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Reasons, Rationality, Reasoning: How Much Pulling-Apart?*

At the heart of John Broome’s research program in the philosophy of normativity, culminating in his magnificent book Rationality Through Reasoning, is a distinction between reasons, on one hand, and requirements of rationality, on the other.1 In my view, Broome’s insistence on pulling these notions apart, and resistance to analyzing either one in terms of the other, is fundamentally correct, and represents a major advance in the field.2 At that level of generality (and in numerous other respects, too), Broome and I are on the same team.

At the heart of John Broome's research program in the philosophy of normativity, culminating in his magnificent book Rationality Through Reasoning, is a distinction between reasons, on one hand, and requirements of rationality, on the other. 1 In my view, Broome's insistence on pulling these notions apart, and resistance to analyzing either one in terms of the other, is fundamentally correct, and represents a major advance in the field. 2 At that level of generality (and in numerous other respects, too), Broome and I are on the same team. This paper is divided into two sections. In the first part of the paper, I'll examine Broome's distinction between reasons and requirements of rationality. Though the remarks come from a position of sympathy with that general distinction, I'll discuss three worries about it, which I'll call the threat of merely terminological debate, the threat of superfluousness, and the threat of disappearing subject-matter. In discussing how these threats can be headed off, I'll suggest some friendly amendments and modifications to Broome's way of presenting and developing the distinction.
The second part of the paper will be more substantively critical. 3 In addition to the notion of a reason and that of a requirement of rationality, there is a third normative notion that Broome is interested in: that of (rules of) correct reasoning. Broome's suggestion is that this third notion, correct reasoning, is closely tied to that of requirements of rationality (or at least to the broader genus of which requirements of rationality are a part). On Broome's view, every rule of correct reasoning corresponds to a "basing permission", which states that it's rationally permissible to base one attitude on one or more other attitudes. I'll argue that this proposal can't be made to work. If I'm right, this suggests that Broome should admit rules of correct reasoning as a third sui generis normative entity, not reducible either to reasons or to requirements (or permissions) of rationality. That is: the same kind of pulling-apart that Broome has effected so persuasively with respect to reasons and requirements of rationality needs to be effected again to separate rules of correct reasoning from both of those other categories.
Parts of this paper will be of necessity programmatic, and in several places I'll have to engage in the annoying habit of referring the reader to other work of mine. I apologize for this in advance. Though this practice may seem self-centered, there is a way in which what it really shows most is how indebted much of my own research program is to Broome's. My own work is often relevant to my discussion of Broome here only because so much of my work addresses philosophical debates that Broome has had such a central role in framing.

I. Reasons and requirements of rationality
Roughly speaking, the distinction between reasons and requirements of rationality is this. Reasons are considerations that speak in favor of attitudes and acts. For example: ȅThat one hears the sound of rain is (typically) a reason to believe that it's raining; ȅThat it's raining is (typically) a reason to carry an umbrella.
Requirements of rationality, by contrast, generally permit or forbid certain combinations of attitudes (and absences of attitudes). 4 For example: ȅIt's rationally required that one not simultaneously believe that it's raining and believing that it's not raining. ȅIt's rationally required that one not simultaneously intend to carry an umbrella if it's raining, believe that it's raining, and yet fail to intend to carry an umbrella.
One way of further strengthening one's grip on the distinction here is to note that we seem to be able to say what the relevant requirements of rationality on an agent are without knowing anything about the situation the agent finds herself in, whereas this is at least often not so for reasons. No matter what the subject is hearing, seeing, and so on, the subject is always rationally required not to both believe that it's raining and believe that it's not raining. By contrast, 4 There's a wrinkle here, since Broome (2013: 153) allows that there's at least one rational requirement that forbids a single attitude: the rational requirement not to believe a conjunctive proposition of the form (p and not-p). This case is, however, like the other examples of rational requirements in the respect that it locates a clash in one's attitudes. It's just that in this case, one single attitude (believing a conjunctive proposition of the form p and not-p) already contains a clash within itself.

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whether the subject has a reason to believe that it's raining depends very much on the subject's circumstances, that is, on what the subject is hearing or seeing (and conceivably, on some views, whether it's actually raining or not). 5 There are some people who are sympathetic to a distinction broadly in the neighborhood of the one being drawn here, but who think that the generally Broomean gloss on it just given already goes wrong in important ways. 6 That won't be the tack I take here. I'm happy to accept the general gloss on the distinction just given (with the caveat that I'll propose a terminological revision in the next subsection). 7 Still, I want to raise three issues that threaten, or may appear to threaten, the depth and significance of the distinction, and discuss how they might be headed off.

