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2 ideas
14623 | Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson] |
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. | |
From: Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 1) | |
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! |
14624 | Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B) [Williamson] |
Full Idea: The counterfactual conditional transmits possibility: (A□→B) ⊃ (◊A⊃◊B). Suppose that if A had held, B would also have held; the if it is possible for A to hold, it is also possible for B to hold. | |
From: Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 1) |