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Set Size and the Part–Whole Principle

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
Creators:
CreatorsEmailORCID
Parker, Matthew W.m.parker@lse.ac.uk0000-0002-7436-2149
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
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
Date: 20 September 2013
Page Range: pp. 589-612
Volume: 6
Number: 4
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/13169

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