Single Idea 9993

[catalogued under 18. Thought / E. Abstraction / 7. Abstracta by Equivalence]

Full Idea

Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'.

Gist of Idea

There is no reason why abstraction by equivalence classes should be called 'logical'

Source

report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.62


A Reaction

This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981.

Related Idea

Idea 9981 Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]