Why Numbers Are Sets

Author: Steinhart E.¹

Source: Synthese, Volume 133, Number 3, December 2002 , pp. 343-361(19)

Publisher: Springer

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Abstract:

I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all natural numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals.

Language: English

Document Type: Research article

Affiliations: 1: Department of Philosophy William Paterson University 300 Pompton Road 265 Atrium Bldg. Wayne NJ 07470-2152 U.S.A.

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