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Full Idea
Whatever ideas follow in the mind from ideas which are adequate in the mind are also adequate.
Gist of Idea
If our ideas are adequate, what follows from them is also adequate
Source
Baruch de Spinoza (The Ethics [1675], II Pr 40)
Book Ref
Spinoza,Benedict de: 'Ethics', ed/tr. Curley,Edwin [Penguin 1996], p.55
A Reaction
This appears to be Modus Ponens, and he calls it (in Sch 1) 'the foundations of our reasoning'. If 'adequate' ideas are knowledge, then this also seems to say that knowledge is closed under known implication.
| 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] |