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July 15th, 2005

Defeaters and Chance

In a paper in today’s issue of Philosophical Quarterly, Michael Bergmann has a discussion of defeaters. Here are the definitions he provides for rebutting and undercutting defeaters.


epistemically appropriate basis for) the belief that oneís actual ground or
reason for b is not indicative of bís truth.

It seems to me these definitions can’t really get at what was driving the identification of these classes. Two examples about chance show this.

Let d be the belief that the objective chance of b is, right now, 0.2. It seems to me that is a rebutting defeater. But since it isn’t sufficient grounds to conclude that b is false, it has to be taken to be an undercutting defeater. And that’s so even if d is not in any sense about my epistemic practices that led me to believe that b.

Second example. Let d be the belief that the objective chance of b is, right now, 0.8. In some circumstances, that is incompatible with believing that b, so it is a defeater. But it is clearly not a rebutting defeater. And, since it is compatible with thinking the processes that led to belief that b are very reliable, it isn’t really an undercutting defeater either. So on this definition rebutting and undercutting defeaters aren’t exhaustive, which seems bad.

Posted by Brian Weatherson in Uncategorized

13 Comments »

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13 Responses to “Defeaters and Chance”

  1. Trent Dougherty says:

    One interesting feature of Bergmann’s account here (and I don’t know how relevant this is) is that there is any interesting asymmetry missing in classical accounts and defeat. That is, his account of undercutting defeaters refers to grounds of belief but his account of rebutting defeaters does not. For Chisholm, defeat is always defeat for evidence for a belief. Here is his account from the third edition:

    d defeats e’s tendency to make h probable =df e tends to make h probable; and d&e does not tend to make h probable.

    Unfortunately Chisholm is unclear whether he means by “made probable” (i) confirmed in the incremental Bayesian sense, or (i) made more probable than not. The main text favors the first interpretation, a footnote favors the latter. It seems wiser to me to work with incremental confirmation. Then we would get defeat spelled out in terms of disconfirmation.

    We could then say that d defeats e for h =df Pr(h/e) > Pr(h) & ~(Pr(h/e&d) > Pr(h/b)). Then strong defeat could be a special case in which Pr(h/e&d)

  2. Trent Dougherty says:

    Oops, that got cut off, here’s the rest, picking up from the last a full paragraph:

    We could then say that d defeats e for h =df Pr(h/e) > Pr(h) & ~(Pr(h/e&d) > Pr(h/b)). Then strong defeat could be a special case in which Pr(h/e&d)

  3. Mike says:

    Let d be the belief that the objective chance of b is, right now, 0.8. In some circumstances, that is incompatible with believing that b, so it is a defeater. But it is clearly not a rebutting defeater. And, since it is compatible with thinking the processes that led to belief that b are very reliable, it isn’t really an undercutting defeater either.

    That’s very interesting. I guess we’re assuming that the process is (nonetheless) reliable since it led to the formation of a belief (viz. b) whose probability we’ve learned is .8 and, after all, .8 is pretty high. But learning that b has probability .8, in this case, shows that the process is not reliable for the sorts of beliefs in question. Were the process reliable it would not have me form the sorts of beliefs in question unless their probability was higher than .8. There is the rejoinder that reliable belief-formation cannot be fine-tuned to every sort of belief. That sounds right. Still a generally reliable process might be unreliable for the sorts of beliefs you have in mind (even if inevitably so). But that seems sufficient to conclude that d is an undercutting defeater.

  4. Michael Bergmann says:

    I appreciate your comments Brian. Let me say a little in response. First, I donít consider it a bad thing to say that defeaters arenít exhaustively divided into rebutting and undercutting defeaters (in some of my work Iíve identified other kinds of defeater that are neither though I havenít claimed that Iíve identified all kinds). So the fact that there are defeaters that are neither rebutting nor undercutting isnít problematic from my perspective. I donít think we can conclude (as you seem to) that if a defeater isnít rebutting it must be undercutting.

    Second, the first example you give suggests that rebutting defeaters for b should include not only the belief (or an appropriate basis for the blf) that b is false but also the strong suspicion (or an appropriate basis for the strong suspicion) that b is false. Iím inclined to think youíre right about that. Hereís a first stab at a revision of D2 to handle that:

    D2*. D is a rebutting defeater for B iff D is a defeater for B that is (or is an epistemically appropriate basis for) the belief or the strong suspicion that B is false.

