more on this theme | more from this thinker | more from this text
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 Ref
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.38