Explaining Higher-order Defeat

Higher-order evidence appears to have the ability to defeat rational belief. It is not obvious, however, why exactly the defeat happens. In this paper, I consider two competing explanations of higher-order defeat: the “Objective Higher-Order Defeat Explanation” and the “Subjective Higher-Order Defat Explanation.” According to the former explanation, possessing sufficiently strong higher-order evidence to indicate that one’s belief about p fails to be rational is necessary and sufficient for defeating one’s belief about p. I argue that this type of explanation is defective or at best collapses into the other type of explanation. According to the latter explanation, Believing that one’s belief about p fails to be rational (in response to higher-order evidence about p) is necessary and sufficient for defeating one’s belief about p. I argue that this type of explanation is better suited to explain higher-order defeat given that what one is rational to believe partly depends on the relations among one’s doxastic attitudes. Finally, I address an peculiar feature of the Subjective Higher-Order Defeat Explanation: higher-order defeat becomes contingent on one’s response to the higher-order evidence.

1 3 mind-distorting drugs, various biases, and peer disagreement. Here is an example to illustrate: HYPOXIA. I am the pilot of an airplane. I need to make a mathematical calculation about which direction to turn the wheel of the plane. I discover that the plane is at a sufficiently high altitude that I am likely suffering from a case of hypoxia. (Hypoxia is a condition brought upon by high altitudes. It makes sufferers prone to errors in their reasoning, including their mathematical calculations. In mild cases, it is introspectively undetectable.) I'm not actually suffering from hypoxia. (Elga n.d.) The higher-order evidence makes me think that I am likely suffering from hypoxia. As a result, it seems that I cannot rationally trust the result of my calculation even if I am not actually suffering from hypoxia. A significant number of philosophers relies on cases similar to hypoxia in order to argue that higher-order evidence has a systematic sort of defeating force with respect to rational or justified belief (in the following, I will use these notions interchangeably). 1 It is not obvious, however, why exactly higher-order defeat happens. 2 Some authors have argued that higher-order evidence has to be misleading in order to have defeating force (e.g., Tal, 2020). The reason for this is that we have to assume that one's belief about p, at least initially, reflects a rational response to the evidence; otherwise, it is difficult to see how it could be susceptible to defeat in the first place. In contrast, if one's belief was not even rational to start with it would not be defeasible and the higher-order evidence would be superfluous. So, given that one's belief was rational at first, we have to presume that potential higher-order evidence to indicate that it was not even rational to start out with is misleading. However, this does not have to change much since misleading evidence is still evidence. An interesting consequence is, nonetheless, that higher-order evidence can leave first-order evidential support intact (Christensen, 2010, p. 195). For this reason, several authors have argued that higher-order evidence lacks this sort of systematic defeating force. 3 Moreover, extant arguments for higher-order defeat do not appear to be in line with one another. Some authors (e.g., Feldman, 2005) emphasize the impact of higher-order evidence on one's total evidence, whereas others (e.g., Horowitz, 2014) emphasize the fact that higher-order evidence will lead one into patently irrational thinking and behavior. Opinions are also split on whether higher-order evidence defeats the rationality of one's belief in a propositional or a doxastic sense. 4 I think 1 3 Explaining Higher-order Defeat that such disagreements among proponents of higher-order defeat further motivates a search for an explanation of why exactly higher-order evidence has the ability to defeat rational belief. I will call the problem of finding a satisfactory explanation to higher-order defeat: the "explanatory problem." In the following, we will consider two competing explanations of higher-order defeat: the "Objective Higher-Order Defeat Explanation" and the "Subjective Higher-Order Defeat Explanation" According to the Objective Higher-order Defat Explanation, possessing sufficiently strong higher-order evidence to indicate that one's belief about p fails to be rational is necessary and sufficient for defeating one's belief about p. I will argue that this explanation is defective or at best collapses into the other type of explanation. According to the Subjective Higher-order Defeat Explanation, believing that one's belief about p fails to be rational (in response to higher-order evidence about p) is necessary and sufficient for defeating one's belief about p. 5 I will argue that this type of explanation is better suited to explain higherorder defeat, at least on the assumption that what one is rational to believe depends on the relations among one's doxastic attitudes.