The threat of merely terminological debate
As the foregoing makes clear, the requirements that Broome calls 'requirements of rationality' pertain to the rational (im)permissibility of certain patterns or combinations of attitudes, independently of the circumstances of the subject. However, many philosophers believe that we are, in some sense, rationally required to respond 5 I won't have anything to say here about another way of bringing out the distinction that is due to Broome (esp. Broome 1999;also Broome 2013: ch. 8), which is to appeal to a difference in the logical form or "scope" of the relevant normative operator. The claim is that reasons have a "narrow-scope" form -if background conditions obtain, one has reason to Ф, where 'has reason to' takes scope only over the attitude in the consequent of that condition -rational requirements have a "wide-scope" form -rationality requires that (if one has some attitude A1, then one has (or lacks) some other attitude A2), where 'rationality requires' takes scope over the whole conditional. I've discussed questions of scope elsewhere (Worsnip 2015b). Independently of my views on that debate, I believe that the idea that rational requirements pertain to combinations of attitudes is more fundamental than the idea that rational requirements are wide-scope: the latter claim is one natural, but not the only possible, way of cashing out the former claim. 6 Cf. esp. Fogal (ms.), who thinks that the notion being distinguished from reasons shouldn't be understood in terms of requirements. 7 See also fn. 38 below for a further wrinkle. appropriately to our reasons: that is, to perform the acts that our reasons (on balance) support performing, and to have the attitudes that our reasons (on balance) support having -or some attenuated version of this claim. 8 In fact, for many philosophers this claim is treated as a truism or axiom. 9 Such philosophers can still, in principle, accept that there is an important distinction between the requirements of rationality that pertain to responding to reasons and the requirements of rationality that pertain to avoiding certain impermissible combinations of attitudes. Still, they hold that both of these are bona fide requirements of rationality. 10 On one view, the dispute between Broome and these philosophers is a merely terminological one. Several philosophers who use the term 'requirement of rationality' to pick out roughly what Broome does present this usage as a matter of terminological stipulation. 11 They're happy to acknowledge that there's a potentially legitimate usage of 'requirement of rationality' whereby there are requirements of rationality to respond appropriately to reasons; still, they don't want to lose sight of the fundamental distinction Broome is after, and so they use 'requirement of rationality' in a narrower way to refer only to requirements pertaining to rationally (im)permissible combinations of attitudes.
But this isn't how Broome himself thinks of things, at least not in his more recent work. Instead, Broome advances the claim that rationality does not require appropriately responding to reasons as a substantive claim, rather than as a matter of terminological stipula- 8 Schroeder (2009);Raz (2011: ch. 5);Parfit (2011: ch. 5);Lord (2014, forthcoming). 9 This is especially so for epistemologists, who generally just take it as axiomatic that it's rationally required to respond to one's evidential reasons. See Worsnip (2018a: fn. 1) for representative citations. 10 Interestingly, Broome himself seemed to imply something like this view in his earliest statement of the distinction, where he uses the term 'normative requirements' for what he later calls 'rational requirements', and writes: "Rationality is often thought to consist in acting for reasons, but following normative requirements is also a major part of rationality" (Broome 1999: 398). 11 Cf. Kolodny (2005: 509-10), Southwood (2008: 9-10 13 His claim is that it isn't irrational to fail to respond to your reasons (as such). As I understand him, Broome's reasons for thinking of this claim as substantive rather than terminological are as follows. According to Broome, it's a conceptual truth that rationality supervenes on the mind. 14 But, Broome thinks that the reasons one has don't supervene on one's mind, and consequently that what is an appropriate response to one's reasons doesn't supervene on the mind. Therefore, rationality is not a matter of responding to one's reasons. A defender of the view that rationality is a matter of responding to one's reasons has only two options to resist this argument. The first is to claim that rationality does not supervene on the mind. This is, in Broome's view, a substantive (though conceptual) falsehood about rationality. The second is to argue for an account of reasons such that reasons (or, at least, the reasons that rationality requires one to respond to) do supervene on the mind. This is, in Broome's view, a substantive falsehood about reasons. So either way, the philosopher who claims that rationality is a matter of responding to one's reasons makes a substantive mistake.
At least for the sake of argument, I'll grant Broome's premise that rationality supervenes on the mind. I'm also happy to grant that there is a reading of 'reason' such that one's reasons do not supervene on the mind. 15 On this reading of 'reason' -sometimes unhelpfully called the 'objective' reading of 'reason'-facts that are totally outside of one's ken can be among one's reasons. For example, to use Williams' classic example, perhaps the fact that the glass contains 12 See esp. Broome (2007Broome ( , 2013; compare fn. 10 above. Likewise, Lord (2014, forthcoming), opposing Broome on these points, takes the debate to be substantive. 13 On his view, it's guaranteed that one ought to do what one has most reason to do, since reasons to Ф are (roughly) explanations of why one ought to Ф (Broome 2013: ch. 4). 14 Broome 2013: 89. 15 Though for dissent, see Kiesewetter (2017).
petrol is a reason not to drink it, even if one is not aware that the glass contains petrol and (justifiably) believes that it contains gin and tonic. Plausibly, this notion of reasons doesn't supervene on the mind: two subjects could have identical mental states, but if the first is in a case where the liquid in the glass is petrol, and the other is in a case where the liquid is gin and tonic, then the former has a reason (in this sense) not to drink that the latter lacks. 16 And -as we would expect, if we agree with Broome that it's a conceptual truth that rationality supervenes on the mind-it does seem that there's no recognizable sense of the term 'rationality' on which the former subject is irrational if she drinks (or intends to do so), given that the reason not to drink is one that she is totally unaware of. Thus, Broome is right that rationality is not a matter of responding to (all of) one's reasons, on this understanding of 'reason'. And this is not just a matter of terminological stipulation: it seems to follow from conceptual truths about rationality. But sophisticated advocates of the view that rationality is a matter of responding to reasons have not claimed otherwise. Instead, they have typically made one of two claims. The first is that rationality requires you to respond to some privileged subset of your reasons: for example, the reasons that are epistemically accessible to you. 17 On this proposal, we still understand the notion of a reason in a way such that facts outside of one's ken are reasons, but we claim that it is only the reasons that are within one's ken that rationality requires one to respond to. The second is that rationality requires one to respond to one's respond to all of one's reasons, but on a reading of 'reasons' where facts outside of one's ken are not reasons at all. 18

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Note that neither view need collapse into the view that rationality is a matter of responding to one's beliefs about the (objective) reasons one has. It might suffice for R's being a reason to Ф in the relevant sense that one is aware that R -one need not believe that R is a reason to Ф. Or it might suffice for R's being a reason to Ф in the relevant sense that one's evidence supports believing that R is an (objective) reason-whether or not one believes that R is a reason to Ф (and perhaps even whether or not one believes that R). 19 Broadly speaking, these sorts of accounts says that the reasons you're rationally required to respond to are your evidence-relative reasons. They thus lie between the two extreme versions of the reasons-responsiveness view that Broome considers in chapters 5 and 6 respectively -on one hand, one that operates on a conception of a reason that is fact-relative and unconstrained by evidence, and on the other hand, one that operates on a conception of a reason that is belief-relative (or that talks of responding to beliefs about reasons). More generally, many ethicists have been stuck in a false dichotomy between so-called "objective" reasons, which are relative to all the facts, and "subjective" reasons, which are relative to one's beliefs. This misses the intermediate notion of an evidence-relative reason. That evidence-relative reasons have been obscured from view in debates in ethics and practical rationality is odd, since they form the basis for the default view in accounts of rationality in epistemology.
On these versions of the reasons-responsiveness view, it is quite plausible that whether one has rationally responded to the relevant reasons does supervene on the mind. Broome takes this possibility to be a threat. 20 Because both his own view and these views might be consistent with the claim that rationality supervenes on the mind, he takes them to be rival views, neither of which is ruled out by the central conceptual truth about rationality that ruled out less sophisticated versions of the view that rationality consists in responding to reasons. But here I think Broome is mistaken. Plausibly, Broome's account of rationality and sophisticated accounts of rationality as responding to reasons are not accounts of the same single thing, rationality simpliciter. Broome seems to be assuming that because both accounts accept the constraint that the notion they're theorizing supervenes on the mind, they must be rival accounts of the same thing. But this patently does not follow. There can be two distinct normative notions, both of which supervene on the mind, and which don't compete as rival accounts of the same thing.
A concrete example may help to illustrate the point. Suppose you know that 99% of scientific experts agree that human activities have contributed to climate change. Call that proposition (or the fact that it corresponds to, if you prefer) E. Assume, as is plausible, that this E is a decisive reason to believe H -the proposition that human activities have contributed to climate change. But suppose that you deny that E is a decisive reason to believe H. For you hold that scientific experts are all involved in a giant global conspiracy to deceive people into false beliefs about climate change. Moreover, suppose that there's no interfering higher-order evidence -your belief that scientific experts are involved in this giant conspiracy is itself unjustified (though we may nevertheless suppose that you believe it to be justified). Finally, suppose that you fail to believe H. Now, the following seems clear. Your failure to believe that H is unjustified, in the ordinary epistemological sense of 'unjustified': it is a failure to correctly respond to your evidence. 21 It is thereby a failure to correctly respond to your reasons, (even) in the sense (or of the kind) that the sophisticated reasons-responsiveness accounts of rationality fix on. 22 The relevant reason that you're failing to re-21 Some epistemologists deny that absence of belief is ever unjustified. I don't agree with this view, but this is inessential to the example. If you have this view, just add to the example that you believe not-H, despite the fact that E is decisive evidence against not-H. 22 Or maybe not. Lord (2014) says that for it to be irrational to fail to respond to a reason (for Ф-ing), you have to be treating it as a reason (to Ф). And you don't seem to meet that condition here. But in my view, this claim of Lord's is a mistake, at least given the ambitions of his own view: it makes his own notion of rationality collapse into something very like (or in fact, perhaps even strictly weaker than)

