文章基本信息

标题：A Note on Identity and Higher Order Quantification
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作者：Rafal Urbaniak
期刊名称：Australasian Journal of Logic
印刷版ISSN：1448-5052
电子版ISSN：1448-5052
出版年度：2009
卷号：7
出版社：Philosophy Department, University of Melbourne
摘要：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 (where the variables range over all subsets of the domain) 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 ( Urbaniak 2006 ), where it has been proven that no actual axiomatization of Leśniewski’s Ontology determines the standard semantics for the epsilon connective.