more from William W. Tait

Single Idea 9981

[catalogued under 18. Thought / E. Abstraction / 2. Abstracta by Selection]

Full Idea

If the sense of a proposition about the abstract domain is given in terms of the corresponding proposition about the (relatively) concrete domain, ..and the truth of the former is founded upon the truth of the latter, then this is 'logical abstraction'.

Gist of Idea

Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete


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

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.47

A Reaction

The 'relatively' in parentheses allows us to apply his idea to levels of abstraction, and not just to the simple jump up from the concrete. I think Tait's proposal is excellent, rather than purloining 'abstraction' for an internal concept within logic.