1. THE BACKGROUND DEBATE – PEER DISAGREEMENT AND THE CONCILIATORY VIEW

In the course of the past ten years, a lively debate has developed around the question of how to rationally form one's beliefs in cases of so called peer disagreement, that is, in cases in which one discovers that someone that one has hitherto regarded as equally competent regarding a certain issue and who apparently possesses the same, or at least equally good evidence regarding the issue in question has a different opinion on this issue. More precisely, someone is my epistemic peer regarding the truth or falsity of a certain proposition p if and only if this person has, at the relevant time t, the same, or at least equally good evidence regarding p and is in general as reliable as I when it comes to forming a judgment on the basis of the kind of evidence in question. The philosophical debate about peer disagreement concerns the question of how to react most rationally in a situation in which one believes (or, more accurately, in which one is rationally required to believe) the disagreeing interlocutor to be one's epistemic peer regarding the issue at hand (that is, it is, in this context, irrelevant whether the interlocutor is in fact the subject's epistemic peer or merely a clever trickster pretending to possess the relevant level of expertise), and in which one does, before being confronted with the disagreement, not regard the interlocutor as any more or less confused, drunk, etc. than oneself. For the purpose of illustration, here is an example of the relevant kind of situation construed by Christensen:

As already mentioned, the relevant question is the following: “How should I react, upon learning of [the interlocutor's] belief?” (193). More specifically, the question at issue is how to form one's belief regarding the issue in question at the very moment of learning about the disagreement. Of course, consulting the bill once again in order to redo the calculation is most reasonable. However, there still remains the question of what to believe regarding the correct amount of the shares until one has a chance to do the math again. (And this question is a legitimate one even if it takes just a few seconds to take another look at the bill.)

The philosophical positions that have seriously been endorsed regarding this question mainly divide into the following three kinds. First, one may regard the kind of situation in question as evidentially symmetric, such that one is rationally required to give the interlocutor's opinion the same epistemic weight as one's own initial stance. This view, which has been called the ‘Equal Weight View’ and which has most prominently been defended by Feldman (Reference Feldman and Hetherington2006), Christensen (Reference Christensen2007a), and Elga (Reference Elga2007), consists in the claim that the subject is rationally required to split the difference between one's own initial degree of confidence in the proposition in question (that is, the degree of confidence one has before learning of the disagreement) and the interlocutor's initial degree of confidence. Thus, if, to use the restaurant case again, one's initial degree of confidence in the proposition that the correct shares are $43 is maximally high, and the interlocutor's degree of confidence that this proposition is correct turns out maximally low, then, according to the Equal Weight View, one is rationally required to adopt a degree of confidence of 0.5 in the truth of the proposition – which simply amounts to withholding one's judgment regarding whether one calculated the shares correctly.Footnote ¹ A second kind of view (defended, for instance, by Wedgwood Reference Wedgwood2007: 261) consists in claiming that in the kind of situation in question, one is always rationally permitted to have an “egocentric epistemic bias” in favour of one's own initial opinion. And finally, one might hold that the most rational confidence distribution depends on who actually did the math correctly, such that the person who did do the math correctly is permitted (and even required) to give less than equal weight to the interlocutor's opinion, while the person who did the math wrong is required to give more than equal weight to the other's opinion. A version of this latter position has been called the ‘Total Evidence View’ and has most prominently been defended by Kelly (Reference Kelly, Feldman and Warfield2010, Reference Kelly, Christensen and Lackey2013).Footnote ²

Even though both the Egocentric Bias View and the Total Evidence View recommend giving less weight to the occurrence of the disagreement than recommended by the Equal Weight View, neither of these two views entails that no weight at all should be given to the occurrence of the disagreement.Footnote ³ Wedgwood (Reference Wedgwood2007), for instance, in defending the Egocentric Bias View, holds that even though learning of the disagreement “need not totally defeat [one's] justification” for one's initial belief, it still “weakens” one's justification (261). And Kelly (Reference Kelly, Christensen and Lackey2013), in defending the Total Evidence View, states that the latter, “no less than the Equal Weight View, counts as a species of” the view according to which “one must give at least some (even extremely minimal) weight to the opinion of a peer” (36, fn. 5).

This latter view according to which one is rationally required to move at least a bit in the direction of the disagreeing peer has (following Elga Reference Elga, Feldman and Warfield2010) been called the ‘Conciliatory View’ (CV). (I will redefine this term in the following section, so as to denote a slightly more demanding, but in the end not significantly less plausible view.) Since the only way to reject CV is to hold that it is rationally permissible to ignore the fact that a person one has hitherto regarded as a peer arrived at a different opinion, and since this latter view (sometimes called the ‘Steadfast View’) appears prima facie implausible even with respect to cases in which one's initial opinion is the correct one, CV should, at least prima facie, be regarded as highly appealing. Accordingly, Christensen (Reference Christensen, Christensen and Lackey2013) describes endorsing CV as no more than

Christensen even goes on to describe CV as “little more than epistemic common sense” (77). I take it that having to deny CV should indeed be regarded as an extremely high theoretical cost, such that any kind of argument showing that endorsing CV involves insuperable difficulties should be regarded as providing a dilemma.Footnote ⁴ As will be described below, such a dilemma in fact arises. As Christensen himself puts it, “the sort of modesty in question has some puzzling consequences” (77). I will now go on to describe these consequences.

2. THE INCOHERENCE OBJECTION AND THE DILEMMA OF CONCILIATIONISM

As already mentioned, Elga (Reference Elga2007) provides one of the most prominent defenses of the Equal Weight View. However, in his 2010 paper “How to Disagree about How to Disagree,” Elga himself argues that not only the Equal Weight View, but also CV – which, as mentioned above, is a much more modest position, and which Elga (Reference Elga, Feldman and Warfield2010) still calls “extremely natural and appealing” (175) – is subject to an insuperable problem. This problem becomes apparent as soon as one considers cases of peer disagreement in which the disagreement is about the truth of CV itself. According to Elga, considering this kind of case reveals that CV is self-undermining and therefore incoherent. The view is self-undermining because, as he argues, it calls for its own rejection in the kind of case in question. He describes the relevant kind of situation as follows:

Since Elga defines CV as the view according to which “finding out that a respected adviser disagrees with one should move one at least a little in the direction of the adviser's view” (Reference Elga, Feldman and Warfield2010: 175), it is not clear why he regards the situation described in the passage just cited as one in which applying CV requires one to give up endorsing the view. After all, moving at least a little bit away from one's initial high credence in CV may still leave one with a relatively high credence in the view, such that one should not be regarded as giving up the view.

