Research: Christopher Pincock

Last update: October 13, 2015

Current Research

My primary research project considers the role of mathematics in science. Mathematics is prominent throughout our best scientific practices, and yet the point of this central place is poorly understood and often generates conceptual confusion. I approach this daunting issue in three complementary ways.
Scientific representation: Mathematical concepts provide some of the best tools for effectively representing phenomena of scientific interest. I argue that the most important contribution that mathematics makes to representation is in terms of facilitating scientific knowledge. That is, in several different ways, using mathematics to represent target systems allows a scientist to know more about those target systems. One way that this can happen is tied to the precise way that mathematics allows one to limit and calibrate the claims being made about some phenomenon. This epistemic approach to mathematized science raises several questions. Can we develop a general account of how models represent that includes mathematical models and other kinds of models like concrete scale models? Also, what sort of scientific knowledge is possible using mathematical models, given that they are highly idealized and of limited scope? My current research on representation is focused on these issues.
Scientific explanation: One of the aims of science is to understand why some phenomenon occurs, and not just to accurately describe how it occurs. Mathematics is often central to a scientific explanation, and yet this apparently indispensable role for mathematics in explanation continues to generate philosophical controversy. I claim that there are some distinctively "abstract" scientific explanations where the mathematics is not representing causes, but instead generating an informative classification of physical systems. At the same time, I reject so-called indispensability arguments for mathematical platonism based on an analysis of the necessary conditions for inference to the best explanation (IBE). My current work on explanation builds on these commitments. I aim to develop an account of scientific explanation that permits several kinds of explanations. A second project here is to refine and improve on Lipton's model of IBE. I argue that IBE can generate knowledge only if it operates under stringent constraints. This limited form of IBE can license belief in the existence of unobservables like atoms, and yet is unlikely to generate support for abstract objects.
Scientific change: The history of science includes many non-cumulative, revolutionary changes in theories, methods and values. In some cases, mathematical concepts survive these changes, and this has suggested some special place for mathematics in understanding scientific change. I argue that scientists have improved their understanding of the costs and benefits of deploying mathematics. This means that one must consider how a mathematical tool is being used in some context in order to predict how that tool will fare in future science. This research project is informed by a series of historical case studies that illustrate the past failures and improved awareness of how mathematics is best used in science. The first case that I consider draws on the mathematical investigations of the tides after Newton.
Other interests: My two other research specializations are the philosophy of mathematics and the history of analytic philosophy. In the philosophy of mathematics I am most interested in tracing how philosophical issues arise out of mathematical practice and in response to pressing mathematical needs. In the history of analytic philosophy I focus on the philosophical development of Russell as well as the logical empiricists.



Work in Progress

'Classics' from the Archives