Tuesday, December 06, 2005

Self-Defeaters

The conference is going well, but for now I just have time now to write up a few quick thoughts on one of yesterday's talks. Lauren Ashwell (MIT/Auckland) was discussing the following widely-accepted principle:

(NBD) It is a necessary condition for S to be justified in believing that p that S not believe that her belief that p is unjustified.

This can be formalized as: "B~JBp -> ~JBp". That is, if you believe that another belief of yours is unjustified, then the latter belief really is unjustified. Self-doubt thus justifies itself. If you start to doubt whether you're justified in believing that you have two hands, then this doubt suffices to remove ("defeat") your justification for the common-sense belief. That seems silly to me, and I'm not really sure why anyone (let alone everyone) would believe NBD. To offer something more than mere intuition, in response to Lauren's talk I thought of an argument which seems to show that NBD leads to a contradiction.

I will assume that knowledge is closed under known entailment:
(Kp & K(p -> q)) -> Kq
If you know p, and you know p implies q, then you (are in a position to) know q.

I will also assume that our beliefs are accessible to us through introspection:
Bp -> KBp
If you believe that p, then you (can) know that you believe that p.

Finally, I assume that it is possible for someone to simultaneously believe that another belief is unjustified, and yet also believe that this former skeptical belief is itself unjustified. So the following is possible:
B~JBp & B~JB~JBp

Now, if someone (S) fitting the above assumptions could know NBD, then we get a contradiction. Here's how:

1. S knows: (i) B~JBp (starting belief, introspection)
(ii) B~JBp -> ~JBp (NBD)
Thus, by closure, S also knows: (iii) ~JBp

2. JB~JBp (knowledge entails justified belief; apply to (iii).)

3. B~JB~JBp (starting belief)

4. B~JB~JBp -> ~JB~JBp (NBD for belief that ~JBp)

5. ~JB~JBp (3,4 modus ponens)

Which contradicts (2)!

So given the other assumptions, NBD cannot be known. So you shouldn't believe it.

[Update: 8 Dec 05] I came up with a parallel argument that's slightly simpler, though with slightly less plausible starting conditions: Bp and B~JBBp. It would be rather odd, but surely possible, to believe p whilst thinking you're not justified in believing that you have the former belief. So consider this:

1) Bp (starting belief)
2) KBp (from 1, introspection)
3) JBBp (from 2, knowledge entails justified belief)
4) B~JBBp (starting belief)
5) B~JBBp -> ~JBBp (NBD for belief that Bp)
6) ~JBBp (4,5 modus ponens)
Contradiction: 3, 6.

Actually, this argument is stronger than the previous one. It doesn't merely show NBD to be unknowable, but indeed straight out false. Neat. (Though I suppose the supporter of NBD would instead reject my introspection principle, and thus (2).)

One final point of interest: it would seem that if NBD were true, then we should try not to doubt our existing beliefs (well, unless we go on to give them up, I suppose). After all, we presumably want to have justified beliefs. But a necessary condition for your belief being justified is that you not doubt it (in the strong sense of believing it to be unjustified). If you don't doubt it, it might be justified or it might not. If you do doubt it, then it's guaranteed to be unjustified. So it seems preferable to take the option where you at least have *some* chance of being justified.

6 comments:

  1. Another problem with NDP:

    (1) I can know p even if I believe I'm not justified in believing p.
    (2) If I know p, I'm justified in believing p.
    (C) NDP is false.

    I suspect there are examples that support (1) to be found in Radford's cases (a 1964 Analysis paper). He took the cases to be K without B, but I think they are better taken as K in which one is uncertain and this uncertainty could lead one to believe one isn't justified in believing when one is in fact justified in believing.

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  2. I suppose NBD has a certain sort of plausibility if you take it in a certain way: i.e., if the idea is that the belief that p is unjustified is itself a significant reason not to believe p. (We often get a little put out when people say that they agree that a belief is unjustified but they'll believe it anyway.) But I think in such cases we are assuming that the belief that p is unjustified is itself a justified belief. If I have an unjustified belief that p is unjustified, then it isn't clear why this would mean that p is actually unjustified. The curious thing about NBD, if I understand it aright, is that it means we are infallible when believing our own beliefs unjustified: it becomes impossible to say, "I believed my belief unjustified, but on further thought it is clear I was wrong, since I had forgotten that I had already found the necessary justification."

    I had to look up Radford, but I think Clayton might be right that a Radford case could be developed to support his (1) (and the argument would be much easier than Radford's actual argument). The basic idea is that there seem to be cases where we think we don't know something, but find that on further, or deeper, inquiry that we actually do. Thus, I can think that I've never learned the Spanish word for 'windshield', but find in actual Spanish conversation that it comes easily to me (my example). This does seem like it might be adaptable to an anti-NBD argument.

    I like your last paragraph, Richard. We can call it the NBD argument for universal dogmatism.

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  3. Brandon, that's exactly right about NBD making skepticism infallible. Regarding unjustified skepticism, Lauren offered the following quote from Bergmann (2005):

    "But what if S's belief that her belief that p is not formed in a reliable way is itself unjustified? Can a justified belief of S's lose its justification as a result of S's coming to hold an unjustified belief? I think it can. It's clear that it is an epistemically bad state of affairs for someone to believe both p and that her belief that p is not formed in a trustworthy way. Thus, if a person has a justified belief that p and then comes to have an unjustified belief that her belief that p is not formed in a reliable way, she will be getting herself into an epistemically bad state of affairs... the best way for S to escape the epistemically bad state of affairs she is in is for her to give up the belief that her belief that p is formed in an unreliable way. But that... doesn't suggest that S's belief that p - when it is held in conjunction with the belief that her belief that p is formed in an unreliable way - remains a justified belief."

