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Monday, June 12, 2006

Luck

After reading Ch. 5 "Luck" in "Epistemic Luck", I wanted to organize a few thoughts/concerns before I forgot them...

(1) An definition of luck which gets presented, and then amended, is L1:

(L1) If an event is lucky, then it is an event that occurs in the actual world but which does not occur in a wide class of the nearest possible worlds where the relevant initial conditions for tha tevent are the same as in the actual world. (p. 128)

This definition is successful in making clear how what we call "lucky" is distinct from what we call "chance" or "accident" (even though, lucky events are usually associated with chance or accident). This is helpful because it isolates respects in which luck differs from these two related concepts, which had previously been taken by some to just "be" what luck is. Pritchard points out, though, that L1 needs some supplementing to be adequate. For one, L1 doesn't capture the "subjective significance" element of luck (and hence, an amendment (L2) is required; secondly, there need to be clear specifications about the initial conditions for events in nearby possible worlds.

There is an especially interesting section about L1 on pp. 129-130 that I think could be grounds for good discussion. Pritchard considers an objection to L1 on the grounds that someone might get a 50-50 guess right on a game show, and we'd intuitively say that person is "lucky", and yet, it isn't the case that in a wide class of the nearest possible worlds (with the relevant initial conditions) the contestant would get the answer wrong. In fact, it would be right at half of them.

In responding to this, Pritchard first offers that he suspects our intuitions would shift to a "non-lucky" assessment if the game-show example were altered so that the contestant gets the answer right, but that rather than having two choices, one right and one wrong, she had four choices, three right and one wrong. Here's Pritchard: "If the contestant guessed correctly in this case then I think it would be unlikely that we would put this down to luck since the odds were squarely in her favour." (130). He adds: "This suggests that the correct reading of "wide class" in L1 is at least approaching half of the relevant nearby possible worlds, and that typically events which are *clearly* lucky will be events which do not obtain in most nearby possible worlds." (130).

My initial response to this suggestion is to think that:

* the guess in the 3-out-of-4-right case is *lucky*
* the guess in the 1-out-of-two case is *luckier*
* both guesses are *clearly* lucky.

It seems intuitive to me, actually, to think that if a man were to play Russian Roulette with a gun with a 99999 blank chambers, and only one loaded chamber, and shot at his head, and got the blank, that he would clearly be lucky, even though with the same initial conditions, the same result occurs in almost all nearby possible worlds. According to (L1) the event of the agent's shooting a blank and not killing herself would not be lucky, and according to the later discussion of the gameshow objection, we could infer that the Russian Roulette case would not be clearly lucky because the worlds in which the chap gets the loaded chamber don't even come close to approaching half. Yet, it just seems wrong to say that "the fact that you didn't kill yourself wasn't a matter of luck."

This line of reasoning led me to think that L1 didn't quite capture the fact that some events are clearly lucky even if they obtain in almost all nearby possible worlds, and that the only thing that changes relative to the number of nearby worlds the events do not obtain in is the "degree" to which we'd say they are lucky. And hence, my thinking was that whilst the Russian Roulette case (and the 3-of-4-case) are both clearly cases of luck, neither is lucky to a very significant degree.

But then... (as happens frequently)... I thought of a different case which makes me think that my initial problem with L1 might be vitiated. What I thought of was a case that is structurally similar to the Russian Roulette case, but which I am not prepared to say is clearly lucky.

Golf case:

Golf legend Ben Hogan was reported to have once gone an entire summer, of playing every day, without missing a single putt inside of six feet. This is quite remarkable, and probably amounted to 500 or so consecutive putts without a miss; let us suppose (justafiedly!) that during that summer, Ben Hogan's putting was exceptionally skillful from that particular range. Now consider the event of Hogan's having successfully holed one of those 500 (or so) putts that he made consecutively that summer. Do we want to say that he was lucky? The intuitive response is... well of course not.

This is probably because, in such a conversation, we would be contrasting luck with skill, and because Hogan was skilled and well-practiced, his having made that particular putt (say, the 350th of 500 putts) doesn't seem to admit of being a matter of luck.

What's odd, though, is that Hogan's chances of missing are much greater than 1 in 100,000 (the chances of getting the loaded chamber in Russian Roulette), and yet we (or at least I) might feel more inclined to attribute the Russian Roulette player's having shot a blank at his head a matter more lucky than Hogan making his 300th of 500 consecutive putts.

And so what should be made of all of this? Perhaps two things:

(1) Granting that the Russian Roulette blank-shooter was lucky might lead us away from accepting L1 insofar as L1 would disqualify as lucky events that take place in almost all nearby possible worlds.
(2) My own initial assessment of the Russian Roulette case must be flawed; this is because I suspected that the degree of luckiness would correspond proportionally to the number of nearby worlds in which the event failed to occur.

I'll end this already-longwinded post by offering two suggestions. They appear like they could be auspicious only with regard to the spefic problem I have of trying to understand how it is that I arrived at the strange intuition that Hogan's event of making one of those 500 putts is not lucky, whereas catching a blank is... (even though it's much more likely that a blank will be caught than that Hogan will make.)

The first avenue of investigation here might be to consider Gricean conversational implicature as an explanation. When we talk of decisively sporting achievements, "luck" seems to be contrasted with "skill" rather than "likelihood of occurring", whereas in the context of a roulette discussion, skill is inherently out of the picture, and so luck would be understood in terms of strictly probability. And so, since it is incontroversial that Hogan is extremely skilled, we might find in a discussion of his feats ourselves inclined to deny luck, even if we would admit of a miniscule chance that his making the putt wouldn't take place (i.e. we might say he was not lucky whilst admitting that there is a 1 in 10,000 chance that he would have a seizure in mid-stroke and whiff the ball completely).

Another avenue here might be to look to Hawthorne's "Knowledge and Lotteries", when he discusses how "parity reasoning" (p. 14) with regard to the likelihood of an proposition's being the case leads the reasoner to feel less sure of a proposition than would be the case if she did not arrive at hear belief that the proposition will be the case through non-parity reasoning.

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