On the Pythagoreanism of modern physics.
Published: 2006
Language: eng
Number of pages: 208
ISBN-13: 9780494220009
Description: Unsympathetic to abstracta, contemporary empiricists have attempted to purge physics of mathematical concepts. But the 'science without numbers' project gradually waned and nowadays many philosophers would agree that mathematics is indispensable to physics. However, even those most sensitive to the importance of mathematics rarely endeavor to further challenge empiricism by examining the question whether mathematics can play even more substantial roles in science, in addition to the seemingly indispensable descriptive and derivational roles. This dissertation is an attempt to argue for an affirmative answer to this question. I first outline and examine a 'Pythagorean' tendency in the 20th century fundamental physics, namely to construct and develop physical theories primarily on the basis of mathematical or formal considerations. Then I spell out the epistemological implications of this Pythagorean idea for the concepts of scientific prediction and scientific explanation.In the first two chapters I investigate some of the greatest physicists' views on the role of mathematics in theory construction and theory discovery. I scrutinize a recent version of Wigner's puzzle, claiming that mathematics was unreasonably effective in leading to the discovery of several fundamental laws of quantum mechanics. Although I criticize the anti-naturalist (or "anthropocentric") conclusions of this neo-Wignerian argument, I maintain that the involvement of mathematics in constructing theories has important epistemological consequences consisting in reframing the concepts of prediction and explanation.In chapter 3 I explore the effectiveness of group theory in the emergence of a new type of predictive strategy in particle physics. I identify the novel methodological features of this type of prediction, showing how the traditional conception of scientific prediction fails to capture them. In chapter 4 I examine the role of group theory in reframing scientific explanation. More precisely, I investigate the doctrine that explanation is unification, the motivation for carrying out this analysis being the prominent role of mathematics in theory unification. I conclude by pointing out an important consequence of this role, that a distinction should be drawn between two kinds of understanding provided by modern physics, causal understanding and mathematical-structural understanding.
Notes: Source: Dissertation Abstracts International, Volume: 68-01, Section: A, page: 0207.

Thesis (Ph.D.)--University of Toronto, 2006.

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