Much of the debate about the mathematical refutation of Zeno’s paradoxes surrounds the logical possibility of completing supertasks—tasks made up of an infinite number of subtasks. Max Black and J.F. Thomson attempt to show that supertasks entail logical contradictions, but their arguments come up short. In this paper, I take a different approach to the mathematical refutations. I argue that even if supertasks are possible, we do not have a non-question-begging reason to think that Achilles’ supertask is possible. The justification (...) for the possibility of Achilles’ supertask lies in the possibility of him completing other supertasks of the same kind, and the justification for the possibility of him completing these other supertasks lies in the possibility of him completing yet more supertasks ad infinitum. (shrink)

There has been a push in recent years to provide better explanations for how AIs make their decisions. Most of this push has come from the ethical concerns that go hand in hand with AIs making decisions that affect humans. Outside of the strictly ethical concerns that have prompted the study of explainable AIs (XAIs), there has been research interest in the mere possibility of creating XAIs in various domains. In general, the more accurate we make our models the harder (...) they are to explain. Go playing AIs like AlphaGo and KataGo provide fantastic examples of this phenomenon. In this paper, I discuss a non-exhaustive list of the leading theories of explanation and what each of these theories would say about the explainability of AI-played moves of Go. Finally, I consider the possibility of ever explaining AI-played Go moves in a way that meets the four principles of XAI. I conclude, somewhat pessimistically, that Go is not as imminently explainable as other domains. As such, the probability of having an XAI for Go that meets the four principles is low. (shrink)

In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...) of accommodating metaphysical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysical vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans' much-disputed argument that vague identities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better explanation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by degree theories. Advisor: Reina Hayaki. (shrink)