Monday, January 23, 2006

A Paradox for Subjective Rationality

I've written before about why rationality can't be too subjective. But here's another reason: it leads to contradiction. Consider Kolodny's two "core requirements" of rationality:
C+: If one believes that one has conclusive reason to have A, then one is rationally required to have A; and
C-: If one believes that one lacks sufficient reason to have A, then one is rationally required not to have A.

Now consider someone who believes that they have conclusive reason to do what they believe they lack sufficient reason to do. (Granted, this is a very odd belief to have. But I think it is possible. Perhaps they've been told that their beliefs have been manipulated by an evil demon into being unreliable [update: this is explained further in my comments below]. Or perhaps they're just incredibly irrational. Whatever.)

It would then follow from C+ that they are rationally required to do what they believe they lack sufficient reason to do. Call this action 'X'. That is, we have so far established that they are rationally required to X. But recall that our agent believes that they lack sufficient reason to X. It thus follows from C- that they are rationally required not to X. Putting these two results together, we find that our poor confused agent is both rationally required to X and rationally required not to X!

This violates what I will call the "consistency of rational requirements" principle:
(CRR) It is not possible for one to be both rationally required to A, and rationally required not to A.

In other words, rationality cannot make contradictory demands of us. It cannot demand both that we do something, and that we don't do it. That's just not a fair ask.

If (CRR) is true, as I think it is, then the case I provide above shows that Kolodny's "core requirements" cannot be true.


  1. Richard,

    I wonder if CRR doesn't rule out too much. Consider the following (plausible, I think) rational requirements:

    RR1: If one believes that A&B, then one is rationally required both to believe that A and to believe that B.

    RR2: If one believes that A, then one is rationally required not to believe that ~A.

    Now suppose someone believes, because of some irrationality, A&(~A). According to RR1, then that person is rationally required to believe A. Hence By RR2, he is required not to believe ~A. But by RR1 he is required to believe ~A. Hence by CRR, RR1 and RR2 cannot both be rational requirements.

    This seems parallel to your paradox case for C+ and C-. You imagine someone who believes
    (1): I lack sufficient reason to X.
    (2): I have conclusive reason to X.

    Now I assume that having conclusive reason to X is a sufficient (but not necessary) condition to having sufficient reason to X. Thus from (2) we can conclude (3) I have sufficient reason to X. But (3) and (1) are contradictory.

    So you show that if someone starts with contradictory beliefs, then C+ and C- will produce conflicting rational requirements. But it seems that any nontrivial system of rational requirements will run afoul of CRR under such conditions.

  2. I like this argument, and I think CRR makes a plausible meta-requirement for .

    I can't remember if Kolodny considers cases like this, but there's perhaps a fairly straightforward counterexample to C-, which at least suggests we should be cautious about it. Suppose someone is a skeptic, of a broadly Humean sort, who finds convincing various arguments both that A may well be wrong and that there is no reason for believing A that withstands critical examination; but who believes on good reasons, and perhaps rightly, that as a matter of our construction we can't avoid believing A. It isn't clear that the skeptic's believing A while not believing he has sufficent reason to believe it is irrational, although obviously it's not an optimal state of rationality. There is no contradiction in the claim that given the way we are set up, it is futile for us to try not to believe A, even though we have what we believe to be conclusive reasons for believing that A is wrong; despite the fact that this will always put us in a state of contradiction (or, as Hume suggests, oscillation between the two - and I think, when considering rational requirements, we need at least to consider whether there is any set of conditions under which the most rational thing to do would be to oscillate between two contradictory beliefs, depending on the context).

    Such a state is consistent with CRR because the skeptic doesn't have to hold that we are rationally required to believe A, but only that we can't avoid doing so It does conflict with Derek's RR2, but I'm not convinced that RR2 is plausible. Suppose I believe B and C, and B implies A but C implies ~A; on accepting these inferences and then, in housekeeping, applying RR2, I would be forced to conclude that I am rationally required not to believe A (because I believe ~A) and not to believe ~A (because I believe A). This doesn't seem reasonable to me, since it must also be rational to reject only one of the two; it would be more plausible to say that (RR3) we are rationally required not believe one member of a contradictory pair ('at least one member' if we reject excluded middle). (RR1 doesn't seem to me to be plausible, either, by the way; it seems to me that what is rationally required given a conjunctive belief depends on the rational status of the conjuncts in the belief, i.e., something like RR1 may be true, but only with qualifications.)

  3. Richard, thanks very much for your comments, and for alerting me to this post.

    Richard raises an important objection. In the paper, I addressed something like it in footnote 22. I'll paste it below and then elaborate a bit.

