Counterfactuals imply some sort of distance between possible worlds [...] predicate P>Q is defined as true in a world ω if, in the closest world to ω in which P is true, Q is also true
What does “closest world to ω in which P is true” mean? Is this still data extracted from a Kripke frame, a set of worlds plus accessibility, or does this need more data (“some sort of distance”)? What sort of distance is this, what if there are multiple worlds in P at the same distance from ω, possibly with different truth of Q?
Keeping to the example at hand, what are the possible worlds/counterfactuals here, just the (row, column) pairs? Their combination with possibly-false-in-that-world beliefs? Something else intractably informal that can’t be divided by equivalence for irrelevant distinctions to give an explicit description? What is the accessibility in the Kripke frame? What are the distances? Is “the result is BE” just the one-world proposition true in the world BE? If some of the assumptions in my questions are wrong (as I expect them to be), what are the worlds where “the result is BE” holds? What does it mean to enact row A in the situation where the result is BE (or believed to be BE)? Or is “he would have instead picked A rather than B” referring to something that shouldn’t be thought of as enactment?
It is indeed correct that “the result be BE” is a false proposition in the real world
(I meant it’s false in the world where it’s believed, where row A would be taken instead as a result of that belief, so that in fact in that world row A is taken rather than B, so that the belief that row B is taken in that world is false. I didn’t mean to imply that I’m talking about the real world.)
What does “closest world to ω in which P is true” mean? Is this still data extracted from a Kripke frame, a set of worlds plus accessibility, or does this need more data (“some sort of distance”)? What sort of distance is this, what if there are multiple worlds in P at the same distance from ω, possibly with different truth of Q?
Keeping to the example at hand, what are the possible worlds/counterfactuals here, just the (row, column) pairs? Their combination with possibly-false-in-that-world beliefs? Something else intractably informal that can’t be divided by equivalence for irrelevant distinctions to give an explicit description? What is the accessibility in the Kripke frame? What are the distances? Is “the result is BE” just the one-world proposition true in the world BE? If some of the assumptions in my questions are wrong (as I expect them to be), what are the worlds where “the result is BE” holds? What does it mean to enact row A in the situation where the result is BE (or believed to be BE)? Or is “he would have instead picked A rather than B” referring to something that shouldn’t be thought of as enactment?
(I meant it’s false in the world where it’s believed, where row A would be taken instead as a result of that belief, so that in fact in that world row A is taken rather than B, so that the belief that row B is taken in that world is false. I didn’t mean to imply that I’m talking about the real world.)