Meta-evidence

Consider the following principle, one lifted from the same Feldman piece that prompted the last post:

Evidence that there is evidence for P is evidence for P.

I’ll call this principle the “metaevidence” principle. According to this principle, no matter how many repetitions of the phrase ‘there is evidence for’ precede P, it is always true that there is evidence for P.

If the metaevidence principle is true, then evidence and probability look quite different. Suppose it is probable that it is probable that P; it doesn’t follow from this claim that it is probable that P (since a claim can be probable and false). But doesn’t this same reason count against the metaevidence principle? That is, can’t there be evidence for something false? Of course there can. So why do things change when the claim is itself a claim about evidence?


Comments

Meta-evidence — 10 Comments

  1. Suppose that 55% of young guckies are males. And, 60% of young male guckies are aggressive, but only 1% of young female guckies are aggressive, while half of all adult male guckies and half of all adult female guckies are aggressive.

    I have Pat, a guckie, in my terrarium. Here is some evidence, which I will call Y: Pat is young. Y is evidence for the following, which I will call YM: Pat is a young male guckie. And YM, in turn, is evidence that Pat is aggressive (which conclusion I call A).

    Y is evidence for YM, and YM is evidence for A, but Y is not evidence for A (indeed, Y is evidence against A). So, Y is evidence that there is evidence for A, without being evidence for A. So the meta-evidence principle is false.

    On the other hand, Jon, while I agree with you that the parallel principle for probability is (also) false, I don’t think I can quite accept your reason, although I’m having a hard time explaining exactly why not.

  2. Jamie, good example! It shows clearly why the probability claim is false, and if we understand evidence as a positive difference between conditional and prior probability, it’s also a counterexample to meta-evidence. But I’m sure Rich would say that such an understanding of evidence is mistaken (for familiar reasons having to do with confirmation paradoxes and the problem of necessary truths, at least, but he may have other reasons as well).

    Maybe you are bothered by my reason because your are strongly inclined toward internalism in epistemology? If so, you’ll maybe look for an account of evidence on which it is reason- and belief-guiding. Then if you have evidence that you have evidence for p, you are on your way to being entitled to conclude that you’ve got evidence for p. And once you get there, you’re entitled to argue from the existence of evidence for p to p itself. That’s one way to talk yourself into the meta-evidence principle, anyway.

  3. I do think that evidence is that which makes a positive probabilistic difference, but does my example depend on that? I don’t think it does. It’s just very plausible (isn’t it?) that Y is evidence for YM and that YM is evidence for A, and very implausible indeed that Y is evidence for A. Denying a general equivalence principle isn’t going to change the plausibility of the example.

    What bothers me about your quick argument

    Suppose it is probable that it is probable that P; it doesn�t follow from this claim that it is probable that P (since a claim can be probable and false).

    doesn’t have to do with internalism. It has to do with my view about the nature of probability judgments. It seems to me that if the probability that the probability of p is .9 is .8, then the probability of p must be at least .72. Since you are an almost-Bayesian, I expect you to agree with me!

  4. I’d agree with Jamie about the .72 claim. I think that the failure of the meta-probability claim has to do with the definition of “probable.” If we take it that for p to be probable, the probability of p must be higher than some x (perhaps contextually determined), then it may be probable that p is probable, while p is not probable. Set x=.75 and Jamie’s example is such a case–it is probable that p is probable, but (if the remaining .1 probability is that the probability of p is 0) p is not probable.

    I’m going to toss in an off-topic question here: Can anyone think of a property of propositions D such that:
    (1) A claim can be both D and false;
    (2) If the proposition “p is D” is D, then p is D.
    It seems to me there should be one, but I can’t think of it. (If you believe in first-person transparency, then “A believes that p” would work, but I don’t think I do believe in first-person transparency.)

    If there is no such property, then the fact that a proposition can be probable and false does entail the denial of the meta-probability claim! Though I think there was more to Jon’s argument than that.

  5. Jamie, my nearly-bayesian side agrees about .72! But I don’t see how this leads to a problem with my argument. To be probable requires a probability of at least .5, and if we simply adjust the numbers you use, we’ll get a case where the metaprobability is over .5, and the base probability can be under .5. And so it is possible to for a false probability claim to be probable. I’m still missing what bothers you here…

  6. On Matt’s question, all we need is something that satisfies S4, not even S5. We just need DDp to entail Dp. Lots of things do that without having Dp entail p.

  7. Jon, sure, that’s a possibility. So, ok, what was it that was bothering me? Oh, I know.

    Suppose it is probable that it is probable that P; it doesn�t follow from this claim that it is probable that P (since a claim can be probable and false).

    A claim can be probable and false, but that fact can’t be used to show that Probable(Probable P) doesn’t imply Probable P, since it could well be that certain kinds of claims cannot be probable and false. Compare the principle â�� â�� P â�� â�� P. It is correct, even though in general a claim can be possible but false.

  8. Oh, man. I was pretty careful about getting the right entity codes, and that principle looked exactly right when I Previewed.
    Anyway, it was supposed to be POSSIBLY POSSIBLY P entails POSSIBLY P. But I tried to get fancy.

  9. Jamie, the comments are limited in terms of what special symbols are allowed, even though the preview function has them showing up. Rats!

    You’re obviously right about the generalization of the argument I gave. You’re reply is also a wonderful example of a philosopher’s predilection. Michael says, “wanna eat,” to which I say, “sure, let’s go to Shakespeare’s,” to which Michael says “why there?”, and I say, “Oh, no special reason, I just haven’t been there for a couple weeks.” Here comes the character trait: Michael says, “Do you always want to go to Shakespeare’s when you haven’t been there for a couple weeks?”

    This is a true story! About Michael Hand, my dear friend, with only the name of the restaurant changed. And, for him, it happens all the time; in my opinion, part of what makes him (and others who have this trait) really good critical philosophers… take a specific reasoning instance and generalize the hell out of it, and see if the generalization is true!

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