However, first, it seems safe to say that not only a view according to which, in the relevant kind of situation, one should be conciliatory to at least some arbitrarily small extent, but also a view according to which one should become doubtful to some significant degree of one's initial stance deserves to be regarded as highly plausible (such that the incoherence of such view should be regarded as striking). In what follows, I will use the term ‘Conciliatory View’ (and ‘CV’) to denote this latter, more demanding but still highly appealing position.Footnote ⁵

And second, one can imagine a situation in which one does not only encounter one single disagreeing peer, but several, all of whom arrived at their opinion independently of each other. It may, however, still be objected that it is not clear whether even the redefined, stronger version of CV in question ever recommends its own rejection in the face of a certain number of independent dissenters. For it would be rather implausible to hold that the number of disagreeing peers proportionally corresponds to the degree of required doubt in one's initial opinion. Rather, the way in which the degree of required doubt in one's initial opinion increases in the face of a growing number of independently disagreeing peers is quite unclear.

In order to resolve this unclarity in a way charitable to Elga, let me specify what the formulation ‘to some significant degree’ in the definition of CV is supposed to mean. It seems that for some degrees of conciliation lower than that required by the Equal Weight View, it is safe to say that a growing number of independently disagreeing peers will push the required degree of conciliation above the threshold of rejection. For instance, if one holds that the presence of one single disagreeing peer requires a degree of conciliation of 0.4, then this arguably commits one to hold that in the face of several independently disagreeing peers, the required degree of conciliation increases such that the subject is required to reject (that is, believe in the falsity of) her initial view. And the same arguably holds for some degrees of conciliation lower than 0.4. Now, in defining CV as the view according to which one should become doubtful of one's initial opinion to some significant degree, I intend to refer to the lowest degree of conciliation that still generates the requirement of rejection of one's initial opinion in the face of an arbitrarily growing number of independently disagreeing peers, whichever degree of conciliation this may be. Given that the number of independently disagreeing peers may be arbitrarily high, it is plausible to assume that the degree in question will be clearly lower than 0.4. Thus, given that even the Equal Weight View has some undeniable intuitive appeal, the resulting version of CV in question may well be regarded as appealing enough in order for its supposed incoherence to be fairly striking.Footnote ⁶

Let me now turn to Elga's argument for the claim that calling for its own rejection makes CV incoherent. He notes that “one's view on disagreement is part of one's inductive method” (Reference Elga, Feldman and Warfield2010: 179), that is, part of one's way of forming beliefs in response to the course of one's experience. Thus, if one's view on disagreement sometimes calls for its own rejection, “[t]hen one's inductive method also sometimes calls for its own rejection.” (Reference Elga, Feldman and Warfield2010: 179). He then goes on to argue that an inductive method that calls for its own rejection is incoherent. He does so by means of illustration, using the following example (adapted from a remark by Lewis Reference Lewis1971: 56):

Arguably, the same problem that besets the consumer ratings magazine in question also besets any inductive method of belief formation that leads one to follow some competing inductive method of belief formation. Elga goes on to conclude:

As stated above, forming one's beliefs in a way rationally required according to CV indeed sometimes leads one to reject the view. However, Elga's conclusion that following CV makes one's inductive method incoherent is too quick. In order to see this, note that CV is merely a view about what kind of belief-formation is rationally required. As already conceded, any advice on belief formation that leads one to follow some competing advice on belief formation should be regarded as incoherent. However, following the advice of CV in the problematic kind of case in question does not consist in starting to follow a competing method (a method recommended by an “uncompromising view,” as Elga coins it), or in no longer following CV. Rather, following the advice of CV in the problematic kind of case in question merely consists (given that one encounters a large enough number of independently disagreeing peers) in adopting the belief that CV is false, that is, in adopting the belief that one is not rationally required to be conciliatory in cases of apparent peer disagreement. And adopting this latter belief is not incompatible with being conciliatory. Christensen puts this as follows:

It should be conceded by defenders of CV, though, that given that the disagreeing peers do not merely hold that one is not rationally required to be conciliatory, but also that one is rationally required not to be conciliatory, following CV (defined in the above-described way charitable to Elga) also leads one to adopt this latter belief. However, even believing that one is rationally required not to be conciliatory is still compatible with being conciliatory. In this way, the analogy to the consumer ratings magazine fails. For following the advice of the magazine does not merely consist in believing that one is rationally required to follow the advice of the competing magazine; rather, it consists in following the advice of the competing magazine, which is indeed incompatible with following the magazine's advice regarding the purchase of toasters. But, as stated above, in contrast to the consumer ratings magazine, following the advice of CV in the problematic kind of case is not impossible, and it does therefore not make one's inductive method incoherent.Footnote ⁸ Elga's argument for the view's incoherence thus fails.

However, defenders of CV still have reason to be worried. For even though it is possible to be conciliatory while believing that one is rationally required not to be conciliatory, it should be acknowledged that this combination constitutes itself some kind of irrationality. As Christensen puts it, “[t]here does seem to be something epistemically wrong with divorcing what it's rational for me to believe in general from what it's rational for me to believe about what's rational for me to believe” (2013: 84). Thus, it seems quite plausible that someone who has come to believe that one is rationally required not to follow CV and who continues to follow the view's advice is subject to irrationality, in virtue of the following level-connecting principle (a term borrowed from Christensen):

Supplementing Elga's objection with LC yields the following problem for defenders of CV. Given CV, one is (in peer situations) sometimes rationally required to believe that one is rationally required not to be conciliatory. And since (due to LC) believing that one is rationally required not to be conciliatory rationally requires one not to be conciliatory, one is, given CV, (in peer situations) sometimes rationally required not to be conciliatory. However, CV is a general principle according to which one is (in peer situations) always rationally required to be conciliatory. Thus, assuming LC, it seems that CV entails contradictory claims and is therefore indeed incoherent. And even apart from LC's indubitable intuitive appeal, rejecting the principle might be regarded as particularly unappealing for defenders of CV:

Thus, it seems that denying LC is no promising option for defenders of CV to block the incoherence argument.

