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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.
| 9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
| 9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
| 9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| 9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
| 9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
| 9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
| 9969 | The empty set is the purest abstract object [Jubien] |