Bibliographic record
Abstract
c:\users\ken\documents\type\red \rj red.docx -- : RUSSELL’S PRINCIPLES OF MATHEMATICS1 G. E. Moore [Bertrand Russell. The Principles of Mathematics. Vol. . Cambridge: Cambridge U. P., . Pp. (), xxix, .] f the philosophical books published in the United Kingdom in the most important is Mr. Russell’s Principles of Mathematics. 2 In this book, Mr. Russell tells us, he has two main objects. His first object is to establish the two very important propositions () “that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts” and () “that all its propositions are deducible from a very small number of fundamental logical principles.” The examination of the principal branches of pure mathematics, which is necessary to establish these two propositions, occupies the last six Parts of the book, which are entitled respectively “Number”, “Quantity”, “Order”, “Infinity and Continuity”, “Space”, and “Matter and Motion”. In these parts there is much which cannot be easily understood without a special knowledge of Mathematics, and much which has little bearing on philosophy, except so far as it helps to establish Mr. Russell’s two main propositions; but there is much also which is of considerable importance for philosophy, quite apart from its bearing on these two propositions: in particular, Mr. Russell examines very carefully the conceptions of Infinity and Continuity, and attempts to shew that they involve no antinomies. Part i, on the other hand, is devoted to Mr. Russell’s second object —“the explanation of the fundamental concepts which mathematics accepts as indefinable”, and is almost entirely philosophical in its nature. I shall endeavour to give some account () of the meaning and consequences of Mr. Russell’s two propositions concerning the relation of Logic and Mathematics () of some of the more important points dealt with in Part i and () of the theory of Infinity and Continuity. Mr. Russell is eminently qualified for his task by a thorough knowledge of Mathematics and by great philosophical acumen ; and it is certain that no philosopher ought in future to handle any of the subjects discussed in this book, without taking account of the arguments advanced in it. 1 The Principles of Mathematics. 2 [Typeset from a photocopy of the manuscript provided to the Russell Archives by Dorothy Moore in (ra Rec. Acq. ). The original ms. is in the Moore papers in Cambridge U. Library. The review is © the Estate of G. E. Moore and is published with the Estate’s permission. Moore revised the ms. a great deal, the foliation being an indication: , a, –(), –(), (), (), –(), (), (), (), a, , (?), –. Proofread by A. Duncan and K. Blackwell.] O Moore’s Review of The Principles of Mathematics c:\users\ken\documents\type\red \rj red.docx -- : Mr. Russell maintains, we have seen, the two very important propositions () “that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts” and () “that all its propositions are deducible from a very small number of fundamental logical principles.” And in order to bring out the philosophical importance of his book, it will be well to explain as clearly as possible precisely what he means by them.There are several points, which require notice, in order that we may form a just estimate of what he is maintaining. In the first place, Mr. Russell makes then two assertions with regard to all the propositions of pure mathematics.What propositions does he mean to include in this description? It is important to recognize that there are certain kinds of propositions to which his assertions do not, and are not meant to, apply. It might, for instance, be thought that the familiar proposition of Euclid that “The three angles of every triangle are equal to two right angles” was a proposition of pure mathematics. It is not, however, one of the propositions of which Mr. Russell is speaking. It cannot be deduced from any logical principles . It follows only if we assume certain of Euclid’s axioms, which cannot themselves be deduced from the principles of Logic. All that can be deduced from logical principles is that if these axioms of Euclid are true, then the...
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 | 0.006 | 0.010 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.004 | 0.013 |
| Scholarly communication | 0.011 | 0.011 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.005 | 0.013 |
| Insufficient payload (model declined to judge) | 0.018 | 0.025 |
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".