The paper will now proceed as follows. In "Section 2," I say something more about what distinguishes higher-order defeat from other types of defeat, and present the Objective Higher-order Defeat Explanation and the Subjective Higher-order Defeat Explanation. Then in "Section 3," I discuss and dismiss two versions of the Objective Higher-order Defeat Explanation; one is based on propositional rationality and the other on doxastic rationality. Finally, in "Section 4," I discuss and defend the Subjective Higher-order Defeat Explanation. "Section 5" concludes.

Higher-order Defeat
Before we go on to have a closer look at the two candidates for an explanation of higher-order defeat, I want to say something more about what distinguishes higherorder defeat from other types of defeat. At the most general level, defeaters are considerations that affect the epistemic status of beliefs in a negative way. Typically, a defeater is evidence to indicate that one's belief regarding the relevant matter fails to be rational. However, defeaters come in different flavors. An often cited distinction is the one between rebutting and undercutting defeaters (Pollock 1970). A rebutting defeater is a consideration that indicates that a belief is false, while an undercutting defeater is a consideration that indicates that a belief fails to be well-grounded. For instance, evidence that there are black swans provides a rebutting defeater for believing that all swans are white. In contrast, undercutting defeaters attacks the grounds for one's beliefs. For example, if I believe that the vase in front of me is red but come to learn that it is in fact illuminated by red lightning, I have an undercutting defeater for my belief that the vase is red. This means that my belief that the vase is red no longer is justified but it does not exclude that the vase in fact might be red.
At first glance, one might think that higher-order defeat is a species of undercutting defeat since it attacks the rationality of one's belief. However, several philosophers have identified features of higher-order defeat that distinguishes it from other types of defeat. 6 Unlike rebutting defeaters, higher-order evidence indicates that one's belief about p fails to be rational and not that it is false. In this sense, higher-order evidence works as an undercutting defeater. However, unlike undercutting defeaters, higher-order evidence has a retrospective effect since it indicates that one's belief about p was never rational to start out with (Lasonen-Aarnio, 2014). In contrast, an undercutting defeater is evidence that one was not initially aware of that changes the picture and thus rationalizes a different belief towards p. So, while undercutting evidence indicates that one's belief about p no longer is rational, higher-order evidence indicates that one's belief about p was never rational to start out with.
But the distinction that matters most for our purposes is the one between objective and subjective undercutting defeaters (Klenk, 2019). An objective undercutting defeater is evidence or some other consideration that makes one's belief about p fail to be rational. For instance, an objective undercutting defeater might be sufficiently strong evidence to indicate that one's belief about p fails to be rational. By contrast, a subjective undercutting defeater is a belief that one's belief about p fails to be rational. For instance, if I believe that my belief about p lacks evidential support, or is epistemically inappropriate for some other reason, then I have a subjective undercutting defeater for my belief about p. Notice that an objective undercutting defeater does not have to be believed to be a defeater in order to provide defeat; it is enough that one comes in possession of the relevant evidence in order for one's belief about p to be defeated in this sense.
Given the distinction between objective and subjective undercutting defeaters, we can outline two different types of explanations to why higher-order evidence has the ability to defeat rational belief: either by providing an objective defeater or by providing a subjective defeater: The Objective Higher-order Defeat Explanation Possessing sufficiently strong higher-order evidence to indicate that one's belief about p fails to be rational is necessary and sufficient for defeating one's belief about p.

The Subjective Higher-order Defeat Explanation
Believing that one's belief about p fails to be rational (in response to higher-order evidence about p) is necessary and sufficient for defeating one's belief about p.
I will now go on argue that the Objective Higher-order Defeat Explanation is unable to provide a satisfactory solution to the explanatory problem and that it at best collapses into the Subjective Higher-order Defeat Explanation. Then, I will go on to argue that the Subjective Higher-order Defeat Explanation, by contrast, is able to provide a straightforward explanation to higher-order defeat at least given a certain conception of structural rationality.

