Turnabout is Fair Play: A New Humean Response in the Old Debate with Kant
Bibliographic record
Abstract
Kant claims that Hume failed to see that mathematics provides us with synthetic a priori knowledge; had he done so, Kant argues, Hume would have to admit the possibility of such knowledge in causal judgments as well. Instead, Kant insists that Hume treats mathematics as analytic, and so missed the key insights of the Critical philosophy. I argue that it is rather Kant who is mistaken: Hume, in fact, endorses a position very similar to the view that mathematics is synthetic and a priori, and arrives at an account of mathematical necessity that stands as a plausible alternative to Kant's. More importantly, recognizing this Humean account of mathematics exposes a potentially grave vulnerability in Kant's system that Hume might exploit: while mathematics can be seen as synthetic a priori knowledge, Hume can argue that this gives us good reason to think that causal judgments cannot meet this standard of necessity.
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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 | 0.013 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.009 | 0.078 |
| Scholarly communication | 0.013 | 0.018 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.014 | 0.013 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".