Workshop on Pragmatism in the Formal Sciences

Idea and Motivation

The workshop is intended to investigate the role pragmatist ideas can play in philosophical thinking about mathematics and its scientific applications. The event is part of the Cambridge–LMU Strategic Partnership project "Pragmatist approaches to the applicability of mathematics".

Speakers

Alexander Bird (Cambridge)
Wouter Cohen (LMU Munich)
Neil Dewar (Cambridge)
John Dougherty (LMU Munich)
Owen Griffiths (Cambridge)
Sophie Kikkert (LMU Munich)
Gabriel Târziu (LMU Munich)

Organizers

John Dougherty (MCMP, LMU Munich)
Neil Dewar (Cambridge)

Registration

In order to register for the workshop, please contact john.dougherty@lrz.uni-muenchen.de

Program

Day 1 (14.04.2025)
09:45-10:00	Opening
10:00-11:00	Alexander Bird: "The Duhem-Quine Thesis Refuted"
11:00-11:30	Coffee break
11:30-12:30	Sophie Kikkert: "Modelling Agentive Modality: What's the Use?"
12:30-14:30	Lunch break
14:30-15:30	Owen Griffiths: "Inferentialism and Identity"
15:30-16:00	Coffee break
16:00-17:00	Wouter Cohen: "Carnapian pragmatism and neo-logicism"
19:00	Workshop dinner

 

Day 2 (15.04.2025)
11:00-12:00	Gabriel Târziu: "Accounting for the role of mathematics in science – A (tentative) pragmatist perspective"
12:00-14:00	Lunch break
14:00-15:00	John Dougherty: "Two varieties of scientific anti-realism"
15:00-15:30	Coffee break
15:30-16:30	Neil Dewar: "What conventionalism demands"

Abstracts

Alexander Bird: The Duhem-Quine Thesis Refuted

I refute the Duhem–Quine Thesis thus. Let a set of hypotheses be collectively responsible for a prediction that is falsified by scientific in‐ vestigation. If one accepts the possibility of scientific knowledge then there is a clear rule that can be used, in the right circumstances, to de‐ termine which hypothesis to reject: ”If all but one of the hypotheses are known to be true, then reject the one hypothesis that is not known to be true”.

Sophie Kikkert: Modelling Agentive Modality: What's the Use?

Agentive modality is often characterised in terms of an agent’s behaviour across some (set of) relevant possible world(s). Notable formalisations include the Modal Analysis (Lewis 1976; Kratzer 1977) and refinements of the Conditional Analysis (e.g., Mandelkern et al. 2017). Recently, analyses of this type have been challenged on the grounds that they fail to provide a reductive account of agentive modality (Maier 2022; Kearl and Wallace 2024). This is thought to constitute a problem not just for possible-worlds analyses as accounts of agentive modality, but also for theories that appeal to agentive modality (understood in terms of what an agent does across other possible worlds) to explain other phenomena.

If these criticisms are correct, this has far-reaching consequences. Agentive modality has been invoked to explain a wide range of philosophically and scientifically interesting issues, including causation, the openness of the future, and conceivability. In addition, philosophers have appealed specifically to modal and conditional analyses of ability to shed light on the possibility of time travel, and free will.
In this talk, I examine what role possible-worlds ‘analyses’ of agentive modality play in our broader philosophical and practical reasoning. What use do they have? The answer to this question affects whether arguments purporting to show that possible-worlds analyses fail as reductive accounts of ability also undermine their potential to help clarify other phenomena.

Owen Griffiths: Inferentialism and Identity

Inferentialists—whether global or logical—will typically want the identity predicate to count as a logical constant. By inferentialist standards, this requires that identity must be capable of harmonious formulation. There’s a problem here from the start: the introduction-rule for identity expresses its reflexivity and its elimination-rule expresses the indiscernibility of identicals, so they appear nothing alike. Stephen Read, Ansten Klev and others have attempted to give identity harmonious formulation but I argue that such attempts fail—a significant problem for inferentialists.

