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Gödel's Argument for Cantorian Cardinality

Parker, Matthew W. (2017) Gödel's Argument for Cantorian Cardinality. Noûs.

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Abstract

On the first page of “What is Cantor’s Continuum Problem?”, Gödel argues that Cantor’s theory of cardinality, where a bijection implies equal number, is in some sense uniquely determined. The argument, involving a thought experiment with sets of physical objects, is initially persuasive, but recent authors have developed alternative theories of cardinality that are consistent with the standard set theory ZFC and have appealing algebraic features that Cantor’s powers lack, as well as some promise for applications. Here we diagnose Gödel’s argument, showing that it fails in two important ways: (i) Its premises are not sufficiently compelling to discredit countervailing intuitions and pragmatic considerations, nor pluralism, and (ii) its final inference, from the superiority of Cantor’s theory as applied to sets of changeable physical objects to the unique acceptability of that theory for all sets, is irredeemably invalid.

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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Parker, Matthew W.m.parker@lse.ac.uk0000-0002-7436-2149
Additional Information: Contact m dot parker at lse dot ac dot uk
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics
Depositing User: Dr. Matthew Parker
Date Deposited: 05 Sep 2017 17:27
Last Modified: 05 Sep 2017 17:27
Item ID: 13390
Journal or Publication Title: Noûs
Publisher: John Wiley & Sons, Inc.
Official URL: http://onlinelibrary.wiley.com/doi/10.1111/nous.12...
DOI or Unique Handle: 10.1111/nous.12221
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics
Date: 29 August 2017
URI: https://philsci-archive.pitt.edu/id/eprint/13390

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