Abstract

This dissertation explores the relationship between our experience and knowledge of the infinite. The first chapter is a critical examination of Shaughan Lavine's project in Understanding the Infinite . Lavine argues that although we do not experience the infinite, we can explain how we acquire knowledge of the infinite by appeal to our experience of the indefinitely large. I argue that Lavine's proposal fails. ;In the second chapter I argue that, contrary to what Lavine and others have claimed, we can have "experiences of the infinite." In particular, I argue that we can have a perceptual illusion of an infinite sequence when we see certain pictures. ;In the third chapter, I argue that the experiences of the infinite discussed in the second chapter help us defend a central tenet of modal structuralism, namely the claim that there could exist infinitely many objects. In order to show that we have evidence for this modal claim, I explain how, in general, we can use pictures to establish that the depicted object could exist. I argue that upon seeing a picture, we can obtain evidence that a picture represents a "coherent" rather than an "incoherent" spatial configuration, and furthermore, that if we obtain evidence that a picture represents a coherent spatial configuration, we thereby obtain evidence that the depicted object could exist. I then use this "picture method" to show that by seeing a picture of an infinite sequence, we can obtain evidence for the modal claim that an infinite sequence could exist