Wouter Cohen: Carnapian pragmatism and neo-logicism

Hume’s Principle, which is the principle on which neo-logicists wish to build arithmetic, is an abstraction principle. Many abstraction principles are unacceptable to the neo-logicist, for instance because they are inconsistent or because they are inconsistent together with Hume’s Principle. What differentiates Hume’s Principle from these unacceptable abstraction principles? This question, which captures the so-called bad company objection, has proved difficult to answer. In this paper, I draw on the philosophy of Rudolf Carnap to develop a Carnapian neo-logicism. I show how the Carnapian neo-logicist can deal relatively straightforward with the bad company objection, namely on pragmatic grounds. In particular, the Carnapian sees value in Hume's Principle because it elucidates the applicability of arithmetic in a way that other foundational systems of arithmetic do not---in this way, having Hume's Principle as a foundation to arithmetic avoids endless philosophical controversies about applicability. The problematic principles are not inherently wrong or incorrect, they just aren't similarly useful. I finally argue that a similar pragmatic consideration motivates the Carnapian to treat Hume's Principle as analytic within their scientific frameworks.

Gabriel Târziu: Accounting for the role of mathematics in science – A (tentative) pragmatist perspective

The aim of this talk is to present a tentative pragmatist account of the utility of mathematics in science. Most commonly, the problem of applicability has been framed as a question of how mathematics "hooks onto" something extra-mathematical, such as a part of the physical world. Many recent answers to this question (e.g., Bueno & Colyvan 2011; Bueno 2016; Bueno & French 2018; Pincock 2004, 2007, 2011; Nguyen & Frigg 2017) can be broadly subsumed under the umbrella term "mapping accounts." These accounts hold that mathematics applies to the physical world by virtue of there being some kind of mapping between a mathematical structure and a physical system, allowing us to learn about the latter from the mathematics, much like we learn about a city by studying its map (Bueno & Colyvan 2011, p. 346).

In this talk, I aim to challenge this way of thinking about the role of mathematics in science and propose an alternative grounded in three pragmatist strands: anti-representationalism, instrumentalism, and pluralism. My account is based on the following claims: (a) mathematics (interpreted or not) doesn't represent anything in the world, and so the problem of applicability is ill-conceived in terms of how it is possible for mathematics to "hook onto" something extra-mathematical; (b) instead of "representation," our inquiry into the epistemic significance of mathematics in science should be based on something that takes into account (i) the dynamic and self-correcting nature of knowledge, and (ii) the fact that nature “does not set the standards for significance” (Kitcher 2015, p. 485), rather, these standards are derived from our practical interactions with the world and other people; (c) there can be a plurality of “correct” ways to think about the physical world.

John Dougherty: Two varieties of scientific anti-realism

I distinguish between two strands of the scientific realism debate. Borrowing a distinction from James Conant, I call them the "Cartesian" and "Kantian" problematics. The Cartesian problematic concerns the truth of our scientific theories. Realism in this problematic attempts to answer a skeptical worry presented by a certain kind of example (as in the pessimistic meta-induction). By contrast, the Kantian problematic concerns the objective purport of our scientific theories. Realism in this problematic attempts to resolve a boggle over how scientific theories can so much as be about the world. I argue that philosophy of science has been dominated by the Cartesian problematic since the 1980s, and I suggest that this is explained by certain assumptions about applied mathematics. I also argue that some recent non-representationalist work in the philosophy of physics is best understood as addressing the Kantian problematic.

Neil Dewar: What conventionalism demands

Conventionalism can seem puzzling, because it appears to be appropriate only in circumstances where (a) there is a choice to be made between two options, and (b) that choice is somehow “empty”, since choosing between the options is a matter of mere pragmatic convention. In this paper, I propose a straightforward account of the circumstances under which (a) and (b) are true, and hence in which conventionalism might be appropriate: when we are faced with pairs of theories that are inconsistent but equivalent. The inconsistency gives rise to the need for choice (as per (a)), and the equivalence gives rise to the choice’s emptiness (as per (b)). I illustrate this with various examples, discuss how this distinguishes the conventionalist from their opponents, and compare my treatment to other recent discussions in the literature.