more from Palle Yourgrau

Single Idea 17821

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory]

Full Idea

We can address a set with any question at all that admits of a numerical reply. Thus we can ask of {Carter, Reagan} 'How many feet do the members have?'.

Gist of Idea

You can ask all sorts of numerical questions about any one given set


Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering')

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.358

A Reaction

This is his objection to the Fregean idea that once you have fixed the members of a set, you have thereby fixed the unique number that belongs with the set.

Related Ideas

Idea 17819 A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau on Frege]

Idea 17820 If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on Frege]