3
Explaining Higher-order Defeat

The Objective Higher-order Defeat Explanation
Let us take a closer look at the Objective Higher-order Defeat Explanation: The Objective Higher-order Defeat Explanation Possessing sufficiently strong higher-order evidence to indicate that one's belief about p fails to be rational is necessary and sufficient for defeating one's belief about p.
A first thing to notice about the Objective Higher-order Defeat Explanation is that it does not require that one comes to believe that one's belief about p fails to be rational. Possessing sufficiently strong higher-order evidence to indicate that one's belief about p fails to be rational is supposed to be enough for higher-order defeat. However, if the higher-order evidence is not sufficiently strong it will not give you reason to believe that your belief about p fails to be rational. I take it that to possess higher-order evidence implies that you have access to the relevant evidence and also the capacity to properly evaluate the evidence. For instance, in order to possess higher-order evidence to believe that I am likely suffering from a case of hypoxia, I have to know what altitude the plane is. Moreover, I also need to be able to interpret the information correctly, e.g., to know about hypoxia. Otherwise, I cannot be said to possess the relevant higher-order evidence at issue.
Advocates of higher-order defeat seem to a large extent rely on something like the Objective Higher-order Defeat Explanation to defend their view. Here are some representative examples: HOE really is best thought of as evidence. It is information that affects what beliefs an agent (even an ideal agent) is epistemically rational in forming. (Christensen, 2010, p. 193) ...one's higher-order evidence often makes a great deal of difference for the status of one's first-order beliefs. (Feldman, 2009, p. 306). ...if one's higher-order evidence indicates that one's first-order evidence does not support belief, then one's total body of evidence does not support belief either. (Matheson, 2009, p. 277) In the passage above, David Christensen describes HOE (higher-order evidence) as information or evidence that affects what one is rational to believe. This seems to be in line with the Objective Higher-order Defeat Explanation. Much in the same way, the quotes from Richard Feldman and Jonathan Matheson imply that merely acquiring higher-order evidence can make one's belief about the relevant matter fail to be rational. If nothing else, these statements all frame what rationalizes a change of belief state in terms of higher-order evidence and not in terms of what one comes to believe in response to higher-order evidence.
The Objective Higher-order Defeat Explanation might be construed either in terms of a defeater for propositional rationality or a defeater for doxastic rationality. There is a difference between saying that it is rational to believe p and saying that one's belief that p is rational. It is normally assumed that propositional rationality is a matter of having on balance good reasons or justification to believe a proposition, whereas doxastic rationality is a matter of believing a proposition in a way that is reasonable or well-grounded. Doxastic rationality entails propositional rationality but not the other way around. Having on balance good reasons to believe p is not enough for doxastic rationality, in addition one's belief must also be properly based on those good reasons. Roughly, this means that one's reasoning has to be sufficiently sensitive to those good reasons.
One possibility is to argue that possessing higher-order evidence suffice to prevent one's belief from being rational in the propositional sense. More precisely, that possessing sufficiently strong higher-order evidence about p makes it impossible for one's total evidence to support one's belief about p. Given that evidential support is necessary for propositional rationality, this means that sufficiently strong higher-order evidence suffice for defeat. Another possibility is to grant that that higher-order evidence does not have to prevent one's belief about p from being rational in the propositional sense, but argue that it nevertheless makes one's belief about p fail to be rational in the doxastic sense. The upshot of this explanation is that higher-order evidence prevents one's belief about p from being reasonable or well-formed. Next, we will consider these two alternatives one by one.

