SET SIZE AND THE PART–WHOLE PRINCIPLE

Citation data:

The Review of Symbolic Logic, ISSN: 1755-0203, Vol: 6, Issue: 04, Page: 589-612

Publication Year:
2013
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Repository URL:
http://philsci-archive.pitt.edu/id/eprint/13169
DOI:
10.1017/s1755020313000221
Author(s):
MATTHEW W. PARKER
Publisher(s):
Cambridge University Press (CUP), Association for Symbolic Logic
Tags:
Mathematics, Arts and Humanities
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article description
Gödel argued that Cantor's notion of cardinal number was 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. Copyright © 2013 Association for Symbolic Logic.

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