Bibliographic record
Abstract
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 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. 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.004 | 0.041 |
| Scholarly communication | 0.006 | 0.011 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.002 | 0.009 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".