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Núm. 12, enero-diciembre de 2018, pp. 59-93 68 spond to -E -is not something outside of your ken; nor does your evidence suggest that E is not a reason to believe H. At the same time, you need not violate a requirement of rationality of the sort that Broome's theory focuses on. That is to say, you are not (or need not be) structurally irrational; there need be no internal incoherence in your belief-set. 23 Moreover, both of these statuses -that you have an unjustified (or reasons-unresponsive) belief, and that your belief-set is internally coherent-are ones that, for all that has been said, supervene on the mind. 24 But that need not mean that, in fact, coherence (see Worsnip 2015a: sec. 2.6 part (d)). As I'm going to suggest below, we ought to distinguish a notion of rationality as reasons-responsiveness from a notion of rationality as coherence -where the former corresponds to the epistemologist's notion of justification and can capture the sense in which our believer is irrational. Adding Lord's "treating condition" frustrates this end. 23 I need to be clear about something here. One might think that I'm resting this claim about the case on the bolder, and more general, idea that as long as you believe that there's nothing wrong with your states, they are coherent. But as Broome (2013: 91-2) himself has persuasively argued, this claim is unsustainable. If there are any exceptionless coherence requirements, they must impose what Broome calls "strict liability". For example, if it's always incoherent to (believe p and believe not-p), then it must be incoherent to be in that combination of states even if one believes the combination to be OK (and even if one believes it to be OK for sophisticated reasons, such as philosophical dialetheism). So the only way to salvage the claim that as long as you believe there's nothing wrong with your states, they are coherent, is to reject the view that there are any exceptionless coherence requirements. Like Broome, I do not want to do this. So I am not claiming that believing there's nothing wrong with your states suffices for coherence. Rather, my claim is simply that there is no requirement of coherence that forbids being in the states involved in my example. There is, in my view, a requirement of coherence that forbids (believing that your evidence decisively supports p and failing to believe p). But you don't violate this requirement in the example. You merely fail to believe what your evidence actually supports. That's not a failure of coherence. The analogy to the moral case, which I will mention shortly, may help to bring this out. 24 Of course, the claim that justification supervenes on the mind is controversial in epistemology. It is associated with internalism -though if one is an externalist about the mental (as Williamson (2000)) is), then it's also compatible with externalism about justification. In any case, it suffices for my purposes that there are many epistemologists who do accept it. My point is merely that in thinking this, such theorists need not collapse justification and coherence. Thanks to Daniel Fogal for help on this point. they are rival accounts of a single notion, rationality. Rather, they seem simply to be distinct normative statuses.
Similarly, consider a structurally analogous moral case. Suppose you're a CEO who knows that some action (say, opening a particular new factory) will gravely damage the environment. And suppose the fact that it will gravely damage the environment is a decisive reason not to open it (and that you lack interfering higher-order evidence that it's not a decisive reason not to open it). But suppose you simply don't care that it will gravely damage the environment, and don't believe that this fact is any reason at all not to open it. Again, you're failing to respond to a reason of the kind that the sophisticated reasons-responsiveness accounts of rationality fixes on. But there's nothing incoherent about your states. Again, both of these statuses may supervene on the mind, yet they seem distinct and not rival account of one single thing, rationality.
That's not to say that there won't be those who insist that the term 'rationality' be reserved for either one or the other of these statuses. But that really is a matter of terminology (and neither usage obviously violates the conceptual truth that rationality supervenes on the mind). The important thing is that we mark the distinction between reasons-responsiveness and coherence somehow.
Interestingly, it seems that when focusing on the epistemic case, it seems to be the usage of 'rationality' to refer to coherence that more often gets jettisoned, whereas when focusing on the moral case, it seems to be the usage of 'rationality' to refer to reasons-responsiveness that more often gets jettisoned. Sometimes, the very same philosopher seems to use the term 'rationality' to refer to (or at least include) reasons-responsiveness in the epistemic case, but to refer to coherence only in the moral (or more generally practical) case. 25 25 This can lead to substantive mistakes. For example, some philosophers affirm a version of expected utility theory where one rationally ought to maximize utility given the evidential probabilities (not one's actual credences) plus one's preferences over outcomes (not the objective value or choiceworthiness of those outcomes). This is a mismatched theory that takes it for granted that rationality requires reasons-responsiveness on the epistemic side, but tolerates any coherent set of preferences on the practical side.

