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. / Master of Arts