Realizability as a Kind of Truthmaking

Abstract

This paper is part of a larger project concerning potentiality in mathematics. The first and simplest case is the traditional Aristotelian notion of potential infinity. An issue much like that of truthmaking arises in our explication of one of the options for potential infinity, namely how to make sense of generalizations from that perspective.We use the traditional intuitionistic notion of realizability to resolve the issue, and to help settle the correct logic for one kind of potential infinity.