The above considerations describe what may be called the ‘dilemma of conciliationism’. (Weatherson Reference Weatherson, Christensen and Lackey2013: 55, for instance, calls it “an odd little dilemma”.) For as already stated, rejecting CV and accepting a view according to which it is epistemically permissible to simply ignore the fact that a respected peer arrived at a different credence is extremely unappealing. Moreover, even if it could be convincingly argued that the intuitive appeal of CV is simply negligible in the face of the incoherence argument, this would still not constitute a satisfying response to this argument. For as pointed out by Christensen (cf. 2013: 86), the incoherence argument does not only apply to CV, but also to more modest and thereby even more appealing principles (call them ‘minimal humility principles’) according to which one should be conciliatory when entering into a disagreement with apparent epistemic superiors. Furthermore, apart from principles about how to react in cases of disagreement, the incoherence argument even applies to any kind of principle according to which one is rationally required to give up one's belief in a proposition p if one encounters some particular kind of evidence (be it a disagreeing peer, evidence that one has been drugged, etc.) suggesting that one's initial belief in p resulted from a defective assessment of the initial evidence. As stated by Frances (Reference Frances2010), “[t]he probability that some such principle […] should be true gives us good grounds to think that there must be something amiss with the Self-Application Objection” (457).

But still, there is no good reason in sight for rejecting any of the steps in the above considerations leading to the conclusion that endorsing CV may result in being irrational. Thus, the debate about peer disagreement is faced with a genuine puzzle. In the following section, I will consider the replies that have been offered so far.

3. SOME (UNSATISFYING) REPLIES

After presenting his version of the incoherence argument (the version that does not take into account the need for a level-connecting principle), Elga concludes that “[t]here is no good reply. Conciliatory views stand refuted” (Reference Elga, Feldman and Warfield2010: 182). However, given that, as already mentioned, he regards CV as “extremely natural and appealing” (175), he attempts to preserve as much of it as possible, by endorsing a partly conciliatory view – a view that “recommend[s] compromise in the face of disagreement about many matters, but not about disagreement itself” (176). That is, since he takes his version of the incoherence argument to show that “in order to be consistent, views on disagreement must be dogmatic with respect to their own correctness” (184f.), he endorses a view according to which one is rationally required to be conciliatory in cases of peer disagreement as long as the disagreement does not concern the question of how to rationally form one's beliefs in cases of apparent disagreement. Even though Elga is not completely explicit regarding whether his partly conciliatory view (PCV) entails that one is rationally required to keep one's initial credence in cases of disagreement about disagreement, or whether PCV simply remains silent about how to form one's beliefs in this kind of case, his remarks suggest the former.

However, PCV should not be regarded as a satisfying answer to the incoherence argument. For exempting cases of disagreement about disagreement from the extremely intuitive requirement to respect the opinions of respected peers is clearly in tension with the intuition behind CV. Christensen puts this as follows:

One might try to violate the intuition behind CV to a lesser extent by endorsing a modified version of PCV which does not exempt all cases of apparent peer disagreement about disagreement, but instead only those cases of apparent peer disagreement about disagreement in which the disagreement constitutes misleading evidence. That is, one might endorse the following principle:

PCV* differs from PCV in two important respects. First, it does not involve the claim that one is rationally required to be dogmatic in the critical kind of case. Instead, it simply remains silent about this issue and is thereby, for instance, compatible with a view according to which one should be conciliatory in the critical kind of case and then go on to follow the advice of whatever kind of position one has arrived at by being conciliatory.Footnote ⁹ Second, PCV*, as already announced, violates the intuition behind CV to a lesser extent than PCV, since PCV* – like CV and unlike PCV – recommends being conciliatory to someone who disbelieves PCV* and who meets an apparent peer disagreeing on this issue. (At least, this is what PCV* recommends if PCV* is correct.)

However, it seems that a view according to which one is rationally required to be conciliatory in cases of disagreement about disagreement only if one's initial opinion is false still violates the intuition behind CV to an unacceptable extent. According to CV, one is rationally required to be conciliatory in all cases of apparent peer disagreement, including those cases in which one's initial opinion is true. And the same holds according to PCV*, with the exception of those cases in which the disagreement concerns rules of rationality. Now, analogously to Christensen's objection against PCV cited above, it seems extremely dubious to regard oneself as being immune from error concerning philosophical questions about rationality while regarding oneself as fallible concerning any other subject matter (including any other supposedly a priori issue).

It thus seems that endorsing a restricted version of CV is not a good way of replying to the incoherence argument. One might, instead, think that the right reply to the incoherence argument is to adopt a position according to which the occurrence of disagreeing peers never creates any rational pressure to revise one's initial attitude, given that one's initial attitude was rationally required on one's initial evidence. This view – the so-called ‘Right Reasons View’ – has most prominently been endorsed by Kelly (Reference Kelly2005) (before he turned to the more moderate position mentioned in section 1 above). Very recently, this view has been endorsed again by Michael G. Titelbaum in a forthcoming paper:

As already indicated, the Right Reasons View has the advantage over restricted versions of CV that it does not involve the extremely unattractive claim that while one should respect one's peers opinions regarding all sorts of issues, one may regard oneself as immune to error when it comes to philosophical claims about rationality. However, endorsing a view that contradicts the intuition behind CV in all cases of peer disagreement (or at least in all those in which one's reaction to the initial evidence was the rationally required one) should not merely be endorsed on the basis of the fact that it avoids the incoherence argument. For what makes the situation concerning CV appear dilemmatic in the first place is that CV's appeal is so strong that simply giving up CV in the face of the incoherence argument is not a way of solving the problem, but rather a way of ignoring one of the horns of the dilemma. Unfortunately, though, Titelbaum rejects CV in favor of the Right Reasons View in essence because the former is ultimately incompatible with the principle that “[n]o situation rationally permits any overall state containing both an attitude A and the belief that A is rationally forbidden in one's current situation” (8). This strategy for rejecting CV is obviously very similar to (and basically the same as) rejecting CV on the basis of the fact that CV is ultimately incompatible with LC – or, in other words, on the basis of the fact that following CV can result in violating LC. Thus, the strategy in effect merely amounts to ignoring one horn of the dilemma, and should thereby not be regarded as a satisfactory way of dealing with it.

