On what we should believe (and when (and why) we should believe what we know we should not believe) Draft for Kevin McCain and Scott Stapleford (ed.) Epistemic Duties. Routledge. Clayton Littlejohn King's College London 0. Introduction Here is a familiar way of thinking about epistemology. Epistemologists are interested in questions about knowledge and they're also interested in normative questions. The first set of questions concern the nature and extent of knowledge. The second concern what we should believe. Imagine this division were reflected on your syllabus. Half of your class is dedicated to each set of questions. Imagine (if you can!) that one of your students read the syllabus. She wants to know how the two parts of the course are connected. One answer, which probably wouldn't be satisfying to her, is simply that these are the questions that epistemologists try to answer.1 That's just how things are and that's why your syllabus looks like this. My answer would be different. If I were to share my own personal views with students, I would say that these two parts of epistemology are connected because knowledge plays an indispensable role in our best normative theory.2 (We shouldn't believe what we don't know! Ignorance enjoins silence!) Since I don't normally share my views with my students, I'd say that some people think these questions are connected and say that it's an interesting and open question whether they are. In this paper, I want to explore a new way of thinking about how they might be connected. Drawing on recent work in ethical theory, I shall offer an account of what we ought to believe on which what we ought to believe is connected to facts about what we can know.3 The idea that the two parts of epistemology are connected isn't new, but the proposal about how they're connected is. While I think that there is something right about the positive proposal offered here, my main interest in writing this chapter is not to defend this proposal about knowledge and its normative role, but to introduce a way of addressing questions about what we 1 See Foley (2012). 2 This way of thinking about the connection reverses a familiar order of explanation, which is that the normative side of epistemology is connected to knowledge insofar as having justification or being justified is necessary for knowledge. An evidentialist (e.g., Conee and Feldman (2004) or 2 This way o thinking about the c nn ction reverses a familiar order of explanatio , which is that the normative side of epistemology is connected to knowledge insofar as having justification or being justified is necessary for knowledge. An evidentialist (e.g., Conee and Feldman (2004) or McCain (2014)) would characterize this (arguably) necessary condition on knowledge in terms of evidential support. This more traditional way of thinking about the relationship explains why the normative side matters to discussions of knowledge, but doesn't give us much to say to someone skeptical of the importance of knowledge if they think that only the normative questions in epistemology matter. 3 The view that it is rational to believe, that we have justification to believe, and/or that we ought (in some sense) believe when the probability that we're in a position to know is sufficiently high is defended by Dutant and Fitelson (MS), Dutant and Littlejohn (forthcoming, forthcoming b), and Littlejohn (forthcoming). I had mistakenly thought that this knowledge-centric view of proper belief was the view of Dutant (forthcoming) and proposed it as a response to Steele's (MS) defence of the idea that we should use statistical evidence as the basis for punishment in criminal trials. Although none of us seemed to like it all that much initially, the view seems to have grown on us. Dutant and Fitelson (MS) develop a version of this view in a consequentialist framework and it's intended to give an account of synchronic wide-scope rational requirements. To my knowledge, this is the first attempt at linking the view to a non-consequentialist framework. ought to believe that might be fruitful. Even if you don't particularly care about knowledge and don't think that it matters whether anyone knows anything, you might extract from this discussion a new way of thinking about what we ought to believe that suits your purposes if you were to strip out all the references to knowledge and substitute in something else that better reflects your values. 1. What is justification? A theory of justification tells us what we should and should not believe. This accords with how we talk about the justification of action. Such talk is talk about what is and what is not consistent with the normative standards that determine what we ought to do. In ethics, we might follow the consequentialists in thinking that value ultimately determines what is and what is not permitted by morality's standards or we might adopt some kind of non-consequentialist view on which the values alone do not determine what is permitted or justified. Either way, we can think of justification as most closely connected to things like permission, obligation, and so on. We have similar choices in epistemology. We might think that epistemic values ultimately determine whether a belief is justified or we might think that something else matters to justification such as conformity to norms.4 In my view, the right approach to justification is one that posits norms that don't simply enjoin us to believe in ways that promote some kind of value. There might be a sense in which it is a bad thing to believe falsehoods or a good thing to believe truths, but we have good reason to think that this isn't the starting point for a good theory of justification because the kinds of trade-offs that would matter to justification if justification were a matter of promoting some kind of good do not matter to justification.5 On the approach to justification that I prefer, a belief is justified if it violates no epistemic norms and it cannot be justified if it violates some such norm without overriding reason to do so. The potentially overriding reasons, in turn, would be provided by norms.6 In short, we can think that a belief is justified when it's not the case that we shouldn't hold it. Questions about the application conditions for these norms are substantive. We can have substantive disagreements