Wednesday, September 27, 2006

Feldman's "essential dependence" theory of Gettierization

This is just a quick thought dashed off after class, but what's the problem with this precisification of Rich's view.

Let LL "for Lucky Lemma" be the general name for the falsehood essentially depended upon.

S's inference from premises P to conclusion C essentially depends on LL iff (i) S infers C from P, and (ii) it is not possibly the case that (a) S infers C from P and (b) C is justified for S and (c)d justifiedly believes LL is not true.

This seems to capture the intuition of the no-defeaters theory without the doomed subjunctive conditional.

That's awefully rough and I probably shouldn't post in a hurry, but I had the idea that something like this might work for what he says in the mid-to-upper 30's of the Epistemology Intro.

14 Comment(s):

  • Trent,
    Is the 'believes' in condition (c) doing any work? It seems preferably to require only that S be justified in believing LL is not true.

    Condition (c) also seems too strong in requiring that S be justified in believing LL is *not true*. Why not just:
    (c): S is justified in believing LL is not true or S is justified in suspending judgment about LL.

    By Blogger jon, at 9/27/2006 9:22 PM  

  • Hmmm... as a first approximation it seems on the right track. But honestly, these kind of analyses leave me a bit empty. It feels more like the kind of analysis that tells you when you've got an essentially depended on proposition, but not really what it is about the proposition that allows it to serve that role.

    So yes, LL is basically a proposition such that if it is denied by S, then that prevents S from being justified in believing C on the inferential basis of P (which, apart from the denial of LL, would have been adequate to be justified), or something like that.

    But that still just doesn't seem that illuminating to me. I why to know WHY the denial of LL can do that. That, for me, would be truly illuminating and satisfying. Is it just me who feels that way?

    By Blogger kdfkwak, at 9/27/2006 9:52 PM  

  • Jon,

    Since it's within the scope of a modal operator, I'm not sure it really makes any difference. The original way seemed more economical, but suppose we put it your way (you seem clearly right on the second point), do you think it works then? Actually, since we are talking about an *inference* here we might actually want occurant belief. However, that might hurt generality (although I'm actually not sure we really want the same account for basic beliefs and inferential beliefs). I'm of two minds here, so let's just have two versions. Do you think the modified version works?

    We now have:

    (ED1) S's inference from premises P to conclusion C essentially depends on LL iff (i) S infers C from P, and (ii) it is not possibly the case that (a) S infers C from P and (b) C is justified for S and (c) S justifiedly believes LL is not true.

    (ED2)
    S's inference from premises P to conclusion C essentially depends on LL iff (i) S infers C from P, and (ii) it is not possibly the case that (a) S infers C from P and (b) C is justified for S and (c) either suspension of judgement or disbelief is the attitude which fits S's evidence.


    John,

    I definitely want a definition of essential dependence which fills your inner void, but I'll settle for extensional correctness to start. In this case, I think we should be looking for anything more "enlightening" here. We'll want that when we try to explain what it is about essential dependence which keeps knowledge at bay, but not, I think, here. First I just want to know when it occurs and when it doesn't so I can apply it to cases.

    Sometimes if we get the extension right we can read the intensions off it. For example, if we examined all the members of the set of "red" things we'd notice something in common.

    re: your last comment, again, this is a two-step: get the notion of ED clear and correct, *then* see why *that* would ward off knowledge.

    By Blogger Trent_Dougherty, at 9/28/2006 12:09 AM  

  • Late-night comments always seem like a bad idea, but I can't resist. Accept the fact that I haven't thought all of this over as much as I'd like to, though:

    Suppose I see a man who looks uncannily like Tom Grabit, one of my fellow students whom I see on a fairly regular basis, and whom I know is prone to stealing, walk into the library, conceal a book beneath his coat, and walk out. Take propositions about my evidence here to be my P. Suppose further that Pinocchio, a student sitting nearby, looks over at me and says, "I don't think that was Tom Grabit." Suppose that I know Pinocchio well, and I know that he's a liar something like at least 90% of the time, and is almost always trying to play tricks on me. So, I (justifiedly) believe he's lying here, and so justifiedly believe that (LL) it is not the case that Pinocchio sincerely believes that that was not Tom Grabit. I thus allow myself to infer from P that (C) Tom Grabit stole a book from the library. So far, it seems to me that I know that Tom Grabit stole a book from the library... Right? Now let's move on.

