Journal article
Frege's Cardinals Do Not Always Obey Hume's Principle
History and philosophy of logic, Vol.38(2), pp.127-153
04/03/2017
DOI: 10.1080/01445340.2016.1270635
Abstract
Hume's Principle, dear to neo-Logicists, maintains that equinumerosity is both necessary and sufficient for sameness of cardinal number. All the same, Whitehead demonstrated in Principia Mathematica's logic of relations (where non-homogeneous relations are allowed) that Cantor's power-class theorem entails that Hume's Principle admits of exceptions. Of course, Hume's Principle concerns cardinals and in Principia's no-classes' theory cardinals are not objects in Frege's sense. But this paper shows that the result applies as well to the theory of cardinal numbers as objects set out in Frege's Grundgesetze. Though Frege did not realize it, Cantor's power-theorem entails that Frege's cardinals as objects do not always obey Hume's Principle.
Details
- Title: Subtitle
- Frege's Cardinals Do Not Always Obey Hume's Principle
- Creators
- Gregory Landini - University of Iowa
- Resource Type
- Journal article
- Publication Details
- History and philosophy of logic, Vol.38(2), pp.127-153
- Publisher
- Taylor & Francis
- DOI
- 10.1080/01445340.2016.1270635
- ISSN
- 0144-5340
- eISSN
- 1464-5149
- Number of pages
- 27
- Language
- English
- Date published
- 04/03/2017
- Academic Unit
- Philosophy
- Record Identifier
- 9984397188802771
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