Two accounts of assertion

In this paper I will compare two competing accounts of assertion: the knowledge account and the justified belief account. When it comes to the evidence that is typically used to assess accounts of assertion—including the evidence from lottery propositions, the evidence from Moore’s paradoxical propositions and the evidence from conversational patterns—I will argue that the justified belief account has at least as much explanatory power as its rival. I will argue, finally, that a close look at the ways in which assertions can be challenged and retracted reveals a certain advantage for the justified belief account. The paper will touch upon a number of further topics along the way, including the logical interaction between knowledge and justified belief, the nature of defeat, and the hypothesis that knowledge and justified belief are normatively coincident goals.

Since knowledge is usually thought to require justified belief, the second rule is more lenient and will, in effect, permit some assertions that the first rule prohibits.
Precursors to the knowledge account are defended in the work of Unger (1975, chap. 6) and Slote (1979), but its prominence in contemporary epistemology is largely due to Williamson, whose case in favour of the account, in chapter 11 of Knowledge and Its Limits (2000), is still widely considered to be the most thorough. Others who have endorsed the knowledge account include DeRose (2002), Hawthorne (2004), Benton (2011) and Kelp and Simion (2017). 1 Douven (2006), Lackey (2007), Hill and Schechter (2007) and Kvanvig (2009) are amongst those who have defended the justified belief account, or close relatives to it. 2 In this paper I will argue that the evidence which is standardly put forward in favour of the knowledge account can be explained equally well, if not better, by the justified belief account. I won't be considering any further accounts of assertion and, as a result, what I offer will fall short of a full defence of the justified belief account. 3 Furthermore, the very idea that assertion is best understood as a kind of rule governed activity-something which both accounts presuppose-will not be argued here (for critical discussion see MacFarlane, 2011;Pagin, 2016). While my enthusiasm for the justified belief account will, I suppose, be obvious, my official conclusion will be a comparative one: the justified belief account is at least as plausible as the knowledge account.
Following Williamson, we can say that one has warrant to assert a proposition P just in case one satisfies all epistemic conditions that are laid down in the rules of assertion (Williamson, 2000, pp. 242-243). Williamson sums up the knowledge account with the slogan 'only knowledge warrants assertion'. This makes it sound as though knowledge is merely being proposed as a necessary condition for warranted assertion-but, arguably, proponents of the knowledge account are also committed to 1 Variations on the knowledge account have been defended by Turri (2011Turri ( , 2016 who proposes an 'express knowledge account' of assertion, and Willard-Kyle (2020) who proposes a 'position to know' account. 2 Epistemologists standardy distinguish between propositional justification-having justification for believing a proposition-and doxastic justification-being justified in believing a proposition. Douven (2006) and Lackey (2007) put forward rules of assertion that feature propositional rather than doxastic justification (Douven uses the phrase 'P is rationally credible for one' and Lackey uses the phrase 'it is reasonable for one to believe P'). Lackey explicitly argues that there is no belief requirement built into the rules of assertion, appealing to cases in which an assertion appears to abide by the rules, even though the asserter does not believe its content (Lackey, 2007, Sect. 2). Many of the things that I say on behalf of the justified belief account will carry over to a 'propositional justification' account as well-but not everything (thanks to two anonymous referees for pressing me to consider this more carefully). In any case, I won't discuss the propositional justification account in the main text, but I will return to it in n16 and n21. 3 Some alternatives include the truth account (Weiner, 2005;Whiting, 2013), on which assertion is governed by the rule that one must only assert P if P is true, the certainty account (Stanley, 2008) on which assertion is governed by the rule that one must only assert P if one is epistemically certain of P, the surety account (Goodman and Holguín, forthcoming) on which assertion is governed by the rule that one must only assert P if one is sure of P and the supportive reasons account (McKinnon, 2013) on which assertion is governed by the rule that one must only assert P if one has supportive reasons in favour of P. (The supportive reasons account is similar to the propositional justification account defended by Douven and Lackey-but, on the relevant interpretation, one can have supportive reasons for a proposition without having justification for believing it.) Others have suggested that the standards for assertion are variable, sometimes requiring knowledge, sometimes less and sometimes more (Brown, 2010;Goldberg, 2015;Levin, 2008;Stone, 2007, part IV). regarding it as sufficient. Assertions can of course be inappropriate or criticisable for reasons that have nothing to do with deficiencies in one's epistemic position-they can be irrelevant, impolite, morally impermissible etc. Assertions that fall into these categories can be taken to transgress broader rules that govern human actions. But if the knowledge rule is the only rule that is specific to assertion, as the knowledge account suggests, then it is difficult to see where additional epistemic requirements on assertion could come from. In any case, the claim that knowledge is sufficient for warranted assertion is explicitly endorsed by some defenders of the knowledge account (DeRose, 2002, Hawthorne, 2004, pp. 23, 87, Simion, 2016a and this is how I will interpret the view here. Accordingly, I will also interpret the justified belief account as offering a necessary and sufficient condition for warranted assertion. 4 Williamson provides three primary pieces of evidence in favour the knowledge account of assertion, which have remained central to the discussion ever since: the evidence from lottery propositions, the evidence from Moore's paradoxical propositions and the evidence from conversational patterns. 5 In the next three sections I will argue, in turn, that each of these pieces of evidence can be accommodated by the justified belief account. I am by no means the first to have attempted such a project and, as a result, I won't be starting from scratch. The point that I make about lottery propositions is similar to that made by Douven (2006, Sect. 3) and the point I make about Moore's paradoxical propositions is similar to that made by Kvanvig (2009, Sect. 3) (and n3 in Hill & Schechter, 2007)-though, in each case, I will be motivating these points in a new way. As far as I'm aware, my treatment of the evidence from conversational patterns is novel, and it is here that a possible advantage for the justified belief account emerges-provided we are willing to take a somewhat broader view of what the relevant evidence includes. This will be the focus of the final section.

The evidence from lottery propositions
Suppose Bruce has bought a ticket in a large fair lottery. Suppose the lottery has just been drawn and Bruce, along with the other ticket holders, is eagerly awaiting the 4 If the proponent of the justified belief account was merely claiming that justified belief is necessary for warranted assertion, then this would be consistent with (indeed entailed by) the claim that knowledge is necessary for warranted assertion. And yet, the original presentation of the two views, in terms of the rules governing assertion, makes it plain that they are genuine competitors, which could not be simultaneously accepted. It can't be the case that assertion is governed solely by the knowledge rule and solely by the justified belief rule. This shows that these accounts cannot be cashed out purely in terms of necessary conditions on warranted assertion. Criticisms of the knowledge account tend to focus on the 'necessity direction'-the claim that knowledge is necessary for warranted assertion (see for instance Weiner, 2005;Lackey, 2007;Stone, 2007;Smithies, 2012;Smith, 2012;McKinnon, 2013;Schechter, 2017). The justified belief account is, for the most part, able to avoid these criticisms. Some, however, have taken aim at the sufficiency direction of the knowledge account (Brown, 2010), and these criticisms will automatically apply to the justified belief account as well-but I won't discuss them here. 5 This doesn't exhaust the evidence that has been thought to favour the knowledge account. In arguing for the account, Turri (2010) and Benton (2011) appeal to conversational patterns that are somewhat different from those emphasised by Williamson. I won't be discussing Turri and Benton's arguments here. There has also been a significant amount of empirical work on accounts of assertion, some of which is purported to support the knowledge account and some of which is purported to support the justified belief account (see Marisili and Weigmann, 2021 for an overview). announcement of the results. If I were to say to Bruce 'Your ticket has lost' purely on the basis of the odds involved, then this assertion would seem unwarranted. On hearing this, it would be natural for Bruce to assume that I had some special inside information about the lottery, or had already heard the result etc. If he were to discover the actual grounds of my assertion, he might well judge that I should have kept my mouth shut. 6 The knowledge account offers a straightforward explanation as to why my assertion would be unwarranted in this case; just as my grounds seem insufficient for me to warrantedly assert that Bruce's ticket has lost, they also seem insufficient for me to know that Bruce's ticket has lost. More generally, many philosophers accept that one cannot know a 'lottery proposition'-a proposition to the effect that a single ticket has lost a large fair lottery-purely on the basis of the odds involved (see for instance Harman, 1968;Armstrong, 1973;chap. 13, Vogel, 1990;Williamson, 2000;chap. 11;Hawthorne, 2004, chap. 1).
Proponents of the knowledge account sometimes suppose that the justified belief account will give the wrong verdict in this case (Williamson, 2000, pp. 259-260;Hawthorne, 2004, p. 21). Since the odds are so strongly in favour of Bruce's ticket losing, surely I would be justified in believing that it has lost-or so one might think-in which case, according to the justified belief account, I must have warrant for asserting this. There are several theories of justification, however, which make the opposite prediction; that one cannot justifiably believe a lottery proposition purely on the basis of the odds involved (see for instance Nelkin, 2000;Bird, 2007;Smith, 2010Smith, , 2016Rosenkranz, 2021, Sect. 7.2). One thing we can say right away is that the justified belief account, if combined with one or other of these theories, would straightforwardly accommodate the evidence from lottery propositions. But we can go a step further than this-for it is no accident that these different theories have converged upon this same prediction.
There are a number of arguments to the effect that one cannot justifiably believe a lottery proposition purely on the basis of the odds involved. One such argument, which I will explore in some detail, appeals to the idea that knowledge and justified belief are normatively coincident goals (Smith, 2014(Smith, , 2016. Say that two goals are normatively coincident just in case it is not possible to aim for one without aiming for the other-though it may be possible to succeed at one without succeeding at the other (see Wright, 1992, pp. 18-19). The clearest examples of normatively coincident goals are those with achievement conditions which are separated solely by factors that lie beyond one's control. If I'm about to compete in a race, and I have no control over the performance of the other runners, then the goals of winning the race in the fastest possible time and of completing the race in the fastest possible time are, arguably, 6 The literature on norms of assertion has tended to focus on all-or-nothing judgments to the effect that an assertion 'should not have been made' or is 'unwarranted' or 'breaks the rules' etc. which are then compared with the predictions made by the different accounts. While I more or less follow this convention here, the way in which we evaluate assertions is certainly much richer than this, and can include comparative judgments-person one is more warranted in asserting P than person two, I'm more warranted in asserting P than Q etc. Giving a necessary and sufficient condition for an assertion to be warranted is, in a sense, just the beginning of the story-warrant for asserting a proposition should, ultimately, be regarded as something that permits of degrees. I am inclined to think that the justified belief account could be easily expanded into a full theory of degrees of warrant (more easily perhaps than the knowledge account) but I won't pursue this here. For detailed discussion of these issues see Carter (2022). normatively coincident. Though I could achieve the second goal without achieving the first, the things that I should do in order to achieve the second (get a good start, pace myself etc.) are exactly the same things that I should do in order to achieve the first. To say that knowledge and justified belief are normatively coincident is to say that they stand in a similar relation to these two goals.
Returning to the lottery case, if I can justifiably believe but cannot know, on the basis of the odds involved, that Bruce's ticket has lost, then this would be a violation of normative coincidence-believing this proposition, on this basis, would be a way of aiming for justified belief without aiming for knowledge. Put differently, if I can't achieve knowledge by believing that Bruce's ticket has lost purely on the basis of the odds involved, and knowledge and justified belief are normatively coincident, then this is no way to achieve justified belief either. 7 Why think that knowledge and justified belief are normatively coincident? One motivation comes from considering the clearest cases in which justified beliefs fall short of knowledge. Consider Chisholm's well-known Gettier case (Chisholm, 1989, p. 93). Suppose I walk past a meadow in which I spot a dog that has been disguised to look like a sheep. Taken in by the deception, I come to believe that there is a sheep in the meadow. My belief would seem to be justified, and it so happens that the belief is also true-there really is a sheep in the meadow, grazing behind a hill out of view. Clearly, though, I don't know that there is a sheep in the meadow. The thing to notice is that, although this is a situation which could befall me, it's not a situation that I could aim to be in. It's not as though I could disguise the dog myself and arrange for the sheep to be hidden behind the hill etc. If I did all of that, then I would know that there's a sheep in the meadow and this would no longer be a Gettier case. It is essential to the case that the deception be something of which I am unaware and over which I have no control. And much the same can be said of all standard Gettier cases, as well as cases of justified false belief. That is, all of these cases involve abnormal or untoward circumstances that lie beyond the believer's awareness and control. The lottery case, however, involves no such factors. If the lottery case really were another situation in which a justified belief fails to constitute knowledge, then it would be quite unlike Gettier cases and cases of justified false belief-it is a situation that one could aim to be in.
Another motivation for regarding knowledge and justified belief as normatively coincident comes from considering the teleological structure of inquiry. If knowledge and justified belief are both deemed to be epistemically valuable, and they are not normatively coincident, then an inquiry could run up against a need to compare the two, 7 If knowledge and justified belief are normatively coincident, then following the knowledge rule for assertion and following the justified belief rule for assertion would, presumably, be one and the same activity. In this case, the knowledge account and justified belief account would make the same predictions about what it is to follow the rule of assertion, but different predictions about what it is to comply with the rule of assertion. Relatedly, if knowledge and justified belief are normatively coincident, then the justified belief account is compatible with the idea that knowledge is the ultimate aim of assertion (see Mehta, 2016) even though it is not necessary in order for an assertion to abide by the rules (for more on the distinction between rules and aims of assertion see Marsili, 2018). While I am sympathetic to the idea that knowledge and justified belief normatively coincide, this plays only a subsidiary role in the present paper. As I try to make clear in the main text, the theses that I will motivate with this idea can all be supported in other, independent ways or simply accepted on their own terms. and to potentially choose between them. But an inquiry never founders for this reason. Lottery propositions provide a vivid illustration of this. Suppose my probabilistic grounds are enough for me to justifiably believe that Bruce's ticket has lost, but not enough for me to know that Bruce's ticket has lost. Should I believe this proposition or should I suspend judgment? There is value in justified belief, but disvalue in holding a belief that falls short of knowledge. Whether I ought to believe that Bruce's ticket has lost would appear to depend, then, on how I weigh up the two. But this, to my mind, presents a completely alien picture of how we go about forming beliefs.
I have sketched here one argument to the effect that lottery propositions cannot be justifiably believed purely on the basis of the odds involved. It's worth emphasising that there are several further arguments that can be given for the same conclusion. 8 Douven (2006), for instance, argues for this conclusion by invoking the lottery paradox, and appealing to a conjunction closure principle for justification. I won't discuss any further arguments here but, suffice it to say, if any one of these arguments is successful then the justified belief account will be able accommodate the evidence from lottery propositions-like the knowledge account, it will predict that asserting a lottery proposition, purely on the basis of the odds involved, is unwarranted.

The evidence from Moore's paradoxical propositions
One version of Moore's paradox focusses on assertions of the form 'It's raining but I don't know that it's raining', 'Dogs bark and I don't know that dogs bark' etc. As many philosophers agree, there seems to be something odd or self-conflicted about assertions like this, even though the proposition being asserted is not contradictory and could perfectly well be true (thus the paradox). The knowledge account straightforwardly predicts that one could never have warrant for asserting a 'Moore's paradoxical' proposition-although such a proposition could be true, it could never be known. Let K abbreviate 'One knows…' and assume, for reductio, K(P ∧~KP). It's plausible that knowledge distributes over conjunction-if one knows a conjunction then one must also know the conjuncts. In this case we can derive KP ∧ K~KP. Since knowledge is factive K~KP entails~KP which gives us the contradiction KP ∧~KP. QED. 9 What does the justified belief account predict about the assertion of Moore's paradoxical propositions? It seems plausible that a Moore's paradoxical proposition isn't something that could be justifiably believed, in which case the justified belief account will make the same predictions as the knowledge account. 10 But can we prove this-in 8 For alternative arguments that appeal to considerations relating to surprise, risk and epistemic resilience see Smith (2021). 9 Another form of Moore's paradox focusses on assertions such as 'It's raining but I don't believe that it's raining'. Since knowledge requires belief, the knowledge account will also straightforwardly predict that one could never be warranted in making an assertion such as this. Let B abbreviate 'One believes…' and assume, for reductio K(P ∧~BP). By distribution we can derive KP ∧ K~BP. Since knowledge is factive K~BP entails~BP and, since knowledge requires belief,~BP entails~KP, which gives us the contradiction KP ∧~KP. QED. 10 There are some who hold that knowledge-type Moore's paradoxical propositions can be justifiably believed (McGlynn, 2013, Mandelkern and Dorst, forthcoming), but this view is often combined with alternative explanations of the infelicity of knowledge-type Moore's paradoxical assertions-explanations the same way that we proved that a Moore's paradoxical proposition cannot be known? The preceding proof is of little help, and will go doubly wrong if we try to run it for the case of justified belief. Assume, for reductio, J(P ∧~KP) where J is read 'One justifiably believes…'. A distribution principle for J will give us JP ∧ J~KP. But from J~KP we cannot automatically infer~KP since justified beliefs can be false and, even if we could infer this, JP and~KP are not contradictory. 11 As a result, we need to try a different tack.
It is commonly observed that justified belief is defeasible. Even if one is justified in believing P, this justification may be lost if one acquires new information that weighs against P, or that undermines one's grounds for believing it. What I propose is that whenever one justifiably believes P, the proposition that one does not know P will serve as one kind of defeater for this justified belief. While the proposition that one does not know P doesn't weigh directly against P itself, there is a clear sense in which it does undermine one's grounds for believing P. Consider a standard example of defeat. Suppose I'm shopping for furniture that will suit the colour scheme of my lounge. Suppose I spy a couch that appears to be red and come to justifiably believe that the couch is red. If I then acquired justification for believing, say, that there is a red light shining on the couch, in such a way that it would still appear to be red even if it were white, my grounds for believing that the couch is red would be effectively undermined. At this point, I would no longer be justified in holding this belief, and would be obliged to give it up. 12 But what if I acquired justification for believing that I don't know that the couch is red? In a way, this would subsume the possibility that there is red light shining on the couch, along with other possibilities as well-if I don't know that the couch is red, then this must be because there's strange lighting or I'm undergoing a hallucination or I've been struck by colour blindness or some other circumstance of this kind. And these circumstances all represent defeaters-if I were to learn about any one of them I would lose justification for believing that the couch is red. Learning that I don't know that the couch is red is, in a way, less specific than any of these other discoveries, but the immediate effect upon my belief is surely no different-I would still be obliged to cease believing that the couch is red. If I learn that I don't know that the couch is red then I might want, or expect, some further information to follow-but this is not Footnote 10 continued which make no appeal to the knowledge account, and could equally well be deployed by a proponent of the justified belief account (McGlynn, 2013, Sect. 8, Mandelkern and Dorst, forthcoming, Sect. 5.3). 11 The proof may work in the case of belief-type Moore's paradoxical propositions as mentioned in n9. Assume J(P ∧~BP) for reductio. By distribution we can derive JP ∧ J~BP. While justified belief is not, in general, factive, we might make an exception for propositions about one's own beliefs. In particular, we might argue that J~BP will entail~BP. Since justified belief requires belief we have it that~BP entails~JP which would allow us to derive the contradiction JP ∧~JP. QED. 12 I pass relatively freely between talk of a proposition D defeating one's justified belief, and one's justification being lost when one acquires justification for believing D. Some have suggested that the defeat relation can be defined in this way: if one justifiably believes P, then D defeats one's justified belief in P just in case were one to acquire justification for believing D, one would no longer be justified in believing P (for one approach along these lines see Klein, 1971). I think that this is approximately right, but can go wrong for the sorts of reasons that subjunctive conditional analyses often do (see, for instance, Feldman, 2003, p. 34). My own view is that the defeat relation is best defined in terms of a justificatory support relation between propositions (Smith, 2016(Smith, , chap. 7, 2018)-but I won't discuss this further here. For present purposes, the approximate correctness of the above will be enough to fix upon the relevant notion. required for defeat to take place. I don't need to wait for more information-indeed I shouldn't wait for more information-before giving up my belief.
Another way to motivate the claim that a justified belief is defeated by the proposition that it falls short of knowledge is by appealing once again to the idea that knowledge and justified belief are normatively coincident. If a justified belief could resist defeat from this proposition then that would offer a way of aiming for justified belief at the expense of knowledge. If my justification for believing that the couch is red could survive the discovery that I don't know that the couch is red, then to continue believing that the couch is red would be to aim for justified belief without aiming for knowledge. The decision of whether to retain the belief or abandon it would then hinge upon the question of whether the value of a justified belief outweighs the disvalue of a belief that falls short of knowledge. By the reflections of the previous section, this is a place to which inquiry never leads.
If it's correct that the proposition that one does not know P always serves to defeat one's justified belief in P, then this will motivate the following principle: J~KP → JP. 13 In words; if one justifiably believes that one does not know P, then one does not justifiably believe P. 14 While logics for knowledge and for justified belief are often discussed, bimodal epistemic logics which feature both a knowledge and a justification operator remain relatively unexplored. It is interesting to note, though, that two recent 13 I don't mean to endorse the claim that whenever D defeats one's justified belief in P it follows that JD → JP should be treated as a general principle. One reason this can fail is that even if D defeats one's justified belief in P, it may be possible for one to justifiably believe P on different grounds, which are impervious to the defeating effects of D. In this case there would be a possible circumstance in which JD and JP both hold. If we relativised the J operator to particular grounds, then we may be able to devise a defensible version of the above claim-but I won't pursue this here. What is important for present purposes, though, is that the instance of this claim in which~KP is substituted for D is not subject to the worry just raised. The reason for this is that the defeating effect of~KP would appear to be completely independent of one's grounds for believing P-something I will return to in the next section. 14 One might think that there is something incongruous about appealing to a principle like this as part of a defence of the justified belief account of assertion. Those who defend the justified belief account are, in the context of contemporary epistemology, naturally seen as trying to downplay the significance of knowledge-but this principle, on the contrary, would appear to assign knowledge a privileged normative role. Willard-Kyle (2020, p. 343) remarks that defences of the justified belief account of assertion often give 'uncomfortable pride of place' to knowledge-and my use of this principle might seem to play into this narrative. I don't myself have any qualms about accepting the justified belief account while also accepting a privileged normative role for knowledge, if this is where the arguments lead-but I'm unsure whether the arguments in the main text necessarily do lead in this direction. I outlined two brief arguments in favour of the principle that a justified belief is always defeated by the proposition that it fails to constitute knowledge. The second argument was based on the idea that knowledge and justified belief are normatively coincident goals. While this might suggest a picture on which knowledge serves as the primary goal and justified belief is a kind of 'consolation prize', it is also consistent with justified belief being the primary goal or with neither goal having special priority (Smith, 2016, pp. 10-11). While this argument does carve out a certain normative role for knowledge, it need not be a predominant one. The first argument, on the other hand, is based on the observation that whenever one justifiably believes a proposition, but doesn't know it, we can always find some true proposition that counts as a paradigm defeater (this is much the same observation that inspired the defeasibility theories of knowledge-see Swain, 1998). To make this argument water-tight we may need to appeal to something like the following claim regarding disjunction and defeat: if D 1 defeats one's justified belief in P and D 2 defeats one's justified belief in P then D 1 ∨ D 2 defeats one's justified belief in P. If every specific way in which one could fail to know P counts as a defeater then, by this principle, the proposition that one fails to know P should also count as a defeater. In any case, this argument appeals, at most, to a certain feature of knowledge, but does not involve assigning it any particular normative role. logics of this kind, developed by Goodman and Salow (2018) and Rosenkranz (2021) both feature this principle as a theorem schema. 15 In any case, the principle allows us to outline a simple proof of~J(P ∧~KP): Assume J(P ∧~KP) for reductio. It's plausible that justified belief distributes over conjunction-in which case we can derive JP ∧ J~KP. By the above principle J~KP entails~JP which gives us the contradiction JP ∧ JP. QED The justified belief account, like the knowledge account, predicts that one can never have warrant to assert a Moore's paradoxical proposition. 16 As I noted above, Kvanvig (2009) mounts a similar argument to the effect that the justified belief account can handle the evidence from Moore's paradoxical propositions. My argument appeals to the thesis that if one justifiably believes that one does not know P, then one does not justifiably believe P: J~KP →~JP. Kvanvig's argument appeals instead to the thesis that if one justifiably believes P, then one justifiably believes that one knows P: JP → JKP (Kvanvig, 2009, Sect. 3). Given some weak assumptions, Kvanvig's principle is logically stronger than mine-it entails it without being entailed by it. 17 Furthermore, Kvanvig's principle (which is very similar to 15 See T16 on pp. 88-90 of Rosenkranz's Justification as Ignorance. It is important to note that Rosenkranz uses different letters to me, with 'D' and 'k' serving as the doxastic justification and knowledge operators (Rosenkranz uses 'J' and 'K' for the propositional justification and 'position to know' operators). It is also important to note that Rosenkranz draws a subtle (and somewhat unorthodox) distinction between doxastic justification and justified belief (see Rosenkranz, 2021, Sect. 6.1) meaning that his D and my J are not perfectly equivalent. But the differences between them are not, I think, relevant to the viability of this principle. Goodman and Salow don't explicitly consider this principle, but it is a consequence of their possible worlds truth conditions for the justification and knowledge operators (Goodman and Salow, 2018, Sect. 5). Goodman and Salow's truth conditions are intended for propositional justification and for being in a position to know, meaning that the principle will, once again, mean something slightly different in their system. 16 It's interesting to note that this argument will not help a defender of the propositional justification account of assertion (as mentioned in n2) to explain the infelicity of Moore's paradoxical assertions-as a propositional justification version of the argument would appear to be unsound. If we let J abbreviate 'One has justification for believing…' then, assuming that propositional justification distributes over conjunction, we could get from the principle J~KP →~JP to the conclusion~J(P ∧~KP). But this principle is not plausible; if one has justification for believing P but does not believe P, or believes P in a way that is not properly based upon one's justification, then one might also have justification for believing that one does not know P. Put differently, the proposition that one does not know P may always defeat a justified belief in P but will not always defeat a justification for believing P. 17 Assume JP → JKP. By contraposition we have~JKP →~JP. If we assume that one cannot justifiably believe both a proposition and its negation then this gives us J~KP →~JKP. By chaining these conditionals together we can derive J~KP →~JP. QED The way that Kvanvig initially formulates his principle, it would seem to be easily refuted by cases in which one justifiably believes a proposition P, but does not believe that they know P (which are surely possible). If one doesn't believe that they know P, then one doesn't justifiably believe that they know P. (Kvanvig does add the requirement that one knows that one believes P, but that is not enough to get around the present difficulty). Kvanvig later suggests that the principle ought to be formulated in terms of propositional rather than doxastic justification (Kvanvig, 2009, p. 150). If we once again let J abbreviate 'One has justification for believing…' we could write this as: JP → JKP. But this is still, arguably, logically stronger than the principle I have defended. Assume JP → JKP. By contraposition we have~JKP →~JP. Since doxastic justification entails propositional justification we also have JP → JP and, by contraposition,~JP →~JP. If we assume that one cannot justifiably believe a proposition while having justification for believing its negation this gives us J~KP →~JKP. By chaining all of these conditionals together we can derive J~KP →~JP. QED. It's important to show, finally, that J~KP →~JP does not entail JP → JKP (or JP → JKP). I will sketch a simple countermodel, cutting various corners along the way. Suppose the J and K operators are each associated with an accessibility relation on possible worlds, such that JP is true at w iff P is true at every world that w accesses via R J and KP is true at w iff P what Smithies (2012) labels the 'JK' rule) may be subject to certain objections that my principle escapes (see Smith, 2012).

The evidence from conversational patterns
The final piece of evidence that has been thought to favour the knowledge account comes from observing the back and forth of conversational exchange, in which assertions are put forward, challenged and retracted. One common way to challenge an assertion is by saying 'You don't know that' or, less forcefully, 'Do you know that?' or 'How do you know that?'. 18 If knowledge is needed for warranted assertion, then these utterances serve to deny that, or to question whether, an assertion is warranted, providing a simple explanation as to why they should function as challenges. There are, of course, other ways in which we can challenge an assertion-like 'That's not true' or 'You have no reason to believe that'-but, in so far as truth and justified belief are both necessary for knowledge, the knowledge account would seem well placed to explain why these utterances will work as challenges too.
The justified belief account can, presumably, provide a simple explanation as to why 'You have no reason to believe that' would pose a challenge to an assertion, but what about the others? Before addressing this question, I want to briefly consider what it means to 'challenge' an assertion. A challenge, in the broadest sense, is a speech act that aims to pressure an asserter into withdrawing or retracting an assertion that they have made-or, at least, into defending it further (more on this below). A challenge could take the form of another assertion or it could be a question, as some of the above examples illustrate. 19 On the justified belief account, one way to oblige a person to Footnote 17 continued is true at every world that w accesses via R K . Consider the following constraint on the interaction between R J and R K : for any world x there exists a world y such that xR J y and for every world z if yR K z then xR J z. As can be easily checked, this will validate the theorem J~KP →~JP. Consider a model consisting of three worlds w 1 , w 2 and w 3 . Suppose that R J and R K coincide and link each world to itself. Suppose further that these relations link w 1 to w 2 and w 2 to w 3 but have no other instances. This model satisfies the above constraint meaning that J~KP →~JP will hold at each world for any P. Suppose, finally, that A is true at w 1 and w 2 , but false at w 3 . JA will be true at w 1 , but~KA will be true at w 2 in which case~JKA will be true at w 1 . It's worth noting that this model also satisfies the most obviously desirable constraints on R J and R K (R K is reflexive giving us KP → P, R J is a subset of R K giving us KP → JP). R J and R K also satisfy some constraints that would not be desirable in general (R J is reflexive and R K is a subset of R J ) but these could easily be relaxed by adding further worlds that are disconnected from w 1 , w 2 and w 3 . 18 According to Williamson, the question 'How do you know that?' presupposes that the addressee does know the relevant proposition, in so far as every question presupposes that it has an answer. As Williamson points out though, asking the question may often serve as a way of expressing doubts about that very presupposition (Williamson, 2000, pp. 252-253). And so it is with how-questions in general. If a mechanic claims that my car has been fixed after working on it for only a few minutes and I ask 'How has it been fixed?' I would naturally be interpreted as disputing, rather than presupposing, the truth of mechanic's claim. If the bank manager says to me 'Don't worry-we're thoroughly investigating why the money has gone missing from your account. Everything is OK' and I respond with 'How is everything OK?', then I'm obviously implying that, as far as I'm concerned, everything is not OK. retract an assertion is by depriving them of justification for believing its content-and one natural way to accomplish this is by supplying a defeater.
Suppose I'm back at the furniture store, and I've brought along Bruce for advice. Suppose I spy a couch that appears to be red and I say 'What about that one? That couch is red.' If Bruce were to reply 'You realise there is red light shining on that couch' then this would work as an effective challenge to my assertion, and the justified belief account offers a straightforward explanation as to why. If Bruce asserts that there is red light shining on the couch then, all else equal, I will acquire justification for believing this, at which point I will lose justification for believing that the couch is red and, according to the justified belief account, lose warrant for asserting it. If Bruce had replied by asking 'Is there red light shining on that couch?' then, all else equal, that would provide me with justification for suspecting that there is red light shining on the couch or for taking the possibility seriously, which may still be enough to have a defeating effect. 20 Challenges like these are not assured to work of course. Perhaps I have good reason to think that the lighting is normal and that Bruce must be mistaken. If so, his utterance may fail to generate justification for believing, or even suspecting, that there is red light shining on the couch. In this case, my justification for believing that the couch is red will stand, along with my warrant for asserting it. But if I don't have any particular reason to distrust what Bruce is saying, the challenge would succeed and I would likely respond by taking the assertion back-saying something like 'OK I guess I might be wrong about the colour of the couch'.
The justified belief account predicts that the introduction of a defeater will serve as one effective way to challenge an assertion. But if a person asserts a proposition P and a challenger responds with 'You don't know that', 'Do you know that?' or 'How do you know that?' then, as discussed in the last section, this is to introduce a defeater. With these speech acts the challenger makes salient the proposition that the asserter does not know P. If the challenger succeeds in providing the asserter with justification for believing, or even suspecting, that this is true, then they will no longer be justified in believing P, and will lose their warrant to assert it. If Bruce replied to my 'That couch is red' by saying 'You don't know that' then I might well expect him to elaborate further, but even if he doesn't (perhaps he's distracted or we're interrupted etc.) the defeating effect is the same: if I don't have any reason to doubt his words, then I ought to give up my belief and retract my assertion. 21 With respect to the question 'Do you know that?' Williamson writes that 'On the hypothesis that not only knowledge warrants assertion, the aggressiveness of the question is hard to understand, for the asserter might truthfully answer 'No' and still have warrant for the assertion.' (Williamson, 2000, p. 253). The justified belief account 20 If one justifiably believes a proposition P, it is plausible that one must have justification for believing, of any defeating proposition, that it is false (see for instance the discussion of 'rational monotonicity' in Smith, 2018). But this is incompatible with one having reason to suspect that a defeating proposition is true-or even reason to suspend judgment on its truth. 21 I have claimed that if one has justification for believing that one does not know P then one cannot justifiably believe P-but, as observed in n16, one could still have justification for believing P. As a result, a defender of the propositional justification account of assertion cannot simply co-opt this explanation of why 'You don't know that' functions as a challenge. is, of course, a view on which not only knowledge warrants assertion-but, contrary to Williamson's claim, it predicts that an asserter could not truthfully answer 'No' to this question and still have warrant for the assertion-to do this would be to acknowledge a defeater. Once again, the knowledge account and the justified belief account make the same prediction here, albeit for somewhat different reasons.
If one way to challenge an assertion is by introducing a defeater, then this explains why 'You don't know that' could, in principle, work as a challenge. But why should this be such a common way of challenging an assertion? Is this something that the justified belief account can explain? I think perhaps it can. One thing we might observe is that the efficacy of most defeaters is going depend upon the grounds of a justified belief. In the couch example, the proposition that there is red light shining on the couch will serve to defeat my justified belief that the couch is red-but this is only because the belief is based on my immediate perceptual impressions. If I had different, or additional, grounds for believing this-if, say, I'd seen the couch described as red in a catalogue-then the proposition that there is red light shining on the couch would not count as a defeater, and Bruce's utterance would fail to raise a challenge.
As a result, Bruce would only seek to challenge my assertion with the words 'There is red light shining on that couch' in so far as he is prepared to make a certain assumption about my grounds (an assumption which might be reasonable enough under the circumstances). But 'You don't know that' requires no such assumption. That is, this utterance will introduce a defeater no matter what. As argued in the last section, one cannot justifiably believe P while simultaneously having justification for believing that they don't know P-and this holds true irrespective of their grounds for believing P. Saying 'You don't know that' may still fail to provide an asserter with justification for believing its content-so the challenge may still fall flat-but if the challenger succeeds in providing the asserter with justification for believing that they don't know P, then they will no longer be justified in believing P, no matter their grounds. The reason 'You don't know that' is such a common challenge for an assertion, I suggest, is that it avoids the need to second-guess an asserter's grounds.
It is not unusual for one to take exception to an assertion without having perfect information about what moved the asserter to make it. And such an attitude may be reasonable-a would-be challenger may be justifiably confident that they could provide a grounds-specific defeater, no matter what an asserter's grounds turned out to be. But, unless the asserter volunteers those grounds, an all-purpose challenge like 'You don't know that' may be the best available option. If the asserter doesn't immediately yield to the challenge and retract their assertion, then they will most likely respond by stating their grounds, at which point the challenger can introduce a grounds-specific defeater, if they are able (and if the challenger is caught out by the asserter's grounds, and is not able to do this, then they should be the one to yield). 22 There is, however, a downside to challenging an assertion with 'You don't know that'. While this challenge doesn't require specific assumptions about the asserter's grounds, it also fails to display any understanding of the asserter's grounds-and this can limit the challenger's authority, in the eyes of the asserter. While 'You don't know that' introduces content that will serve as a defeater, irrespective of the asserter's grounds, it may be more difficult for this utterance to provide an asserter with justification for believing that defeating content. This is precisely why a confident asserter would tend to respond to this by stating their grounds, and shifting the onus back to the challenger, rather than making an immediate retraction.
'You don't know that' is not the only 'all-purpose' challenge that one can make to an assertion-'That's not true' would also have this status. After all, one cannot justifiably believe P while simultaneously having justification for believing~P-irrespective of their grounds for believing P. If someone asserts P and a challenger responds by saying 'That's not true' then this may fail to provide an asserter with justification for believing P-but if it succeeds, the asserter will no longer be justified in believing P, no matter their grounds. By uttering 'That's not true', however, a challenger obviously commits themselves to the falsity of the asserted content, while 'You don't know that' carries no such commitment. 23 The main upshot of this discussion is that, according to the justified belief account, 'You don't know that' may have a unique status as the least-committal all-purpose challenge to an assertion, giving an explanation for its common usage. But the discussion may also serve to highlight something more general: if we accept the justified belief account, then this opens up the possibility of explaining various aspects of conversational exchange by using resources from the epistemology of testimony and the epistemology of defeat. I have already indicated a few areas in which this approach may be fruitful, and I will pursue this theme further in the final section.

Prospective vs retrospective retraction
Following Kvanvig (2009, Sect. 2) we can distinguish between two different ways in which an assertion can be retracted. First, one could indicate that they are no longer willing to repeat or endorse an assertion that they have made. This kind of retraction is purely forward-looking or prospective. Second, one could admit that their assertion should never have been made in the first place. This kind of retraction is backwardlooking or retrospective. The second kind of retraction goes significantly further than the first, and involves an element of self-criticism or self-censure that the former lacks. One can make a prospective retraction with the words 'I take it back' or 'I might be wrong', 24 while a retrospective retraction would involve something like 'I never should have said that' or 'I didn't mean that '. 25 Corresponding to these two ways in which an assertion can be retracted, we can distinguish between two ways in which an assertion can be challenged: a prospective challenge aims to elicit a prospective retraction, while a retrospective challenge aims to elicit a retrospective retraction.
On the justified belief account, as we've seen, one way to challenge an assertion is to introduce a defeater. Suppose a person asserts a proposition P. If a challenger succeeds in providing the asserter with justification for believing or suspecting that a defeating proposition is true, then they will no longer be justified in believing P, and will have reason to concede that the assertion might be false. But the introduction of a defeater will not, in and of itself, give the asserter any reason to deny that they were justified in believing P in the past, and thus no reason to concede that the assertion should never have been made.
The justified belief account predicts that the introduction of a defeater will pose only a prospective challenge to an assertion-and consideration of examples suggests that this prediction is correct. Suppose I assert 'That couch is red', Bruce responds with 'There's red light shining on that couch' and I reply 'OK, I guess I might be wrong about the colour'. Suppose Bruce then tries to force a retrospective retraction by saying 'Right. You never should have said that it was red in the first place'. I'd likely protest at that-'Hold on-how was I supposed to know there was red lighting?!' On the justified belief account I'm right to protest-Bruce's challenge has only prospective scope. Bruce may have provided new information in light of which I would no longer be justified in believing that the couch is red-but that doesn't mean that my belief was unjustified all along.
