Dates: **11-13 May 2022**

**Organization: **the Centre for Logic and Philosophy of Science (Ghent University)

**Workshop chairs:** Erik Weber & Karim Zahidi.

**Local organising team:** Kristian Gonzalez Barman, Pawel Pawlowski, Qianru Wang, Erik Weber & Karim Zahidi.

## Topic

The relationship between mathematics and science continues to be of considerable philosophical interest. Within contemporary philosophy of science, for example, pinpointing the exact role of mathematics in the sciences remains a hotly debated issue. Does mathematics play a mere inferential role in that it allows for the derivations of one substantial truth from another or is mathematics more than a ‘theoretical juice-extractor’? Are there distinctive mathematical explanations of physical phenomena? Similar questions can be asked about the role of logic in science.

These issues connect with discussions within the philosophy of mathematics (and the philosophy of logic) concerning the nature of mathematics (or logic). Within the philosophy of mathematics, Platonists, nominalists and structuralists consider mathematics to be fundamentally different in kind from empirical science, while empiricists have argued that mathematics is, just like other sciences, fundamentally about aspects of the empirical world. Different positions within the debate about the nature of mathematics will, arguably, lead to different answers to the question as to how mathematics and science are related.

In this workshop we want to focus on how these different philosophies of mathematics fare in giving an account of mathematical practice and the role of mathematics in scientific practice.

Examples of topics of interest therefore include (but are not restricted to):

– How do we get mathematical knowledge?

– What is the role of sensory perception in mathematics?

– Can there be mathematical experiments? If so, how do they relate to experiments in other disciplines?

– What is (are) the role(s) of proof in mathematics?

– What is the epistemic role of mathematical communities (dependence, peer review, joint commitments, …)?

– Are there explanations in mathematics? Are mathematical explanations similar to scientific explanations?

– Are there distinctively mathematical explanations in science?

– What is the role of aesthetic virtues (beauty, symmetry, simplicity, …) in mathematical practice?

– What role does mathematics play in empirical science?

– Does empirical science play any role in mathematics?

– How can mathematics be successfully applied in empirical science and engineering?

We welcome contributions that approach these (and related) topics either from a systematic or a historic angle. In other words, we welcome contributions that elaborate and defend your own position, but also contributions that discuss the views that philosophers and scientists had on these topics in the past.

## Keynote speakers

Joachim Frans (Vrije Universiteit Brussel)

Valeria Giardino (Institut Jean Nicod – Paris)

Victor Gijsbers (Leiden University)

## Abstract submission

We welcome submissions on any topic that fits into the scope as described above. Send your abstract of 300 to 500 words to: lrr@ugent.be before **18 October 2021**. Notification of acceptance: 25 October 2021.

## Programme

**Day 1 (Wednesday 11 May)**

13:30-14:00 *Registration*

14:00-15:10 Victor Gijsbers (Leiden University), *Causal Interventionism for Science, Grounding Interventionism for Mathematics?*

15:10-15:45: *Coffee Brea*k

15:45-16:30 Viktor Blasjo (Utrecht University), *The operationalist philosophy of ancient Greek geometry.*

16:30-17:15 Francesca Biagoli (Torino), *Mathematics in the relativization of the Kantian a priori: A reconsideration of Cassirer’s **functional account.*

17:15-18:00 Rami Jreige (Ecole Normale Supérieure), *How an Historical In Re account of mathematical Structuralism Sheds Light on Applicability*

19:00 *Diner*

**Day 2 (Thursday 12 May)**

09:30-10:40 Joachim Frans & Bart Van Kerkhove (Vrije Universiteit Brussel), *Exploring disagreements about explanatoriness in mathematics.*

10:40-11:00 *Coffee Break*

11:00-11:45 Karim Zahidi (Ghent University),*On the explanatory strength of proofs by mathematical induction.*

11:45-12:30 Ann Wyverkens (Ghent University), *The Intermediate Value Theorem: Proofs, Graphs, Narratives and Explanations*

12:30-13:30 *Lunch Break*

13:30-14:15 Robert Knowles (The University of Bristol), *Distinctively mathematical explanation: A deflationary proposal*

14:15-15:00 Jose Perez Escobar (ETH Zürich), *Paradigmatic examples of “genuine mathematical explanations” in biology are only indicative of mathematical *

* heuristics.*

15:00-15:45 Kristian Campbell Gonzalez Barman (Ghent University), *Distinctively Mathematical Explanations of physical facts? Some examples are dubious at best*.

15:45-16:15 *Coffee Break*

16:15-17:00 Erik Weber (Ghent University), *The weird metaphysics behind distinctively mathematical explanations.*

17:00-17:45 Lieven Decock (Vrije Universiteit Amsterdam), *Frege’s Theorem and mathematical cognition.*

**Day 3 (Friday 13 May)**

09:30-10:40 Valeria Giardino (Institut Nicod), * Experimenting with Triangles.*

10:40-11:00 *Coffee Break*

11:00-11:45 Michal Sochanski (Adam Mickiewicz University Poznan), *On the different ways of understanding “mathematical experiments”*

11:45-12:30 Matthew Garrett (University of Tilburg), *Deep Learning as Experimental Mathematics at Science’s Border.*

12:30-13:30 *Lunch Break*

13:30-14:15 Colin Rittberg (Vrije Universiteit Brussel), *On the epistemological relevance of the ethics of mathematics.*

14:15-15:00 Nicola Bonatti (LMU München), *Extremal axioms and the reflective equilibrium of intended models.*

15:00-15:45 Maria Martinez-Ordaz (Federal University of Rio de Janeiro), *Understanding (defective) mathematical theories.*

16:00 *Drinks*

## Venue

Royal Academy of Dutch Language and Literature (KANTL), Koningstraat 18, Ghent, Belgium.

## Registration

Registration will be possible from 1 November. The registration fee is 60€ and has to be paid in cash at the registration desk. Coffee, lunches and the workshop dinner are included in this fee.

## Book of abstracts