Another reply to the incoherence argument – a reply more eager to respect the intuition behind CV – can be found in Frances (Reference Frances2010). Frances is not directly concerned with CV, but instead with an even weaker view, according to which one should not be a so-called “reflective epistemic renegade” – i.e., a person who “knows that she believes P and she knows that [her] epistemic superiors believe [non-P] and are her epistemic superiors regarding P” (422). Let the view that one is rationally required not to be a reflective epistemic renegade be called ‘ANTI-R’. It ranges between CV and Minimal Humility, and it is subject to the incoherence argument to the same extent as the other two. Regarding the problematic kind of situation (i.e., situations in which following ANTI-R consists in giving up the view), Frances holds that incoherence can be avoided in the following way. According to Frances, one should stop believing ANTI-R, but one should still believe that ANTI-R is “in the vicinity of an important truth” (459), and that it is “closer to the truth than other principles (such as: it's virtually always okay to be a reflective epistemic renegade)” (459). And this epistemic situation is one in which, according to Frances, one should still arrange one's doxastic life (that is, form one's beliefs) “in accord with” ANTI-R (459), for even though the person in question now disbelieves ANTI-R, she still believes in the truth of some principle close enough to ANTI-R so as not to differ from ANTI-R in any practically relevant way.

The claim that disbelieving ANTI-R while arranging one's doxastic life in accord with it does not violate the relevant kind of level-connecting principle may appear dubious – especially since Frances provides no clear rationale in favour of it. However, even if it is granted that this claim is true, his solution is unsatisfactory for a different reason. In his discussion of Frances' proposal, Christensen (Reference Christensen, Christensen and Lackey2013: 87f.) holds that the kind of retreat position held by the person in the scenario – i.e., the view that ANTI-R is closer to the truth than an uncompromising view – is itself subject to the incoherence argument, to no lesser extent than CV and ANTI-R. But it may be pointed out, in defense of Frances' proposal, that it is actually quite unclear in how far the view that ANTI-R is approximately true (let's call it ‘APPROX-ANTI-R’) is subject to the incoherence argument. For given that APPROX-ANTI-R differs from ANTI-R in some way, it might differ from it in exactly the way required in order to circumvent the incoherence threat. However, the fact that Frances does not specify in which way APPROX-ANTI-R differs from ANTI-R, his proposal can hardly count as a solution to the supposed dilemma. Moreover, he also leaves it unclear in how far this required difference between APPROX-ANTI-R and ANTI-R could still be compatible with his claim that following the former still amounts to arranging one's doxastic life in accord with the latter. In any case, unless it is specified how far APPROX-ANTI-R fares better in the light of the incoherence argument than ANTI-R, Frances' proposal can essentially merely count as an overly sanguine way of stating that a solution is somehow available. In particular, it remains completely unclear how proponents of APPROX-ANTI-R can circumvent the incoherence threat without exempting their view from cases in which the view itself is under dispute – in which case APPROX-ANTI-R would not fare any better than the proposals already discussed above.Footnote ¹⁰

Christensen's own reply to the incoherence objection is to endorse what he calls the ‘Conflicting-Ideals View’ (CIV). It consists, first, in biting the bullet by accepting that following CV leads to irrationality, and second, in maintaining that being conciliatory is nonetheless a rational ideal. In other words, endorsing CIV consists in claiming that both following LC and following CV are rational ideals, and that in certain situations, there is no way to avoid violating one of them. Christensen puts it as follows:

However, he himself admits that this position “is not an entirely comfortable one” (2013: 92). This kind of unease may be justified by pointing out that while it seems plausible to hold that conflicts may arise between ideals across different normative areas (such as the epistemic ideal to maximize knowledge and the moral ideal to minimize suffering), it seems much harder to accept that genuine dilemmas may arise with respect to one single norm, such as the norm of rationality. Schechter (Reference Schechter2013), who also tends towards accepting CIV in the face of the incoherence argument, expresses similar doubts:

Some of Christensen's earlier remarks on ideals may suggest interpreting his position as less radical than it may initially appear. That is, some of his earlier remarks indicate that he employs a relatively weak notion of ideals – a notion according to which a conflict between two ideals may still be compatible with there being a so-called Über-rule, that is, a rule that trumps the two conflicting ideals and recommends one single course of behaviour:

Furthermore, he does not rule out the possibility of there being a Über-rule trumping conflicting epistemic ideals (cf. 203).

Employing a notion of ideals allowing for the possibility of there being a Über-rule which generates one single maximally rational way of forming one's beliefs would, as already mentioned, render CIV less radical than it may initially appear. However, in the face of the incoherence argument, the prospects for finding this kind of Über-rule are quite dim. One self-suggesting candidate for such rule is the kind of restricted version of CV proposed by Elga. But as explained above, accepting the corresponding kind of rule should be regarded as unsatisfying. And as also stated above, any other rule of belief-formation significantly falling short of complete steadfastness, including (as Christensen Reference Christensen, Christensen and Lackey2013: 93 concedes) any remaining promising candidate for an Über-rule, is itself subject to the incoherence objection, and could therefore not be an adequate mediator between LC and CV, given that the search for a mediating rule was initiated by CV's being subject to the incoherence objection.

It thus seems that biting the bullet in the face of the incoherence argument consists in accepting that there are conflicts between rational ideals that cannot adequately be resolved by any promising kind of Über-rule. This further justifies the kind of unease expressed by Schechter and Christensen regarding CIV.Footnote ¹¹ For endorsing the view, while accepting that the kind of conflict in question cannot be adequately resolved, amounts to accepting that the notion of rationality is incoherent. The fact that this position may indeed be regarded as radical is by itself of course not a sufficient reason for rejecting it. However, the fact that all existing replies to the incoherence argument are either radical or implausible certainly provides a good reason to search for a better solution. In the following sections, I will suggest what such a solution plausibly looks like.

4. TOWARDS A SOLUTION: WHAT EPISTEMIC RATIONALITY STRICTLY REQUIRES

As I will argue now, there is a promising strategy available for showing that the supposed dilemma described in the preceding sections can be resolved in a relatively elegant way – a way not involving the claim that the notion of rationality (taken in its most relevant sense) is incoherent. The strategy consists in taking a step back and considering in what exact sense rationality requires one to be conciliatory in cases of apparent peer disagreement. In order to see how far this question is relevant for present purposes, consider a case of apparent peer disagreement in which the disagreement is about the correct answer to a moderately difficult but easily formulable arithmetic question, say: what is the square number of 123? Suppose that person A is quite confident in the result she comes up with, and that she then comes to know that her friend, a respected peer regarding calculating square numbers, is quite confident that a different result is correct. Suppose further that A's initial answer is in fact the correct one. According to CV, this is a situation in which A is rationally required to become less confident in her initial answer, even though this answer is correct.

As already stated, CV's intuitive appeal stems from the indubitable fact that there is something epistemically wrong in completely ignoring the opinion of a respected peer. The question to ask now is whether this latter fact is really one in virtue of which A should become less confident in her initial answer. Consider the following, admittedly unrealistic, extension of the above-described scenario. In the very moment in which A comes to know that her friend came up with a different answer, she does the math again, and she does it arbitrarily many times and arbitrarily quickly, reassuring her – to some arbitrarily high degree – that her initial answer is correct. And suppose further that her recalculations are all faultless and also maximally reliable. As already admitted, this is not a realistic scenario. The kind of instantaneous recalculations involved may even be regarded as humanly impossible. Nevertheless, it can hardly be denied that A's way of reacting to the disagreement is cognitively preferable to not instantaneously recalculating. And given the arbitrarily high number of recalculations, is it not plausible to assume that the degree to which A should become less confident in her initial answer is arbitrarily small? (Of course, A might enter into a disagreement with arbitrarily many peers who came to their opinion independently of one another. But given A's unlimited recalculation capacities, one may hold that no concrete number of disagreeing peers can significantly change the picture.) If this is so, then being conciliatory, understood as becoming less confident (to any non-arbitrarily small degree), is actually not rationally required in the scenario in question.Footnote ¹²

Given that the kind of arbitrarily intensive reassessment in question may be regarded as humanly impossible, one might still claim that there is a useful notion of rationality in the light of which one should become less confident in one's initial opinion in the kind of situation in question – a notion of rationality taking into account that certain cognitive processes are simply out of human reach and can therefore not usefully be required. Let what is rational in this sense be called ‘humanly rational’, or ‘rational_H’, and let what is rational in the sense of being in principle achievable be called ‘strictly rational’, or ‘rational_S’. Applying this terminology to cases like the one described in the previous two paragraphs, it seems that becoming less confident in one's initial opinion is rationally_H required, since every other humanly possible way of reacting to the disagreement would be cognitively worse. (More on this at the end of this section.) However, in the light of the above considerations, becoming less confident in one's initial opinion in the kind of situation in question is not rationally _S required, since there is in principle a cognitively preferable kind of reaction available.

At this point, it might appear as if I am giving a wrong picture of the role played by cognitive limitations when it comes to issues concerning rationality. That is, my above claim that becoming less confident in one's initial opinion in the kind of situation in question is not rationally_S required, due to there being in principle a cognitively preferable reaction available, might provoke the following question: Why isn't it – in any legitimate sense of the term ‘rational’ – rationally required for beings with cognitive limitations to be conciliatory in the kind of situation in question? That is, shouldn't one rather hold that cognitive limitations regarding the speed of thought, loss of memory, etc., affect what a person is rationally required to believe – in any legitimate sense of the term ‘rational’?

My answer to these questions is the following. There is a (strict) sense in which all the cognitive limitations relevant here simply amount to violations of rational requirements. Take, for instance, limitations regarding the speed of deducing a conclusion from certain premises that the subject believes to be true. Any limitation of this kind amounts to there being a period of time in which the subject believes the premises without believing what is logically deducible from them (given that she does not already believe the conclusion for other reasons). And it does not seem far-fetched to hold that there is a strict sense of the notion of rationality in which the subject violates a rational requirement in the (however small) period of time in question. Next, consider the kind of cognitive limitation consisting in a loss of memory. In the example regarding the square number of 123, loss of memory may, for instance, play a role if the subject forgets about the result of one of the substeps that she has undertaken in order to arrive at the overall result. Here, she ceases to hold a belief (a belief about the result of the substep in question) without the occurrence of any evidence against the truth of this belief. Again, it does not seem far-fetched to hold that there is a strict sense of the notion of rationality in which the subject violates a rational requirement by ceasing to hold the belief in question.

I will not discuss all other possible kinds of cognitive limitation that might play a role in the kind of example in question. I take it that the above considerations already strongly suggest that whenever a cognitive limitation affects one's belief formation in the example in question, one violates some rational requirement, in a strict sense of the term ‘rational’. And insofar as it is therefore plausible to hold that the kind of arbitrarily intensive reassessment in question is rationally_S required, it is even more plausible to hold that the latter is rationally_S permitted.

Of course, the subject may not only be kept from realizing the intensive reassessment in question due to cognitive limitations, but also due to practical concerns (such as laziness or sheer lack of curiosity). However, in addition to the above-stated assumption regarding the relation between cognitive limitations and violations of rational_S requirements, it may also be assumed that there is a useful distinction between practical and epistemic rationality, and that the notion of rationality relevant with respect to the present debate is the epistemic one. In order to illustrate this distinction, imagine a person who, for whatever reason, tends to get headaches when not remaining completely steadfast in situations of apparent peer disagreement. Moreover, this person is aware of this causal relation. Imagine further that, in a particular case of apparent peer disagreement, not getting a headache is more important to the person in question than being right about the disputed proposition. Finally, in order to make the point as uncontroversial as possible, imagine that in the situation in question, the subject's initial opinion regarding the truth of the disputed proposition is actually false. Now, I suppose that none of those who have hitherto defended CV would be willing to hold that the subject's interest in not getting a headache exonerates her from the epistemic requirement to be conciliatory. Rather, not being conciliatory in this situation (without any reassessment of the disputed issue) remains epistemically irrational, regardless of whether some expected side-effect of being conciliatory is unwelcome for practical reasons.

Speaking more generally, practical considerations like the one just mentioned do not make an otherwise epistemically irrational way of belief formation epistemically permitted. In any case, they certainly do not make an otherwise epistemically preferable way of belief formation epistemically irrational. Thus, practical factors such as laziness or lack of curiosity do not make a reassessment of the disputed issue epistemically irrational.

Given this assessment of the example regarding the square number of 123, CV – understood as a claim about what epistemic rationality strictly requires – turns out to be false, for there is then no general rational_S requirement not to reassess the disputed issue to an arbitrarily intensive degree, and therefore no general rational_S requirement to become significantly less confident in one's initial opinion in cases of apparent peer disagreement. However, the supposed dilemma of conciliationism does not disappear merely by observing that CV turns out to be false, for this observation might still be compatible with the correctness of a restricted version of CV – a version according to which one is rationally_S required to be conciliatory only in certain cases of apparent peer disagreement, and according to which the case concerning the square number of 123 is not among them. And one might suspect that the restricted version in question is still subject to the incoherence objection. But it seems quite plausible to assume that my above considerations regarding disagreements about the square number of 123 extend to all disagreements about a priori matters, including the correctness of restricted versions of CV. (More detailed remarks regarding an analogous issue will be provided in the following section.) And my above considerations thereby extend to all those restricted versions of CV that could be subject to the incoherence objection. The supposed dilemma therefore seems to disappear.

However, as already pointed out towards the end of section 2, trying to solve the supposed dilemma by rejecting CV does not only involve the heavy burden of having to explain away CV's intuitive appeal, but also the even heavier burden of having to explain away the intuitive appeal of so-called Minimal Humility principles, according to which one should be conciliatory whenever entering into a disagreement with apparent epistemic superiors (cf. Christensen Reference Christensen, Christensen and Lackey2013: 86). For this latter kind of principle is subject to the incoherence objection to the same extent as CV. However, my above considerations regarding what strict rationality requires in cases of apparent peer disagreement about the square number of 123 also apply to cases of disagreement about the square number of 123 with apparent epistemic superiors, such as persons who have spent more time on doing the calculation. For given the demanding notion of rationality employed here, the arbitrarily intensive reassessment in question makes up for any asymmetry regarding the amount of time or concentration that the subject has invested in arriving at her initial opinion. (Admittedly, there still remains the issue of how to react in those cases of disagreement in which one has independent evidence of being drugged, or of being cognitively impaired in any other way. I will discuss this kind of case in section 5 below.)

Another possible reason for being unsatisfied with my proposed solution might consist in the fact that even though CV, understood as a claim about what strict rationality requires, has turned out to be false, CV still seems to be true if it is understood as a claim about what I have called ‘rationality_H’ (i.e., what can usefully be required taking into account the cognitive limitations of actual human beings). Let this latter view be called ‘CV_H’. Given that in cases of apparent peer disagreement about the truth of CV_H, proponents of CV_H appear to be rationally_H required to become less confident in their initial opinion, and given that a version of LC employing the notion of rationality_H also appears prima facie plausible, the incoherence argument, applied to CV_H, stands unrefuted. For this reason, it might be held that I have, in the end, not succeeded in arguing that there is no genuine rational dilemma in the light of the incoherence objection.

I will now argue that this worry results from a misunderstanding of the notion of rationality_H (which, in turn, results from the fact that this notion has not been properly described in my above considerations). In the course of introducing this notion, I stated that becoming less confident in one's initial opinion in the example concerning the square number of 123 seems to be rationally_H required, since it is preferable to every other humanly possible way of reacting to the disagreement. What this rationale amounts to is that in the case in question, being conciliatory is the least irrational_S reaction allowed by one's limited human condition. That is, in the case in question, one's cognitive limitations happen to allow for one way of belief formation which is more rational_S than all competing ways of belief formation allowed by one's limited human condition. However, examining cases like this provides no good reason for assuming that one's cognitive limitations always leave available exactly one most rational_S way of belief formation. In fact, in cases of apparent peer disagreement about the truth of CV_H, the limited human condition does not leave available exactly one most rational_S way of belief formation, given the considerations regarding LC_H mentioned in the previous paragraph.Footnote ¹³ That is, given that the most rational_S reaction that is in principle available (namely, instantaneous, arbitrarily intensive reassessment) is out of reach for the kind of being in question, the latter can either refrain from being conciliatory without the kind of intensive reassessment in question, or she can be conciliatory and violate LC_H. I take it that there is no clear sense in which one of these reactions is preferable to the other.

However, the fact that there is not always one most rational_H way of belief formation should not at all be viewed as dilemmatic. For the human condition is a contingent matter, and it should be expected that these contingent limitations can be such that the two least irrational_S ways of belief formation in a certain kind of situation that are allowed by one's limited cognitive condition are equally bad. For instance, there are certainly possible worlds in which humans (or other beings) are in a cognitive condition such that whenever they are to evaluate the prospects of some practically relevant issue, they are either overly optimistic or overly pessimistic, both ways of belief formation being equally irrational_S. The fact that these beings' cognitive condition happens to leave available only these two equally irrational_S ways of belief formation should not give rise to postulating any genuine dilemma. And an analogous conclusion should be drawn regarding the way in which human beings happen to be limited in the actual world.