The Propositional Objective Higher-order Defeat Explanation
The first alternative is to try to explain higher-order defeat in terms of propositional rationality. In this case, possessing sufficiently strong higher-order evidence about p makes it so that one's belief about p no longer is rational in the propositional sense. In order to see how this explanation is supposed to work, let us first consider how acquiring additional evidence in general can affect what one is propositionally rational to believe. Suppose that it is propositionally rational for S to believe p at t1 given a certain body of evidence E. Then at t2, S acquires new first-order evidence (E´) that bears directly on what she ought to believe about p. Let's say that E´ speaks very strongly against believing p. Given the more expansive body of evidence (E and E´) it seems plausible to assume that it is no longer rational for S to believe p in the propositional sense at t2. There is nothing peculiar about the fact that additional evidence can make a difference in this way with respect to what one is propositionally rational to believe regarding p. Some authors (e.g., Feldman, 2005;Matheson, 2009) argue that higher-order evidence has the ability to undermine evidential support in this way. Suppose again that E makes it rational for S to believe p at t1 in the propositional sense. Then at t2, S acquires higher-order evidence (HOE) that indicates that her belief about p is the result of an unreliable belief-forming process. Given the more expansive body of evidence (E and HOE), it might be argued, just like before, that it is no longer rational in the propositional sense for S to believe p at t2. So, on the supposition that this case is analogous to the one above it seems that we can explain propositional higher-order defeat in terms of (lack of) evidential support. So, given that 1 3 Explaining Higher-order Defeat higher-order evidence provides additional evidence regarding p in this sense, it seems that the Objective Higher-order Defeat Explanation works satisfactorily.
However, as several authors have pointed out, it seems possible for one's total evidence to be self-misleading in a certain sense. 7 That is, one's total evidence might support believing that it does not support believing p, when it in fact supports believing p. Or it might support believing that one's evidence supports believing p, when it in fact does not support believing p. As Maria Lasonen-Aarnio points out: "Very few think that there is a viable account of evidence on which evidence always has perfect access to itself, and the kinds of reasons for thinking this support the idea that sometimes evidence might have poor access to itself" (2020, p. 599-600).
Intuitions about hypothetical cases like the following seem to further support this possibility: HOLMES AND WATSON. Holmes is a detective who is famously good at evaluating evidence. Watson is a promising apprentice of Holmes. One day Watson accompanies Holmes to a crime scene. They carefully examine the available evidence. Watson correctly evaluates the evidence and concludes that the butler did it. However, in this case, Holmes makes a rare mistake and tells Watson that he thinks that the evidence does not support believing that the butler did it. 8 On the one hand, Watson has strong first-order evidence to believe that the butler did it, but on the other hand, he has strong higher-order evidence to believe that the first-order evidence does not support that the butler did it on the basis of Holmes' expert testimony. In this case, it seems plausible to assume that the total evidence supports both believing that the butler did it and believing that the evidence does not support believing that the butler did it.
Note that in cases like Holmes and Watson, the Propositional Objective Higher-order Defeat Explanation does not works satisfactorily. Watson's total evidence supports believing that the butler did it despite higher-order evidence to indicate that that the evidence does not support believing that the butler did it. In other words, the mere possession of strong higher-order evidence about p does not make one's belief about p fail to be rational in the propositional sense. So, when the evidence is self-misleading, the Propositional Objective Higher-order Defeat Explanation is unable to account for higher-order defeat. Of course, the higher-order evidence must not always be misleading in this way but a satisfactory explanation of higher-order defeat has to be able to account for cases like hypoxia and Holmes and Watson as well. Cases involving misleading higherorder evidence are also considered to be paradigmatic examples of higher-order defeat in the literature.
Perhaps, there are other ways in which possessing sufficiently strong higher-order evidence can lead to defeat. Feldman argues that reflection on one's higher-order evidence can affect the rationality of one's first-order beliefs (2006, p. 436-38). He suggests that in response to higher-order evidence one might reason in the following way: I only have reason to believe p if p is supported by the evidence; the evidence does not support p; therefore, I should suspend judgment about p. Believing that one ought to suspend judgment over p is in turn supposed to defeat the propositional rationality of one's belief that p. One might consider the belief to be additional evidence that counts against one's belief about p. Let us call Feldman's argument the "Argument From Reflection." In a sense, the Argument from Reflection provides a straightforward explanation of higher-order defeat. Reasoning about one's higher-order evidence in cases like this is likely to make one conclude that one ought to suspend judgment about p. However, the Argument from Reflection makes the Propositional Objective Higherorder Defeat Explanation collapse into the Subjective Higher-order Defeat Explanation. Notice that it is crucial for the Argument from Reflection that one actually comes to believe that one ought to suspend judgment about p; otherwise, it does not seem that reflection will lead to defeat. It does not have the same effect if one reflects on the higher-order evidence but concludes that one might rationally maintain one's belief about p. So, in the end it seems that the Argument from Reflection lends support to the Subjective Higher-order Defeat Explanation rather than to the Propositional Objective Higher-order Defeat Explanation.
