FICTSTRUCT · Fictionalist Mathematical Structuralism
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2020-07-01 → 2024-05-29
- EU contribution
- €224,934
- Participants
- 1
- Scheme
- MSCA-IF
Lines connect the coordinator with its partners.
Results in brief
Fictionalist Mathematical Structuralism
This project addresses the abstract nature of mathematics and the philosophical questions surrounding the existence of mathematical entities such as numbers, functions, and sets. Traditionally, the philosophical perspectives of structuralism and fictionalism have offered competing views: realist, or ‘ante rem’, structuralism views mathematical theories as descriptions of abstract structures, while fictionalism denies the existence of these entities, treating mathematical discourse as fictional. This project has been implemented to develop a comprehensive theory of mathematical structure, based on the fictionalist approach, which can advance long-standing debates in the philosophy of mathematics and the philosophy of science. Understanding the nature of mathematical entities and the applicability of mathematics is crucial not only for philosophical inquiry but also for enhancing our comprehension of mathematical practice and its applications in science. Core objectives: 1. To develop a comprehensive theory of mathematical structure by integrating structuralism and fictionalism. 2. To advance debates in the philosophy of mathematics and the philosophy of science. 3. To promote interdisciplinary research and collaboration among philosophers, mathematicians, and scientists.
Data: CORDIS, © European Union
Project objective
Mathematics is ubiquitous throughout the sciences and in everyday language and thought. Its applications across all disciplines - science, economics, engineering, computing and more - are central to the future development of a robust, creative, and driven society. 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 in the philosophy of mathematics, viz. ""mathematical structuralism"" and ""mathematical fictionalism"". Both structuralism and fictionalism capture important aspects of how many working mathematicians approach their practice. But in contemporary philosophy of mathematics, structuralism and fictionalism are widely thought of as presenting competing views of the nature of mathematics. In contrast, this project will develop a new theory of mathematical structure that unifies structuralism and fictionalism, thereby shifting the debate and promoting new and fruitful lines of research in the philosophy of mathematics and mathematical practice. Crucially, this research will be informed and supported by interdisciplinary discussions of mathematical practice with mathematicians, mathematical scientists, linguists who work on meaning and reference, 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.""
Original text from CORDIS.
Participants
- UNIVERSITY OF YORK · YORK NORTH YORKSHIRECoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union