# Structuralism and Fictionalism in the Philosophy of Mathematics

ENV/005

University of York

York YO10 5DD

United Kingdom

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About the conference:

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 conference will explore such questions from the perspective of two different traditional approaches, viz. “mathematical structuralism” and “mathematical fictionalism”. The main objective of the conference is to re-evaluate these perspectives and to consider the relationship between them. Specifically, the following research questions will be addressed in the conference:

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

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

- What are the connections between the structuralist and fictionalist approaches to the philosophy of mathematics?

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

Provisional schedule:

Monday May 13th, 2024

09:45 - 10:00 Welcome

10:00 - 11:15 Otávio Bueno Why a Mathematical Fictionalist Should Be a Structuralist about Mathematics

11:15 - 11:45 Coffee break

11:45 - 13:00 Mary Leng and John Wigglesworth Fictionalist Mathematical Structuralism

13:00 - 14:30 Lunch break

14:30 - 15:30 Georg Schiemer What is implicit structure?

15:30 - 16:00 Coffee break

16:00 - 17:15 Elaine Landry Breaking Benacerraf

Tuesday May 14th, 2024

10:00 - 11:15 Bahram Assadian Cross-structural identities

11:15 - 11:45 Coffee break

11:45 - 12:45 Ludovica Conti Arbitrary Logicism and Structuralism

12:45 - 14:15 Lunch break

14:15 - 15:15 Alex Paseau Four Metaphysical Objections to Plenitudinous Platonism

15:15 - 15:45 Coffee break

15:45 - 17:00 Jessica Carter Structuralism in mathematical practice

Participation Cost: Free admission. Everybody is welcome.

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.

## Registration

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May 12, 2024, 11:00pm BST

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