Date of Award
Doctor of Philosophy
Mary Beth Mader
This dissertation attempts to resolve a central problem in the metaphysics of science. This problem is the conflict in ontologies that our best scientific theories seem to imply. Our best scientific theories tell us that the universe and everything in it is contingent, changing, and finite. Yet this model of the universe cannot even be formulated without the tools of contemporary mathematics. The objects that mathematics describes are necessary, unchanging, and involve infinities. If we take the statements of mathematics literally, we find all sorts of fantastic objects which cannot possibly fit within the bounds of our scientific picture of reality. Therefore, simply populating our ontology with the objects implied by our best theories leaves us with a radically inconsistent picture of reality. To address this problem, this dissertation proposes a metaphysics of modality which makes possible the grounding of mathematical truths as necessary and eternal in a materialist and finitely bounded universe. The building blocks of this account come from the work of Gilles Deleuze and his metaphysics of the primacy of difference over identity. I argue for a modal interpretation of Deleuzes concepts of the virtual, the intensive, and the actual. I then explicate them in relation to a process of generation which can give rise to new objects and objective generalities, a process Deleuze calls individuation. This makes possible a grounding of the propositions of mathematics as expressions of this universe rather than as representations of it. This grounding allows one to then rightfully say that the objects mathematics describes are not a part of the ontology of this universe while still maintaining that mathematics can then be rightfully said to be true as a result of the structures of this universe. That is, the objects which mathematics describes (numbers, points, etc.) are not the objects which make mathematics true. What makes mathematics true is instead, the modal structure of difference itself.
Dissertation or thesis originally submitted to ProQuest
Ardoline, Michael J., "Difference and Necessity: Dispositionalism, Deleuze, and the Finite Genesis of Transfinite Truths" (2021). Electronic Theses and Dissertations. 2426.