about, say, whether the norms have internal or external application conditions (i.e., conditions that do or do not supervene upon internal conditions). We can have substantive disagreements about whether they are concerned with knowledge, truth, evidential support, coherence, etc. Questions about whether justification can be understood in terms of some connection to norms, by contrast, don't strike me as substantive. We should be able to represent every possible view about justification in terms of some connection to a norm. The real debates in epistemology are about the kinds of things that can figure in genuine epistemic norms, not whether we can state a theory of justification by specifying them. Because I think that the fundamental norms that govern belief are knowledge norms, they figure centrally in the discussion below.7 These norms can be stated as follows: K-: If we are not in a position to know p, we should not believe p. K+: If we are in a position to know p, we should believe p. 4 See Dorst (forthcoming) and Easwaran (2016) for a discussion of how considerations of epistemic utility support a kind of Lockean view of rational belief. For defences of that view of rational belief, see also Sturgeon (2008). 5 For discussions of trade-offs and their (ir)relevance to epistemic status, see Firth (1981), Jenkins (2007), and Littlejohn (2012). For sophisticated responses to such concerns, see Ahlstrom-Vij and Dunn (2014), Singer (2018), and Talbot (2014). 6 This view is compatible with the view that a thinker's evidence ultimately determines what a thinker should believe. We can represent the evidentialist as someone who thinks that what we ought to believe is determined by what we have sufficient evidence to believe. 7 See Williamson (2000). Readers know that there is a standard objection to the claim that Kis a genuine epistemic norm. Even epistemologists who think that some externalist views are worthy of consideration are put off by the idea that a belief isn't justified if it happens to be false. When we think about brainsin-vats, for example, people often say that (a) their beliefs must be justified if ours are and (b) they should believe the false propositions that appear to them to be true (e.g., that they have hands). These judgments about the case of systematic but undetectable error are sometimes taken to show that knowledge couldn't be the norm of belief and often taken to show that justification doesn't require knowledge. In my view, this reaction is a sign that many epistemologists are conflating justification and excuse. I don't want to argue for that point here having argued for it extensively elsewhere.8 Instead, I want to describe a way of accommodating these kinds of intuitions without abandoning the idea that there are externalist epistemic norms that tell us we shouldn't believe what we don't know or that we shouldn't believe falsehoods. This will, in turn, give us room to define justification in terms of different connections to what we ought (in some sense to be specified) believe.9 Let me mention one more case that might seem to pose a problem for the externalist about epistemic norms, the preface case.10 Agnes has completed her first book. She heads to the library because she wants to see it on the shelves when she discovers that it's been shelved in a special section of the library reserved for books that contain precisely one false claim. She has researched each of the claims in the book very carefully, but it shouldn't come as a shock to her that her book contains an error. If anything, she should be pleased that it was only one. In such a scenario, I think that she could come to know that her book contains an error. She could also continue to know that the true claims that she put into the book were true. Under these conditions, it seems that each claim we pointed to might be one that she could continue to justifiably believe provided that she was initially justified in believing it. If, however, she ought to believe each claim in a set of claims that is inconsistent (i.e., each claim in the body of the book and the claim that the book contains an error), then isn't it wrong to say that she should only believe what she knows or that she should only believe what is true? These norms imply that we ought to have sets of beliefs that are consistent, but this seems like a difficult view to defend in light of these preface cases.11 2. An argument against externalist epistemic norms Suppose that ten miners are trapped in one of two shafts, shaft A or shaft B.12 You think it's just as likely that they'd be in one shaft as the other. It starts to rain. If you don't act the shafts will fill with water and all the miners will drown. If you do act, you have to choose between three options. You can block shaft A completely. This would ensure that there is enough air in this shaft for all 10 miners to live if they're in A, but it will guarantee that the miners in B would all 8 Littlejohn (2012). For a contrasting view, see Simion, Kelp, and Ghijsen (2016). 9 At various points I will shift between claims about what we do know and what we are in a position to know. On the one hand, I think that if we believe but don't know there is a sense in which we shouldn't hold this belief, not unless we were to hold it in such a way that it constituted knowledge. On the other, I think that we want to focus on questions about what we are in a position to know when we are thinking about what we ought to believe because we want to be able to say that there are some things that we ought to believe or ought not believe that we don't currently have any beliefs about. 10 Makinson (1965). 11 For defences of this verdict, see Christensen (2004), Dutant and Littlejohn (forthcoming b), Easwaran and Fitelson (2015), and Worsnip (2016). For a dissenting view, see Ryan (1991, 1996). 