The Ideal in mathematics: A Spinozist Marxian Elaboration and Revision of the Theory of Knowledge Objectification
Bibliographic record
Abstract
The theory of knowledge objectification, initially presented and developed by Luis Radford, has gained some traction in the field of mathematics education. As with any developing theory, its presentation contains statements that may contradict its stated intents; and these problems are exacerbated in its uptake into the work of other scholars. The purpose of this study is to articulate a Spinozist-Marxian approach, in which the objectification exists not in things—semiotic means that mediate interactions—but as real relation between people. As a consequence, the (problematic) concept of mediation is unnecessary and can be abandoned. A concrete classroom example from Radford’s own studies is used to exemplify and develop pertinent issues. In particular, the societal nature of the ideal—a synecdoche of relations between objects that reflect relations between people—should be added and the notion of (sign) mediation no longer is required.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.012 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.006 | 0.064 |
| Scholarly communication | 0.010 | 0.014 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".