Bibliographic record
Abstract
This thesis presents an anti-realist account of mathematics as ‘recreational’, and argues that such a view can answer the central dilemma for the philosophy of mathematics as presented in Benacerraf's ‘Mathematical Truth’. I argue that we should only be satisfied with a naturalistic solution to this dilemma, where I understand ‘naturalism’ minimally as requiring natural scientific explanations of our mathematical knowledge. In Chapter 2 I thus discuss several broadly naturalist attempts to understand mathematical statements as having standard (referential) truth conditions while not referring to non-natural objects, and argue that these attempts to grasp the first horn of Benacerraf's dilemma have failed to satisfy a minimal adequacy condition of accounting for ordinary mathematical practices. In order to ensure that my own account takes seriously the actual practices of mathematicians, I discuss in Chapters 3–5 various stages of mathematical activity. These chapters include my own case study of mathematical proof, in which I present my observations from two semesters participating in a research seminar at the Fields Institute for Research in Mathematical Sciences in Toronto. Chapter 6 returns to the argument for anti-realism; showing that the standard Quinean realist arguments from indispensability leave too much standard mathematical practice unaccounted for. Chapter 7 makes explicit the commitments of the anti-realist alternative I have argued for, including an explanation of the various things that could be meant by ‘mathematical truth’. It is concluded that there is an important sense in which mathematical statements may be said to be true even though they are not true of any objects. However, if Benacerraf is right to insist that, for a predicate to be considered a genuine truth-predicate, its applicability conditions must be explained in terms of reference, then the radical conclusion of this thesis is that there is no such thing as mathematical truth.
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How this classification was reachedexpand
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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; both teacher heads agree on what is shown here.
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".