Combining Philosophers

Ideas for Michael Burke, Alfred Tarski and David Bostock

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6 ideas

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

13341

Using the definition of truth, we can prove theories consistent within sound logics [Tarski]

13540

A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock]

13541

For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock]

13542

A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock]

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

13544

Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock]

13618

Compactness means an infinity of sequents on the left will add nothing new [Bostock]