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As I've argued elsewhere, 26 there is no justification for this asymmetry. Only confusion will result from using 'rationality' to refer to (or include) reasons-responsiveness in epistemology, but to refer to coherence (only) in ethics. Indeed, Broome himself may be guilty of this. In a brief but telling passage, he writes: No doubt one or more requirements connect a belief that you ought to F with your evidence that you ought to F; I do not try to specify those requirements in this book. So there are a number of states you might be in -call them 'grounding states'-that ensure you are not rational unless you believe you ought to F (140). 27 Here, Broome seems to allow that there are rational requirements that require one to have beliefs that are appropriately responsive to one's evidence. But appropriate responsiveness to one's evidence is just appropriate responsiveness to a particular kind of reason -evidential reasons. So, if there are such rational requirements, they are rational requirements to respond to one's reasons. This is striking, since as we've seen, Broome denies -with primary attention to the practical, rather than the epistemic case-that it's rationally required to respond to one's reasons. Of course, if evidence supervenes on the mind, Broome's concession here doesn't violate his guiding principle that rationality supervenes on the mind. But that just reinforces my point that there is a notion of reasons-responsiveness that supervenes on the mind. It's most familiar from epistemology, 28 but it can be extended to the practical case also. Indeed, anyone who denies that there's at least an evidence-relative sense of the term 'reason' will have great difficulty accounting for the epistemic case.
Still, any requirements to respond to one's evidence (or reasons more generally) are of a fundamentally different kind from the requirements of coherence that Broome is primarily engaged in theorizing, and the two should be kept apart. So, although I'm not taking a stand on whether 'rationality' should be used to refer to reasonsresponsiveness or coherence, I do think we should strive to make our usage consistent across domains. One disadvantage of working simply with the term 'rationality' is that it obscures possible inconsistencies of this kind.
The result of all of this is that, once we have the best reasons-responsiveness view on the table, the debate about whether rationality is about reasons-responsiveness or about coherence does seem to be close to being terminological. This might seem like a disappointment for Broome's project, since two whole chapters of Rationality Through Reasoning are devoted to arguing that rationality doesn't require responding to reasons. But in fact, I think that it doesn't really compromise the ultimate project at all (indeed, I think it strengthens it). My proposal is that we use the term 'coherence requirements', or 'structural requirements', to refer to the sorts of requirements that Broome is engaged in theorizing, and 'coherence' or 'structural rationality' to refer to the phenomenon that they're a part of. 29 It would be a change of vocabulary for Broome to talk this way, instead of just talking of 'rational requirements' and 'rationality', simpliciter. But the crucial point is that it's compatible with this change of vocabulary to continue to think that the distinction between reasons and structural requirements is deep and important -in contrast to the many philosophers who have ignored it, equivocated on it, and so on. The change in vocabulary also preserves the possibility of asking many questions about the relationship (or lack of) between reasons and structural ra-

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Núm. 12, enero-diciembre de 2018, pp. 59-93 72 tionality, and to translating Broome's claims about the relationship of reasons and rationality simpliciter into those terms. Finally, suppose I'm wrong that the issue between the reasonsresponsiveness view and the coherence view is terminological. Though the constraint that rationality supervenes on the mind won't rule out the (best version of the) former view, perhaps there's some other conceptual constraint that does. Note that the change in vocabulary I'm proposing wouldn't preclude recognizing this. We would simply present this claim as the further claim that structural requirements exhaust the requirements of rationality as a whole. Indeed, I think it's more perspicacious to present this claim as just what it is: a further claim -rather than using 'requirements of rationality', in effect, to refer to structural requirements by stipulation. So I think that however things shake out, we should adopt my proposed change in vocabulary, and this is what I'll do in what follows.
To have a single set of terminology, I'll use the vocabulary of structural requirements and of structural rationality. But that of coherence requirements and of coherence would do just as well.

The threat of superfluousness
A different threat to the significance of the distinction between reasons and structural requirements comes from the thought that structural requirements might be superfluous. The idea here is that, as long as one responds appropriately to one's reasons, this will guarantee that one obeys all the structural requirements. 30 In that 30 Cf. Kolodny 2007; Lord 2014. Interestingly, Easwaran & Fitelson (2015), who (unlike Kolodny and Lord) think that structural requirements, as distinguished from reasons, are both real and interesting -and who (unlike Broome, cf. section I.3 below), give a kind of analysis of what structural requirements are, seem to define structural requirements (or 'coherence requirements', as they call them) in a way that guarantees their superfluousness. On their analysis, a combination of attitudes is forbidden by a structural requirement iff we know a priori that anyone who has such attitudes must (whatever their particular circumstances, evidence and reasons) be failing to respond appropriately to their reasons in some way (that is, that at least one of the attitudes must be one that they have most reason to abandon). But that means that all instances of structural irrationality are already forbidden by sense, structural requirements are superfluous, because they don't introduce any further demands on one's attitudes that one's reasons don't already impose. An example will help here. One might think that, whatever one's evidence is, it could never both permit believing p and permit believing not-p. If that's so, correctly responding to one´s evidential reasons guarantees that one satisfies the (structural) requirement to avoid contradictory beliefs. The superfluousness charge aims to extend this general sort of challenge to other structural requirements.
Of the three threats I am exploring here, this is the only one that Broome directly discusses. 31 He discusses it in the context of his aforementioned contention that rationality is not a matter of responding appropriately to reasons. Part of what Broome is claiming is that even if rationality did require responding to reasons in some sense, responding to reasons is not the only aspect of rationality. 32 But if structural requirements are superfluous, there's a sense in which that is not so. On such a view, once we have said what our reasons demand of us, we are done saying what rationality requires. Or, if rationality consists only in structural rationality, and does not require responsiveness to our reasons, then rationality as a whole is superfluous: we can capture all the demands on our attitudes by talking only about our reasons.
There's a stronger and a weaker way of construing the threat of superfluousness. On the stronger version of the threat, showing that putative structural requirements are superfluous shows (or at least provides strong reason to think) that there in fact are no such structural requirements. Once these requirements are superfluous, we can simply eliminate them from our ontology. 33 So, for example, it will be true that it's never permissible to both believe p and believe not-p, but not because there's a requirement banning this combination as such, but rather because, for any proposition and any evidential state, one's evidence will forbid (at least) one of these two one's reasons, delivering the superfluousness of structural requirements. 31 Broome 2013: 84-87. 32 Cf., e.g., Broome 2013: 90;also, again, Broome 1999: 398. 33 This seems to be the view of both Kolodny (2007) and Lord (2014 beliefs. On the weaker version of the threat, structural requirements might be real in spite of their superfluousness, but they are nevertheless uninteresting, since they don't tell us anything to do anything that our reasons don't already tell us to do (and fail to tell us to do some of the things that our reasons do tell us to do). They can, on this view, be fairly ignored by those interested in normativity. I'm not sure I agree that, were structural requirements superfluous, they would be completely uninteresting. It might be that failures to conform with structural requirements represent a deeper kind of irrationality than failures to respond appropriately to reasons, or that there is a distinctive mode of criticism involved in charging someone with structural irrationality. 34 Moreover, structural requirements may play a constitutive role in the attribution of mental states, or in the explanation and prediction of behavior, that reasons (or requirements to respond appropriately to reasons) do not. 35 Still, it's clearly at least something of a disappointment for those who want to draw attention to structural requirements if they turn out to be superfluous. I'll mention two ways in which the superfluousness result might be blocked.
The first is offered by Broome himself, and attempts to exploit cases where one's reasons are permissive. 36 The trick is to find cases 34 Cf., e.g., Elga (2005: 115). 35 Cf. Davidson (1985); Worsnip (2018b). 36 I'll grant for the sake of argument that reasons can be permissive. In fact, though, I don't think that reasons-talk handles permissions very well. In the reasons literature, it's typically taken for granted that if you have most reason to Ф, you ought to Ф. But, it's an elementary principle of most deontic logics and deontic semantics that if you ought to Ф, then it's impermissible not to Ф. Putting these two seemingly innocuous principles together, we get the claim that if you have most reason to Ф, then it's impermissible not to Ф. If we combine this with a picture where all reasons have weights that must, when added up, either be equal or not equal, then we get the startling result that the only way for more than one option to be permissible is for each option to have reasons supporting it that are of precisely equal weight. In my view this result turns on an equivocation: the kind of 'ought' that features in the first principle is not the same as the kind of 'ought' that features in the second: the 'ought' that is guaranteed by having most reason is a kind of "optimal" 'ought', whereas the 'ought' that is the dual of natural permissibility-talk is a stronger notion corresponding to something more like obligation. But that suggests where one's reasons permit one to have some attitude A, and permit one to have some attitude B, but having both attitude A and attitude B is structurally irrational. 37 For example, it might be that it's permitted by one's evidence to have a credence for p anywhere in the range between 0.32 and 0.33, inclusive. It plausibly follows from this that it's permitted by one's evidence to have a credence for not-p anywhere in the range between 0.67 and 0.68, inclusive. Nevertheless, it would be structurally irrational to have credence 0.33 in p while also having credence 0.68 in not-p. Or, to take an example from the practical domain: it might be permissible, so far as one's reasons go, either to intend to go the office or to intend to work from home, and thus also be permissible either to intend what you believe to be that the concepts of obligation and permissibility aren't simply a matter of adding up all the reasons; reasons on their own can't explain what's permissible and what isn't. Of course, this is quick and could be objected to at a number of points. 37 I suspect that, interestingly, we cannot give a definition of what so-called "permissive cases" are without appealing to structural requirements. In the literature in epistemology on permissivism, it's often said that one counts as a permissivist, or believes in permissive cases, if one thinks that there can be cases where, even holding fixed a body of evidence, there's more than one doxastic attitude that it can be rational to take toward a proposition (White 2005: 445;Ballantyne & Coffman 2011: 1;Schoenfield 2014: 194). Strictly speaking, though, this definition is clearly too inclusive. Here are two doxastic attitudes that virtually all epistemologists think can sometimes both be rational toward the same proposition p: believing p, and having credence 0.99 in p. (I'm thinking here of epistemologists who don't think of belief as incompatible, either descriptively or rationally, with credence 0.99.) Surely they don't qualify as permissivists thereby. What's instead wanted to define permissivism is the idea that sometimes, more than one "incompatible" attitude toward p is permissible. But "incompatible" in what sense? If we define "incompatible" attitudes as attitudes that it is impossible to hold at once, then our definition of permissivism is now too exclusive: surely someone who thinks that there are cases where it is rational either to believe p or to disbelieve p (where disbelieving p involves believing not-p) counts as a permissivist, even if they think that it's possible to both believe p and disbelieve p by having contradictory beliefs. So it seems that "incompatible" needs to be understood in terms of structural rationality: a permissivist is someone who thinks that there are cases such that: attitude A1 toward p is permissible, attitude A2 toward p is permissible, even though A1 and A2 are incompatible in the sense that they would be structurally irrational to hold together. In fact, once we have this definition, we can drop the "toward p" qualification, which provides a nice generalization of our definition of permissive cases beyond the doxastic realm.

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Núm. 12, enero-diciembre de 2018, pp. 59-93 76 necessary means toward going to the office (say, asking to borrow the car), or to not intend those believed means. But it's structurally irrational to intend to go to the office but fail to intend to ask to borrow the car (while believing that you need to ask to borrow the car in order to go the office). There are, however, some complications here. In general, it doesn't follow from its being permissible to Ф and its being permissible to Ψ that it's permissible, even by the same set or kind of norms, to (Ф and Ψ). Thus, one's reasons might permit two things individually, without permitting them jointly. For example, it might be that your reasons permit you to propose marriage to your partner tonight, and that your reasons also permit you to watch a gory horror movie with your partner tonight. But for all that, your reasons might not permit doing both: it might be that although each plan is an individually reasonable course of action, the two together are a very unreasonable course of action. This isn't, it bears stressing, a matter of structural irrationality. 38 On its own, there's nothing structurally irrational about intending to propose and simultaneously intending to watch the gory horror movie. You might be structurally irrational if you also have certain further attitudes: say, believing that conditional on watching the horror movie, you shouldn't propose. But it's possible for there to be no structural irrationality here (you might wrongly think that it's a great idea to propose while watching a gory horror movie), compatibly with its still being the case that it is in fact unreasonable to (intend to) do both. Your reasons forbid doing both jointly not because of the structural irrationality or incoherence of having both intentions, but rather because the reasons that speak in favor of each individual plan are undermined by pursuing the other one: the reason-generating benefits of proposing are unrealized if you do it while watching a gory horror movie, and the reason-generating benefits of watching a gory horror movie are unrealized if it is interrupted by a proposal. 39 Having clarified that one's reasons can forbid doing two things jointly even while permitting each individually, it's now open to someone defending the superfluousness of structural requirements to claim that in the permissive cases where it is structurally irrational to have both attitudes, one's reasons also forbid having both attitudes (though they permit each individually) -so that the structural requirement is in fact superfluous after all. For example, perhaps it's unreasonable (and not just structurally irrational) to intend to go to the office, while not intending to ask to borrow the car. After all, one might say, the primary point of intentions is to help us get things done. The point of the intention to go to the office is (typically) in the actually going to the office; but if one doesn't intend to ask to borrow the car, one won't actually go the office, and so the reason-generating benefit of intending to go is unrealized. So perhaps, though taken individually, both intending to go to the office and not intending to ask to borrow the car are reasonable, jointly they are unreasonable (and not just structurally irrational). Admittedly, it's a bit harder to see how to generalize this to doxastic permissive cases. But perhaps it can be done, and besides, doxastic permissive cases are more controversial than practical permissive cases. So it's uncertain, I think, whether permissive cases really do save us from superfluousness. By this, I really do mean that it's uncertain. Permissive cases are a good way to put some pressure on the claim that structural requirements are superfluous, but more work remains to be done to show that they defeat it.
Elsewhere, I've pursued a different way to undermine the claim that structural requirements are superfluous, namely, to argue that there are cases where reasons and structural requirements conflict with each other, in the sense that it's impossible both to take the attitudes your reasons support and to satisfy the structural require-