    Under those conditions, it seems that I've got to justifiedly believe that LL in order to justifiedly infer C from P. At least, (somewhat weaker) it seems clear that it is not possible for me to infer C from P while justifiedly believing NOT-LL, i.e., while justifiedly believing that Pinocchio *is* being sincere. If I were to justifiedly believe anything like that, it would seem that I would have good reason to withhold my assent to C; after all, an otherwise competent observer like myself, and in the same situation as myself, has just declared to me that that was *not* Tom Grabit, and if I take him to be sincere then it seems I should have reason for concern about my inference to C. So I think that, according to your analysis, my inference to C from P essentially depends on LL. Let me know if you think that's right.

    Okay. You suggest you want to capture the intuitions of the no-defeaters theory with this, so I assume that you want to say something like:

    S knows that p iff (i) p is true, (ii) S believes that p, (iii) S is justified in believing that p, (iv) S's justification for p does not essentially depend on any falsehood.

    Now, it just so happens that I haven't told you the full story here. The above situation was one of those rare cases where Pinocchio was being sincere; it was the case that he sincerely believed that that was not Tom Grabit. So LL, in the above scenario, is false. If I've got it right, your theory therefore says that my inference to C essentially depends on a falsehood (LL), and so it says that I don't have knowledge that Tom Grabit stole a book from the library in the above scenario. But suppose that there's another fact about this scenario that I haven't mentioned: it just so happens that Pinocchio, despite his strange sincerity, was still wrong; it was indeed Tom Grabit who stole the book. So it seems that I would have in fact known that Tom Grabit stole a book if only Pinocchio hadn't spoken up, in a rare moment of sincerity, albeit mistakenly, about him, and thereby given me cause for forming beliefs about his lying.

    I don't know if I think that result is quite right; to me, it seems awfully close to the "misleading defeater" problems for other no-defeaters theories. My familiarity with Tom Grabit strongly suggested to me that it was him who stole the book; my familiarity with Pinocchio strongly suggested that there was no good reason to believe that he was being sincere about what he was saying, and so that there was no reason to pay attention to his misgivings. It seems that I really did know, based on all of my evidence, that Tom stole the book (in fact, I would have said, "I knew it all along!"); I had good sensory evidence, good memory evidence, etc., and also strong evidence that Pinocchio was being insincere (given his track record). In fact, if Pinocchio hadn't said anything, I apparently would have known -- it is Pinnochio's entirely mistaken utterance that indirectly destroys my knowledge, and through what seems like a fluke. Just because Pinocchio was mistaken about Tom and sincerely told me so, I don't know that Tom stole the book (because, recall, LL is a falsehood about Pinocchio's sincerity, yet apparently essential for my justifiedly inferring that Tom stole a book, in the conditions described above). I would have been better off if I hadn't known anything about Pinocchio's mistaken utterances.

    In other words, I'm saying that I have knowledge in the above scenario, despite my (apparent) essential dependence on a falsehood in my inference. If that's right, non-essential-dependence on a falsehood, as "essential dependence" is spelled out here, is not a necessary condition for knowledge.

    By Blogger Jason Rogers, at 9/28/2006 2:05 AM  

  • Jason,
    you say:
    "In fact, if Pinocchio hadn't said anything, I apparently would have known"
    If that is right, then there is no essential dependence in this case

    By Blogger jon, at 9/28/2006 9:17 AM  

  • Jason,

    That sounds like a good case, it seems structurally similar to one of the newspaper cases. I'll have to think through it in detail after I finish my formal semantics homework and class. One quick thing, though: I would make the following substitution in the definition of knowledge.

    "p is well-founded for S"

    for

    "S is justified in believing p"

    As it happens, I think my functional credit view gets that case right handily. So I'm going to think about the case really hard when I'm done.

    I also can't tell yet whether what Jon just said as I was typing is right, though it sounds plausible. Can't wait to think about this case!

    By Blogger Trent_Dougherty, at 9/28/2006 9:35 AM  

  • Jon,

    Quick, off-the-cuff comment before I run to class (and so this one's not that well-thought-out either; hopefully I'm not muddying the waters).

    What you say seems intuitively right, but I don't know that it's captured in the analysis of essential dependence presented here. If Pinocchio hadn't said anything, I also wouldn't believe that LL is not true -- I wouldn't believe that it is not the case that Pinocchio does not sincerely believe that that was Tom Grabit (because I probably wouldn't believe anything about Pinocchio). But then, given the scenario as I described it, it still seems true that "it is not possibly the case that (a) S infers C from P and (b) C is justified for S and (c) [S?] justifiedly believes LL is not true." I can't think of a case where I do justifiedly believe LL is not true but still infer C from P (at least in these few seconds I have before class). So it seems like I still have essential dependence in the above, according to the analysis.

    Maybe you can accomodate this with your revised analysis (above) that does not require occurrent justified belief that LL is not true? I don't know; I admit I haven't read over that analysis yet, and so haven't thought about it.