Other authors, most notably Sophie Horowitz (2014), argue in a similar vein that a subject's total evidence cannot support an incoherent set of attitudes. The reason for this, in turn, is supposed to be that "ideally rationally agents will never be akratic" (p. 718). Roughly, to be epistemically akratic is to believe that one ought not to believe p, but yet believe p. Horowitz goes on to defend what she calls a "Non-Akrasia Constraint" on rationality by arguing that having akratic combinations of beliefs of this sort will lead one into patently irrational reasoning and behavior. For instance, a person who believes p but the evidence does not support p should be willing to bet a lot of money on the fact that p is true but not on the fact that the evidence supports p, which is odd. I think, however, that the appeal to epistemic akrasia is misguided, at least if used in an attempt to defend the Propositional Objective Higher-order Defeat Explanation. Remember that according to this type of explanation it is acquiring sufficiently strong higher-order evidence that is supposed to be responsible for defeat, and not the fact that one comes to believe that one's belief about p fails to be rational. In order for Horowitz's argument to work we have to presume that one, in addition to maintaining one's belief about p, also comes to believe that one's belief about p fails to be rational; only then could we say that one is akratic in the relevant sense. But then, once more, this would make the Propositional Objective Higher-order Defeat Explanation collapse into the Subjective Higher-order Defeat Explanation. 9

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Explaining Higher-order Defeat At the end of the day, the Propositional Objective Higher-order Defeat Explanation appears to be defective or it will at best collapse into the Subjective Higherorder Defeat Explanation. I therefore think that we should reject the propositional version of the Objective Higher-order Defeat Explanation and go on to explore the doxastic version instead.

The Doxastic Objective Higher-order Defeat Explanation
A more promising alternative might be to hold that rational belief is defeated by higher-order evidence in the doxastic sense. The idea would then be that possessing sufficiently strong higher-order evidence in some way or the other prevents one's belief from being doxastically rational; not because one fails to form the relevant belief, but rather because it prevents one from properly basing one's belief regarding the relevant matter on the evidence.
According to the orthodox view about basing, it is rational in the doxastic sense to believe p iff (i) believing p is propositionally rational for S in virtue of S having evidence E, and (ii) S believes p on the basis of E. So, does possessing sufficiently strong higher-order evidence to indicate that one's belief about p fails to be rational prevent one's belief about p from being rational in the doxastic sense? Not necessarily. As we have seen, S's total evidence can support believing p despite higherorder evidence to indicate that one's belief about p fails to be rational. Given that S bases her belief about p on that evidence, it should be rational for her to believe p in the doxastic sense. At least granted that it is possible for one's total evidence to be self-misleading in the way we discussed above. So, given the orthodox view about basing it is not obvious why higher-order evidence should prevent one's belief from being rational in the doxastic sense. Unless doxastic rationality requires something more than propositional rationality plus basing, it seems that the Doxastic Objective Higher-order Defeat Explanation is unable to account for higher-order defeat.
However, John Turri has argued in an influential paper (2010), which doxastic rationality cannot be understood simply as propositional rationality plus basing. Turri provides convincing examples to illustrate that basis is not enough. In order to be doxastically rational to believe p, it seems that one also has to properly reason from the evidence to one's belief about p. Say that S has good evidence E to believe p and bases her belief about p on E. But suppose also that S believes that E supports p because the tea leaves say that E supports p. According to the orthodox view about basing, it might be rational for S to believe p in the doxastic since her belief that p is based on good evidence. However, since S has reasoned improperly in concluding that E supports p because of the tea leaves, it seems that it is not rational for S to believe p after all. The lesson is: there is more to doxastic rationality than just propositional rationality plus basing.
Following up on Turri's critique of the orthodox view it might be argued that doxastic rationality requires something more than just a basing requirement. A number of authors have attempted to formulate a further constraint on doxastic rationality that makes it sensitive to higher-order evidence. 10 For example, Han van Wietmarschen (2013) suggests that doxastic rationality requires that "the subject engages in the right kind of process of reasoning" (p. 414). He goes on to argue that higher-order evidence prevents the subject from reasoning properly. The higherorder evidence is supposed to force one to "bracket" one's actual reasoning process about the relevant proposition. Call this the "Proper Reasoning Argument." The argument is in turn inspired by David Christensen's "Independence principle": Independence: In evaluating the epistemic credentials of another person's belief about P, to determine how (if at all) to modify one's own belief about P, one should do so in a way that is independent of the reasoning behind one's own initial belief about P. Christensen (2010, p. 196) holds that Independence not only applies in cases of disagreement but also in cases involving higher-order evidence more generally. The upshot is that one cannot rationally use one's initial reasoning about p in order to dismiss higherorder evidence about p. As a result, higher-order evidence about one's belief about p will prevent one's belief about p from being rational in the doxastic sense. If this is correct, Independence seems to support the Proper Reasoning Argument.
However, I think that the Independence as well as the Proper Reasoning Argument are problematic for several reasons. First of all, Independence is controversial. Christensen himself points out that Independence is the focal point of the debate over the significance of higher-order evidence. For this reason, it seems somewhat question-begging to appeal to this principle in order to defend higher-order defeat. Moreover, a number of philosophers (e.g., Kelly, 2013, Lackey, 2010, Lord, 2013, Moon, 2018 have constructed counterexamples to show that Independence might be false, at least in the way it was originally formulated by Christensen. But the fact that Independence is controversial and subject to many objections does not rule out that the Proper Reasoning Argument is sound. I believe, however, that the there is a deeper problem with the argument.
According to the Proper Reasoning Argument, it is necessary that you engage in the right kind of reasoning process in order for your belief about p to be rational in the doxastic sense. In order to engage in the right kind of reasoning process, you need to take the higher-order evidence into consideration and the only reasonable thing to do in response to higher-order evidence, according to the argument, is to bracket your reasoning process about p. For this reason, your belief about p cannot be rational in the doxastic sense if you possess sufficiently strong higher-order evidence about p according to the Doxastic Higher-order Defeat Explanation. But why should refraining from bracketing your reasoning process about p in cases like this be considered to be bad reasoning? Naturally, there seems to be something bad about not properly taking the higher-order evidence into consideration from an epistemic point of view, but it is not obviously an example of bad reasoning from the evidence to one's belief about the relevant mater.
For instance, suppose that Watson in response to the higher-order evidence (Holmes's testimony) comes to believe that Holmes must be mistaken and that the evidence in fact supports believing that the butler did it. Now, Watson's reasoning about the higher-order evidence might be defective but this does not imply that his reasoning about whether the butler did it is defective as well. 11 Unless, of course, one presumes that Watson's reasoning about the higher-level proposition, the evidence supports that the butler did it, also must be proper in the relevant sense in order for Watson's belief about the object level proposition, the butler did it, to be rational in the doxastic sense. But this seems to open up for a viscous regress. Moreover, it does not seem to be relevant in relation to Watson's reasoning process from the first-order evidence to the conclusion that the butler did it. Watson's reasoning from the evidence to the conclusion might very well be impeccable. However, if Watson had come to believe that his belief that the butler did it fails to be supported by the evidence, in response to Holmes testimony, things would be different. In that case, it would be a case of bad reasoning to conclude that the butler did it from Watsons' perspective. But if the Doxastic Objective Higher-order Defeat Explanation where to require this, it would collapse into the Subjective Higher-order Defeat Explanation.
