Single Idea 10772

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

Full Idea

The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models.

Gist of Idea

Compactness blocks infinite expansion, and admits non-standard models

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