Sly Pete and “The Conditionals of Deliberation”

About a year ago, Jon blogged here about Allan Gibbard’s Sly Pete example, inspiring quite a discussion in the comments. I’ve finally finished a draft of the paper that, when I gave it as a talk, got Jon thinking about the example. It’s “The Conditionals of Deliberation,” and it’s available here [pdf document]. Sly Pete doesn’t make his first appearance until about half-way through the paper, but once he’s on the scene, he stays in the spotlight pretty much for the rest of the paper. There are lots of variations of the example. It turns out that, on the matter of whether Pete will win if he plays, much depends not only on who is talking to whom (and also on who is thinking about the matter to themselves), but also, in interesting ways, on just what purpose the conditional is being asserted/thought about for. There’s also a bit of Newcomb’s problem in the paper. So, even if you don’t like what I do with this material, at least you know that a couple of the coolest examples of recent philosophy are discussed.

So, why did it take a whole year to get a draft out after having all the ideas together for a talk? It took longer than that! I first gave that paper as a talk more than 4 years ago (at Michigan, with Gibbard present!), and I think I’ve had all the main ideas in my head for more than 5 years. I don’t know why, but for some of my papers, I find it extremely difficult to get myself to write them up. Very frustrating. I think that giving them as talks will spur me on to get these papers written up, but that usually doesn’t seem to work. But who knows? Maybe it would have taken even longer if it weren’t for the talks.


Sly Pete and “The Conditionals of Deliberation” — 2 Comments

  1. Keith, glad to see it written up. Can’t believe you presented it in 45 minutes!

    I’m still worried about the argument on p. 24. The passage I’m referring to says this: “So, if this fact — that Pete holds the lower card — were enough to make Sigmund’s claim false, then from Sigmund’s own point of view, his claim had a very high probability of being false.”

    Here’s my worry. Take any claim that I believe (and assume that means I assign a high subjective probability to it). For any such claim, I can find a number of things whose truth would explain why the propositional content in question is true, and a number of other things whose truth would explain why the propositional content in question isn’t true. Now, if these explainers are conceived of as things that entail the truth or falsity of the proposition in question, that would make a difference, since probability is supposed to track entailments in a certain fashion (though, as we know, rational belief really doesn’t. . .). But if the explainers are thought of more in terms of pretty conclusive evidence (and I doubt in the Sigmund story, the claim in question would be claimed to be an entailer of the falsehood of the conditional), then I don’t see why the probabilities need to be related much at all. If I’m running a statistical study, I can tell you in advance what the effect on my probability of the hypothesis I’m testing would be of lots of samples I might collect. Lots of these will be pretty conclusive evidence regarding the hypothesis. Perhaps the sample has already been collected. I might even know that it is a pretty conclusive sample, but not whether for or against the hypothesis. I still have whatever evidence I had initially that led me to want to test further. I was pretty confident that the hypothesis is false, but not certain. So I wanted to test it further. When I get further information, I’ll adjust. But nothing about the probability of getting a particular sample (which is bound to be very low) should control my probability for the hypothesis in advance of learning that it is the actual sample.

  2. I didn’t do the whole paper in 45 min. I did different parts (in addition to the essential parts, which I did whenever I gave the paper) of it at different presentations of it. At the Missouri conference, though, I also did material that’s not in this draft — the stuff about the “middle knowledge” debate.

    As for the argument you ask about…
    The argument starts from a datum about the Sly Pete story: that Sigmund’s claim that Pete will win if he plays is appropriate. (This is the original version of the story, where Sigmund is talking to someone just making derivative bets on Pete’s game; everything changes in the later variation where the person Sigmund is talking to is considering telling Pete what to do.) It then utilizes a principle to the effect that we shouldn’t make a speaker’s perfectly appropriate claim come out false unless there’s some fact that the speaker is mistaken about or unaware of that makes the speaker’s claim false and the speaker’s ignorance of this fact explains why the speaker would appropriately make his claim even though it is in fact false. So, what fact can be making Sigmund’s claim false? The most obvious candidate is that Gus holds a higher card than Pete. That fact, together with other facts that Sigmund knows (about the rules of the game, etc.) seems like it might have the potential to make Sigmund’s claim false. And Sigmund is ignorant of that fact — though he thinks it probably obtains. But wait! *That* fact can’t be enough to make Sigmund’s claim false, because Sigmund thought it was quite likely that that fact obtained (in fact, from Sigmund’s point of view, the fact had a probability of .83), and yet he still appropriately made his claim. If that fact were enough to make Sigmund’s claim false, then Sigmund made a claim that from his own point of view had a probability of .83 of being false – and you can’t appropriately assert something that from your own point of view has that high a probability of being false. But what fact or facts, then, *could* be making Sigmund’s claim false? None: there are no good candidates. So his claim is not false.

    *That’s* how the argument goes. The situation you describe doesn’t seem to clearly test either of the principles the argument uses. The principles don’t have much to say about all that’s going on in your example, unless in light of the evidence that might be coming in, your speaker gets into a position in which it’s already highly probable from her own point of view that p is false. In that case, what the principle says is that she then is not a position to appropriately assert that p – which, of course, seems right to me. If she is expecting evidence but the nature of the case results in there not yet, from her point of view, being a substantial probability of p’s being false, then we have no block to the appropriate assertion of p so far as the principles of this argument are concerned.

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