Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, George Boolos and A.George / D.J.Velleman

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6 ideas

5. Theory of Logic / K. Features of Logics / 2. Consistency

10119

Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman]

10126

A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman]

5. Theory of Logic / K. Features of Logics / 3. Soundness

10120

Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman]

5. Theory of Logic / K. Features of Logics / 4. Completeness

10834

Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]

10127

A 'complete' theory contains either any sentence or its negation [George/Velleman]

5. Theory of Logic / K. Features of Logics / 6. Compactness

13841

Why should compactness be definitive of logic? [Boolos, by Hacking]