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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 Ref
'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.
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| 9984 | We can have a series with identical members [Tait] |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |