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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!
| 7803 | Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle] |
| 14286 | In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker] |
| 14283 | A conditional probability does not measure the probability of the truth of any proposition [Lewis, by Edgington] |
| 13768 | Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington] |
| 13853 | It is a mistake to think that conditionals are statements about how the world is [Edgington] |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| 14623 | Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |