| In this dissertation, I defend unorthodox conceptions of continuity: I argue that they're both conceptually viable and philosophically fruitful. After a brief introduction in the first chapter, I argue in the second chapter that the standard conception of continuity---which comes to us from Georg Cantor and Richard Dedekind, and which uses the real numbers as a model---doesn't satisfy all of pretheoretic intuitions about continuity and indeed that no conception of continuity does. This opens up conceptual room for unorthodox conceptions of continuity. In the second chapter, I argue that an unorthodox conception of continuity based on infinitesimals---numbers as small as infinity is large---provides the basis for a novel account of contact: of when two material bodies touch. In the third chapter, I argue that two other unorthodox conceptions of continuity provide the basis for novel solutions to Zeno's paradox of the arrow. |