    Iíd be curious to know if you think that would handle concerns in the neighborhood of those raised by your first example.

    I also want to say something about Doughertyís comments. He notes that other accounts of defeaters focus on defeaters for evidence for blfs rather than on defeaters for beliefs. And he notes that my account of undercutting defeaters refers to blf grounds and my account of rebutting defeaters doesnít. To make the journal editors happy, I left out of my PQ paper a discussion I had comparing my account of defeaters for blfs with Pollockís account of defeaters for reasons for beliefs. That discussion can be found in my forthcoming book (Justification Without Awareness). I explain there why I think itís easy to translate back and forth between my way of speaking and Pollockís. Moreover, contrary to what Doughertyís comments might suggest (though I couldnít tell whether Dougherty meant to suggest this), my account of both rebutting and undercutting defeaters focuses on defeaters for beliefs, not on defeaters for reasons (or evidence) for beliefs.

    If there is some further discussion of this and I donít get back to it for a while, itís because Iím on vacation. But Iíll try to check up on it while Iím away.

  5. Carrie Jenkins says:

    Michael,

    On your new proposal:
    “D2*. D is a rebutting defeater for B iff D is a defeater for B that is (or is an epistemically appropriate basis for) the belief or the strong suspicion that B is false.”

    This doesn’t look to me like it quite gets it. Suppose I believe the chance of this coin’s coming down heads when I flip it is 0.2. I don’t think it sounds quite right to say that that means I have a strong suspicion that it won’t come down heads. I allow that it might come down heads, I just think it’s more likely that it won’t. But I needn’t nail my colours to the mast one way or the other.

    I was thinking you might want something more like:
    D2**: D is a rebutting defeater for B iff D is a defeater for B that is an epistemically appropriate basis for considered non-belief in B.

    In thinking about defeat , aren’t we interested in what makes it rational to give up belief in B, rather than (necessarily) what makes it rational to adopt some other belief (or other attitude)?

    Also, considered non-belief would handle cases where you come to believe the chance of the coin’s landing heads is 0.5 and this new belief defeats your previous belief that it will land heads. Maybe you wouldn’t want to include these cases (perhaps you’ll think ‘rebutting’ is too strong a word for what’s going on here), but there are surely interesting affinities with rebutting cases (more than with ‘undermining’ cases, at least) that we might want to capture.

  6. Michael Bergmann says:

    Thanks for your thoughts Carrie. I’ll have to think more about your reason for not liking my proposed D2*. I’m not yet convinced by what you say against it. As for your proposed D2**, the analysans would be true of undercutting defeaters too, I think (if considered non-belief amounts to being either disbelief or withholding — as the latter is defined in my paper). In fact, your D2** sounds closer to what I say in defining defeaters generally (see D1 in my paper and my discussion of it).

  7. Carrie Jenkins says:

    Michael,

    “As for your proposed D2**, the analysans would be true of undercutting defeaters too”

    That’s right, of course – I wasn’t being careful enough. What I meant D2** to convey is perhaps better captured by:
    D2***: D is a rebutting defeater for B iff D is a defeater for B that is an epistemically appropriate direct basis for considered non-belief in B.

    (By a ‘direct’ basis I mean a basis which bears on B itself, rather than affecting our attitude towards B only via its bearing on some other proposition, e.g. some proposition about the status of our ground for believing B.)

  8. Brian Weatherson says:

    Sorry for taking so long to get back to this – I was away from email/blogs for a little.

    I should have known that rebutting and undercutting weren’t meant to be exhaustive. I’m glad I know that now!

    I think Carrie’s right that ‘strong suspicion’ is too strong here. A chance of 0.2 is actually fairly high. A card is going to be drawn from a deck that’s about to be well shuffled, and p is the proposition that it’s a non-face-card diamond. Do we have a ‘strong suspicion’ that p is false? Hardly. It wouldn’t be much of a surprise that p turns out to be true.

    But maybe the problem here was the assumption that we really have a rebutting defeater. We don’t have an undercutting defeater. But not all defeaters that aren’t undercutting are rebutting. So maybe we should just live with the thought that this is neither rebutting nor undercutting.

