Single Idea 10769

[catalogued under 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic]

Full Idea

The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated.

Gist of Idea

Second-order logic isn't provable, but will express set-theory and classic problems

Source

Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)

Book Reference

'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.38