Parker, Matthew W. (2013) Set Size and the Part–Whole Principle. Review of Symbolic Logic, 6 (4). pp. 589-612.
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Abstract
Gödel argued that Cantor’s notion of cardinal number is uniquely correct. More recent work has defended alternative “Euclidean” theories of set size, in which Cantor’s Principle (two sets have the same size if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). Here we see from simple examples, not that Euclidean theories of set size are wrong, nor merely that they are counterintuitive, but that they must be either very weak or in large part arbitrary and misleading. This limits their epistemic usefulness.
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| Item Type: | Published Article or Volume | ||||||
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| Keywords: | Gödel, Cantor, cardinal number, set theory, part-whole principle, Hume's principle, infinity, numerosity, Euclidean theories of set size | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics |
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| Depositing User: | Dr. Matthew Parker | ||||||
| Date Deposited: | 03 Jul 2017 14:35 | ||||||
| Last Modified: | 03 Jul 2017 14:35 | ||||||
| Item ID: | 13169 | ||||||
| Journal or Publication Title: | Review of Symbolic Logic | ||||||
| Publisher: | Association for Symbolic Logic | ||||||
| Official URL: | https://www.cambridge.org/core/journals/review-of-... | ||||||
| DOI or Unique Handle: | https://doi.org/10.1017/S1755020313000221 | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics |
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| Date: | 20 September 2013 | ||||||
| Page Range: | pp. 589-612 | ||||||
| Volume: | 6 | ||||||
| Number: | 4 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/13169 |
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