About.

The event will take place via Zoom on Tuesday January 16, 2024

Explanation and understanding are central topics in the philosophy of science. This discipline has made important developments to account for the role explanations play in scientific activities. A current trend is that philosophers emphasize the relation between explanation and understanding, and stress the need for theories of scientific understanding. This events wants to bring together scientists from different fields tackling the question of mathematical explanations both: in the sense of explanation within mathematics as well as mathematical explanations in the sciences. 

You can see this event as an informal continuation of Explanation and Understanding in Mathematics which took place in December 2019 in Brussel and lead to the following issue of Axiomathes. It is clearly a continuation of the first iteration happening in 2022.

This event is part of the World Logic Day 2024 

Registration is free, but needs to be done. 

"What Kind of Understanding Do Explanatory Proofs Provide?" by Otávio Bueno

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"Explanation and the Methodology of Philosophy of Mathematical Practice" by William D'Alessandro 

Practice-based approaches to philosophy of mathematics have gone mainstream over the past several decades. This approach is perhaps nowhere more clearly on display than in recent work on mathematical explanation. But there’s been little sustained meditation, and still less any explicit consensus, on what exactly it means for philosophy to take practice seriously. What, for instance, counts as a mathematical practice in the relevant sense? Are some practices (or practitioners) more epistemically weighty than others? Which methods are acceptable for learning about mathematicians’ practices? As the banner of practice-based philosophy is taken up in increasingly diverse ways, the field’s lack of a clear common methodology has begun to make itself felt. In this talk, I review the methodological situation and suggest some ways forward, with the explanation debate as a guiding case study.

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"The Potential Explanatoriness of Examples in Mathematics" by Ellen Lehet

The philosophical discussion of intra-mathematical explanation has primarily focused on explanatory proof. It seems, however, that other forms of explanation naturally arise in the practice of mathematics. In this talk, I will focus on the use of examples within mathematical practice and will consider the ways in which examples may be explanatory. I will argue that when the main goal of mathematical explanation is understanding, examples play a crucial explanatory role. To do so, I will consider examples from both the practice of researching mathematics and of teaching mathematics.

The consideration of examples as potential sources of explanation will shed light on the overall nature of mathematical explanation and the significance it has for mathematical practice.

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"Explanatory proofs and their virtues" by Christopher Pincock
There are two views about how an explanatory proof relates to its explanatory virtues. According to what I call the traditional view, a proof explains due to an explanatory relevance relation obtaining between the proof and what is proven, and the virtues arise as symptoms of this relevance relation. What I call the virtue-based view reverses this order of analysis: a proof explains due to the proof exhibiting various explanatory virtues to a sufficient extent, and an explanatory relevance relation obtains as a consequence of the presence of these virtues. The virtue-based view is widely endorsed (Colyvan, Cusbert & McQueen 2018, D’Alessandro 2021, Wilhelm 2023). In this paper I raise three objections to the virtue-based view. First, to deliver a determinate class of explanatory proofs, it must somehow aggregate the virtues and clarify how a given combination is sufficient for a proof to be explanatory. This is not possible. Second, some of the virtues emphasized by defenders of the virtue-based view are tied to individuals, and so a virtue-based approach leads to an unacceptably subjectivist view of explanatory proof. Third, a virtue-based approach undermines the use of inference to the best explanation in pure mathematics. For IBE requires the traditional view that the virtues are symptoms of the presence of an explanatory relevance relation, which entails the truth of the assumptions of the proof. By making some combination of virtues sufficient for explanatory proof, the crucial link between explanation and truth is severed.

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