12 This case is a modified version of the case from Parfit (1988). Regan (1980) was the first to present structurally similar cases. drown. You can block shaft B completely. This would guarantee that all ten miners would survive if they were in B but that all would die if they were n A. You can partially block off the openings to both shafts. Some water would get it, but most would be kept out. The result would be that there is enough air in both shafts for 9 miners to live. In this scenario, we know that the objective consequentialist would say that you ought to save all the miners by blocking the shaft that they happen to be in, but this doesn't sit well with the intuition that we ought to partially block both shafts. Bearing this in mind, consider this argument against objective consequentialism: The Mineshaft Argument P1. According to objective consequentialism, you either ought to completely block shaft A or ought to completely block shaft B. P2. We ought to partially block both shafts. C. Objective consequentialism is false. Many people think that this is a decisive argument against objective consequentialism.13 My interest in this argument is that it seems that we need to address similar arguments in epistemology: The Preface Argument P1. According to some externalists about epistemic norms, you should not believe falsehoods. P2. If so, you should not believe an inconsistent set of propositions. P3. If so, you should not believe each of the propositions in Agnes's book and believe that the book contains an error. P4. You should, however, believe each of the propositions in the book and that the book contains an error. C. These externalists are wrong about the norms of belief.14 What should we make of second argument? One might conclude in both cases that the arguments show us something important about norms. They might show us that the norms in question (i.e., those of the objective consequentialist, the knowledge norm, etc.) aren't genuine norms because they deliver the wrong verdicts in these cases. This response might appeal to some, but it might seem unwarranted to someone who thinks that our talk of what we 'ought' to do or 'should' believe might concern different readings of the normative language. Even if it were true (in some sense) that we ought to partially block both shafts and save only nine of the miners, it might be true (in some other sense) that we ought to save them all. And even if it were true (in some sense) that we ought to believe each of the claims in a book known to contain an error, it might still be true (in some other sense) that we ought to believe only truths. Following Sepielli (2018), let's distinguish the debater from the divider. The debater thinks (roughly) that there is one reading of 'ought' and 'should'. They would say that it couldn't be true (in any sense) that a thinker should have an inconsistent set of beliefs if it's true (in some sense) that a thinker shouldn't believe falsehoods or shouldn't believe what she doesn't know. A divider thinks (roughly) that there are different ways of reading 'ought' and 'should' and that these seemingly incompatible claims about what we ought to believe or do are perfectly compatible 13 See Zimmerman (2008), for example. He notes that objective consequentialists cannot say that we would be excused for partially blocking both shafts since we know that this is the one thing that we should not do. 14 The preface case also presents interesting challenges to some seemingly plausible claims about the normativity of logic since it is difficult to see how logic might be normative if we might find that we ought to hold inconsistent beliefs. See Steinberger (2019). when they're properly understood.15 Let's explore the prospects of a divider's view on which claims about what we ought or ought not believe can be interpreted in different ways to see if it gives the externalist a way of capturing intuitions that would seem to be problematic for their view. 3. What shouldPRO we believe? According to the divider, questions about what we 'should' believe and claims about what we 'shouldn't' believe can be read in different ways. Even if it's true to say that we 'ought' to believe each claim in an inconsistent set of claims it might be true that we 'ought' not believe falsehoods, provided that we're talking about different senses of 'ought'. On one reading, 'ought' might be read objectively.16 On such a reading, facts that an individual might not be cognizant of might nevertheless help to determine whether the individual ought to believe something or ought not believe something. On another reading, 'ought' might be read in such a way that the truth or falsity of claims about what an individual ought to do or ought to believe would depend upon the individual's perspective on things. Let's call these the 'objective' and 'prospective' readings of 'ought' (i.e., oughtOBJ and oughtPRO). We want an account of what we oughtPRO to believe. 17 It makes sense to turn to ethics to look at accounts of what we oughtPRO to do to see if it would be fruitful to model our account of oughtPRO to believe on one of them. Here is a simple account of what we oughtPRO to do. Whenever we face a choice between some feasible set of options, we can think of each option as being associated with various states that will result as a consequence of choosing an option. Some of these states will realize value, good or bad. The value of an option can, in turn, be understood in terms of the total value realized by these states. We can rank the options in terms of their values and say that someone ought not choose an option if there is a better one available and ought to choose an option if it is best. In cases of ties, we are free to choose amongst the best options. People often object to this account on the grounds that the ranking of options isn't sensitive in any way to the agent's information and this view is widely believed to be problematic because it gives us the wrong verdict in cases like the mineshaft case. So, we make a small modification. When we are uncertain about what will happen if an option is chosen, we think about the possible outcomes associated with each option and we rank the options by thinking about the values that attach to the possible outcomes and the probabilities that these outcomes would eventuate. If we were to take this approach to oughtPRO to believe, we would need to identify the relevant outcomes, assign values to them, and offer some account as to how the probabilities and values determine how our options should be ranked. If we adopt a veritist view, we would say that the fundamental epistemic goods have to do with accuracy and inaccuracy.18 If we adopt a gnostic view, we would say that the fundamental epistemic goods have to do with knowledge 15 For a discussion of the divider's view and its virtues in dealing with cases of uncertainty and/or ignorance, see Graham (2010) and Smith (2011). The response to the Preface Argument is similar to Graham's (2010) response to the Mineshaft Argument, but it incorporates some ideas from Lazar (forthcoming) and Olsen (2018). 