    But, as I pointed out during question time, Bergmann is implicitly relying upon a sort of scopal fallacy. We can all agree that there's something wrong with believing the conjunction in question. We might phrase this as a wide-scope requirement, e.g. RR(if B~JBp then ~Bp). That is: You're rationally required that: if you believe you're not justified in believing p, then you do not believe that p. (The combination of beliefs is somehow defective or unjustified.)

    This must not be confused with the narrow scope requirement: if B~JBp then RR(~Bp). That is: if you believe ~JBp then you are rationally required not to believe p. (The particular latter belief is unjustified.)

    As John Broome drummed into us last semester, you cannot infer a narrow-scope requirement just from the corresponding wide-scope one. The inference is simply fallacious. So Bergmann's observation that there's something defective about the conjunction of beliefs does nothing at all to show that there's anything defective about one in particular, even in the presence of the semi-contradictory other.

    In light of this, I have trouble seeing the motivation for NBD. I wonder whether I have adequate justification for believing it to be "widely accepted"? ;)

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  4. Wow. As far as I know, I’ve never been blogged before. Or tried to respond to one, so let’s hope I do ok. Thanks for your comments, Richard. I enjoyed the conference; it was very nice to get to a NZ division AAP – haven’t managed to be in the country for one since 2000.

    Note that S might not know (2), as it seems you’ve assumed she does, and in this case we won’t be able to apply closure at the transition to (5). To get that she knows this, one has to assume the KK-principle. I assume this is something an externalist wants to reject on other grounds - in many cases, you don't believe you know what you do in fact know (there's no positive higher-level requirement on knowledge, although there is supposedly this negative one: NBD). In any case, the contradiction in your argument comes from this assumption that she knows (2), together with the fact that she doesn’t believe (2) (from (3)).

    I have to run off to a Christmas lunch now so I’ll have a look at the 2nd argument after that.

    Anyway, there certainly seem to be problems if you think that anyone can know NBD. For example, the “unreasonable procedure” for gaining knowledge which I mentioned (but stuffed up!) in response to you at question-time was supposed to be this (if I remember right):

    Teach S the NBD principle. Make sure you’re a respected reliable epistemologist, so she knows this. Now, when she gets into the situation where she finds herself believing that p in conjunction with believing that this belief is unjustified, she will know exactly what to do to resolve the problem. If she gives up the higher-level belief, she has a chance of having a false belief. However, the higher-level belief is both true, and justified (if the assumption of closure is correct – I’m not entirely sure about this). But it seems a strange epistemic procedure to follow.

    I’m trying to get a web-page up and running (I might finally have time now teaching for the year is over with!) so when I do I’ll post the paper up. There will be a link from http://web.mit.edu/philos/www/phil-grad.html

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  5. Hi Lauren,

    I was hoping not to need the KK principle, but only the weaker introspection (KB?) principle mentioned in the main post and employed in step 1 (i).

    Note that in the first argument, I'm only assuming that S has knowledge of those propositions listed under step (1). In step two, I assume only that "JB~JBp" is true, not that it is known. Because 1 (iii) states that S knows that ~JBp, it follows that S has a justified belief that ~JBp, which is to say that JB~JBp is true.

    To get the result in (5), I simply use modus ponens on the NBD principle (4) and the second starting belief (3). I don't require S to make this inference herself, so she doesn't need to know about it (it just needs to be true in fact), and the knowledge closure principle is not involved. If S believes that her belief that ~JBp is unjustified, then it follows from NBD that the latter belief really is unjustified (thus ~JB~JBp), regardless of whether S or anyone else knows this fact.

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  6. Whoops - shouldn't have tried to look at that so quickly! You're right that you don't need the KK principle - which is good, because I really don't think NBD is plausible, and it would be good to have even more reasons to think it's implausible. Thanks for clarifying that for me. Hopefully I understand the argument now, having had a closer look at it.

    I think the argument, given the assumptions, might be even stronger than it seems at first. As far as I can see at the moment, you can replace "JBp" as "has a justified belief that p" with "Jp" = "is justified in believing that p" (if you think believers can have such a property) which doesn't imply that S actually believes that p, and the argument still goes through. Then you don't even need S to go through the deduction at step 1; you only need that they potentially could (which is more in-line with your closure principle anyway). Although perhaps there is some problem with S believing that ~Jp on some basis, and being justified in believing ~Jp on another, so that S doesn't know (iii).

    I wonder if Bergmann's response would be that reasoning using NBD is itself defeasible. The refinement would be to claim that NBD should be stated with a caveat that of course such higher-level beliefs only act as defeaters in the absence of neutralising defeaters, such as the belief found in (3).

    After all, there's nothing wrong with:
    1. Knowing the widgets look red to you
    2. Knowing that, in the absence of defeaters, if they look red then they are red
    3. Not knowing that they are red because you believe that they are being irradiated by red light.

    I'm not sure what I think of this response – after all, if Bergmann’s reason for accepting NBD is that S gets herself into an "epistemically bad state of affairs” when she believes that p and also that that belief is not justified, surely one should say that she’s in an even worse state of affairs regarding these beliefs when she also believes that this higher-level belief is not justified. It doesn’t seem like things are getting any better for S (although maybe things do get better for S’s belief that p)? It seems to me that (3) should, on this line of reasoning, be what I called a "standard defeater-defeater" (and Bergmann calls an "intrinsic defeater-defeater" - a term which I didn't want to use because I'm not sure it lines up with Plantinga's use of the term) which only removes the justification of the defeated-defeater, rather than removes its defeating power (remember that defeaters don't have their defeating power in virtue (apparently) of being justified themselves, so it's perfectly fine (apparently) to have standard defeater-defeaters which aren't neutralising defeater-defeaters).

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