Workshop: The Mathematical Turn in Philosophy
On 7–8 May 2026 we will host a workshop at the University of Warwick to inaugurate the AHRC–DFG project 'The mathematical turn in philosophy: measurement, computation, (de)idealization'. The workshop will also celebrate the 60th birthday of the University of Warwick and the Department of Philosophy.
The workshop will start on Thursday 7 May at 12:30, and finish on Friday 8 May at 17:00.
Registration is not required, but please email Benedict Eastaugh at benedict.eastaugh@warwick.ac.uk if you would like to attend the dinner on May 7.
Speakers
Andrew Arana (Université de Lorraine), Catrin Campbell-Moore (University of Bristol), Benedict Eastaugh (University of Warwick), Ben Ferguson (University of Warwick), Martin Fischer (LMU München), Juliet Floyd (Boston University), Volker Halbach (University of Oxford), Zuzana Haniková (Czech Academy of Sciences), Sam Sanders (Ruhr-Universität Bochum).
Programme
Thursday 7 May
| Time | Speaker | Title |
|---|---|---|
| 12:30 | Welcome | |
| 13:00 | Walter Dean | Opening remarks on the mathematical turn in philosophy |
| 13:30 | Volker Halbach | Incompleteness, Reflection, and Implicit Commitment |
| 14:30 | Catrin Campbell-Moore | Probabilities and finite entailment: the probability filter model of belief |
| 15:30 | Coffee | |
| 15:45 | Ben Ferguson | Moral maximisation |
| 16:45 | Benedict Eastaugh | Squeezing probabilism |
| 17:45 | ||
| 19:00 | Dinner |
Friday 8 May
| Time | Speaker | Title |
|---|---|---|
| 9:30 | Welcome | |
| 10:00 | Sam Sanders | Three topics in reverse philosophy |
| 11:00 | Coffee | |
| 11:15 | Andrew Arana | Varieties of reversals |
| 12:15 | Lunch | |
| 13:30 | Martin Fischer | Potentialist Unfolding and Idealizations |
| 14:30 |
Zuzana Haniková |
Feasibility and nonclassical mathematics |
| 15:30 | Coffee | |
| 15:45 | Juliet Floyd | Wittgenstein on Turing's 1936 Diagonal Argument: Variations on a Theme |
Abstracts
Catrin Campbell-Moore, Probabilities and finite entailment: the probability filter model of belief
I will present and discuss a model of belief taking seriously the idea that imprecise probability frameworks consider constraints on probabilities. By just requiring that these be closed under finite consequence, we result in a new model of imprecise probabilities, which I call the probability filter model. It is compatible with a version of regularity.
We show that finitary probabilistic logic of statements about comparative expectations results in exactly the usual axiomatisation in the so-called desirable gambles model of belief, showing the probabilistic underpinnings of that model as against the arguments against probability-based accounts due to their inability to capture appropriate behaviour when the sample space is infinite.
A prominent decision theory for imprecise probability is E-admissibility. We show how to apply it to this model and the axioms it results in.
I will also try to flag a challenge by applying this decision theory to the question of which decision theory to use. It seems to recommend following precise expected utility theory rather than its own imprecise recommendations.
Volker Halbach, Incompleteness, Reflection, and Implicit Commitment
When we accept a formal system S, we are implicitly committed also to statements partially or fully expressing the soundness of S in the language of S. This claim is a simple version of the Implicit Commitment Thesis (ICT). A paradigmatic example of a statement partially expressing soundness is the arithmetized consistency claim for Peano arithmetic with PA as S. I will try to sharpen ICT. In particular, I will investigate what exactly these additional statements are, what their relative strengths are, and what supports the claim that we are implicitly committed to them. I will consider less familiar systems as base theory S and present cases where the addition of soundness statements to an arithmetically sound system S leads to an inconsistency. Finally, I will consider the overall plausibility of ICT.
Zuzana Haniková, Feasibility and nonclassical mathematics
This talk will look into modelling the concept of feasible natural number, as discussed some decades ago by Yessenin-Volpin. A number is said to be feasible if one can count up to it. Feasible numbers are a natural example of a vague concept, and as such, susceptible to paradox. In particular, it seems a matter of common sense to admit that there are numbers that are not feasible, and perhaps we can even name some. On the other hand small natural numbers appear feasible and one can argue some closure properties for feasible numbers. To Yessenin-Volpin this was an initial consideration in a foundational programme, known as 'ultrafinitism' or 'strict finitism'. Dummett took up his work and provided an influential analysis of strict finitism, suggesting that it is coherent only if there are weakly infinite, weakly finite totalities, under definitions he provided for both notions. I will discuss how these notions may help to mediate the problem of modelling feasible numbers in Vopěnka's axiomatic Alternative Set Theory, a nonstandard and formally weak formal system with some but, as I will try to point out, not quite all suitable properties. I also plan to comment on competing ways of modelling feasible numbers, and on related applications of the term 'feasible'.
Sam Sanders, Three topics in reverse philosophy
We discuss the following applications of reverse mathematics in philosophy of mathematics:
- The role of the intensionality of computation: a well-known property of algorithms is argued to be as important as computational/logical strength in analysing philosophical arguments.
- Vagueness and the Axiom of Choice: how the Colyvan–Weber definition of vagueness depends on AC and related axioms.
- Countable sets and structuralism: we analyse the notion of "countable set" from the pov of structuralism and observe that the restrictions imposed by the latter keeps things inside predicativist math.