Why numbers are sets
type: Item
instance of: scholarly article
title: Why numbers are sets
zbMATH Open document ID: 1033.03003
DOI: 10.1023/A:1021266519848
author: Eric Steinhart
published in: Synthese
publication date: 2003-04-27T00:00:00Z
review text: In opposition to the general opinion that there are infinitely many different structures that can play the role of the natural numbers, the author holds that the natural numbers are, in fact, the finite von Neumann ordinals (FVNO). He points out the well-known fact that, in addition to Peano's Postulates, there are other nice properties that will ensure that the structure consists of the natural numbers and he seems to believe that the natural numbers must have those properties, although he gives no justification for that belief. But, beyond this, he claims to give a proof (on pp. 355--356) that the natural numbers are the FVNO. The reviewer was unable to understand this ``proof''. Among other things, the author uses the concepts of NN-universe and NN-conditions and asserts various properties of these concepts, but he does not clearly define or explain the concepts.
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03C62
Mathematics Subject Classification ID: 00A30
zbMATH DE Number: 1901274
zbMATH Keywords: natural number
zbMATH Keywords: finite von Neumann ordinals
reviewed by: Elliott Mendelson
MaRDI profile type: Publication
full work available at URL: a:1021266519848
OpenAlex ID: W149979176
description: scientific article; zbMATH DE number 1901274