16 For reasons discussed below, we might instead want to talk about 'primary' and 'derivative' readings for someone who didn't believe that objective conditions matter in any sense to what we 'ought' to do or believe might find a need to draw distinctions between different readings of the relevant parts of our normative language. 17 For reasons discussed in Littlejohn (2012), I don't think this is a theory of justification in the primary or most important sense, but it might give us an important part of a theory of when we can defend the individual from criticism for failure to meet an obligation. 18 See Goldman (1999) and Joyce (1998), for example. and failed 'attempts' to know.19 On the first view, we oughtPRO to believe iff it maximises expected epistemic value as the veritist conceives of it. On the second, we oughtPRO to believe iff this maximises expected epistemic value as the gnostic conceives of it. To see how this might work in practice, we can try to set things up using a belief-matrix that represents the options, states, and the values of outcomes as follows: Veritist Belief-Matrix p ~p Believe p a b Believe ~p c d Believe Neither e f Believe Both g h Gnostic Belief-Matrix Kp ~Kp Believe p a b Believe ~p c d Believe Neither e f Believe Both g h The first matrix captures a simple veritist approach that is concerned with accuracy and inaccuracy. The second captures a gnostic approach where our concerns are with whether our beliefs would or would not constitute knowledge.20 To determine the expected epistemic value of each option (i.e., believe p, believe its negation, believe both, etc.), we assign cardinal numbers to each cell that represents the value of the outcome, multiply each by the probability that the relevant state obtains, and sum across the rows. If, as seems plausible, we shouldn'tPRO believe both p and ~p whatever probabilities we assign to the relevant states, the absolute value associated with g and h will be less than that of e or f.21 If we want to avoid the sceptical conclusion that we shouldn'tPRO believe anything, we would want the values of a and d to exceed those of e and f. In my view, the main problem with this approach is that it gives an account of what we oughtPRO to believe in terms of the values realized by the states that result from believing as opposed to the norms that determine what we oughtOBJ to believe. The externalist norms that I like drop out of the picture. Of course, you might not like such norms, but that doesn't mean that you should embrace some kind of epistemic consequentialist view. I am sceptical of consequentialist views because I doubt that there are epistemic values that call for promotion.22 19 See Hyman (2015), Littlejohn (2015), and Williamson (2000) for discussion and defences. 20 We can think of 'Kp' and '~Kp' as standing for being in a position to know and not being in a position to know respectively. For reasons discussed in Dutant and Fitelson (MS) we might further refine this so that the options include ways of believing propositions. 21 See Dorst (forthcoming) and Steinberger (forthcoming) for discussions of the significance of and motivations for this assumption. 22 For arguments that there aren't epistemic values that call for promotion, see Littlejohn (2018). For a defence of an opposing view, see Talbot (2014). While I think that there might be a sense in which epistemic norms are sensitive to considerations about value (and hence might be thought of as teleological), the relevant values might not be ones that call for promotion. The relevant notion of the good here might be attributive goodness, for example. While it might be an important truth about belief that the good ones are suited for certain functional roles (and are so suited iff they constitute knowledge, say) we shouldn't say that we ought to have as many such beliefs as possible just like we shouldn't say that we ought to have as many good toasters or Imagine that there were such values and they determined what we oughtPRO to believe. Recall Foot's (1985) point about consequentialism. The thought that it's never rational to prefer an acknowledged lesser good to a greater one makes consequentialism seem quite compelling. Consequentialist views retain this intuitive motivation if they rank options in terms of total value (i.e., the total epistemic value realized as a consequence of coming to believe). Because of this, the view is designed to allow for trade-offs.23 Indeed, one of the key selling points of a consequentialist framework is that it explains when and why trade-offs are justified. We don't like epistemic trade-offs. We don't think, for example, that the explanation as to why I shouldn'tPRO believe (or shouldn'tOBJ believe) is that the opportunity costs associated with forming the relevant belief are too great. We need an approach that isn't consequentialist. We don't have to go far to find an alternative view that doesn't assume that normative status is determined by how well an option promotes some value. Instead of looking for an epistemic axiology that tells us which states of affairs would be good or bad, better or worse, and so on, we can start with our preferred view about the identity of the epistemic norms that tell us what we oughtOBJ to believe. From this, we can extract a theory of what we oughtPRO to believe. Others have tried this, but the details are difficult to get right. Let's try a new approach. We begin by consequentializing our theory of what we oughtOBJ to believe and use some tools from decision-theory to generate our theory of what we oughtPRO to believe. Here is a crude recipe for consequentializing a non-consequentialist epistemological theory. Each non-consequentialist epistemological theory purports to tell us which options are permitted and which ones are not. For example, suppose that we think that the knowledge norms govern belief: K-: If we are not in a position to know p, we should not believe p. K+: If we are in a position to know p, we should believe p. When we're in a position to know neither p