The Value of Mathematics for Scientific Representation and Knowledge

FAIN: FA-54005-08

Christopher John Pincock
Purdue University (West Lafayette, IN 47907-2040)

My project will provide the first systematic overview of the philosophical options for accounting for the role of mathematics in science and then argue for my preferred proposal. Briefly put, the value of mathematics for scientific representation is epistemic. That is, by appealing to mathematical concepts and theorems, scientists are able to formulate theories that can be highly confirmed by the available evidence. Without mathematics, scientific theories would still be possible, but they would be less well confirmed. I reach these conclusions through a careful consideration of the different ways in which mathematics can be useful in science and by reviewing the main alternative accounts of how mathematics is applied. After articulating my epistemic proposal, I test it using an extended case study from the history of meteorology. My project concludes by exploring the consequences of this view of applied mathematics for the metaphysics and epistemology of pure mathematics.