Kuczynski, John-Michael (2025) Numbers as Ordered Pairs. [Preprint]
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Abstract
According to Frege, n=Kn, where n is any cardinal number and Kn is the class of all n-tuples. According to Von Neumann, n=Kpn, where Kpn is the class of all of n's predecessors. These analyses are prima facie incompatible with each other, given that Kn≠Kpn, for n>0. In the present paper it is shown that these analyses are in fact compatible with each other, for the reason that each analysis can and ultimately must be interpreted as being to the effect that n=Cn, where Cn is the class of all ordered pairs <Kn#,Rn#>, where Kn# is an arbitrary class and Rn# is an arbitrary relation such that a class k has n-many members exactly if k bears Rn# to Kn#.
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| Item Type: | Preprint | ||||||
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| Keywords: | cardinal number, Frege, Von Neumann | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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| Depositing User: | Dr. John-Michael Kuczynski | ||||||
| Date Deposited: | 20 Apr 2025 17:00 | ||||||
| Last Modified: | 20 Apr 2025 17:00 | ||||||
| Item ID: | 25117 | ||||||
| Official URL: | https://www.analyticphilosophy.ai/post/numbers-as-... | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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| Date: | 20 April 2025 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/25117 |
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