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Full Idea
All demonstrations involve the principle that 'anything implied by a true proposition is true', or 'whatever follows from a true proposition is true'.
Gist of Idea
Demonstration always relies on the rule that anything implied by a truth is true
Source
Bertrand Russell (Problems of Philosophy [1912], Ch. 7)
Book Ref
Russell,Bertrand: 'The Problems of Philosophy' [OUP 1995], p.40
A Reaction
This is modus ponens, a broad principle of rationality, rather than of strict logicality, because it covers practical inferences and vague propositions. Presumably truth is a prior concept to implication, and therefore more metaphysically basic.
| 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] |
| 13617 | MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock] |
| 13614 | MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [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] |