Logic & Philosophy of Science Colloquium

Paolo Mancosu
U.C. Berkeley

"The varieties of mathematical explanation"

Contemporary work in scientific explanation has pursued to a great extent the project of a single unified account of the nature of explanation. Unfortunately, the drive towards unfication has also left by the wayside an important number of phenomena. In particular, many theories of scientific explanation do not address mathematical explanation, either because they rule mathematical explanations out of court from the outset or because they hold that their account of explanation automatically takes care of mathematical explanation. In this paper we begin by providing evidence for the claim that mathematicians seek explanations in their ordinary practice and cherish different types of explanations. We go on to suggest that a fruitful approach to the topic of mathematical explanation would consist in providing a taxonomy of recurrent types of mathematical explanation and then trying to see whether these patterns are heterogeneous or can be subsumed under a general account. We maintain that mathematical explanations are heterogeneous. However, neither giving the taxonomy nor arguing for the previous claim is what we have set for ourselves in this paper. Rather, we would like to provide a single case study of how to use mathematical explanations as found in mathematical practice to test theories of mathematical explanation. This can be seen, as it were, as a case study of how to show that the variety of mathematical explanations cannot be easily reduced to a single model. The case study will focus on Steiner's theory of mathematical explanation and Pringsheim's explanatory proof of Kummer's convergence criterion in the theory of infinite series.

Friday, May 2, 2003
SST 777
3 pm

Refreshments will be served