The Confirmation of Mathematics and its Relationship to Science

Dissertation, The University of Wisconsin - Madison (1994)

Anthony F. Peressini
Marquette University
How are mathematical theories and statements confirmed? This is the central question of my dissertation. The received view, the Quine/Putnam indispensability account, views science as holding the key to the confirmation of mathematics. The influence of the Quine/Putnam indispensability approach cannot be overstated; however, new and important doubts are being raised concerning its efficacy. The first part of my dissertation is directed toward the Quine/Putnam indispensability account. I examine the approach and recent critiques of it and offer my own critique, which turns on a distinction between pure and applied mathematics. ;In the second part, I attempt to take a fresh look at the issue of the confirmation of mathematics. I break the problem into two parts: the confirmation of individual mathematical statements relative to a body of accepted formal theory, and the confirmation of the mathematical theory as a whole. The paradigm case of the first, relative kind of mathematical confirmation is mathematical proof. I argue that a reliability condition inspired by the reliability theory of knowledge provides a framework that helps make sense of the epistemological priority given proof. ;In considering the confirmation of a mathematical theory as a whole, I draw on a van Fraasen-like distinction between accepting the adequacy of a theory and believing the truth of a theory. An important question is under what circumstances are we justified in moving beyond the acceptance of a theory to belief in its truth. I argue that the prospects for justifying this move are worse in mathematics than they are in science
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