Combining Philosophers
Ideas for Lynch,MP/Glasgow,JM, Paul O'Grady and David Bostock
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6 ideas
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
13623
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The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
13347
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Validity is a conclusion following for premises, even if there is no proof [Bostock]
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13348
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It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock]
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13349
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Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
13614
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MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock]
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13617
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MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock]
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