A note on identity and higher-order quantification.
Title | A note on identity and higher-order quantification. |
Publication Type | Journal Article |
Year of Publication | 2009 |
Authors | Urbaniak, R |
Journal | Australasian Journal of Logic |
Volume | 7 |
Pagination | 48–55 |
Abstract | 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 Key | urbaniak2009note |