But how is this different from the case with the tea leaves above? Remember that S believed that E supports p because the tea leaves say that E supports p. For this reason, Turri argued that S's belief that p cannot be rational in the doxastic sense even if it is based on E (that supports p). I do not think that the cases are analogous though. Watson correctly reasons from the evidence to the conclusion that the butler did it and presumably he also believes that the conclusion follows from the evidence for the right reason. In contrast, the subject in Turri's example does not believe that his evidence supports p for the right reason (E). Instead, S believes that the evidence supports p in virtue of the tea leaves, which is obviously the wrong reason.
In sum, the Objective Higher-order Defeat Explanation is either defective or it collapses into the Subjective Higher-order Defeat Explanation. Next, I will argue that the Subjective Higher-order Defeat Explanation does a better job explaining higher-order defeat than the Objective Higher-order Defeat Explanation.

The Subjective Higher-order Defeat Explanation
Recall the Subjective Higher-order Defeat Explanation: The Subjective Higher-order Defeat Explanation Believing that one's belief about p fails to be rational (in response to higher-order evidence about p) is necessary and sufficient for defeating one's belief about p.
What is crucial in this type of explanation is that one (in response to higher-order evidence about p) comes to believe that one's belief about p fails to be rational. Whether or not one actually has good evidence to believe this seems to matter less. For instance, say that Watson is at a crime scene without Holmes. He carefully evaluates the evidence and correctly concludes that the butler did. However, as a result of a sudden whim, he suspects that someone has slipped a mind-distorting drug in his coffee and concludes that he cannot trust his evaluation of the evidence. As a result, Watson comes to believe that his belief that the butler did fails to be rational. According to the Subjective Higher-order Defeat Explanation, this means that Watson's belief that the butler did suffers higher-order defeat. It does not matter that Watson's whim provides poor evidence to indicate that he has been drugged since the quality of one's higher-order evidence is not crucial for higher-order defeat according to the Subjective Higher-order Defeat Explanation.
But why should one's belief about p be defeated by the mere fact that one comes to believe that one's belief about p fails to be rational? As we have seen above, possessing sufficiently strong higher-order evidence does neither seem to rule out that one's belief about p can be rational in the propositional nor the doxastic sense. So, in the end it seems that it is possible for one's total evidence to support believing p despite possessing higher-order evidence to indicate that one's belief about p fails to be rational. Given that rationality is a matter of evidential support or epistemic reasons, it becomes somewhat difficult to see what difference it would make that one comes to believe that one's belief fails to be rational.
The familiar view that epistemic rationality is a matter of evidential support or epistemic reasons is sometimes called the "substantive view of epistemic rationality." But there is also another approach to epistemic rationality. Some authors (e.g., Broome, 2013) have argued that rationality above all is a matter of satisfying certain structural, coherence requirements. In order to be coherent one cannot have certain combinations of attitudes. This is sometimes called the "structural view of epistemic rationality." For example, not having the intention to ψ when one intends to φ and believes that one must ψ in order to φ appears to be a paradigmatically irrational combination. It has therefore been argued that there is a non-akratic (enkratic) constraint on rationality. To be practically akratic is to fail to intend to do what one believes that one ought to do. Much in the same way, one is epistemically akratic if one fails to believe what one believes that one ought to believe.
Epistemic Enkrasia Rationality requires that [if you believe that your belief about p fails to be rational, you give up your belief about p]. 12 Given that Epistemic Akrasia is a plausible constraint on rational belief it seems that the Subjective Higher-order Defeat Explanation provides a straightforward 12 I formulate Epistemic Enkrasia as a wide scope rather than as a narrow-scope requirement. This means that the rational requirement takes a wide-scope over the relevant conditional. However, as some writers have pointed out, the wide scope formulation makes structural requirements symmetrical in a certain sense: "Wide-scope requirements do not discriminate between the different ways in which you might avoid irrationality" (Way, 2011, p. 229). I will not enter the vexed debate over the nature of rational requirements here. But for whatever it is worth, I think that a wide scope formulation might be appropriate given the misleading nature of higher-order evidence. In contrast, the narrow scope formulation is problematic since it entails that one is rationally required to believe what one believes one is rational to believe. For instance, if one believes that it is rational to believe that the moon is made of green cheese, then one is rationally required to believe that the moon is made of green cheese, which is clearly absurd.

