Bibliographic record
Abstract
In this paper, I provide a soft defence of the Platonist conception of mathematics, which posits mathematical objects as having substantial and necessary meaning independent of human constructions or compulsions. I defend the Platonist account of mathematics against two interpretations of Wittgenstein's theory of mathematics. The first interpretation, which I term the 'Independent Instantiation' interpretation, maintains that mathematical claims only have meaning within a linguistic framework, and thus correspond to no generalizable essences. The second, the Psychological Predilection interpretation, argues that humans are psychologically, rather than socially compelled to accept mathematical claims, but still rejects any metaphysical necessity in mathematics. I accuse the first interpretation of committing the genetic fallacy and failing to account for our ability to apply mathematics in new ways. The second interpretation I claim to be neither true nor false, but nonsensical by Wittgenstein's own standards, leaving us to find criteria other than truth for choosing a theory of mathematics.
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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 | 0.005 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.003 | 0.030 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.002 | 0.007 |
| Research integrity | 0.003 | 0.007 |
| 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".