Furthermore, it should be pointed out that – contrary to what the distinction between rationality_S and rationality_H might initially suggest – it is not the case that the notion of rationality_H is supposed to capture what might be called the ‘ordinary language notion’ of rationality, while rationality_S is only some artificial notion that can usefully be applied outside the realm of everyday rationality judgments. To the contrary, it is quite plausible to assume that the notion of rationality which is most commonly applied in everyday rationality judgments is already one involving standards that abstract from the actual cognitive condition of humans – as also noted by Christensen:

Rather than the notion of rationality_S, the notion of rationality _H may thus be regarded as an artificial one. For this reason, as well as for the reason mentioned before, worries regarding genuine rational dilemmas should only be directed at the notion of rationality_S. The above-mentioned possible objection against my response to the supposed dilemma of conciliationism should thereby not be regarded as a serious threat.

In the following section, I will present a hitherto unmentioned advantageous aspect of my proposed solution, by describing in how far this solution – despite involving a rejection of CV – is still compatible with respecting CV's intuitive appeal.

5. PRO TANTO CONCILIATIONISM

My above argument against CV, understood as a claim about what epistemic rationality strictly requires, is perfectly compatible with respecting the strong intuition behind CV according to which one should take into account the fact that an apparent peer disagrees. For the person described in the above scenario does treat the disagreement as a pro tanto reason (that is, as a reason that may still be outweighed by opposing reasons) to lower her confidence in her initial opinion; but given her arbitrarily intensive reassessment of the issue at the time of hearing about the disagreement, the pro tanto reason in question for lowering her confidence in her initial opinion is outweighed. The corresponding view may accordingly be called ‘Pro Tanto Conciliationism’, and it can roughly be formulated as follows:

According to the so-called ‘Steadfast View’, the fact that an apparent peer disagrees does not even constitute a pro tanto reason for lowering one's confidence in one's initial opinion, and accordingly, no further reassessment of the disputed matter is needed to authorize sticking to one's initial confidence distribution. Strictly speaking, though, PTC is not incompatible with the Steadfast View, if the latter is merely formulated as a claim about changes of degrees of confidence. However, taking into account the issue of pro tanto reasons, PTC may well be regarded as quite congenial to intuitions underlying existing defenses of CV, and it may thus be regarded as a hitherto overlooked niche between a steadfast and a conciliatory attitude.

Given that PTC, in contrast to CV, stands unrefuted in the face of considering what rationality strictly requires, and given that endorsing PTC enables one to respect the intuitive appeal of CV, rejecting CV (as a claim about rationality_S) while endorsing PTC appears to be an elegant way of dealing with the incoherence argument.

However, in giving up CV, while still endorsing PTC, one does not absolve oneself from having to deal with the general kind of dilemma in question. That is, if it turned out that there are situations in which one is rationally_S required to believe that one is rationally_S required not to follow PTC, and in which one then enters into a situation of apparent peer disagreement, a dilemma arises for those endorsing both PTC and the following modified version of LC:

Fortunately, though, my above argument for there being no rational_S requirement, in the face of disagreement, to become significantly less confident in one's initial (correct) take on the square number of 123 also works as an argument for there being no rational_S requirement, in the face of disagreement, to become significantly less confident in PTC. An important aspect of the scenario concerning the square number of 123 is that all the evidence necessary for A in order to check her initial answer is still assessable at the time of coming to know about the disagreement. Many cases of disagreement differ in this respect. Take, for instance, Christensen's example of the restaurant bill mentioned above. The person in this example is probably not in a position to reassess her initial calculation before having another look at the bill – simply because she no longer remembers all the numbers written down on the bill. It seems that in this kind of case, the considerations presented above do not apply. However, it seems plausible to assume that situations of disagreement about PTC are in this respect more like the example involving the square number of 123 than the restaurant example. For the question whether PTC is true may well be regarded as a priori, and even though a professional way of forming an opinion about philosophical issues normally consists in considering arguments written down in the literature, it is still plausible to assume that given the apriority of the subject matter, any competent speaker of English is in principle in a position to come to know whether PTC is true without consulting any literature on the issue.Footnote ¹⁴ Thus, analogously to the scenario involving the square number of 123, it may seem that in cases of disagreement about the truth of PTC, proponents of PTC are (at least if PTC is true) rationally_S required not to become significantly less confident in their approval of the view.

Unfortunately, though, matters turn out to be more problematic. For there are possible situations in which someone endorsing PTC is not just confronted with a disagreeing peer, but also with some good independent empirical evidence that one's own philosophical capacities are drastically impaired in the current situation. Think, for example, of a drug that drastically impairs one's reliability regarding any kind of abstract thought for a long period of time. The kind of case in question shall be imagined as one in which the subject has not in fact been administered this drug,Footnote ¹⁵ but as one in which she is confronted with very good evidence that she had been administered the drug before having started to consider whether PTC is true (with the drug's effect not having ceased since then). Moreover, the subject shall be imagined as being confronted with an arbitrarily high number of apparent peers, rejecting PTC independently of each other. Furthermore, the apparent peers do not only reject PTC (thereby claiming that there is no rational_S requirement to treat apparent peer disagreements as pro tanto reasons to lower one's confidence in one's initial opinion), they also claim that one is rationally_S required not to follow PTC (that is, not to treat apparent peer disagreements as pro tanto reasons to lower one's confidence in one's initial opinion).

One might claim that in this kind of case, even completely rational_S beings are required to believe that one is rationally_S required not to follow PTC, since the empirical evidence in question provides good reason for the subject to be suspicious of whatever instantaneous reconsideration regarding the truth of PTC she comes up with. Given LC_PTC, it may thus seem that not only forming one's beliefs in accord with what is rationally_H required, but also forming one's beliefs in accord with what is rationally _S required can, in the end, involve genuine dilemmas.

However, the objection fails, as I will now argue. In particular, I will argue that contrary to what has been suggested in the formulation of the objection, the kind of case in question is not one in which the subject is rationally_S required to believe that she is rationally_S required not to follow PTC. I will try to make my point by contrasting the case in question with the following one.

