Workshop on Structuralism and Fictionalism in Mathematical Practice

Workshop on Structuralism and Fictionalism in Mathematical Practice

University of York, Department of Philosophy

May 27, 2022

About the workshop:

The abstract character of mathematics raises difficult philosophical questions as to the nature and existence of mathematical entities, such as numbers, functions, sets, groups, graphs, and number systems.  This workshop will explore such questions from the perspective of two different traditional approaches, viz. “mathematical structuralism” and “mathematical fictionalism”. The main objective of the workshop is to re-evaluate these perspectives on the foundations of mathematics within the context of mathematical practice.  Specifically, the following research questions will be addressed in the workshop:

- Do either structuralism or fictionalism offer a philosophically viable foundation for modern mathematics?

- To what extent are structuralism and fictionalism faithful to mathematical practice?

- How do mathematicians think about meaning, reference, and truth in mathematics?

Location:

The Treehouse

Humanities Research Centre

Berrick Saul Building

University of York

Heslington

York  YO10 5DD

UK

We will also aim to offer online participation.

Time: 27 May 2022, 10:00 - 17:30

Tentative Programme:

10:00 - 10:15 Welcome

10:15 - 11:30 Paola Cantù (Aix-Marseille) - Peano’s views about meaning and their relation to structuralism

11:30 - 12:00 Coffee

12:00 - 13:15 John Wigglesworth (York) - Practice-based philosophy of mathematics

13:15 - 14:30 Lunch

14:30 - 15:45 José Ferreirós (Sevilla) - A conceptualist take on structuralism

15:45 - 16:15 Coffee

16:15 - 17:30 Concha Martínez Vidal (Santiago de Compostela) - An answer to the fictionalist from a metaontologically-minimalist perspective

19:00 Dinner

Participation Cost:

Free admission. Everybody is welcome. Coffee and lunch will be provided. 

Registration:

If you are interested in participating, either in person or online, please register your interest by sending an email to [email protected] .

Organizers:

Mary Leng and John Wigglesworth

University of York, Department of Philosophy

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 890376.