Structure and Ontology: On Quine's Relational Theory of Object
Philosophy of Mathematics, Philosophy of Science, Philosophy of Logic, Metaphysics, and Recent History of Analytic Philosophy (particularly Quine)
The philosophy of mathematics is concerned, primarily, with the following three interrelated questions: What is the ontological status of mathematical objects, if there are any? What do mathematical statements mean? And, how do we come to know mathematical truths, if there are any? These questions are made especially difficult by the desire to make answers consistent with answers to the same questions in other domains, particularly science. Recently, the notion of structure has emerged as a key candidate for resolving many of the problems that arise when trying to answer the above questions systematically and in ways that are compatible with our naturalistic world view. Often, however, structuralist views run into issues analogous to those they try to resolve, particularly problems with “epistemic access” to their proposed ontologies (or modal claims). My project is aimed at explicating a version of structuralism proposed by W.V.O. Quine that I think offers a plausible solution to the issues that contemporary philosophers of mathematics face. Quine’s view is systematic and requires a detailed account of its epistemic and semantic foundations in order to fully understand. Thus, the first parts of the thesis will provide an analysis of Quinean naturalism, his naturalistic epistemology and his naturalistic account of meaning. This will be followed by a detailed account Quine’s theory of object. The problems that arise from Quine’s views on meaning and knowledge are remarkably similar to those that interest philosophers of mathematics. Consequently, his solution to these problems, i.e. his relational theory of object, is of deep interest. I will argue that Quine’s theory of object provides key insights into how we come to understand and know mathematical claims. Additionally, the solutions Quine provides for philosophers of mathematics are not different in kind from those available to the philosopher of science.
My PhD research is generously funded by The Monist: An International Journal in General Philosophical Inquiry and The University of Manchester School of Social Sciences. I completed my B.A. in philosophy at Wichita State University and my M.A. in philosophy at The University of Kansas.