    By Blogger Jason Rogers, at 9/28/2006 9:39 AM  

  • As an addendum to the above, and also in further response to Jon's comment: Clearly it is the case that, in different circumstances, I could infer (C) that Tom Grabit stole a book from the library, from my premises (P) and not entertain any beliefs at all about whether or not (LL) it is not the case that Pinocchio sincerely believes that that was Tom Grabit. So, in that sense, there is no essential dependence on LL. However, it still seems to be true that (1) I infer C from P, and (2) it is not possibly the case that (a) I infer C from P and (b) C is justified for me and (c) I justifiedly believe LL is not true. Whenever I justifiedly believe LL is not true, I believe that Pinocchio, a competent observer in the same conditions as myself, sincerely believes that that was not Tom Grabit, which would seem to undercut my justification for C, and so it is not possible that (a)-(c) are all satisfied together. It seems that, in that case, I satisfy the right side of the biconditional for "essential dependence," and so there is in fact essential dependence on LL according to the proposed analysis. That result doesn't match with the intuitions mentioned at the outset of this comment, though. Does that seem right?

    By Blogger Jason Rogers, at 9/28/2006 11:35 AM  

  • Trent,
    I like where (ED2) is headed, but I don't think it's there yet. More must be done to strengthen the connection between C and LL. As things now stand, C and LL can be *completely* unrelated. We don't want it to be the case that my belief that Grabit took the book essentially depends upon the LL: I exist/bachelor are unmarried males/2+2=4..... those all of these LL's would fit the criteria.

    I'm not sure how to strengthen the correlation, but hopefully someone can help.

    By Blogger jon, at 9/28/2006 2:12 PM  

  • I should add that the problem here is not solely with necessary truths. There could be contingent propositions such that one's evidence make it impossible that one could be justified in suspending judgment or believing it despite the evidence justifying belief in C. This would be the case when LL and C are unrelated.

    By Blogger jon, at 9/28/2006 3:00 PM  

  • Earlier, I said: "maybe you can accomodate this [my Pinocchio example] with your revised analysis (above) that does not require occurrent justified belief that LL is not true? I don't know; I admit I haven't read over that analysis yet." Well, now I have read over it, and I think that (ED2) might work, as far as the Pinocchio example goes. Keep my C, P, and LL the same as they are in the original example. (ED2) says that my inference from P to C essentially depends on LL only if it is not possibly the case that (a) S infers C from P and (b) C is justified for S and (c) either suspension of judgement or disbelief is the attitude [toward LL -- this needs to be included] which fits S's evidence. So I need to show that it is false that it is not possibly the case that . . . [etc.] . . . In other words, I need to show that it is possibly the case that I infer C from P, C is justified for me, and either suspension of judgment or disbelief is the attitude toward LL which fits my evidence.

    Suppose that in some world, I have the same evidence and so the same P as in the example I described above, but Pinocchio sits silently nearby and says nothing to me. I infer C from P. C is justified for me. The attitude that fits my evidence in that scenario regarding (LL) -- the proposition that it is not the case that Pinocchio believes that that was not Tom Grabit -- seems to be suspension of judgment. I have no evidence either way about whether Pinocchio even has beliefs about Tom Grabit. ED2 therefore says that my inference does not essentially depend on LL, and so that protects it from leading to improper results when combined with a no-defeaters sort of analysis for examples like the one I described.

    So, right now it seems to me that (ED2) works for that case. I like Jon's point about contingent propositions which one is always justified in believing, though, if such propositions exist. It does seem like there needs to be some more explicit connection between C and LL, but I don't know what that connection is.

    In the meantime, I'll see if I can think of any more potential counterexamples. ;)

    By Blogger Jason Rogers, at 9/28/2006 6:44 PM  

  • (ED3) Conclusion C's being justified for S essentially depends on falsehood F iff (i) C is justified for S and (ii) ~<>(S's evidence remains the same with the sole exception of learning that F is false & C remains justified for S)

    By Blogger Trent_Dougherty, at 9/29/2006 8:06 AM  

  • Jon (or anyone else), can you spell out in more detail the threat you see from necessary truths or necessarily-ever-justified contingent truths.

    I think I'm not seeing it.

    By Blogger Trent_Dougherty, at 9/29/2006 8:12 AM  

  • Slightly cleared up version.

    (ED2) S's inference from premises P to conclusion C essentially depends on falsehood F iff (i) S infers C from P, and (ii) it is not possibly the case that [(a) S infers C from P and (b) C is justified for S and (c) either suspension of judgement or disbelief is the attitude to F which fits S's evidence].

    By Blogger Trent_Dougherty, at 9/29/2006 8:22 AM