Combining Philosophers

Ideas for Lynch,MP/Glasgow,JM, Marcus Rossberg and David Bostock

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8 ideas

5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence

10753

Logical consequence is intuitively semantic, and captured by model theory [Rossberg]

5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-

13623

The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock]

10752

Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=

13347

Validity is a conclusion following for premises, even if there is no proof [Bostock]

13348

It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock]

13349

Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock]

5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens

13614

MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock]

13617

MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock]