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Full Idea
The empty set is the pure abstract object par excellence.
Gist of Idea
The empty set is the purest abstract object
Source
Michael Jubien (Ontology and Mathematical Truth [1977], p.118 n8)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.118
A Reaction
So a really good PhD on the empty set could crack the whole nature of reality. Get to work, whoever you are!
Related Ideas
Idea 13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
Idea 10811 The null set plays the role of last resort, for class abstracts and for existence [Lewis]
| 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] |