November 09, 2007

Intution Check

O three remaining readers, do you think I say anything fishy in the following story?

I'm playing bridge against Allison. Allison has bid spades and then hearts, and then led diamonds. Since she bid that way, she must have five spades and four hearts. But if she doesn't have five spades and four hearts, she might have four clubs.

Posted by Matt Weiner at November 9, 2007 07:26 AM

My first reaction was to evaluate the inference as a bit of bridge playing, and so I was going to complain about something else: You don't say what Allison's partner bid after her Spade bid. Without that information, I don't know what to make of her Heart bid-- if partner jumped to a 3 Heart bid and she bid it up to 4 Hearts, then she might just have two or three Hearts but good ones.

My second reaction: The 'must' in the third sentence seems wrong to me. It seems like it should be a 'probably' or 'almost certainly'.

Posted by: P.D. at November 9, 2007 09:28 AM

"P must be the case, but if it weren't then q" sounds fine to me where q is something like a contingency plan, but really strange where q is a state of the world inconsistent with p. P.D. gets at this too, the speaker doesn't believe their own "must."

Posted by: washerdreyer at November 9, 2007 11:51 AM

i was thinking either Allison's partner bid 1NT or was silent in a competitive auction? I don't know, it's been over ten years since I played bridge with other people.

Anyway, I find myself agreeing with you guys -- can't have "must p" followed by an indicative "if q then might r" where p and q are incompatible. In fact I wonder whether the "might" makes a difference; it could just be the indicativity. (This would go along with some of Frank Jackson was arguing in a talk on indicative conditionals that he gave here, that they're always about the actual world.)

I was thinking about the claim made in the Thony Gillies paper discusssed here, that "If P then might Q" (again, indicative) means "Might (P and Q)." (If Jackson's theory is correct, perhaps this is true partly because "if p then q [indicative]" always entails "Might P"?) It looks to me as though you can't cause any trouble for it this way. Maybe you can cause trouble for it with an impossible antecedent?

"If the elliptic curve defined by [x, y, z, n] is semistable but not modular, then [x, y, z, n] might constitute a solution to the Fermat equation. But, as we will show, all semistable elliptic curves are modular."

Posted by: Matt Weiner at November 9, 2007 01:04 PM

Make that "All semistable elliptic curves must be modular," even.

Actually I don't think this yields a problem for Gillies' claim. [Slopes off.]

Posted by: Matt Weiner at November 9, 2007 01:05 PM

Yes. I find it strange to say that she "must have" such and such and then to go on and say, "but if she doesn't ...". So I guess I read the "must" as an epistemic modal. (I didn't read the comments so as not to spoil anything, but now I see I have nothing to add. Oh well, its a datum point.)

Posted by: marc at December 3, 2007 10:36 AM
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