Abstract

Informally speaking, the Principle of Identity, one of the so-called “Laws of Logic”, grants us in one of its most well-known formulations that every object is identical to itself. Non-reflexive logics, roughly speaking, are systems of logic in which this principle is not valid in general. One of the problems associated with non-reflexive logics concerns quantification: it has been argued that quantification only makes sense if we presuppose the identity concept, and consequently, non-reflexive logics employing quantifiers presuppose some form of the principle of identity we wanted to restrict in their formulation. In this paper we argue that it is possible to make sense of quantification in non-reflexive logics without presupposing identity. We argue both from a syntactical as well as from a semantical point of view. We close the paper with some reflections on natural language and its relation to non-reflexive logics.