This project is initially generously funded by the European Commission through a Marie Sklodowska-Curie Individual Fellowship (101063639).
Proposal Scheme : UKRI Postdoctoral Fellowships Guarantee
Proposal Type : Horizon Europe Guarantee MSCA Postdoctoral Fellowships 2021
Host Institute: University of Leeds, School of Philosophy, Religion and History of Science
Mathematics seems to be about abstract entities such as sets, numbers, lines, points, etc. But mathematical objects, if they exist, cannot be picked out by their role in the causal nexus of the universe: unlike ordinary objects, we cannot see, smell, or touch them. The abstract character of mathematical discourse raises long-standing philosophical questions concerning the nature and the identity of mathematical objects, and our capacity to gain knowledge of them. This research project aims to tackle such questions by offering a novel approach to the philosophy of mathematics that unifies two seemingly divergent perspectives: mathematical structuralism and abstractionism.
The project’s principal objectives can be summarized as follows:
1. Laying down the logical and mathematical foundations of abstractionist structuralism
2. Articulating the metaphysics of mathematical structures
3. Addressing the challenge of referential indeterminacy