Single Idea 10768

[catalogued under 5. Theory of Logic / K. Features of Logics / 8. Enumerability]

Full Idea

Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one.

Gist of Idea

Effective enumeration might be proved but not specified, so it won't guarantee knowledge

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

The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job.