What will the knowledge account predict about the status of Bruce's challenge? Many accept that knowledge, like justified belief, can be defeated, in that it can be lost as a result of the acquisition of new information (Williamson, 2000, pp. 205-207, pp. 265-266, Goodman & Salow, 2018 26 . And yet, it's clear that defeat cannot work Footnote 24 continued score and opening up further possibilities (Stalnaker, 1970, pp. 286-287, Yalcin, 2007 This would provide one explanation as to why 'I might be wrong' amounts to a (prospective) retraction of an assertion-it can be seen as an attempt to reverse whatever changes the assertion wrought to the conversational score (MacFarlane, 2011, Sect. 3). 25 Kvanvig frames this distinction in a slightly different way, contrasting cases in which one 'takes back the content' of an assertion with cases in which one 'apologises for and regrets' the assertion itself (Kvanvig, 2009, pp. 145-146). The idea of taking back the content of an assertion, if that is supposed to be somehow different from taking back the assertion, is not, I think, a helpful way to conceive of prospective retraction-indeed, it's unclear whether this is even coherent (Simion 2016b, Sect. 3). Also, while I agree that an apology is often appropriate in a case of retrospective retraction and would sometimes seem excessive in a case of prospective retraction, I wouldn't want to use the presence of an apology as a criterion for determining whether a retraction is retrospective-I don't think the connections are quite tight enough for that (Williamson, 2009, p. 345). We should in any case be wary of overcomplicating the distinction between prospective and retrospective retraction-there is an obvious difference between indicating that one is no longer willing to endorse or repeat an assertion and indicating that one should not have made the assertion in the first place. 26 Some suggest that knowledge may not be defeasible in this way (Lasonen-Aarnio, 2010, see also Williamson,forthcoming,Sect. 4). If this is correct then the proponent of the knowledge account will be prevented from appealing to the notion of defeat in explaining how challenges work and will, I suspect, be unable to make any sense of the idea of a prospective challenge. As I argue soon, however, even those defenders of the knowledge account who accept the possibility of knowledge being defeated may, in the end, be saddled with the same conclusion. in quite the same way for knowledge as it does for justified belief. After all, if what Bruce says is true, and there really is red light shining on the couch, then this wouldn't be a case in which my knowledge is defeated-rather, it would be a case in which I never had knowledge to begin with. What are the possibilities here? If the couch is white and bathed in red light, then this would be a case of justified false belief. If the couch is red and bathed in red light, then this would be a Gettier case. Either way, my belief would never have amounted to knowledge in the first place. If I yield to Bruce's challenge, and the knowledge account is correct, then it looks as though I would be obliged to make a retrospective retraction after all.
Proponents of the knowledge account often emphasise the fact that rules can be broken in a way that is blameless or excusable (see for instance Williamson, 2000, Sect. 11.4, DeRose, 2002. So even if I were to retrospectively retract my assertion that the couch is red, that is compatible with my regarding the assertion as blameless. Could this make the idea of a retrospective retraction more palatable in this case? On the face of it, though, Bruce is not laying any blame in the above exchange-he is merely trying to force a retrospective retraction. And even if he made it clear that blaming was not his intent, this wouldn't necessarily make any difference to my reaction. If Bruce were to say 'You never should have said that the couch was red in the first place-but I guess you have an excuse', I would still push back against that-I wouldn't concede that I had done anything for which an excuse is needed. In any case, I won't pursue this further, as I'm inclined to think that the present issue is just a symptom of a deeper problem for the knowledge account-and one that cannot be avoided by manoeuvres of this kind.
If the knowledge account is correct, then not only would Bruce's particular challenge above turn out to be retrospective-it may be impossible in principle for Bruce to make a prospective challenge to my assertion. According to the knowledge account, in order for me to make a prospective retraction I would have to take the view that I knew that the couch was red but, having heard from Bruce, I no longer do-but this just doesn't seem like a coherent attitude for me to adopt. Whatever Bruce says, if it makes me reluctant to assert that the couch is red it will also make me reluctant to believe that I knew this in the past. The problem for the knowledge account isn't, then, just about the status of this or that specific challenge-rather, the account seems to preclude the very possibility of a prospective challenge to an assertion.
From the perspective of the justified belief account, however, things look very different. According to the justified belief account, in order for me to make a prospective retraction I would have to take the view that I was justified in believing that the couch was red but, having heard from Bruce, I no longer am-which is not at all incoherent. The justified belief account allows for the possibility of both prospective and retrospective challenges; a prospective challenge involves trying to defeat an asserter's justified belief in the asserted content while a retrospective challenge involves accusing the asserter of lacking justified belief in that content-perhaps with the words 'You have no reason to believe that'. Saying 'You have no reason to believe that' is not an attempt to change an asserter's epistemic position but, rather, to draw attention to its deficiencies 27 . On close inspection, though, I think it's plausible that this kind of challenge really does have a different status to the challenges we have been focussing on thus far.
One thing we can observe about 'You have no reason to believe that' is that it serves as a natural follow-up when an initial challenge is ignored. This pattern already suggests that the challenge may have retrospective scope-we would expect that a demand for prospective retraction, when ignored, will quickly give way to a demand for retrospective retraction. Suppose again that I assert 'That couch is red' and Bruce responds 'You realise there's red light shining on that couch'. Suppose that, rather than making a retraction, I dismiss the challenge and continue to make the assertion-perhaps I run into another friend and say 'See that red couch there? I'm thinking of getting it!' At this point, it would be perfectly legitimate for Bruce to interject with 'I told you there's red light over there-you have no reason to believe that the couch is red!' Bruce would not have been entitled to make this challenge initially, but is within his rights to do so now. And the right response from me, at this point, would be to make a retrospective retraction-something like 'Oh right the lighting. I shouldn't have said that it was red. I really do need to check the colour'.
In the previous section, I argued that the knowledge account and the justified belief account can equally well explain the evidence from conversational patterns-where this evidence is conceived as a list of the kinds of utterances that might be used to challenge an assertion. In this final section, I have argued that there is more to the evidence than this. Once we are attuned to the distinction between prospective and retrospective challenges, and to the kinds of utterances that are associated with each, it is the justified belief account that has an explanatory advantage.
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