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Full Idea
We want to know How many what? You must first partition an aggregate into parts relevant to the question, where no partition is privileged. How the partitioned set is to be numbered is bound up with its unique members, and follows from logic alone.
Gist of Idea
How many? must first partition an aggregate into sets, and then logic fixes its number
Source
Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'New Problem')
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.357
A Reaction
[Compressed wording of Yourgrau's summary of Frege's 'relativity argument'] Concepts do the partitioning. Yourgau says this fails, because the same argument applies to the sets themselves, as well as to the original aggregates.
| 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] |