Single Idea 10771

[catalogued under 5. Theory of Logic / K. Features of Logics / 6. Compactness]

Full Idea

It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms.

Gist of Idea

Compactness is important for major theories which have infinitely many axioms

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


A Reaction

An example of infinite axioms is the induction schema in first-order Peano Arithmetic.