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10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
From: George Boolos (On Second-Order Logic [1975], p.52) | |
A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |