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'On What Grounds What', 'Must We Believe in Set Theory?' and 'On Second-Order Logic'
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
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Why should compactness be definitive of logic? [Boolos, by Hacking]
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