Single Idea 9972

[catalogued under 18. Thought / E. Abstraction / 8. Abstractionism Critique]

Full Idea

Why should abstraction from two equipollent sets lead to the same set of 'pure units'?

Clarification

'Equipollent' means they map one-to-one onto each other

Gist of Idea

Why should abstraction from two equipollent sets lead to the same set of 'pure units'?

Source

William W. Tait (Frege versus Cantor and Dedekind [1996])

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.42


A Reaction

[Tait is criticising Cantor] This expresses rather better than Frege or Dummett the central problem with the abstractionist view of how numbers are derived from matching groups of objects.