Abstract

I take some initial steps toward a theory of real definition, drawing upon recent developments in higher-order logic. The resulting account allows for extremely fine-grained distinctions (it can distinguish between any relata that differ in their syntactic structure, while avoiding the Russell-Myhill problem). It is the first account that can consistently embrace three desirable logical principles that initially appear to be incompatible: the _Identification Hypothesis_ (if _F_ is, by definition, _G_, then there is a sense in which _F_ is the same as _G_), _Irreflexivity_ (there are no reflexive definitions), and _Leibniz’s Law_. Additionally, it possesses the resources needed to resolve the paradox of analysis.