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Single Idea 9963

[filed under theme 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism ]

Full Idea

If the intuition of mathematical objects were general, there would be no real debate over platonism.

Gist of Idea

If we all intuited mathematical objects, platonism would be agreed

Source

Michael Jubien (Ontology and Mathematical Truth [1977], p.111)

Book Ref

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.111


A Reaction

It is particularly perplexing when Gödel says that his perception of them is just like sight or smell, since I have no such perception. How do you individuate very large numbers, or irrational numbers, apart from writing down numerals?


The 8 ideas from 'Ontology and Mathematical Truth'

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