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 defined in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantifiers 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 in which the identity relation is not definable. The point is that the definability of identity in higher-order (...) languages not only depends on what variables range over, but also is sensitive to how predication is construed. This paper is a follow-up to , where it has been proven that no actual axiomatization of Leśniewski’s Ontology determines the standard semantics for the epsilon connective. (shrink)

With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...