Turnabout is Fair Play: A New Humean Response in the Old Debate with Kant
Why this work is in the frame
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it