Applicability of Mathematics: Explanation and Representation

I am very grateful to the British Academy for supporting this workshop, as part of the project Mathematics: The Unlikely Engine of Scientific Discovery.

Date: 12/12/2017

Location: University of Leeds, Botany House Research Room, 1.03

Provisional schedule:

9:30am: Coffee

10am: Rob Knowles (University of Leeds)

Title: Mathematics, Explanatory Generality, and Ontological Commitment

Abstract: There is a little-acknowledged assumption at the heart of the debate surrounding the ‘enhanced’ indispensability argument: that increasing explanatoriness is a matter of representing new explanatory features of reality. By providing a detailed analysis of the explanatory virtue that mathematics supposed to contribute–explanatory generality–I argue that this assumption is mistaken. Mathematics increases explanatoriness by making explanatory information that can be expressed non-mathematically easier for creatures such as ourselves to grasp and reason with. (This work has been developed in collaboration with Juha Saatsi.)

11: 30am: Daniel Kostic (IHPST, CNRS/Université Paris 1 Panthéon-Sorbonne)

Title: Asymmetries and Levels of Mathematical Dependencies in Distinguishing Explanatory and Representational Roles of mathematics in Topological Explanation

Abstract: I propose a heuristic for distinguishing explanatory and representational roles of mathematics in topological explanation, that is based on a simple question: Would any change in the network always change the global pattern of connectivity? I argue that, if a change in the network doesn’t affect a global pattern of connectivity, we are talking only about a representational role of mathematics. In this case, there is a causal asymmetry between the system and the particular mathematical values of topological properties. Conversely, a change in the network that changes the global pattern of connectivity, in an explanatorily relevant way, will have nothing to do with this sort of causal asymmetry. It has to do with mathematical asymmetries between different levels of mathematical dependencies.

13:00pm: Lunch (Provided by Opposite)

2:30pm: Mary Leng (University of York)

Title: Explanations by Constraint, Structural Explanations, and the Demand for Asymmetry

Abstract: TBA

4:00pm: Sorin Bangu (University of Bergen)

Title: Having your (Strawberry) Cake and Dividing it too. On ‘Distinctively’ Mathematical Explanations’

Abstract: In a recent book, Because without Cause (2017), Marc Lange proposes what he takes to be a new form of explanation – distinctively mathematical. I examine this proposal critically, as well as some of Lange’s specific examples, and I articulate a dilemma: either these explanations are old fashion causal, or they are no explanations at all. Along the way I will make several remarks on the kind of understanding one gets from scientific explanations involving mathematics in a seemingly indispensable way.

6:00pm: Drinks (The Reliance)