Abstract

I have two main objectives in this paper. First, I attempt to make sense of the Aristotelian notion of infinity or the notion of potential infinity. I show that the so-called notion of “potential infinity” should be understood as the notion of infinite potentialities. Second, I consider how well different theories of modality may fare as accounts of the notion of potential infinity. I discuss well-known theories of modality such as genuine modal realism, ersatz modal realism, and modalism. Then I introduce my own theory of modality, modal quantificationalism. I argue that only modal quantificationalism offers an adequate formulation of the notion of potential infinity.