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Full Idea
If we are allowed in the case of sets to construe the number question as 'really': How many (elements)?, then we could just as well construe Frege's famous question about the deck of cards as: How many (cards)?
Gist of Idea
If you can subdivide objects many ways for counting, you can do that to set-elements too
Source
comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Palle Yourgrau - Sets, Aggregates and Numbers 'New Problem'
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.358
A Reaction
My view is that counting is not entirely relative to the concept employed, but that the world imposes objects on us which thus impose their concepts and their counting. This is 'natural', but we can then counter nature with pragmatics and whimsy.
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 17821 You can ask all sorts of numerical questions about any one given set [Yourgrau]