Abstract

The objective of this dissertation is to determine whether a formalist interpretation of classical mathematics is tenable. We first argue that the best theories of linguistics and mathematics characterize both linguistic objects and mathematical objects as abstract. This eliminates one objection to a formalist construal of mathematics. These results are interesting in themselves, since they address and resolve a problem largely ignored by formalists: the ontological status of expressions. ;A second objection to formalism stems from Godel's work. He demonstrated that truth could not be identified with derivability within a formal system. However, it has been suggested that formalism need not be abandoned but can still be defended on epistemological grounds. We argue, to the contrary, that there is no epistemological motivation for formalism. ;Thus, while on the one hand we show that formalism is ontologically tenable, our demonstration that the objects of both mathematics and linguistics are abstract removes the epistemological motivation for formalism.