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

[rule that the entailment of a true formula is also true]

9 ideas
 8078 Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
 20309 If our ideas are adequate, what follows from them is also adequate [Spinoza]
 5395 Demonstration always relies on the rule that anything implied by a truth is true [Russell]
 3094 You don't have to accept the conclusion of a valid argument [Harman]
 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]
 10257 Intuitionism only sanctions modus ponens if all three components are proved [Shapiro]
 14184 In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read]
 15341 Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]