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Núm. 12, enero-diciembre de 2018, pp. 59-93 78 ments. 40 In such cases, taking the attitudes one's reasons support would put one into violation of the structural requirements; a fortiori, taking the attitudes one's reasons support does not suffice for satisfying the structural requirements. Thus, it directly follows from the possibility of such conflicts that the structural requirements are not superfluous. My particular strategy is to appeal to cases of misleading higher-order evidence, where one has misleading evidence either about what one's evidence is, or about what it supports. I argue that in some such cases, one's total evidence can support a doxastic attitude A, yet one's total evidence also supports the belief that one's total evidence does not support A. In such cases, the only way to have the attitudes one's evidence (and thus, assuming no interfering non-evidential reasons, reasons) supports is to have attitude A, but also believe that one's total evidence does not support A. And that, I claim, is structurally irrational. So, we have a conflict between reasons and structural requirements. I won't rehearse my defense of this line of argument here, and I am not pretending that it is uncontroversial. I do think that, if it succeeds, it can be extended to the practical domain, giving us cases where one ought to (intend to) Ф, but also decisive reasons to believe that one ought not Ф -again, a combination that would make one structurally irrational. 41 40 Worsnip (2018a). Interestingly, Broome's early view (Broome 1999) seemed to disavow the possibility of such conflicts, by holding that rational requirements can be expressed using the same 'ought' that corresponds to what one has most reason to do. 41 One might think that this is actually easier to get than conflicts of the purely doxastic kind, since one might think it's just obvious that one can have misleading evidence about whether one ought to Ф. However, we must be careful not to make this look too easy by tacitly relying on an evidence-insensitive notion of 'ought' and 'reasons' when it comes to action and intention, but an evidence-sensitive notion of 'ought' and 'reasons' when it comes to belief (cf. the discussion in the previous section). It's not so obvious that one can have (all-things-considered) misleading evidence about whether one ought to Ф, where 'ought' in that claim is itself read as evidence-sensitive. Kiesewetter (2016) and Way & Whiting (2016) both deny that one can, and thus deny the possibility of the sort of conflict described here. Still, I think that the doxastic case, where 'Ф' itself refers to a belief, illustrates how such a thing is possible, and certainly shows that it is at least conceptually possible. For the claim that one's evidence decisively supports the first-order proposition p is not the same thing It's worth mentioning a two other, perhaps simpler, ways in which we might hope to get conflicts between reasons and structural requirements. First, there are cases where having some structurally irrational combination of attitudes is beneficial. For example, some eccentric madman might offer you millions of dollars to violate a structural requirement (or threatens to do something awful to your family if you don't). If the madman's offer is a reason to have the attitudes that violate the structural requirement, then it seems like it should be strong enough to, in principle, be decisive; a conflict would then follow. Whether this is a successful example of a conflict case turns on whether there are so-called "wrong kinds of reasons" for attitudes that are nevertheless genuine reasons for those attitudes (as opposed to something else, such as wanting to have the attitude or trying to get yourself to have it). 42 Secondly, if one thinks that it's incoherent to have inconsistent beliefs, then preface paradox-style cases, where one's evidence seems to support inconsistent beliefs (due to the agglomeration of risk of error), might be examples of conflicts between (evidential) reasons and structural requirements. Whether this is a successful example of a conflict case turns on whether it really is incoherent (even in preface-style cases) to have inconsistent beliefs. 43 Overall, then, the two ways of trying to head off the superfluousness problem have different virtues and vices. The existence of permissive cases is relatively uncontroversial (at least in the practical domain), but the argument from permissive cases to the claim that structural requirements are not superfluous turns out not to be straightforward. By contrast, the existence of conflict cases is more controversial and takes some work to establish, but the argument as the claim that one's evidence decisively supports the higher-order proposition that one's evidence decisively supports believing p. So similarly, I think it's at least not ´conceptually impossible for it to be the case that one ought (even in an evidence-relative sense) to perform an action Ф but also that one has decisive (evidential) reason to believe that it's not the case that one ought (in an evidence-relative sense) to Ф. 42 For discussion, see among many others Hieronymi (2005); Parfit (2011: Appendix A); Way (2012); Howard (2016). 43 Unfortunately (for my purposes here), I believe that it is not. See Worsnip (2016a).

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Núm. 12, enero-diciembre de 2018, pp. 59-93 80 from conflict cases to the claim that structural requirements are superfluous is straightforward. Either way, if I'm right, those who (like both Broome and I) want to stress the importance of the distinction between reasons and structural requirements have substantive work to do here.

The threat of disappearing subject-matter
As Broome clarifies several times, his use of 'requirement' is not such that a requirement is necessarily normative in a robust sense. 44 In a robust sense of 'normative', something is normative if it helps determine what you ought to do. It follows from Broome's discussion of the relationship between reasons and 'ought' that reasons are normative in this sense. But -and here we find another important element of the distinction between reasons and structural requirements-it is not guaranteed that structural requirements are normative in this sense. Broome says that he although believes that rational requirements (i.e., structural requirements) are normative, he "has no argument" for this claim. 45 This may leave some readers puzzled. In what sense could a structural requirement be a requirement if it were not normative? But as Broome points out, the idea of a non-normative requirement can be made sense of. To use his example, the claim that Catholicism requires you to abstain from eating meat on Fridays is both intelligible and true even from the point of view of someone who thinks that we have no reason whatsoever to comply with the requirements of Catholicism. 46 Similarly, we can talk about requirements of etiquette, of grammar, of Mafia morality, and so on, without committing ourselves to thinking of these requirements as normative.
However, there is a major disanalogy between all of these (potentially) non-normative requirements, on one hand, and structural requirements of rationality on the other. The difference is that every

Problema. Anuario de Filosofía y Teoría del Derecho
Núm. 12, enero-diciembre de 2018, pp. 59-93 clear example of the former seems to be in some way fixed by facts that are (in a broad sense) conventional. For example, what 19 th century British etiquette requires is simply a matter of what the conventional practices and beliefs of 19 th century Brits are. By contrast, I want to suggest, we do not have clear examples of requirements that are both non-normative and non-conventional. Yet structural requirements of rationality do not seem to be conventional. So perhaps it is, after all, hard to make sense of the idea that structural requirements of rationality are non-normative. This creates a puzzle even if one, like Broome, suspects that structural requirements are, ultimately, normative. For Broome still takes it to be a possibility worth taking seriously that structural requirements are not normative. But he never seems to take it to be a possibility worth taking seriously there simply are no genuine structural requirements. Assuming that structural requirements are not conventional, this combination of attitudes requires us to be able to at least make sense of the idea of a non-normative, but also nonconventional requirement.
The problem would go away if we took the specification of structural requirements to be essentially a matter of stipulation. Some philosophers do talk about 'coherence' this way. For example, epistemologists typically call any set of credences that do not obey the axioms of the probability calculus "probabilistically incoherent". In doing so, they are just stipulatively using the term 'incoherent' to refer to any set of credences with those probabilities. Indeed, some of these philosophers go on to deny that probabilistic incoherence is in fact irrational, or that there is any genuine requirement on us to avoid it. 47 Similarly, some may treat it as a matter of stipulation that any set of deductively inconsistent beliefs is incoherent. Broome, however, doesn't treat the specification of structural requirements as a matter of stipulation. Chapters 9 and 10 of Rationality Through Reasoning are concerned with trying to determine, as a substantive matter, which putative structural requirements are genuine requirements of rationality, and which aren't. For example, for Broome, it's a substantive question for debate whether (e.g.) there is a genuine

