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.