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Full Idea
It makes no sense to suppose there might be just one natural number, say seventeen.
Gist of Idea
There couldn't just be one number, such as 17
Source
Michael Jubien (Ontology and Mathematical Truth [1977], p.113)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.113
A Reaction
Hm. Not convinced. If numbers are essentially patterns, we might only have the number 'twelve', because we had built our religion around anything which exhibited that form (in any of its various arrangements). Nice point, though.
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| 17877 | The number series is primitive, not the result of some set theoretic axioms [Almog] |