nor ~p, our theory ranks believing neither above believing p, believing ~p, and believing both. If we're in a position to know, it ranks believing the relevant proposition ahead of the others. If, however, we think that belief is governed by truth norms, we might have this instead: T-: If ~p, we should not believe p. T+: If p, we should believe p. We needn't worry about conflicts between these positive and negative norms, not when we're considering a thinker's attitude concerning some particular proposition.24 We can represent the violations of the relevant norms as if they were bad outcomes. A value function that assigned numbers to 'outcomes' (i.e., situations in which we believe in conformity to or in violation of the norms) would give a faithful representation of the ordering of options associated with our theory. Oddie and Milne (1991) show that every non-consequentialist moral theory's deontic ordering can be faithfully represented by a value function that assigns cardinal numbers to the assassins as possible. The view that tries to account for epistemic norms in terms of values that call for promotion seem to face the trade-off problems that seem to make epistemic consequentialism implausible. 23 These matrices are misleading precisely because they don't capture the situation in cases where coming to believe some proposition necessitates believing or failing to believe others. When we take account of this complexity, we can start to see that however probable p might be, believing p might fail to maximize expected epistemic value as the veritist conceives of it. This is why I said the approach sketched was naïve. 24 A fully developed view might want to limit assessment to questions that the thinker is or ought (in some sense to be specified) to be trying to settle and the attitudes that are the thinker's answers to these questions. Being able to answer questions that don't or needn't interest us shouldn't have a bearing on whether we oughtPRO to believe things that we do know. various norm conforming and violating acts. There is no obstacle to generalizing their result to the epistemic case. Let's see how this would look by assigning values to our cells. We can represent the violation of a norm as a bad outcome where we might decide that we want to weight the violation of the different norms differently. We might think, for example, that it would be worse to violate Tby forming a false belief (e.g., -3) than it would be to violate T+ by failing to form a true belief (e.g., -1). This might have a matrix like this: Truth-Centred Belief-Matrix P ~p Believe p 0 -3 Believe ~p -3 0 Believe Neither -1 -1 Believe Both -3 -3 According to this truth-centred account of what we oughtPRO to believe, we get the result that we oughtPRO never believe both p and believe ~p whatever evidence we happen to have. Because every proposition is either true or false there is no situation in which we oughtOBJ to suspend, but on our view, we oughtPRO to suspend if the expected value of believing neither is greater than that of believing p or believing ~p. If someone flips a fair coin and you have no more reason to believe that it landed heads than tails, you oughtPRO to suspend because the expected value of suspension (-1) exceeds that of believing p or of believing ~p (-1.5). This is thus a case in which you can know that you ought (in some sense) have attitudes that you ought not (in some other sense) have. You oughtPRO to suspend even though you're certain that you oughtOBJ to believe (i.e. oughtOBJ not suspend). And we know why you oughtPRO to have attitudes that you know you oughtOBJ not have. Given the norms that you're supposed to follow (e.g., T-, T+) and your uncertainty about what it takes in your present situation to conform to them (i.e., the probability that you violate the first or violate the second if you believe one way or the other is .5), you have to rationally respond to the risks you face. That requires a sensitivity to the comparative weight of the normative considerations and the chance of failing to meet the relevant standards. Readers might wonder how we should decide on the numbers. In the truth-centric approach, you might think of it this way. Imagine a set of books arranged in terms of length. The shortest book contains one claim. The longer books contain many more. You know that each book contains one false claim, but one that you know you won't recognize as false provided that the book contains two or more claims. You might think that it would be overly sceptical to say that someone shouldn't believe what they read in a book containing 1,000,000 claims and that someone is being insufficiently sceptical if they believe what they read in a book containing two or three claims. The weights we attach to the two truth norms should decide when the risk of forming a false belief is too great. The resulting view is basically the Lockean view, a view that says that we oughtPRO to believe when the truth of our belief is sufficiently probable. The numbers assigned to the outcomes determine the probability threshold. Let's look at things from the perspective of a theory that takes Kand K+ to be the fundamental norms that govern belief: Knowledge-Centred Belief-Matrix Kp ~Kp & ~K~p K~p Believe p 0 -3 -3 Believe ~p -3 -3 0 Believe Neither -1 0 -1 Believe Both -3 -6 -3 In this matrix, we've represented the possibilities of coming to know p by believing, coming to know ~p by believing, and believing where you're not in a position to know either way. One difference between this matrix and the previous one is that if you were a BIV and you were to believe correctly that you were a BIV, the veritist would say that this is good in one way even though it is irrational or what you oughtPRO not believe. On this knowledge-centred account, you oughtOBJ not believe that you're a BIV even if you are (because that belief, while true, couldn't constitute knowledge) and oughtPRO not believe that you're a BIV even if you are (because the probability that you could know that you're a BIV won't be high). Unlike the previous view, this approach says that we sometimes oughtOBJ to suspend. Since we cannot know whether the number of stars is even or odd, this account says that we oughtOBJ to suspend judgment while the truth-centred approach says that we oughtOBJ to believe the truth about the number of stars and oughtOBJ not suspend. 25 The knowledge-centred view also differs from the truth-centred view in how it handles lottery propositions and Moorean absurdities.26 The probability that a ticket lost is high, so our previous view makes it hard to deny that we oughtPRO to believe that a ticket we've been gifted is worthless. In turn, it makes it hard to deny that we oughtPRO believe this Moorean absurdity: I don't know if this ticket lost, but it did. Since the probability of knowing such things is (i.e., that a ticket lost or the complex proposition that the ticket lost and I don't know whether it did), on some views, 0, this account delivers the verdicts that I would want it to. As with truth-centred view just discussed, it allows for the possibility that we might know that we oughtOBJ not have some beliefs and still oughtPRO to have the beliefs in question. In preface cases, each belief might be very likely to be knowledge even if it's certain that one of the beliefs in the set is mistaken. The knowledge-centred and truth-centred views tell us that while it might be the case that we oughtOBJ not believe the false claims in the preface case, we still oughtPRO to believe each of the claims. Thus, these views can retain the idea that logic is normative for thought (i.e., that we oughtOBJ not hold inconsistent sets of beliefs) even if we oughtPRO to believe as if probability is the guide to our doxastic life and that we have to tolerate inconsistency in some special cases. One advantage, to my mind, of the knowledge-centred view is that the knowledge-centred view gives a better explanation as to why we oughtPRO to hold inconsistent beliefs. The truth-centred view explains this in terms of the high probability of the truth of each belief and thus doesn't distinguish the preface-type cases from the lottery-type cases. The knowledge-centred view treats them differently because the probabilities of knowing in these cases are very different. There is no chance of knowing in the lottery case and a good chance of knowing in each case where you consider a claim made in a book known to contain an error. Once we have consequentialized the theory in this way (i.e., by replacing the deontic ordering with a value-function that preserves this ordering), we're back in business. We can say that we oughtOBJ to believe in ways that the norms require and oughtOBJ not believe in the ways that the norms forbid. Provided that opportunity costs don't have any direct bearing on whether we might conform to the norms that determine what we oughtOBJ to believe, we have a view that mirrors in some superficial ways the consequentialist views described above but without adopting a view that encourages us to believe that trade-offs can require us to, say, refrain from 25 In general, I think that the knowledge-centred view is a more natural fit for the best views we have about the norms of suspension and the interaction between the considerations that determine when we ought to suspend and those that determine when we may believe. See Miracchi (forthcoming) and Raleigh (forthcoming) for helpful discussions of suspension and the role of reflection. 26 The importance of getting the lottery case right comes out clearly in discussions of the right kind of evidence for criminal trials. See Moss (2018) and Steele (MS) for two very different approaches to these issues. believing what we know or to believe what we know to be false or unsupported by the evidence.27 The knowledge-centred view is like the Lockean view in that it is a kind of threshold view. It thus differs in important ways from some prominent attempts to capture more subjective aspects of normative evaluation without a knowledge-centred framework.28 It says that when the probability of a certain 'outcome' is sufficiently high, we oughtPRO to believe. If it is low, we oughtPRO not. 29 This gives us an elegant solution to a Harman-esque puzzle about lottery cases.30 How could it be rational to form beliefs on the basis of perception and/or testimony if it's not rational to form lottery beliefs on the basis of statistical evidence? Defenders of the knowledge-centred view will say that the difference isn't to be found in the different probabilities of truth, but in terms of the different probabilities of knowing. This difference matters because it matters whether we're responding appropriately to risks of violating the norms that determine what we oughtOBJ to believe. The knowledge-centred proposal is not unique in classifying some perceptual and testimonial beliefs as justified when it classifies lottery beliefs as unjustified. Smith (2016) proposes a view designed to deliver just this verdict. If we adopt the knowledge-centred proposal and characterize justification either in terms of what we oughtOBJ to believe or what we oughtPRO to believe, we follow Smith in breaking from the view that justification is fundamentally about minimizing the risk of error. The knowledge-centred proposal has at least two virtues that a view like Smith's might lack. First, it gives us a natural response to a forceful challenge to explain why we should stick to rules that forbid belief in lottery cases. Consider Horowitz's observation: ... a rational agent should be doing well by her own lights, in a particular way: roughly speaking, she should follow the epistemic rule that she rationally takes to be most truth-conducive. It would be irrational, the thought goes, to regard some epistemic rule as more truth-conducive than one's own, but not adopt it (2014: 43). If our fundamental concerns (in our axiology or in our account of what we oughtOBJ to believe) concern truth and nothing but the truth, it's not clear why we should stick to rules that we know to be suboptimal. Second, there is the issue of naturalness. Someone can offer a theory of justification that fits well with our intuitions without offering one that seems to have any underlying theoretical rationale as to why, say, the evidential support relation would favour believing propositions that would be true in most normal worlds in which our evidence is true over believing propositions known to be highly probable in the kinds of situations we know 27 For helpful discussions of how consequentializing a non-consequentialist theory and importing tools from decision-theory can help non-consequentialists handle uncertainty, see Lazar (forthcoming) and Olsen (2018). My crude recipe for consequentializing draws from their work on decision-theory for non-consequentialists in ethics. 28 My hope is that this approach to derivative normative status addresses some of Brown's (2018) concerns about Williamson's (forthcoming a) approach to derivative normative status. It also might improve upon a suggestion of DeRose's (2002) where he suggests that we can characterize a kind of secondary normative status in terms of what we take to be proper in some primary sense. In many cases, we neither take something to be proper or to be improper but should think about the risk of the different kinds of norm violations to determine what is proper in this secondary sense. 29 Just as truth doesn't imply the high probability of truth, I don't think knowledge implies that it's particularly probable that we know. This account suggests that Lasonen-Aarnio (2010) is right that there can be unreasonable knowledge. 30 See Harman (1968). ourselves to be in.31 The knowledge-centred proposal sketched here should score well on the naturalness front since it simply appropriates the natural account to give about how we oughtPRO to proceed in light of uncertainty. The approach sketched here has other virtues that have been discussed elsewhere.32 One virtue is that it gives us a response to the Preface Argument because it explains why we shouldPRO sometimes believe what we know we shouldOBJ not believe. Even if you don't think that the knowledge-centred view gives us the right account of what we oughtOBJ to believe, you know now how to give an account of what we oughtPRO to believe given a theory of what we oughtOBJ to believe. If you don't believe there are any genuine externalist epistemic norms, you might think that even internalist views will need to draw the kinds of distinctions that we've drawn here. The proposed account of the connection between oughtOBJ and oughtPRO might be helpful. Suppose that you're uncertain whether some large collection of beliefs meet the standards that determine what you oughtOBJ to believe. If a guru tells you correctly that there is one belief in this set that you oughtOBJ not believe, what should you do? If you cannot identify which belief is the bad one, dropping lots of beliefs might raise the probability that you don't hold the belief that the guru has in mind, but the consequence might be failing to believe many things that you oughtOBJ to believe. In such a case, you might survey each belief individually and be quite confident that each of them is what you oughtOBJ to believe even if you are certain that one of them must not be. The suggestion that you oughtPRO to continue to maintain each of them in spite of your knowledge that one of the beliefs oughtOBJ to go might seem attractive even if your account of what we oughtOBJ to believe is given in purely internalist terms. While the account gives externalists a useful way of responding to objections (e.g., those having to do with error cases), it also gives internalists a way of thinking about how to deal with a kind of uncertainty that can be problematic for them as well.33 Conclusion Let me say in conclusion that the approach being sketched here can be appropriated by anyone who believes that there are norms that determine (in some sense) what we ought to believe or do provided that they concede that it's at least possible for a rational agent to be uncertain to some 31 Similar concerns might arise for truth-centred views that insist that evidential support only confers justification if a stability condition (e.g., Leitgeb (2017) or explanatory condition (e.g., Nelkin (2000)) is met or if the supported beliefs don't contain any known falsehoods (e.g., Ryan (1991, 1996)). 32 In Dutant and Littlejohn (forthcoming), we show how this view unifies various kinds of defeaters in a single framework. On our view, defeaters partially defeat the justification of belief by lowering the probability that we know and fully defeats it by lowering it below a threshold. This allows us to say that there is some single mechanism by which defeaters defeat and we think that this is preferable to a view that posits a multitude of different kinds of defeaters without any underlying explanation of their rational toxicity. 33 An interesting case study would be the evidentialist view. Suppose (with Conee and Feldman (2004) and McCain (2014)) that a thinker's evidence supervenes upon her internal mental states and determines what she ought (in some primary sense) believe. And suppose that while evidence of evidence might in some weak sense be evidence (see Feldman (2005)), a rational thinker might be uncertain about what her evidence is and what it supports, rules out, etc. Given some very modest claims about the limitation of our access to our evidence, Dorst (forthcoming b) and Williamson (forthcoming b) argue that even very strong evidence of strong evidence might ensure only that we have very weak first-order evidence for our beliefs. In light of this, even the evidentialist might want to allow that there might be things that we ought not believe (in light of the first-order evidence) that we ought to think we ought to believe (in light of the higher-order evidence) and the approach sketched here might help us make sense of this. degree about whether in a given situation the norm applies. As it happens, I think there are powerful reasons to believe that every set of norms is like this. I think that anyone who isn't a committed epistemic consequentialist should be pleased to see that we can borrow some ideas from consequentialists and work out a theory of what we oughtPRO to believe when we're uncertain about whether our beliefs meet the standards that we take to be of fundamental normative significance. As it happens, I think that the implications of the view that combines this framework with a knowledge-centric approach to epistemic norms looks very good. I have sketched one of the few views on the market that explains why we can think that perceptual beliefs differ in justificatory status from lottery beliefs without committing ourselves to implausible views about what we ought to believe in preface-type situations. I cannot think of a single alternative view in the literature that delivers verdicts about these cases that draws the distinctions in the right place. Moreover, it explains why there should be these distinctions without forcing us to say strange things about the evidential support relation.34 References Ahlstrom-Vij, Kristoffer and Dunn, Jeffrey. 