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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
Source
Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering')
Book Ref
'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]
17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
17822 | Nothing is 'intrinsically' numbered [Yourgrau] |