Bibliographic record
Abstract
Certain advocates of the so-called "neo-logicist" movement in the philosophy of mathematics identify themselves as "neo-Fregeans" (e.g., Hale and Wright), presenting an updated and revised version of Frege's form of logicism.Russell's form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of inWnity, reducibility and so on).In this paper I have three aims: Wrstly, to identify more clearly the primary meta-ontological and methodological diTerences between Russell's logicism and the more recent forms; secondly, to argue that Russell's form of logicism oTers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics.i. introduction I t was for a while fashionable to say that logicism was dead.Even now we see the sentiment repeated.1 As recently as 2010, a website developed for a popular logic textbook 2 claimed that "in the 1920's, the German mathematician and logician Kurt Gödel made an astonishing discovery, a discovery that eTectively ended the hopes of the logi-128 kevin c. klement 3 What is particularly strange about Herrick's way of putting the point is that he somehow thinks Gödel's results pose a greater problem for reducing mathematics to logic than to set theory, whereas of course Gödel's results equally show that no recursively axiomatized set-theoretic foundation for mathematics is complete.4 See especially Crispin Wright, Frege's Conception of Numbers as Objects (Aberdeen: Aberdeen U. P., 1983), and Bob Hale and Crispin Wright, The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics (Oxford: Clarendon P., 2001).Neil Tennant and Stewart Shapiro have also done work in sympathy with their programme, though without the same kind of commitment to the project.Moreover, George Boolos, Richard Heck and Kit Fine have contributed in important ways, though none of them, I think, actually endorse the position in the end.cists", namely, that "there are truths of arithmetic that are in principle not provable", and "with tight deductive proofs that convinced everyone" (!), Gödel proved that "logicism is false", and indeed: Today, logicians agree that although mathematics can be derived from set theory, it cannot be derived from pure logic alone.Thus was an exciting new theory Wnally proven false.
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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 | 0.008 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.031 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| 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; 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".