Relational Possibility

Abstract

This dissertation consists of three papers. The first is about relational possibilities, which are possibilities that compare or otherwise relate things across worlds. We might say, for example, that Socrates could have been taller than he is or that the Athenians could have been happier than they are. The standard view is that such claims require quantification over further things like heights or degrees of happiness. But as we will see, this approach stands in the way of an especially promising strategy for doing science with only particles. In response, I develop and defend an alternative view that I call modal relationalism. According to the modal relationalist, modality is ultimately about how things could have differed, not just how things could have been, and so can naturally accommodate the needed comparisons without quantifying over further things.

The second paper presents a paradox: Counterfactuals are somewhat tolerant. Had Socrates been at least six feet tall, he need not have been exactly six feet tall. He might have been a little taller. He might have been six-foot one or six-foot two. But while counterfactuals are somewhat tolerant, they are also bounded. Had Socrates been at least six feet tall, he would not have been a thousand feet tall, for example. Surprisingly, given these simple assumptions, we can prove a flat contradiction using principles validated by our best semantic theories. These include the familiar similarity analysis from David Lewis. After sketching the paradox, I describe what I think is the solution.

The last paper is a kind of technical companion to the first. It describes a hierarchy of multi-dimensional quantified modal languages that are modeled using a corresponding hierarchy of multi-dimensional Kripke models. We then show how to build multi-dimensional proof systems and prove completeness. This is relevant to the first paper because, if modal relationalism is true, then we are going to need an appropriate multi-dimensional modal language. This third paper shows that such languages are in good working order from a certain technical perspective.