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SET SIZE AND THE PART–WHOLE PRINCIPLE

Published online by Cambridge University Press:  20 September 2013

MATTHEW W. PARKER
MATTHEW W. PARKER*
Affiliation:
Centre for Philosophy of Natural and Social Science, London School of Economics and Political Science
*
*CENTRE FOR PHILOSOPHY OF NATURAL AND SOCIAL SCIENCE LONDON SCHOOL OF ECONOMICS AND POLITICAL SCIENCE HOUGHTON STREET, LONDON WC2A 2AE, UK E-mail: m.parker@lse.ac.uk
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Abstract

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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 4 , December 2013 , pp. 589 - 612
Copyright
Copyright © Association for Symbolic Logic 2013 

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