Bibliographic record
Abstract
introduction In his 1893 Grundgesetze der Arithmetik Frege sought to demonstrate a thesis which has come to be called Logicism. Frege maintained that there are no uniquely arithmetic intuitions that ground mathematical induction and the foundational principles of arithmetic. Couched within a proper conceptual analysis of cardinal number, arithmetic truths will be seen to be truths of the science of logic. Frege set out a formal system - a characteristica universalis - after Leibniz, whose formation rules and transformation (inference) rules were explicit and, he thought, clearly within the domain of the science of logic. Confident that no nonlogical intuitions could seep into such a tightly articulated system, Frege endeavored to demonstrate logicism by deducing the principle of mathematical induction and foundational theorems for arithmetic. In his 1903 The Principles of Mathematics , Russell set out a doctrine of Logicism according to which there are no special intuitions unique to the branches of non-applied mathematics. All the truths of non-applied mathematics are truths of the science of logic. Russell embraced this more encompassing form of logicism because, unlike Frege, he accepted the arithmetization of all of non-applied mathematics, including Geometry and Rational Dynamics. Both Frege and Russell regarded logic as itself a science. Frege refrained from calling it a synthetic a priori science so as to mark his departure from the notion of pure empirical intuition ( anschauung ) set forth in Kant’s 1781 Critique of Pure Reason . In Frege’s view, Kant’s transcendental argument for a form of pure empirical (aesthetic) intuition that grounds the synthetic a priori truths of arithmetic is unwarranted. Russell concurred, but spoke unabashedly of a purely logical intuition grounding our knowledge of logical truths. Russell wrote that Kant “never doubted for a moment that the propositions of logic are analytic, whereas he rightly perceived that those of mathematics are synthetic . . . It has since appeared that logic is just as synthetic . . .” ( POM , p. 457).
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.003 | 0.013 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 0.005 |
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".