Problema. Anuario de Filosofía y Teoría del Derecho
Núm. 12, enero-diciembre de 2018, pp. 59-93 82 structural requirement of rationality forbidding all inconsistent beliefs (in fact, he thinks there is not). 48 But, to reframe the problem, what does that substantive question come to? One might think the question of whether there is a genuine structural requirement forbidding inconsistent beliefs just is the question of whether we really ought (or at least, have some reason) to refrain from having inconsistent beliefs. But as we've just seen, for Broome, this can't be so, since saying that something is a (genuine) structural requirement of rationality is not supposed to commit one to the claim that this requirement is normative. (He turns to the question of whether the requirements of rationality are normative only in Chapter 11, independently of and after asking which putative requirements of rationality are genuine requirements.) Broome's method of uncovering requirements of rationality is to "appeal largely to our intuitions". 49 But our intuitions about what? It's not clear how to have an intuition about whether a putative structural requirement is genuine without at least tacitly asking ourselves questions like "is this really a (putative) requirement that I ought to comply with?".
Of course, you could ask yourself "is this a (putative) requirement that it would really be irrational to violate?". But, as I've already argued in section I.1, the bare concept of rationality (as a status that supervenes on the mind) doesn't automatically zero in on the relevant notion: given the right interpretation, the notion of a failure to respond to one's reasons can be thought of as irrational, in a good sense that respects the supervenience constraint. Rather, we have to zero in on structural rationality, or coherence, specifically. But then the question is just: is this a requirement that it would be structurally irrational to violate?. And it's hard to know how to have intuitions about that question without an answer to the question of what makes a putative requirement a requirement of structural irrationality.
The final threat to the depth of the distinction between reasons and structural requirements, then, is that when the two are cleaved apart so that calling something a structural requirement does not in itself commit one to saying there is reason to comply with it, the very substance of the subject-matter of a theory of structural requirements (that is, a theory of which structural requirements are genuine and which aren't) may seem to disappear. 50 Heading off this problem, I think, requires us to give a more substantive account of what structural rationality, or coherence, is. 51 It's not enough to have a purely formal account -that is, one that tells us only the form of structural requirements, for example that they govern combinations of attitudes, or are "wide-scope". For this, at most, enables us to see which things are of the right form to be putative structural requirements. 52 The putative requirement not to have inconsistent beliefs, for example, clearly has the right form. So do absurd putative requirements, like the claim that it's rationally required not to both hope that p and simultaneously believe that if p then q. This purely formal account, then, doesn't help us say which requirements are actually genuine and which aren't. Especially if it is not necessarily normative, we need a substantive account of what structural rationality is in order to know what we are looking for when we accept or reject putative structural requirements as genuine.

II. Rational permissions and correct reasoning
For someone who wants to separate reasons and structural requirements sharply, as both Broome and I ultimately do, a further question is how the notion of correct reasoning, and of a rule of correct 50 To be clear, however: even if this problem were to force Broome to commit to the claim that calling something a structural requirement is to commit oneself to the claim that there is reason to comply with it, this would not collapse the distinction between reasons and structural requirements entirely. There could be a distinctive category of reasons to comply with structural requirements that do not exhaust the reasons as a whole. 51 For my own attempt, see Worsnip (2018-b It's part of the concept of correct reasoning that reasoning can be correct even if the attitudes involved are not supported by reasons. For example, even if the belief p and the belief if p then q are both hopelessly unsupported by the evidence, it's still true that if one were to reason from these beliefs to the belief q, one would be reasoning correctly. This might make us suspect that correct reasoning is tied, not to reasons, but to structural rationality. 53 And that's exactly what Broome claims. It's this link that I want to put pressure on in what follows. I'll be suggesting that correct reasoning and structural rationality are less intimately related than Broome thinks, and that we may thus need to make room for correct reasoning as a third sui generis normative notion, alongside reasoning and structural rationality, that cannot be analyzed in terms of the other two. In attempting to tie correct reasoning to structural rationality, one might think that the place to start is with the claim that reasoning is correct just when it brings one into satisfaction of structural requirement of rationality. 54 However, Broome argues (correctly) that this not right: it is neither necessary nor sufficient for reasoning to be correct that it bring one into satisfaction of a structural requirement. 55 One reason that it isn't necessary is that there are many instances of correct reasoning that are trivial extensions of one's existing beliefs (for example, inferring from a belief that p to the disjunction of p and any other proposition). Such reasoning is correct when one does it, but there is no rational requirement to believe all these trivial extensions of one's beliefs, and so the reasoning 53 Some philosophers have argued for other ways of linking between (rules of) correct reasoning and reasons. Way & Whiting (2016), for example, argue that correct reasoning from attitudes supported by your reasons always issues in attitudes supported by your reasons. See Worsnip (forthcoming) for criticism of this view. 54 On one interpretation, this is Hussain's (ms.) view. 55 Broome (2013: 246-7).
does not bring one into satisfaction of any structural requirement. One reason that it isn't sufficient is that, if rationality requires you to hold some attitude given other attitudes you have (for example, if it requires you to intend to Ψ, given that you intend to Ф and believe that to Ф you must Ψ), and you currently lack the intention to Ψ, it's always possible for some other, incorrect process of reasoning to happen to lead you to form the intention to Ψ. This would bring you into satisfaction of a structural requirement, but would not count as correct reasoning thereby. Broome attempts to deal with this problem by tying correct reasoning not to structural requirements but to structural permissions. As he claims, "if it is correct to reason to some conclusion, that is because rationality permits you to reach that conclusion" (Broome (2013: 219). So correctness of reasoning is understood in terms of structural rationality: but not structural requirements; rather, structural permissions. According to Broome, (correct) reasoning will often bring one into satisfaction of rational requirements, and is one of our main ways of doing this. 56 But equally, "in many cases, you commit no offense against rationality by failing to do a piece of reasoning that would have been correct had you done it". 57 Broome develops his account by appealing to the notion of a "basing permission", which specifies that it is rationally permissible to base some particular attitude on some other attitude or attitudes. 58 Though basing permissions make appeal to a notion of basing that has not featured in the structural requirements we have considered so far, they are still permissions of structural rationality: they pertain to the rationality of how one combines one's attitudes. 59 56 Op. cit.: 207. 57 Ibid.: 219. 58 Ibid.: 189-90. 59 One can imagine basing permissions that are content-specific in a way that takes them out of the realm of pure structural rationality. For example, I might claim that it's permissible to base a belief that England will win the cricket match on a belief that the conditions for swing bowling are favorable. Here, I am partly relying on claims about which kinds of considerations (viz. the conditions for swing bowling being favorable) provide adequate reasons to draw further conclusions (viz. the belief that England will win the cricket match), which is not a matter of structural

