more from William W. Tait

Single Idea 9980

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

Full Idea

If the power |A| is obtained by abstraction from set A, then if A is equipollent to set B, then |A| = |B|. But this does not imply that A = B. So |A| cannot just be A, taken in abstraction, unless that can identify distinct sets, ..or create new objects.


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

Gist of Idea

If abstraction produces power sets, their identity should imply identity of the originals


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

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.46

A Reaction

An elegant piece of argument, which shows rather crucial facts about abstraction. We are then obliged to ask how abstraction can create an object or a set, if the central activity of abstraction is just ignoring certain features.