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Full Idea
A first-order model can be viewed as a kind of ordered set, and if the domain of the model contains only concrete entities then it is a 'fundamental' model.
Gist of Idea
A model is 'fundamental' if it contains only concrete entities
Source
Michael Jubien (Ontology and Mathematical Truth [1977], p.117)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.117
A Reaction
An important idea. Fundamental models are where the world of logic connects with the physical world. Any account of relationship between fundamental models and more abstract ones tells us how thought links to world.
| 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] |