86
According to Broome, "each permission will determine a rule, and reasoning by correctly following that rule will be correct". 60 For instance, reasoning by the modus ponens rule is correct because it is always (structurally) rationally permissible to base a belief that q on believing that p and believing that if p then q. Here is the way Broome writes out the basing permission corresponding to the modus ponens rule (with the notation slightly adjusted): Modus Ponens Permission. Rationality permits N that (N believes q at some time on the basis of believing p at some time and believing (if p then q) at some time). 61 It's crucial to understand that this is a supposed to be a schema that holds for all possible propositions p and q. Thus, it claims that it's always structurally permissible to base a belief q on a belief p and a belief if p then q. 62 This is a very strong claim. I will argue that, even rationality. But Broome's structural permissions are not like this. They say, for example, that it's permissible to believe q on the basis of the believing p and believing (if p then q). Since this relies only on the logical relations between these variables that stand in for propositions, it doesn't turn on any particular substantive theory of which particular considerations provide adequate reason for particular conclusions. And so I think it makes sense to think of them as remaining within the domain of structural rationality. Broome is talking about which attitudes it's permissible to base on others by the lights of structural rationality, not which attitudes it's permissible to base on others in light of what's a reason for what. 60 Op. cit.: 247; see also 255. 61 Ibid.: 191. 62 One might be misled by the fact that Broome says that a basing permission is a negation of a basing prohibition, which is a requirement that forbids basing one attitude on another. If requirements were understood as universally quantified, rather than as schemata, then the negation of the basing prohibition would simply be the claim that it is sometimes permissible to base a belief q on a belief p and a belief if p then q. Understood this way, basing permissions are evidently too weak to correspond to rules of correct reasoning. For some propositions p and q, it's permissible to base a belief in q on a belief in p, but evidently there's no general rule of reasoning telling one to go from a belief in p to a belief in q. However, since basing prohibitions (like all other requirements) are, for Broome, in fact to be understood as schemata, we can think of basing permissions as negating each of their instances. Thus, the right way to read the modus ponens permission is itself as a schema that yields individual permissions for all propositions p and q -that is, as saying that it's confining ourselves to purely structural rationality (and so bracketing whether your beliefs in p and (if p then q) are themselves justified), there are cases where, in believing q on the basis of believing p and believing (if p then q), you are not structurally rational.
For a first example, suppose that you believe that it is raining, and believe that if it is raining then it is not raining. And suppose that on the basis of these two beliefs, you believe that it is not raining. This combination of states is structurally irrational, since it involves your believing that it is raining and believing that it is not raining; that is, believing contradictory propositions. For all that, though, the application of the modus ponens rule is still correct reasoning here. 63 So we have a failure of correspondence between correct reasoning and structural rationality: there is a rule of correct reasoning for which there is no genuine corresponding basing permission.
In conversation, Broome suggested two lines of response to this objection. The first is this. As he sets out basing permissions in his book, 64 the basing permission says that it's (structurally) permissible to be in the following combination of states in this case: {believing that it's raining, believing that if it's raining then it's not raining, believing that it's not raining on the basis of the first two beliefs}. However, Broome denies the axiom of deontic logic that says that if p is permitted, and p entails q, then it follows that q is permitted. So, Broome says, he can deny that the basing permission entails that it's permitted to be in the following combination of states: {believing that it's raining, believing that it's not raining}. I do not agree with Broome's rejection of the relevant axiom here. Though he has independent purported counterexamples to this axiom and other closely related ones, I think these counterexamples can be easily dealt with by accepting a standard contextualist semantics for deontic modals.
always permissible to believe q on the basis of believing p and believing (if p then q). Thanks to Broome for setting me straight on this. 63 One might take the lesson of these two examples to be that the modus ponens rule itself is not a rule of correct reasoning as it stands, and needs revision. I don't think this is the right response, but can't argue this here. See Worsnip (forthcoming) for discussion. 64 Broome (2013: 190).
But it would take me too far off-track to argue for this here. 65 Fortunately, I have another response, which is that it is already an unacceptable result to say that any total state involving a belief that p and a belief that not-p is structurally rational. Even if Broome denies the relevant axiom of deontic logic, he is still committed to this unacceptable result. Broome's second line of response is different. It is to revise his statement of the relevant basing permission, so that it says the following: rationality permits that (if you believe that it's raining, and you believe that if it's raining then it's not raining, then you believe that it's not raining on the basis of the first two beliefs). So what's permitted is not a conjunction but a (material) conditional. But once we switch to this reading of basing permissions, they become too weak to vindicate the purported connection between basing permissions and rules of reasoning. Consider the following permission: Rationality permits of you that (if you believe that it's raining, and you believe that it's not raining, then you believe that pink elephants will invade China on the basis of your belief that it's raining and your belief that it's not raining).
If we read the conditional here as material, it is permissible to be such that this material conditional is true. Specifically, it's permissible to make it true by making its antecedent false: by not having the contradictory beliefs in question. Of course, there's also a way of making the material conditional true that is not structurally permissible, namely making both the antecedent and the consequent true. But no-one accepts the principle that if it's permissible to Ф only if any way of Ф-ing is permissible. So this is no objection to the basing permission as stated. But clearly, this basing permission does not correspond to a rule of correct reasoning. It definitely isn't correct reasoning to go from the belief that it's raining and the belief that's it not raining to the belief that pink elephants will invade China.
A better option for Broome might be simply to claim that it's the basing on its own that is permissible. Both attempts at stating the bas-ing permission just considered mention the state of basing the belief that it's raining on the belief that it's raining and the belief that if it's raining, then it's not raining. So perhaps we can say that this state on its own is permissible. But even this doesn't strike me as the right result. There is something distinctively (structurally) irrational about basing a belief that it's not raining, in part, on the belief that it is raining. This is not a structurally rational way to be.
So much for the first example of a case where it's not structurally rational to base a belief q on a belief p and a belief (if p then q). Suppose that, although the agent believes each (underived) premise in this long chain of deductions (i.e. both P1 and each conditional premise), there is a slight risk of error associated with each premise. These risks aggregate so that eventually the probability of the conclusion, Pn, is low, and as such doesn't warrant belief. And let us suppose that the agent herself recognizes these risks of error, and even recognizes how they aggregate. Would she be even structurally rational to base belief on the conclusion of the basis of these premises? I think not.
But consider what would be so if it were always structurally rational to base a belief q on a belief p and a belief (if p then q). It would be structurally rational for her to believe P2 on the basis of P1 and (if