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- Title
Frege's Cardinals and Neo-Logicism.
- Authors
Cook, Roy T.
- Abstract
Gottlob Frege defined cardinal numbers in terms of value-ranges governed by the inconsistent Basic Law V. Neo-logicists have revived something like Frege's original project by introducing cardinal numbers as primitive objects, governed by Hume's Principle. A neo-logicist foundation for set theory, however, requires a consistent theory of value-ranges of some sort. Thus, it is natural to ask whether we can reconstruct the cardinal numbers by retaining Frege's definition and adopting an alternative consistent principle governing value-ranges. Given some natural assumptions regarding what an acceptable neo-logicistic theory of value-ranges might look like, successfully implementing this alternative approach is impossible.
- Subjects
CARDINAL numbers; SET theory; ETHNOMATHEMATICS; COMBINATORIAL set theory; MATHEMATICAL ability
- Publication
Philosophia Mathematica, 2016, Vol 24, Issue 1, p60
- ISSN
0031-8019
- Publication type
Article
- DOI
10.1093/philmat/nkv029