Bibliographic record
Abstract
With a series of important papers in the 1960s, Jaakko Hintikka initiated a surge of interest in Kant's philosophy of mathematics, developing an interpretation which has in some ways defi ned the fi eld.Because I can't do justice to all of the details of Hintikka's view here, I propose to stand back and consider the broader context.In a later paper revisiting the topic, Hintikka complained that subsequent discussions of his interpretation of Kant paid no attention to "the overall picture of Kant's thinking about mathematics in its historical setting or to my view of the role of Kant's theory of space, time, and mathematics (including the whole of his transcendental aesthetics) within the structure of his philosophical system" 1 .In the intervening years, Kant scholars have taken up these two tasks, so it seems worthwhile to consider the implications of this work for Hintikka's interpretation of Kant's theory of mathematics.The key question at issue is the role of intuition in Kant's philosophy of mathematics.On the logical approach developed by Hintikka, the primary role of intuition is formal or inferential.By following Hintikka's suggestion and reconsidering the historical setting -both philosophical and mathematical -and the structure of Kant's philosophical system, I want to suggest that we can make a case for a richer role for intuition in Kant's philosophy of mathematics than the merely formal one.2 1. Hintikka [1981], pp.201-215.2. As Hintikka recognizes, the formal role of intuition is compatible with its playing other roles (ibid., p. 213), so the following considerations are not intended to undermine his positive arguments for the formal role for intuition.
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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 | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.015 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
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".