construed.

Citation Keyurbaniak2009note