    22. Glenn Ross raises the following objection against the narrow-scope readings of I+ and I-. If someone, at one and the same time, believes that she has conclusive reason to X and believes that she lacks sufficient reason to X, then I+ and I- will require incompatible things of her. She will be required, at one and the same time, to intend to X and not to intend to X. Whatever she does next, she will be in some way irrational. This seems to me, however, the right thing to say about such a case. She has backed herself into a corner. So it is unclear, on reflection, what the objection is supposed to be. Why can’t it be the case that rationality requires one to intend to X and not to intend to X? Because ‘ought’ of reason implies ‘can’? But it would beg the question, at this point, to assume that the ‘ought’ of rationality is the ‘ought’ of reason. If the ‘ought’ of rationality is understood along the lines of the Transparency Account, then it is entirely explicable how one could be under conflicting rational requirements. If someone believes that she has conclusive reason for an attitude, then, as it seems to her, she ought to have it. And if she also believes that she lacks sufficient reason for that attitude, then, as it seems to her, she also ought not to have it. She feels two conflicting normative ‘pressures,' and whatever she does next, she will be resisting one of them.

    To restate: Why should we accept CCR? It doesn't seem to me that it captures our judgments about particular cases. Whatever the subject whom Richard describes does next, he will be being in one way irrational. ("What if he believes some contents on the basis of which he might rationally revise one of his beliefs about his reasons regarding doing X?" In the end, I'm not sure that it matters. But, at any rate, it suffices to consider a case in which he doesn't believe any such contents. The CCR ought to be valid in such a case.)

    The fact that CCR doesn't capture our judgments, if it is a fact, might not be decisive. There might be some theoretical reason for accepting CCR. The question is what this reason might be. We can't appeal to the principle that ought implies can without begging the question of what sort of normativity rationality has.

    It is perhaps worth noting that John Broome sent me a draft of a reply in which he raises a related objection: that one might believe that one had conclusive reason to X and conclusive reason not to X. In this case, the conflict would be one of intending to X and intending not to X, as opposed to intending to X and not intending to X. My reponse is similar.

    I might be willing to accept a different principle: that if one complies fully with reason, then one does not violate any requirements of rationality (which means that one is not confronted with conflicting rational requirements).

    I agree, then, in the main, with Derek's reply on my behalf. I think Brandon is right, though, that the rational requirements of logical consistency and closure in belief, when spelled out, need to appeal to the "rational status" of the relevant beliefs. It isn't clear which conjunct one is rationally required to give up until we consider what the subject believes about the evidence for those beliefs. This is important for the argument for my claim that even these rational requirements are derived from requirements like C+ and C-, which mediate beliefs about reasons for attitudes and attitudes themselves. I suspect that there is a way for Derek to reformulate the reply, however, taking this into account.

    I haven't thought much about Brandon's objection, which is also well taken. My initial response, I suppose, is to think that the skeptic is being irrational, even though, if the skeptic is right, he can't help but be. Why should "is irrational in X-ing" imply "could have done otherwise"? Because ought implies can?

  4. Brandon,

    Doesn't your RR3 imply my RR2?

    RR3: One is rationally required not to believe one member of a contradictory pair.
    If one believes that A, then one will believe both members of a contradictory pair unless one does not believe that ~A.
    If one believes that A, then one is rationally required not to believe not ~A.

    Note that there are two ways to be in compliance with a rational requirement like RR1 and RR2: one can either comply with the consequent or make the antecedent false. But for as long as you do neither, you are in violation of the requirement and, in that respect, irrational. That somtimes one of those ways is manifestly more rational than the other does not show that the conditional requirement itself is faulty.

  5. I think that your initial premise is simply contradictory.

    I would re-phrase to not use the word conclusive, which you are perhaps using to escape the contradiction.

    "Consider someone who believes that they have sufficient reason to do what the believe they lack sufficient reason to do".

    That is clearly absurd -- one cannot consistently believe something and its negation at the same time.

    Perhaps you could explain what constitutes a "conclusive reason" which is different from sufficient reason.


  6. Niko - thanks for your reply, and for pointing out that crucial footnote I missed!

    "Whatever she does next, she will be in some way irrational. This seems to me, however, the right thing to say about such a case. She has backed herself into a corner."

    I agree with that, but I don't think it necessarily supports your position. To say "you will be irrational if you do not X" is not the same thing as saying "you are rationally required to X". For instance, perhaps they are simply irrational to begin with, and their X-ing has nothing to do with it. (This seems plausible in the cases we are discussing, where the confused agent begins with irrational or even contradictory beliefs.) So I'm not convinced that we can move from your evaluation quoted above to the claim that rationality positively demands that our agent performs a contradiction. Perhaps the following isn't much of an argument, but it just strikes me as a bizarre thing for rationality to ask of us! CCR captures the intuitive idea that rationality offers sensible guidance. "Do both X and not-X" is not sensible guidance!

    On the other hand, I have to agree that your Transparency account makes it clear why CCR is (purportedly) false. If rationality is merely a matter of doing what it seems to you that you ought, then having contradictory beliefs about the latter will straightforwardly lead to contradictory rational requirements. But if we find CCR independently plausible (as I think I do) then that might lead us to reject your Transparency account.

    Derek - as stated, your proposed requirements were narrow-scope ones, and false. The true versions are wide-scope: as you say, they can be satisfied by rejecting the antecedent rather than complying with the consequent. That is, the true version of RR2 would say:

    (RR2-wide) Rationality requires that: if one believes that A, then one does not believe that ~A.
    Equivalently: Rationality requires that: one either does not believe that A, or does not believe that ~A.

    This won't lead to any violation of CCR, because you cannot conclude from my believing that A that rationality requires me to not believe that ~A. Perhaps it rather requires me to reject my prior A-belief.

    (If this doesn't entirely make sense, don't worry, I'll probably write another post tomorrow on "wide-scope" stuff.)

    MP - it isn't contradictory for a person to have contradictory beliefs. "Sam believes that P and not-P" is perfectly possible. What isn't possible is for Sam to be correct in this. Too bad for Sam. But our theories should be able to cope with his irrationality nonetheless :-)

    Incidentally, I was hoping my scenario might even be able to avoid ascribing outright lunacy to our agent. Suppose (in that distant possible world where something like Christianity is true) that an angel tells Sally that she is about to be possessed by the devil. The angel warns Sally that this will make her faculties very unreliable, and she will become disposed to initially conclude the very opposite of what she ought. Heeding this advice, Sally decides to outwit the devil by, in each new case, doing the opposite of whatever she initially concludes she ought.

    Sally thus believes that she ought to do whatever she initially believes she ought not to do, and vice versa. This is complicated, but, I think, coherent. She might reason about a problem and initially conclude "I ought to do X". And then she might further reason "Ah, but the devil fools me! I ought instead to not-X." In the middle of her reasoning, we can run through the argument in my main post to show that Kolodny's requirements make contradictory demands of her. But I don't think rationality is making contradictory demands of her in this case. (I do not think that she is rationally required to X at all.)

    I hope filling out the scenario like this makes it a little clearer what I'm trying to get at here.

  7. I don't have much more to contribute to this thread, but I'm enjoying it considerably.


    RR2 implies RR3, I think, but I don't think the reverse is true. Given an initial contradictory conjunction, and an additional RR2 implies that I ought not to believe either conjunct, whereas an additional RR3 implies that I ought not to believe one of them. The same cases will violate either, of course; but, unless I misunderstood you, they are not the same requirement.

    But you're right that I seem to be thinking of rational requirement in a different way, and I'll have to think further about it. Part of my reason for thinking about it this way that I'm inclined to think that any account of rational requirements has to take into account paraconsistent initial conditions, for much the same reason that AI theorists are interested in paraconsistent logics: rational people will, in fact, very often be in a paraconsistent state, due to changing beliefs, etc. An account of rational requirements has to account for rationality under these circumstances -- otherwise, we're really just talking about logical implication in an unnecessarily round-about way. And talking about logical implication doesn't on its own tell us anything about what we ought to do, rationally speaking, which is what I was taking rational requirement really to be about.


    I don't think it's so much a matter of 'is irrational in X-ing' implying 'could have done otherwise', but the sort of inability to do otherwise that's on the table. It's analogous to Berkeley's argument against skepticism about the external world: the skeptic about the external world uses a prejudgment about the way things are to split the world into a merely apparent external world and a real external world, and then identifies the former with what we call the external world and the latter with something we can't know. Berkeley's point is that this isn't a serious attempt to give an account of external world, but instead an attempt to fit the external world to arbitrary assumptions. Likewise, the skeptic in the rationality case could (as Hume does in Treatise 1.4.1) regard his scenario as a general scenario to which everyone is subject, and then conclude that we can't seriously do anything with an account of rational requirement which understands it in such a way that, whether in general or on a given point, we are always and necessarily in violation of our rational requirements. If we had a good argument for taking rational requirements to be necessities recognized as such a priori, we could get around this; if they are not necessary, or not recognizable a priori, I think the skeptic has a bit more wiggle-room for arguing that he's being rational.

  8. It doesn't make things much clearer to me. You can prove anything from a contradiction, this is well-known. Including your theories. (As an aside, it it possible to prove a contradiction from a contradiction?)

    Regardless, I fail to see what is interesting about pointing out that someone with inconsistent beliefs is going to be caught up in a conflict of intentions.

    What do you mean by rationality other than logic? Rationality and logic can certainly make contradictory demands of us -- it does so all the time. There is a phrase in computer science -- "Garbage in Garbage Out".

    The way I see it, conflict plays a central role in forcing us to re-evaluate our beliefs. Clearly we don't operate on boolean logic, but numerical probabilities and strengths. We frequently have conflicting goals and desires, and we don't vanish into a puddle of logic.

    I haven't read Kolodny, but I think it's only fair to reasonable to accept that Kolodny's arguments are based on having noncontradictory beliefs. Maybe I'll get round to it sometime when I'm not at work :)


  9. I have no reason to leave a comment.

  10. MP, as explained in my previous comment, none of my premises were themselves contradictory. (To say "X is a contradiction", or "S believes a contradiction", or to otherwise talk about contradictions, is not itself a contradiction.)

    Update to my response to Derek: the promised post is here.


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