Imagine, once again, that subject A enters into an apparent peer disagreement situation with respect to the square number of 123. Imagine further that in addition to an arbitrarily high number of disagreeing peers, A is also confronted with very good evidence that she has been administered a certain drug – namely, a drug drastically impairing one's ability to multiply. Imagine, for example, that the effect of the drug is that the result the subject comes up with when trying to do the calculation in her head is always higher than the correct result, and imagine that A knows the drug to have this effect. Thus, since the error caused by having been administered the drug is a systematic one, the fact that A, when recalculating, always comes up with the same result is no evidence that she has not been administered the drug. And given that the result the disagreeing peers come up with is lower than the result of A's calculation, it indeed seems rationally_S required for A to believe that the result of her calculation is the wrong one, even if in fact no drug of the kind described has been administered.

I now claim that there is a crucial difference between the case just described and the case regarding the correctness of PTC – a difference in virtue of which while the subject in the math case is rationally_S required to believe that her initial answer is wrong, the subject in the case regarding PTC is not rationally_S required to believe not-PTC (let alone to believe that one is rationally_S required not to follow PTC). The difference in question is the following. The drug described in the math example is such that it impairs one's reliability in determining the square number of 123. One may assume that it does not impair one's reliability in judging whether the empirical evidence that the drug has been administered is a kind of evidence that should be trusted; and one may also assume that it does not impair one's reliability in judging whether one should in principle take into account the opinions of disagreeing peers. In short: the effect of the drug does not interfere with one's ability to determine how in principle to react to disagreeing peers and evidence of being drugged. In the case regarding the correctness of PTC, matters are different. That is, if the effect of the drug is such that it drastically impairs one's ability to determine whether PTC is true – which amounts to an impairment of one's ability to determine whether one should take into account the opinions of disagreeing peers – then it is very plausible to assume that it also impairs one's ability to determine how in principle to react to the occurrence of disagreeing peers and to evidence of being drugged. Thus, the maximally rational reaction in the case regarding the correctness of PTC cannot be to start disbelieving PTC, while at the same time trusting one's inclination to take into account (and even to give some significant weight to) the opinions of the disagreeing peers and the evidence of having been administered the kind of drug in question. Rather, if one is rationally_S required to mistrust one's ability to determine whether PTC is true, then one is also rationally_S required to mistrust one's inclination to take into account the opinions of the disagreeing peers and the evidence of being drugged.

The situation just described is rather complicated, since mistrusting one's inclination to take into account the evidence of being drugged should reduce the degree to which one mistrusts one's ability to determine whether PTC is true, which, in turn, should raise the degree to which one trusts one's inclination to take into account the evidence of being drugged and the opinions of the disagreeing peers, and so forth. However, the above considerations strongly suggest that the case in question is not one in which one is rationally_S required to disbelieve PTC. Given the kind of complications just mentioned (and given that a completely rational_S subject is aware of these complications), it seems most plausible to assume that the subject is rationally_S required to suspend her judgment regarding issues about conciliation, including the correctness of PTC.Footnote ¹⁶ Thus, even though the kind of situation in question is one in which one is rationally_S required to not just take into account the opinions of the disagreeing peers, but also to significantly adjust to their opinion by suspending one's judgment regarding the correctness of PTC, it is still not a kind of situation in which one is rationally_S required to violate either PTC or LC_PTC. For LC_PTC is merely a claim about situations in which one believes that one is rationally_S required not to follow PTC, and as just stated, the kind of situation in question is one in which one is not rationally_S required to hold this belief.

Thus, so far, no dilemma arises. However, my assessment of the kind of situation in question might still be taken as one in the light of which a dilemma arises – namely, if PTC is combined with the following modified version of LC_PTC:

Given my assessment of the kind of situation discussed in the present section – according to which the subject is rationally_S required to suspend judgment regarding issues about conciliation – those endorsing both PTC and LC*_PTC would have to admit that a genuine dilemma arises. However, LC*_PTC clearly lacks the intuitive appeal of LC_PTC. Hence, those claiming, on the basis of endorsing both PTC and LC*_PTC, that a genuine dilemma arises carry the burden of presenting a convincing reason for accepting LC*_PTC. As long as no such reason has been presented, the incoherence argument against PTC should be regarded as unsuccessful.

It thus seems that preserving what is so intuitively appealing about CV by endorsing PCV is not only an elegant way of dealing with the incoherence argument against CV, as presented in section 2, but also an elegant way of dealing with the general kind of supposed dilemma in question.

6. SUMMARY

In sections 1–3, I have described the current state of the debate on the incoherence argument against conciliationism, and I have explained why the current state of this debate should be regarded as unsatisfying. That is, while all existing attempts at avoiding the dilemma turn out implausible, accepting the dilemma amounts to the radical view that the notion of rationality is ultimately incoherent, and that there are conflicts between rational ideals that cannot adequately be resolved by any promising kind of Über-rule.

In section 4, I have proposed a different response to the supposed dilemma, according to which – taking seriously what epistemic rationality strictly requires – the Conciliatory View (as well as all those weakened or restricted versions of it that could be subject to the incoherence objection) turns out to be false. In section 5, I have pointed out that my considerations leading to this conclusion still respect CV's indubitable intuitive appeal, for they are compatible with what may plausibly be regarded as a central intuitive motivation for a prima facie acceptance of CV. That is, my considerations against CV are still compatible with what I have called ‘Pro Tanto Conciliationism’ – namely, with the view that one is rationally required to treat an apparent peer disagreement as a pro tanto reason to lower one's confidence in one's initial opinion. In the remainder of the section, I have argued that in contrast to CV, Pro Tanto Conciliationism is not subject to any serious incoherence threat.

I have therefore proposed what may be regarded as an elegant response to the supposed dilemma of conciliationism, in virtue of being non-radical in the following two important respects. First, it is non-radical insofar as it does not amount to accepting the possibility of genuine rational dilemmas.Footnote ¹⁷ Second, it is non-radical insofar as it respects much of CV's intuitive appeal.Footnote ¹⁸