Matt Sayball

In this paper, I analyze Kit Fine’s account of the logic and semantics of vagueness. The overall aim of Fine’s project is to develop an account of the logic and semantics of vague language which accommodates distinctive characteristics of vagueness including penumbral connections and higher-order vagueness. I begin Chapter 1 with a discussion of what vagueness is and is not. Next, I trace the development of supervaluationism, and summarize Kit Fine’s supervaluationism and specification space approach to vagueness. I also discuss the more salient features of vagueness and I discuss them in relation to specification space models. I close with a look at the logic of vagueness and the logic of higher-order vagueness. Chapter 2 deals with penumbrae and penumbral connections. I analyze Fine’s account of penumbral connections before arguing that his characterization of penumbral connections is too broad. Fine mistakenly identifies logically valid formulae and their instances as though they exhibited penumbral connections. After arguing that Fine’s misidentification of penumbral connections results in an analysis of penumbral connections which is built for too wide a notion of penumbral connections, I suggest a more refined characterization of penumbral connections. I take up higher-order vagueness in Chapter 3. I begin with an overview of some characterizations of higher-order vagueness. Next, I revisit Fine’s accounts of the D operator and higher-order vagueness. Lastly, I argue that higher-order vagueness is not a distinct feature of the vagueness of natural language, but, rather, it is an artifact resulting from the analysis of the vagueness of natural language.

Throughout the twentieth-century, philosophers of language and logic have produced massive amounts of literature on conditionals, and the issues involved continue to receive much scholarly attention today. In our daily lives, conditionals are commonly used in communication, in decision-making, and in drawing inferences. My project focuses on the syntax, semantics, and pragmatics of conditional statements in classical logic, modal logic, and ordinary English. The major issues that I take up include the classification, interpretation, and meaning(s) of conditional statements. Roughly the first half of my thesis focuses on the syntax and semantics of three conditionals of logic, namely, the material, strict, and counterfactual conditionals. After considering each of these individually, I acknowledge the many troubles that arise when each is analyzed philosophically. Next, in order to evaluate the pragmatics of ordinary English conditionals, I focus on H. P. Grice’s theory of conversational implicature. Here, too, several troubles arise. I proceed by presenting several philosophical accounts, all of which focus on the discrepancies between the material conditional and the ordinary English ‘if’. The study of the ordinary English ‘if’ led me to consider some ordinary English if-statements, the meanings of which are clearly not conditional. Although many philosophers recognize that there are non-conditional ordinary English uses of ‘if’, there is no comprehensive account to be found in the literature on conditionals. Hence, I produce the most comprehensive explanation of non-conditional if-statements, or pseudo-conditionals, that I am aware of. Lastly, I suggest a novel approach to conditionals designed to account for the classification and meaning of the conditional statements of logic and ordinary English.