2014. A Defence of Epistemic Consequentialism. The Philosophical Quarterly 64: 541–51. Brown, Jessica. 2018. Fallibilism: Evidence and Knowledge. Oxford University Press. Christensen, David. 2004. Putting Logic in Its Place. Oxford: Oxford University Press. Conee, Earl and Feldman, Richard. 2004. Evidentialism. Oxford University Press. DeRose, Keith. 2002. Assertion, Knowledge, and Context. Philosophical Review 111: 167-203. Dorst, Kevin. Forthcoming. Lockeans Maximize Expected Accuracy. Mind. Dorst, Kevin. Forthcoming b. Evidence: A Guide for the Uncertain. Philosophy and Phenomenological Research. Dutant, Julien. Forthcoming. Knowledge-First Evidentialism about Rationality. In F. Dorsch and J. Dutant (ed.), The New Evil Demon Problem. Oxford University Press. Dutant, Julien and Fitelson, Branden. MS. Knowledge-Centered Epistemic Utility Theory. Dutant, Julien and Littlejohn, Clayton. Forthcoming. Defeaters as Indicators of Ignorance. In J. Brown and M. Simion (ed.), Reasons, Justification, and Defeat. Oxford University Press. Dutant, Julien and Littlejohn, Clayton. Forthcoming. Justification, Knowledge, and Normality. Philosophical Studies. Easwaran, Kenny. 2016. Dr. Truthlove or: How I Learned to Stop Worrying and Love Bayesian Probabilities. Nous 50: 816–33. Easwaran, Kenny and Fitelson, Branden. 2015. Accuracy, Coherence, and Evidence. In T. Gendler and J. Hawthorne (ed.), Oxford Studies in Epistemology. Volume 5. Oxford University Press. Feldman, Richard. 2005. Respecting the Evidence. Philosophical Perspectives 19: 95-119. Firth, Roderick. 1981. Epistemic Merit, Intrinsic and Instrumental. Proceedings and Addresses of the American Philosophical Association 55: 5–23. Foley, Richard. 2012. When is True Belief Knowledge? Princeton University Press. Foot, Philippa. 1985. Utilitarianism and the Virtues. Mind 94: 196–209. Goldman, Alvin. 1999. Knowledge in a Social World. Oxford University Press. Graham, Peter. 2010. In Defense of Objectivism about Moral Obligation. Ethics 121: 88-115. Harman, Gilbert. 1968. Knowledge, Inference, and Explanation. American Philosophical Quarterly, 5: 164–73. Horowitz, Sophie. 2014. Immoderately Rational. Philosophical Studies 167: 41–56. Hyman, John. 2015. Action, Knowledge, and Will. Oxford University Press. 34 Discussions of their gnostic utility theory with Julien Dutant and Branden Fitelson were incredibly helpful in thinking about the issues discussed here. I want to offer a special thanks to Kevin McCain for providing extensive feedback on a previous draft. Jenkins, Carrie. 2007. Entitlement and Rationality. Synthese 157: 25–45. Joyce, James. 1998. A Nonpragmatic Vindication of Probabilism. Philosophy of Science 65: 575–603. Lasonen-Aarnio, Maria. 2010. Unreasonable Knowledge. Philosophical Perspectives 24: 1–21. Lazar, Seth. Forthcoming. Deontological Decision Theory and the Grounds of Subjective Permissibility. Oxford Studies in Normative Ethics. Leitgeb, Hannes. 2017. The Stability of Belief. Oxford University Press. Littlejohn, Clayton. 2012. Justification and the Truth-Connection. Cambridge University Press. Littlejohn, Clayton. 2015. What Cares What You Accurately Believe? Philosophical Perspectives 2015: 217-48. Littlejohn, Clayton. 2018. The Right in the Good. In J. Dunn and K. Ahlstrom-Vij (ed.), Epistemic Consequentialism. Oxford University Press. Littlejohn, Clayton. Forthcoming. Truth, Knowledge, and the Standard of Proof in Criminal Law. Synthese. McCain, Kevin. 2014. Evidentialism and Epistemic Justification. Routledge. Makinson, David. 1965. The Paradox of the Preface. Analysis 25: 205-7. Miracchi, Lisa. Forthcoming. When Evidence Isn't Enough: Suspension, Evidentialism, and Knowledge-First Virtue Epistemology. Episteme. Moss, Sarah. 2018. Probabilistic Knowledge. Oxford University Press. Nelkin, Dana. 2000. The Lottery Paradox, Knowledge, and Rationality. Philosophical Review 109: 373–409. Oddie, Graham and Milne, Peter. 1991. Act and Value: Expectation and the Representability of Moral Theories. Theoria 57: 42-76. Olsen, Kristian. 2018. Subjective Rightness and Minimizing Expected Objective Wrongness. 99: 417-441. Parfit, Derek. 1988. MS. What We Do Together. Raleigh, Thomas. Forthcoming. Suspending is Believing. Synthese. Regan, Don. 1980. Utilitarianism and Cooperation. Oxford University Press. Ryan, Sharon. 1991. The Preface Paradox. Philosophical Studies 64: 293–307. Ryan, Sharon. 1996. The Epistemic Virtues of Consistency. Synthese 109: 121–41. Sepielli, Andrew. 2018. Subjective and Objective Reasons. In D. Star (ed.), The Oxford Handbook of Reasons and Normativity. Oxford University Press, pp. 784-800. Simion, Mona, Kelp, Christopher, and Ghijsen, Harmen. 2016. Norms of Belief. Philosophical Issues 26: 374-392. Singer, Daniel. How to be an Epistemic Consequentialist. The Philosophical Quarterly 68: 580–602. Smith, Holly. 2011. The 'Prosective View' of Obligation. Journal of Ethics and Social Philosophy. Smith, Martin. 2016. Between Probability and Certainty. Oxford University Press. Steele, Katie. MS. Crime, Punishment, and 'Individualized' Evidence. Steinberger, Florian. 2019. Three Ways in Which Logic Might be Normative. Journal of Philosophy 116: 5-31. Steinberger, Florian. Forthcoming. Accuracy and Epistemic Conservatism. Analysis. Sturgeon, Scott. 2008. Reason and the Grain of Belief. Nous 42: 139–165. Talbot, Brian. 2014. Truth Promoting Non-Evidential Reasons for Belief. Philosophical Studies 168: 599–618. Williamson, Timothy. 2000. Knowledge and its Limits. Oxford: Oxford University Press. Williamson, Timothy. Forthcoming a. Justifications, Excuses, and Sceptical Scenarios. In F. Dorsch and J. Dutant (ed.), The New Evil Demon Problem. Oxford University Press. Williamson, Timothy. Forthcoming b. Evidence of Evidence in Epistemic Logic. In M. SkipperRasmussen and A. Steglich-Petersen (ed.), Higher-Order Evidence: New Essays. Oxford University Press. Worsnip, Alex. 2016. Belief, Credence, and the Preface Paradox. Australasian Journal of Philosophy 94: 549–562. Zimmerman, Michael. 2008. Living with Uncertainty. Cambridge: Cambridge University Press.