Thursday, March 23, 2006

The Limits of Divine Defeation

I previously noted an interesting phenomenon: if you hear from a source that you know with certainty to be infallible, "P is true but you cannot know it," then you'll be thrown into such a state of epistemic confusion that you truly won't know that P, despite having heard it from an infallible source! This suggests that God could undermine or 'defeat' what would otherwise amount to knowledge - and even certain knowledge! - simply by asserting to you that you lack sufficient justification for knowledge. God's assertion here is "self-fulfilling", since it itself is the cause of your epistemic confusion, and is the only reason why your belief fails to constitute knowledge in this case. Speaking generally, we might recognize the phenomenon of "self-fulfilling defeation claims": claims of epistemic defeation in which the claim itself constitutes the defeater. But I'll refer to this phenomenon by the snazzier title of "divine defeation".

Now, I'm wondering just how far God's powers of defeation extend here. (Not that God exists, of course, but it can be a useful philosophical heuristic to pretend otherwise.) His arbitrary proclamations can defeat knowledge, but can they do any more than that? In particular, can they defeat claims of justification, or of high rational subjective probability?

If we stipulate that God cannot utter falsehoods, then he won't be able to say things like, "P is true but you cannot believe it" (for arbitrary P). For that would simply be false; even after hearing God say this, I might go on to believe P (perhaps alongside the second-order belief that I do not believe that P -- hi Moore!). This yields the contradiction that you cannot believe P and you can believe P, thus providing a reductio of the claim that God could utter such a statement.

But what of the divine proclamation, "P is true but you cannot justifiably believe it?" Is this impossible, like the belief case? Or is it instead "self-fulfilling", like the knowledge case? Would hearing such a statement throw a rational agent into such a state of epistemic confusion that they would lose all justification for their belief? That seems implausible to me. You might be confused, but still, testimony from an infallible source has got to count for something, right? If I heard God say that, I would believe that P, and justifiably so! (I might also believe the latter conjunct, i.e. that my former belief is unjustified; but I would simply be mistaken on that point.) So the proclamation would be false, so God could not say it.

The key difference between this and the knowledge case seems to concern the possibility of "meta-defeation". By this I mean the idea that ("meta") doubts about your epistemic status can themselves influence this status. Plausibly, if you doubt whether you know that P, then you actually lack knowledge that P. (This principle seems debatable, however. And if rejected, one might deny that any sort of 'divine defeation' is possible, even for strict knowledge.) But it is far less plausible to hold that such 'meta' considerations defeat justification. One can be justified in believing that P, even if they doubt whether they're so justified.

We could close this gap by building the "meta" considerations into the case. God could say, "P is true, but you cannot justifiably* believe that P (where justification* supplements standard justification with the additional internal requirement that you rationally recognize your belief as being justified)."

Or perhaps that won't work either, since you might believe that P, and recognize this justification ("I heard it from an infallible source!"), all the while mistakenly taking yourself to lack this recognition. That is, much like before, your belief is in fact justified*, even though you don't believe it is justified*. The incongruity is simply pushed back a step. So one-step recursion isn't enough. We're going to need infinite recursion, e.g. by saying: "P is true, but you cannot justifiably** believe that P (where justification** supplements standard justification with the additional internal requirement that you justifiably** recognize your belief as being justified)." If that even makes sense.

(The idea is to close all the "meta" gaps, by rendering it impossible for one to be in this super-justified state without realizing it. In addition to your belief being justified, you must recognize this fact, and also recognize that fact, and then recognize... ad infinitum.)

I'm going to give myself a headache if I go on any further. But it looks like divine defeation is fairly limited in power. Just as well, since I just had an experience as of God telling me that I couldn't justifiably accept the conclusions of this post. That actually isn't true, but you'll never know for sure.



  1. I wonder were, in this scenario, the certainty that God is infallible comes from? This experiment presupposes the possibility of certain knowledge, which I don't think we should admit to without a fight :)

  2. Heh, pity I can't edit my stupid fumbling typos :)

  3. > "P is true but you cannot believe it" (for arbitrary P). For that would simply be false

    Well I'd suggest that after god saying it you would simply be unable to believe. Regardless of that being rational.
    rationality is often breached in humans so I'd tend towards bending that rule than bending the proposed god is infallible rule (which is a stated assumption in this post as opposed to the rationality one which is, err... less clearly stated).

    Still I should know that you wish to hold rationality as an assumption and god’s lack of interference as an assumption etc (which relates to your mroe recent post) I wonder how many of these things we have to add to make it foolproof?

  4. (I tried to post this earlier but Blogger was acting funny.)

    I think that God could assert "P is true, but you will not believe P."

    Your argument against this is that "even after hearing God say this, I might go on to believe P", but I don't see why that has to be so. At first glance, it seems that you might go on to believe P or you might not, but surely God can arrange to only make such statements in cases where you are not going to believe P (or in cases where He can make it that you will not believe P).

    We can even make the same epistemic confusion argument that you make in the case of "know". Indeed, in your earlier post you described epistemic confusion as leading to a suspension of belief, which is exactly what we'd need in this case: "If God says I cannot know X, and he's never wrong, then there must be something dodgy about it... I'd better suspend belief." Just replace "know" with "believe" (and "X" with "P") and you can run the exact same argument.

    Even if you continue to insist that no perfectly truthful being could utter such a sentence in real life, you must at least concede that something like this could at least happen in fiction, since I've already written such a fiction. (The relevant portion begins with the last two paragraphs of this post, though in this case P is only deducible rather than being directly asserted.)

  5. Blar, yes, there are some instances of P (e.g. where it's independently true that I'll never believe P) for which God could assert that. I meant to suggest that he couldn't say it in general, for any arbitrary P. Such assertions are not self-fulfilling or guaranteed to be true, unlike in the knowledge case.

    Regarding the "suspension of belief" argument, it isn't clear that God's belief-assertion will create epistemic confusion of the right sort. In the knowledge case, his claim that I cannot know provides me with reason to doubt my justification or evidence. But in the belief case, there don't seem any evidential implications. God is making a merely psychological claim about what I will or will not end up believing. (If I take him to be infallible, I might form the second-order belief that I will never believe that P; but this belief of mine might well turn out to be false. It is still possible for me to believe that P, even while I doubt that I do so.) Since God's assertion gives me no reason to revise my epistemic assessment of P itself, it isn't clear why I should suspend belief about it. But even if I rationally ought to suspend belief, that's no guarantee that I will in fact do so. (I am not perfectly rational, after all.)

    G. - "I'd suggest that after god saying it you would simply be unable to believe." Why? There doesn't seem any psychological mechanism preventing me from forming such a belief, even after learning of God's assertion (see my response to Blar above about 2nd-order beliefs). Perhaps you are suggesting a brute metaphysical barrier, but that's just bizarre. We shouldn't think that an infallible being's assertions would make false things true. Rather, we should think that an infallible being can't possibly assert falsehoods.

  6. So is this what happened to Socrates? He heard something was true from the oracle but also couldn't know it? (LOL)


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