JOHN
WIGGLESWORTH
FICTIONALIST MATHEMATICAL STRUCTURALISM
A Marie Skłodowska-Curie project at the University of York
The main goal of this research project is to establish a comprehensive approach to the philosophy of mathematics that draws on mathematical practice. The abstract character of mathematics raises difficult philosophical questions about the nature of mathematical entities (such as numbers, functions, and sets), how we have knowledge of such entities, and how they can be applied in the real world. This research project tackles such questions by integrating two perspectives on the philosophy of mathematics, viz. "mathematical structuralism" and "mathematical fictionalism". Crucially, this research will be informed and supported by interdisciplinary discussions of mathematical practice with mathematicians, mathematical scientists, and psychologists whose research focuses on mathematical cognition. Drawing on aspects of their research, this project will build a new and distinctive positive theory of the nature of mathematics. With this comprehensive theory established, the project will show how it can be deployed to make progress on long-standing problems in the philosophy of mathematics and the philosophy of science.
The project is located in the Department of Philosophy at the University of York.
Project Themes
Research on the project is based on three interrelated subprojects:
1. Structuralism and fictionalism in mathematical practice: The aim here is to explore the extent to which these approaches in the philosophy of mathematics align with mathematical practice.
2. A fictionalist theory of mathematical structure: Building on the previous investigations, this subproject develops versions of structuralism, based on structural abstraction principles, that are nominalistically acceptable.
3. Applications of fictionalist mathematical structuralism: With a comprehensive fictionalist theory of mathematical structure in hand, this subproject focuses on applications of this theory to problems in the philosophy of mathematics and the philosophy of science.
Publications
Wigglesworth, J. Review of Conceptions of Set and the Foundations of Mathematics By Luca Incurvati, Analysis 81, 1 (2021), Pages 184–189, https://doi.org/10.1093/analys/anaa089.
Schiemer, G., Wigglesworth, J. Structuralism and informal provability. Synthese 202, 55 (2023). https://doi.org/10.1007/s11229-023-04274-4.
Events
2024 - International Conference: Structuralism and Fictionalism in the Philosophy of Mathematics
University of York (and online via Zoom)
May 13 - 14, 2024
Confirmed speakers: Bahram Assadian (University of Leeds), Otávio Bueno (University of Miami), Jessica Carter (Aarhus University), Ludovica Conti (IUSS Pavia), Elaine Landry (University of California, Davis), Mary Leng (University of York), A. C. Paseau (University of Oxford), Georg Schiemer (University of Vienna), John Wigglesworth (University of York).
2022 - Workshop: Structuralism and Fictionalism in Mathematical Practice
University of York (and online via Zoom)
May 27, 2022
Confirmed speakers: Paola Cantù (Aix-Marseille Université), José Ferreirós (Universidad de Sevilla), Concha Martínez Vidal (Universidade de Santiago de Compostela), John Wigglesworth (University of York)