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Full Idea
The strict conditional implies the counterfactual conditional: □(A⊃B) ⊃ (A□→B) - suppose that A would not have held without B holding too; then if A had held, B would also have held.
Gist of Idea
Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B)
Source
Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 1)
Book Ref
'Modality', ed/tr. Hale,B/Hoffman,A [OUP 2010], p.81
A Reaction
[He then adds a reading of his formula in terms of possible worlds] This sounds rather close to modus ponens. If A implies B, and A is actually the case, what have you got? B!
| 14531 | Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals [Williamson, by Hale/Hoffmann,A] |
| 14624 | Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B) [Williamson] |
| 14625 | Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation [Williamson] |
| 14623 | Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson] |
| 14626 | In S5 matters of possibility and necessity are non-contingent [Williamson] |
| 14628 | Imagination is important, in evaluating possibility and necessity, via counterfactuals [Williamson] |