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

[a set of sentences are held to be simultaneously true]

10 ideas
Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P]
Using the definition of truth, we can prove theories consistent within sound logics [Tarski]
A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock]
For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock]
A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock]
P-and-Q gets its truth from the truth of P and truth of Q, but consistency isn't like that [Fodor]
Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
Consistency is semantic, but non-contradiction is syntactic [Mares]
Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman]
A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman]