2.1 Rational instability of belief

Now that we've seen how problems can arise for the rational instability of credences, we are in a position to consider how they extend to belief. Reed (Reference Reed2012) argues that agents whose all-or-nothing beliefs shift in response to pragmatic factors can also be Dutch Booked, and so rationally unstable belief is problematic in the same way as rationally unstable credence. To put his point at its highest level of generality, if all-or-nothing belief plays any independent role in decision-making, then what choices you should be willing to make when you have a belief are different from those that you are willing to make when you do not have that belief, and this is the ammunition that we need to exploit in order to construct Dutch Books.

For example, here is a simple example of how such a Dutch Book might go.Footnote ⁴ Sam is riding a Ferris wheel at the carnival, and she is secured in her seat by a seatbelt. While she is at the bottom of the wheel, it is rational for her to act as if the seatbelt will hold her weight if she leans out, because the worst thing that can happen is that she would fall four feet. But when she is at the top of the wheel, it is not rational for her to act as if the seatbelt will hold her weight if she leans out, because if that is false, then she could fall to her death. Sam never tests the seatbelt by leaning out, so she never collects any new evidence about the security of her seatbelt, but she rides the Ferris wheel for five full circuits. Finally, let us suppose, since we have already seen how to construct a Dutch Book for Sam if her credences shift, that Sam's credence that the seatbelt will hold her weight if she leans out remains at .98 throughout her ride.

While Sam is at the top of the Ferris wheel, she doesn't believe that the seatbelt will hold her weight or that it will not hold her weight. But she would be willing to pay 2 cents for a bet that pays out $1 if the seatbelt would not hold her weight and $0 otherwise, because her credence that it will hold her weight is .98. When she reaches the bottom of the Ferris wheel, in contrast, although by hypothesis her credence stays the same, her belief changes – now she believes that the seatbelt will hold her weight if she leans out. So if beliefs make any difference for action, this belief should make a difference, here, and she should be willing to pay 99 cents for a bet that pays out a dollar if the seatbelt will hold her weight and $0 otherwise, since she believes that this is a winning bet. But in combination, these two bets lead to a guaranteed loss of a cent.

But this result has limited significance. And that is because not all pragmatic encroachers accept that binary beliefs actually do make any difference for action. According to one prominent family of views – pragmatic credal reductivism – all action is rationalized by credences, and all-or-nothing belief reduces to having a credence above a threshold that depends, in part, on the stakes.Footnote ⁵ This view is a form of single-tier pragmatic encroachment, because on this view, the stakes do not affect which credence it is rational to have, but only whether rationally having that credence counts as rationally believing. And on this view, Sam's belief comes and goes as she goes around the Ferris wheel, but which actions she is committed to taking does not shift, because her credences are constant and rational action depends only on credences. So on this view, Sam is not Dutch Bookable, despite the instability of her beliefs. So the Dutch Book problem is not a perfectly general one for shifty pragmatic encroachers – just for those who think that belief can play some independent role in choice or action.

But Dutch Books are only one familiar sort of reason for thinking that credences should not shift in response to practical factors that are independent of the evidence. And once we see how reasons to think that credences should not shift in response to practical factors can extend to the case of binary belief, we can see that other standards applying to credences can also be extended to apply to belief. So even if shifty believers are not Dutch Bookable, they still fail by other familiar standards that we use to evaluate believers.

For example, at the bottom of the Ferris wheel, Sam knows that she will soon – fully rationally – give up her belief that her seatbelt will hold her if she leans out. But since at the bottom of the Ferris wheel, Sam believes that her seatbelt will indeed hold her, it follows that she is committed to drawing the conclusion that in revising her belief, she will be believing less of the truth. So by her own lights, it is a problematic way of governing her own beliefs in service of the goal of believing the truth.

Similarly, at the bottom of the Ferris wheel, Sam believes that she will soon rationally come to give up her belief that her seatbelt will hold her. So she violates a kind of reflection-like principle on rational belief – she is committed to something that she knows she will be rationally required to give up. In the case of credences, it is not rational to be more or less confident in something than you believe that you will be rationally required to be in the future, absent forgetting something or other rational lapses. Similarly, in the case of intention, it is not rational to intend to do something that you believe that you will soon be rationally required to give up the intention to do. When Sam is at the bottom of the Ferris wheel, she violates a very similar principle with respect to belief. This still looks like a serious objection to the rational instability of belief in cases like Sam's.

2.2 Instability is optional

So far, we've seen why some pragmatic encroachers are committed to the conclusion that rational belief will be unstable in the face of shifts in the practical stakes. This commitment is suggested by the common examples used in case-based arguments for pragmatic encroachment, and it follows from arguments drawing on knowledge-action principles. And we've briefly seen some of the reasons why you might think that this kind of instability could be bad – at the very least, it seems to require reflective thinkers to see their own beliefs as not fully attuned to the truth, and to allow that it is rational to violate analogues of the principle of Reflection for binary belief – believing something that you know it will soon be rational for you not to believe.

But rational instability is not a mandatory feature of pragmatic encroachment. It is optional. There are two reasons why it does not follow from the bare thesis of pragmatic encroachment that it is rational for beliefs to be unstable over time. The first is that even if different beliefs are rational at different times (due only to pragmatic factors that are independent of evidence), it doesn't follow that it is rational to shift your belief over time in response to those factors, because there could be diachronic constraints on rational belief that forbid it. For example, even if the rational thing for Sam to believe about whether the seatbelt will hold her weight if she leans out while she is at the bottom of the Ferris wheel is that it will, but this is not rational for her to believe while at the top of the Ferris wheel, it could be that, having formed this belief while at the bottom of the Ferris wheel, it is not rational to give it up at the top, merely because she is at the top.

It turns out that the best empirical evidence about belief formation in the face of stakes suggests that actual belief formation behaves in this way. This is the phenomenon that Arie Kruglanski (Reference Kruglanski2004) calls “seizing and freezing.” If you put an agent in a situation in which it makes sense for them to form some belief, then they will continue to hold that belief even if subsequently put in a situation in which other agents do not form the belief. Having ‘seized’ on the information to form the belief, we then ‘freeze’ in that state, absent a sufficient jog to push us out of it. Any philosopher who has tried to use the same argument to convince both someone without prior commitments and someone who has already published a paper on a topic can recognize this same phenomenon anecdotally.

Abelard Podgorski (Reference Podgorski2016a, Reference Podgorski2016b) goes further, and defends a general view on which the rationality of belief is fundamentally a constraint on the diachronic process of belief maintenance over time. On Podgorski's view, there may be synchronic facts about the level of rational support that some proposition has at a given time, and those synchronic facts may or may not depend on practical factors in addition to evidence, but those facts bear only on what belief it is rational to form at that time, if the agent is considering the question. It is perfectly rational, on Podgorski's view, for an agent to have a belief that it would not be rational for her to form afresh at some time, or to lack a belief that it would be rational for her to form, provided that she is not rationally required to consider or reconsider, at that time. Podgorski's view offers an explanation of why the seizing and freezing phenomenon observed by Kruglanski could be a feature of rational belief formation and maintenance.

So earlier in this paper, I was being sloppy to talk about ‘rational instability.’ We need to distinguish between instability in what it is rational for an agent to believe, if she is considering the question afresh, and the rationality of being unstable in what one believes. If pragmatic encroachers are committed to rational instability at all, they are committed in the first instance only to instability in what it is rational to believe. But the problems of instability are all problems about an actual agent being unstable over time.

But even the conclusion that what it is rational to believe is unstable over time is optional for pragmatic encroachers. And that is because we don't need bank cases or knowledge-action arguments in order to motivate the thesis of pragmatic encroachment. Pragmatic encroachment might be true even if the only practical differences between cases that make a difference for what it is rational to believe are constituted by differences in the cross-temporal practical adequacy of some belief.

Because pragmatic encroachment has seemed so unorthodox a position in the climate of contemporary epistemology, much discussion of it has been focused on the arguments to think that it is true. So under those circumstances, it is not surprising that commitments of particular ways of arguing for pragmatic encroachment, including commitments of strong knowledge-action principles, would come to seem like parts of the package deal. But it is important to keep in view that this is what they are – commitments of certain ways of arguing for pragmatic encroachment, not commitments of the bare thesis of pragmatic encroachment, itself.

3.1 The significance of stable high stakes

I've just been arguing that denials of self-attributions of penicillin allergies are stably high-stakes – they make it rational to hold out for more evidence that one has no such allergy before forming a positive belief that one does not have it, and they do so in a way that does not carry risks for rational believers to end up vacillating in their beliefs over time, for these costs stay high across times. What I am now going to argue is that this – and many other cases like it – have been the best cases for pragmatic encroachment all along. A theory that gets to explain how there is pragmatic encroachment in these cases but has to give up on bank cases will not lose out on the best of what makes pragmatic encroachment an attractive view. On the contrary, it will keep the heart of it.

Consider the case of judgments of self-worth. Falsely believing yourself to be better than you are at, say, playing chess, or the piano, is a vice. But falsely believing yourself to be much worse than you really are is not a virtue – modesty, which is a virtue, is concerned with how you comport yourself, and perhaps what you attend to in thought, not with what you actually believe about yourself. In fact, falsely believing yourself to be much worse at something than you actually are is quite tragic. Compare the example of Virgil, who devotes seven years of his life to writing a PhD dissertation that documents the influence of Ralph Cudworth on Immanuel Kant's thinking. Years later, news comes to light on DailyNous.com of hitherto-undiscovered correspondence in which Kant asks, in 1794 “Wer ist diese Cudworth Person, die du in deinem letzten Brief erwähnt hast?”Footnote ⁸ If Virgil now concludes, along with other casual readers of DailyNous.com that his dissertation was worthless, this isn't modesty, but tragic. Given his personal investment, it is surely rational, rather than immodest, for him to hold out for better authentication of the letter.

Or consider a case from Marušic (Reference Marušic2012, Reference Marušic2015). You are a long-time smoker and are trying to work up a resolution to quit. The empirical evidence is compelling that it takes the vast majority of smokers many attempts before they successfully quit. But if you believe that you will be unsuccessful, you won't be able to intend to quit. Marušic argues persuasively that what makes quitting even possible, in such circumstances, is that quitters don't believe that they will fail. He actually goes farther, and argues that it is rational for someone trying to quit smoking to believe that they will succeed, but we needn't follow him so far in order to appreciate how his case raises trouble for the idea that the only conditions governing rational belief are truth-related. The evidence that smokers fail to quit on their first attempt compares very favorably to matters about which we seem to rationally form beliefs all of the time. We even rationally expect others to fail to quit smoking on their first attempt. But if that evidence is so compelling, then it wouldn't be rationally possible to actually quit smoking. Treating the proposition that we will fail in the same way as we would treat any other proposition with respect to belief would make it impossible to rationally form an intention – much less a resolution – to quit.

Marušic's point plausibly generalizes. Jennifer Morton and Sarah Paul (Reference Morton and PaulMS), for example, have explored the phenomenon that psychologists call grit – the capacity to stick with a task in the face of evidence of failure. Many achievements worth their salt require effort and commitment extended across time in the face of difficulties and setbacks. People with greater grit manage to stick to these tasks over the full range of time required, rather than being deterred when bad news arrives, deciding not to continue because of the unlikelihood of success. But there are low points along all difficult paths – points at which evidence that one will fail predominates over recent evidence that one will make it. So arguably, grit requires not concluding that one will fail, in the face of this evidence. To falsely conclude that one will not be able to succeed at one of the low points along the path is not only to unnecessarily fail, but it is to unnecessarily fail after a great deal of expended effort. So if rationality requires us to conclude that we will fail, at these low points, then rationality requires us to miss out on the capacity for most achievements worth their salt.

All of these cases so far are first-personal, and are relatively stable cases of high-stakes propositions, because they are based in relatively enduring features of ourselves – our biology, as with the penicillin allergy case, our self-worth or ability, or our long-term projects. But stable high-stakes cases can also arise with respect to others – particularly when they are grounded in relatively enduring background facts. For example, Simon Keller (Reference Keller2004) and Sarah Stroud (Reference Stroud2006) have explored the epistemic dimension of friendship, each arguing that it is incompatible with the demands of friendship that we apply the same evidential standards to conclusions about our friends as to similar conclusions about strangers.

For example, Billy and Stan are driving through Alabama, and are arrested for the murder of a convenience store clerk. When he is arrested, Billy confesses that they did it, and there are eye-witnesses to two young men of their description hopping into a lime-green convertible that looks just like theirs. There is even forensic evidence showing that the getaway car from the crime wore the very same tires as the car they are arrested driving. Billy and Stan's only defense is that when Billy confessed, he thought he was being arrested for stealing a can of tuna – which he had – and that there must have been another mint-green convertible with two similar-looking young men that drove by at the same time. Vinny – Billy's cousin – owes it to Billy not to respond to the evidence of guilt in the same way as local bystanders do.Footnote ⁹

Both Keller and Stroud claim that epistemic rationality and the demands of friendship are simply in conflict – that it is irrational to be a good friend. But this is an unattractive conclusion. If they are right about what friendship requires, perhaps that is because friendship changes the nature of the wrong that you inflict on someone by forming false negative beliefs about them. Since the kinds of friendships that plausibly come with such epistemic demands are relatively enduring, that means that these stakes are high in a way that is relatively stable.

The role of pragmatic factors in rational belief formation about loved ones is revealed not only in the contrast between how we form beliefs about friends versus strangers, but in asymmetries in how it makes sense to form beliefs about our loved ones. For example, if my wife comes home from work and compliments me on how dinner smells, there is probably something wrong with our relationship if my first thought is to wonder whether she found a coin in a vending machine return this afternoon. Yet if she comes home and complains about how dinner smells, our relationship is in trouble if it's not part of my interpretive repertoire to consider the possibility that she has had a rough afternoon. Yet unusual compliments might be just as good of evidence that she has had an unusually good afternoon as unusual complaints are that she has had an unusually bad one.

This asymmetry, too, can be explained by the role of costs of error in belief formation. Close interpersonal relationships like this one, as Steve Bero (Reference Bero2017) argues, are structured around caring deeply about what each other think of one. So forming false negative beliefs about a loved one is hurtful. But whereas it is negative to interpret a spouse's attempt at a compliment as caused by a coin in a vending machine return rather than by goodwill, it is positive to interpret her complaint as caused by her bad afternoon rather than by ill will. So one of these beliefs is hurtful in a way the other is not, and it is the one for which greater evidence is required. Again, the considerations that raise the stakes are the stable features of our interpersonal relationship, and so they are not liable to shift easily over time.

Even outside of the context of close interpersonal relationships, there are positive/negative asymmetries in how we form beliefs about others. For example, Tamar Gendler (Reference Gendler2011) considers the case of the distinguished African-American historian John Hope Franklin, who was awarded the Presidential Medal of Freedom in 1995. The night before he received the award, he hosted a small party with friends at the Cosmos Club in Washington, DC, a historically white club of which he was one of the very first black members, and where most staff were black. While walking through the club, a woman calls him out, presents him with her coat check, and orders him to bring her his coat. Given that all of the club attendants were in uniform and Hope Franklin was not, it is clear that she has formed a belief that he is staff on the basis of his race alone – a statistically promising basis, given the underlying demographic statistics at the club.

Gendler argues that in cases like this one there is a conflict between epistemic rationality and avoiding implicit bias – given underlying statistical regularities in the world, many of which are directly or indirectly caused by past injustice, perfect respect for the evidence will require sometimes forming beliefs like the woman in the club. But the belief that the woman forms is racist. And I hold out hope that epistemic rationality does not require racism. If it does not, then the costs of this belief must play a role in explaining why the evidential standards are higher, for believing that a black man at a club in Washington, DC is staff. And I believe that they are – a false belief that a black man is staff not only diminishes him, but diminishes him in a way that aggravates an accumulated store of past injustice.

3.2 How stable?

I've now touched on all of the main points that I promised to try to make in this paper: I've shown why it is natural for pragmatic encroachers to be committed to the claim that it is rational for one's beliefs to be unstable over time, illustrated why it is natural to worry about this commitment, explained why it does not follow directly from the thesis of pragmatic encroachment itself, but only from some of its motivations, and argued that the Reasoning Disposition account of belief defended in Ross and Schroeder (Reference Ross and Schroeder2014) lends itself to pragmatic encroachment on the rationality of belief that is relatively stable. Finally, I've been briefly rehearsing a range of cases that support pragmatic encroachment but for which there is no need to think that rational belief need ever be unstable. All of these cases are I think more compelling than the traditional train and bank cases that have been appealed to so regularly in the literature on pragmatic encroachment. I'll close in this section by addressing one prominent worry.

I've said that pragmatic encroachment is not committed to any rational instability in belief in response to pragmatic factors. But the actual account that I have sketched, grounded in the Reasoning Disposition account of belief, does not quite support the idea that it is never appropriate to alter one's belief in response to a change in stakes – just that this will be relatively rare. And so this brings back the possibility that even though the view that I prefer only makes it rational to believe bad things about one's spouse after that relationship ends, and doesn't allow Ferris wheel type shifts, that is still enough to be problematic.

The first objection that we gave to the rational instability of belief was the extended Dutch Book argument. This argument, as we noted, turned on the assumption that all-or-nothing belief can make a difference to action, but that assumption is accepted by the Reasoning Disposition view. So to construct a Dutch Book, all we need is to find someone who knows in advance that (for example), their friendship will end. Such a person will lack some negative beliefs about her friend that she may rationally come to endorse after the friendship ends, and we could use this to construct a Dutch Book. The problem with this is that if she knows in advance that her friendship will end in this way, then that is a problem with the friendship itself. Similarly, if we try to construct the Dutch Book with someone who knows in advance that she will have a close personal friendship with someone in the future, that won't work because knowing in advance that you will have such a close friendship with someone already raises the stakes for believing negative things about them now. Similar considerations apply, I believe, for Dutch Books about the other cases I've considered where the sources of the high stakes might end. So an agent who revises her beliefs in the way that I'm suggesting won't easily be able to predict in advance that she will be susceptible to a Dutch Book.Footnote ¹⁰

Another objection that I leveled to the rational instability of belief was that it violates a natural extension of the principle of Reflection. Strictly speaking, the principle of Reflection applies to credence, not belief or intention, and it needs to be carefully qualified to be free of counterexamples. But the intuitive idea of extended Reflection for belief is that you shouldn't believe what you are very confident that in the future you won't (or shouldn't) rationally believe. Similarly, you shouldn't intend what you believe that in the future you will (or should) rationally cease to intend. Easily unstable believers run afoul of this principle.

It's important to distinguish this principle – which I accept – from a closely related principle, which I do not. The closely related principle says that you should believe what you are very confident you will (or should) rationally believe. Notice that the analogous principle for intention is false: it makes perfect sense to wait to make decisions that you are very confident you will make in one way rather than another, provided that the cost of making the wrong decision is high, and there is some chance that information might come in before you have to decide, which could allow you to avoid the wrong decision. In such cases, it makes perfect sense to make only a conditional decision, or even just to put the decision off. In contrast, it makes no sense at all to intend now to do something that you are very confident you will change your mind about before the time comes to act – this defeats the point of intending.

Similarly, since beliefs are much like intentions, there is nothing strange, I contend, in not yet making your mind up about something that you expect to make it up about in the future. But there is something strange about making your mind up about something you expect it to be rational to change your mind about in the future. This is because whereas believing something, like intending something, is being committed to it, but not believing something, like not intending something, is just lacking a commitment.

What it is rational to believe, given the Reasoning Disposition account of belief, depends on the long-run expectation of the costs of error, in comparison to the long-run expectation of the benefit of simplifying thought. The long-run expectation of the costs of error is not affected by how far into the future those costs are. So it's simply not possible to be in a low-stakes context now but expect to be in a high-stakes one in the future. That means that believers who conform their belief formation to this advice will never violate the belief Reflection principle. In contrast, it is possible for the expected costs of error to be mostly in the short term. And when that happens, a believer should expect that after the short term has passed, absent any new evidence coming to light, it may be best to form the belief. When this happens, it may be rational for a believer who follows my advice to fail to believe something that she expects that it will be rational for her to believe in the future. But as I have just argued, this is not problematic in the same way.

So although, on my view, stakes can both go up and go down, stakes never predictably go up – they only predictably go down, and then only rarely in a way that will change what it is rational to believe. This isn't perfect stability, but it is a lot – and it just may be enough.Footnote ¹¹