Zack Garrett

There has been a sharp increase in the use of impossible worlds as theoretical tools for solving difficult philosophical problems. Some philosophers, however, warn against their use. For example, Timothy Williamson argues that impossible worlds should not be used in an analysis of conditionals because they do not provide a compositional semantics. In this paper, we set out to resolve some of the potential problems associated with impossible worlds, thereby providing justification for their uses in a variety of contexts and applications. Graham Priest provides two directives for an account of impossible worlds. We argue that Priest’s directives, and, thus, the traditional view on impossibility, overextend the class of impossible worlds. We argue that all worlds, possible or impossible, are describable and that nonsense cannot play a role in a proper description. So, putative worlds that include nonsense are not worlds at all, possible or impossible. The exclusion of nonsense sentences from worlds undermines Priest’s two directives, but by separating nonsense from impossibility, we can resolve many of the worries about the use of impossible worlds.

Epistemological accounts that make use of a safety condition on knowledge, historically, face serious problems regarding beliefs that are necessarily true. This is because necessary truths are true in all possible worlds, and so such beliefs can be safe even when the bases for the beliefs are epistemically problematic. The existence of such problematically safe beliefs would undermine a major motivation for the condition itself: the ability to evaluate how well a belief tracks the truth. This paper argues that incorporating impossible worlds into the evaluation of beliefs solves this problem, but only if the relevant account of impossible worlds entails that many impossible worlds are incredibly similar to the actual world. Further, the paper argues that, as a result of including impossible worlds, some philosophical beliefs are unsafe, and many more are potentially unsafe. But, it argues, even if this is the case, we can still make philosophical progress.

There has been a sharp increase in the use of impossible worlds as theoretical tools for solving difficult philosophical problems. Some philosophers, however, warn against their use. For example, Timothy Williamson argues that impossible worlds should not be used in an analysis of conditionals because they do not provide a compositional semantics. In this paper, we set out to resolve some of the potential problems associated with impossible worlds, thereby providing justification for their uses in a variety of contexts and applications. Graham Priest provides two directives for an account of impossible worlds. We argue that Priest’s directives, and, thus, the traditional view on impossibility, overextend the class of impossible worlds. We argue that all worlds, possible or impossible, are describable and that nonsense cannot play a role in a proper description. So, putative worlds that include nonsense are not worlds at all, possible or impossible. The exclusion of nonsense sentences from worlds undermines Priest’s two directives, but by separating nonsense from impossibility, we can resolve many of the worries about the use of impossible worlds.

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.

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.

Logical form is thought to be discovered by keeping fixed the logical constants and allowing the non-logical content in the sentence to vary. The problem of logical constants is the problem of defining what counts as a logical constant. In this paper, I will argue that the concept ’logical constant’ is vague. I demonstrate the vagueness of logical constancy by providing a sorites argument, thereby showing the sorites-susceptibility of the concept. Many prior papers in the literature on logical constants hint at this vagueness, but do not explore how theories of vagueness apply to logical constants. In the second half of this paper, I do just this. I consider approaches to logical constants that resemble nihilism about vagueness and more recent theories that relativize truth to precisifications. Finally, I argue that approaches that accept the potential indeterminate status of putative logical constants are preferable to nihilism or relativism about logical constancy.

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.