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Dissertation Defense: Symmetry and Reformulation: On Intellectual Progress in Science and Math

Joshua Hunt
Friday, June 3, 2022
1:00-3:00 PM
1164 Angell Hall Map
COMMITTEE:
Ruetsche, Laura (co-chair)
Belot, Gordon (co-chair)
Baker, David
Elvang, Henriette (cognate, Physics)

ABSTRACT:
Scientists and mathematicians routinely make progress by reformulating their problem-solving plans. Whereas many philosophers focus on competing theories, methodologies, or foundations, I focus on what I call "compatible formulations." In these cases, different problem-solving plans peacefully coexist, mutually illuminating their subject matter. My dissertation defends an account of the nature and value of compatible formulations. I argue that reformulations often provide a kind of objective, non-practical, epistemic value, which I call "intellectual significance." Meeting the constitutive aims of science and mathematics requires reformulating.

Of course, not all reformulations are intellectually significant: some are trivial notational variants. To distinguish trivial from significant reformulations, I consider four different accounts of the value of reformulating, based on instrumental, intellectual, explanatory, and metaphysical value. According to what I call "conceptualism," reformulations are significant when they provide an epistemically distinct plan for solving problems. The intellectual value of reformulating does not require corresponding explanatory or metaphysical differences, and it goes beyond practical or instrumental value. To avoid more weighty commitments, I provide expressivist accounts of (i) what it means for one formulation to provide better understanding than another and (ii) what it means for one formulation to be more fundamental. Finally, I analyze what it means for a formulation to make a property manifest or perspicuous, e.g. by "wearing it on the sleeves."
Building: Angell Hall
Event Type: Other
Tags: Dissertation
Source: Happening @ Michigan from Department of Philosophy