Whittle, B. (2018) Size and function. Erkenntnis, 83(4), pp. 853-873. (doi: 10.1007/s10670-017-9917-z)
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Abstract
Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections (i.e. one-to-one correspondences) between them. These results (which I of course do not dispute) settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: for any sets A and B, if A is the same size as B, then there is a bijection from A to B. The aim of the paper, however, is to argue that this question is in fact wide open: to argue that we are not in a position to know the answer, because we are not in one to know the principle. The aim, that is, is to argue that for all we know there is only one size of infinity.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Whittle, Bruno |
| Authors: | Whittle, B. |
| College/School: | College of Arts & Humanities > School of Humanities > Philosophy |
| Journal Name: | Erkenntnis |
| Publisher: | Springer |
| ISSN: | 0165-0106 |
| ISSN (Online): | 1572-8420 |
| Published Online: | 12 July 2017 |
| Copyright Holders: | Copyright © 2017 The Author |
| First Published: | First published in Erkenntnis 83(4): 853-873 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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