### Single Idea 17818

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure]

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 Reference

'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.