HYPER-REF: A General Model of Reference for First-Order Logic and First-Order Arithmetic

Abstract In this article I present HYPER-REF, a model to determine the referent of any given expression in First-Order Logic (FOL). I also explain how this model can be used to determine the referent of a first-order theory such as First-Order Arithmetic (FOA). By reference or referent I mean the non-empty set of objects that the syntactical terms of a well-formed formula (wff) pick out given a particular interpretation of the language. To do so, I will first draw on previous work to make explicit the notion of reference and its hyperintensional features. Then I present HYPER-REF and offer a heuristic method for determining the reference of any formula. Then I discuss some of the benefits and most salient features of HYPER-REF, including some remarks on the nature of self-reference in formal languages.