    If we can’t do that, I think some variant on Carrie’s last suggestion is the way to go. Actually I think we can motivate something like Carrie’s idea the following way. Start with a fairly flat footed counterfactual analysis.

    D is a rebutting defeater for B iff D is a defeater for B that would be a defeater whatever evidence the subject had.

    The idea is that rebutting defeaters don’t need to interact with the evidence we actually have, so they should apply whatever our evidence. But it doesn’t take much imagination to see that this will be subject to the usual arguments against counterfactual analyses. So we should try the following instead:

    D is a rebutting defeater for B iff D is a defeater for B and the fact that D is a defeater in this context is not explained (in whole or in part) by the interaction of D with the evidence supporting the belief that B.

    And that’s just about equivalent to Carrie’s definition, except that my version has some redundant double negations.

  9. Michael Bergmann says:

    Both Brian and Carrie think D2* fails because “strong suspicion” is too strong. Again, I’m not sure this worry is right. But if it is, I’m not inclined to make the moves they propose to fix it. Instead, I think the following simpler proposal would be better:

    D2*-revised: D is a rebutting defeater for B iff D is a defeater for B that is (or is an epistemically appropriate basis for) the belief or the inclination to think that B is false.

    One can be inclined to think something is false without blving it is false or even strongly suspecting it is false (since the inclination can be quite weak). Notice that the first clause in this account of rebutting defeaters says that D is a defeater for B (so I’m not saying that all instances of being inclined to think B is false count as rebutting defeaters for B). If the defeater in question doesn’t get you to lean at all in the direction of thinking B is false, then I’m inclined to think it isn’t a rebutting defeater.

  10. Carrie Jenkins says:

    I guess I’m inclined to think you can rebut something either by giving reason for thinking it’s false or just giving (direct) reason for not thinking it’s true. But that’s a just a terminological issue. Even if we go with Michael’s terminology, however, I think what matters is that there are similarities (that it might be helpful to draw out) between rebutting defeaters for B and defeaters for B which defeat it by giving (direct) reasons for not thinking that B is true.

    Another thing I wondered: what’ll happen to the notion of rebutting if we operate with a multi-valued logic? Consider e.g. a three-valued logic with values 1, .5 and 0 with 1 the only designated value. Would you want to say that something is not a rebutting defeater for B if what it does is give you reason to think that the value of B is .5?

    (Of course, even if you don’t want this conclusion, the terminology that Brian and I seem to prefer is still not enforced: one might still say that the thing rebutting defeaters for B do is give you reasons to think B is not true. That’s stronger than saying all it need do is give you direct reasons for not thinking B’s true.)

  11. Michael Bergmann says:

    Carrie, you seem to want to distinguish a defeater which is a reason for “not thinking p is true” from undercutting defeaters for the belief that p. But undercutting defeaters for Bp give us a reason for “not thinking p is true”: they give us a reason to give up the belief in question, and giving up a belief that p counts as “not thinking p is true”. I’m sure there’s some other distinction you’re after here but it seems to me that what you’ve said isn’t the way to identify it.

  12. Carrie Jenkins says:

    Michael,

    “undercutting defeaters for B give us a reason for ‘not thinking p is true’”

    They do, but not the kind I’m calling direct (see my second comment on this thread).

  13. Trent Dougherty says:

    Two things strike me about this conversation. First, how complicated the definitions have become (can you say post-Gettier). Second, Michael has moved toward notions such as suspicion (with a strength modifier) and inclination both of which admit of degrees. So it seems to me that when things get complicated and degree-involving a formal apparatus has a good deal of utility. That is, rather than trying to identify any number of ever more complex types of defeaters, why not accept Chisholm’s notion of defeat in some degree-theoretic interpretation (the simplest of which is a probability structure, but there are other options). Then we would have a simple central notion of defeat whose species are individuated by their strength (of the inclination or the evidence or the logical probability or whatever your conceptual anchor is).

    d makes S at least as inclined to suspend judgment as to believe p

    d makes S more inclined to suspend judgment than to believe p

    d makes S more inclined to believe ~p than to believe p

    d makes S more inclined to believe ~p than to suspend judgment