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Full Idea
Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world.
Gist of Idea
In nearby worlds where A is true, 'if A,B' is true or false if B is true or false
Source
Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.18
A Reaction
This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you.
| 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] |