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Explaining Higher-order Defeat explanation of higher-order defeat. 13 The reason why one's belief about p fails to be rational if one (in response to higher-order evidence about p) comes to believe that one's belief about p fails to be rational is that one ends up with an akratic combination of beliefs, and in that situation one is rationally required to give up one's belief about p according to Epistemic Enkrasia. I cannot provide a defense for Epistemic Enkrasia here but let me just say that the principle is deeply rooted in intuitions about rationality and endorsed by a great number of philosophers. 14 To believe against one's best judgment appears to be at least as odd as not to intend to do what one believes one ought to do. 15 For this reason, a number of philosopher have emphasized the Moore-paradoxical nature of believing things like the butler did it but the evidence does not support that the butler did it.
Notice that Epistemic Enkrasia cannot be used in the same way in order to support the Objective Higher-order Defeat Explanation. Epistemic Enkrasia is a requirement which determines which combinations of attitudes one rationally may occupy, and not a requirement on what combinations of attitudes one's total evidence possibly might support. Put differently, Epistemic Enkrasia says that one is rationally required to take certain beliefs conditional on one's other beliefs and not conditional on one's total evidence. For example, if I come to believe (in response to higherorder evidence about p) that my belief about p fails to be rational, it will not be rational for me to believe p. But it does not follow from Epistemic Enkrasia that one's belief fails to be rational merely by the fact that one possesses higher-order evidence to indicate that one's belief about p fails to be rational.
The Subjective Higher-order Defeat Explanation also enjoys an explanatory advantage over the Objective Higher-order Defeat Explanation. The Subjective Higher-order Defeat Explanation seems to be better suited to accommodate intuitions about skepticism. The view that higher-order evidence provides a defeater threatens to lead to skepticism in controversial areas of inquiry like philosophy (Whiting, 2020). According to the Objective Higher-order Defeat Explanation, possessing sufficiently strong higher-order evidence about p will always make it so one's belief about p fails to be rational. Much in the same spirit, it has been argued by proponents of the conciliatory view that higher-order evidence of peer disagreement rationally requires one to suspend judgment or at least to have significantly less confident in one's belief about the disputed matter. 16 In epistemic domains where peer disagreement is prominent, it seems to follow that large amounts of our beliefs will fail to be rational in this sense given the Objective Higher-order Defeat Explanation. This might lead to local skepticism in areas like philosophy, morality, 13 There are also philosophers who have called Epistemic Enkrasia into question, e.g., Coates (2012), Lasonen-Aarnio (2020), and Reisner (2013. Notice that if one does not accept Epistemic Enkrasia, one is not likely to accept the Subjective Higher-Order Defeat Explanation either. 14 See, e.g., Broome (2013), Horowitz (2014, and Kolodny (2005). 15 Adler (2002) argues that it is impossible to hold akratic combinations of beliefs, but for the sake of argument I will assume that this is possible. 16 For instance, according to the conciliatory view about higher-order evidence, one ought to suspend judgment or at least have significantly less confidence in one's view in the face of disagreement, given that one has reason to believe that one's opponent is an epistemic peer.

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and politics, where peer disagreement is pervasive. But this does not square well with our intuitions about knowledge in these areas. For instance, in general we do not accept local skepticism about morality.
By contrast, the Subjective Higher-order Defeat Explanation does not lead to skepticism as easily. Whether or not one comes to believe (in response to higherorder evidence about p) that one's belief about p fails to be rational is a contingent matter. In the ideal case, we can assume that one in response to higher-order evidence to indicate that one's belief about p fails to be rational, also comes to believe that one's belief about p fails to be rational. However, in a non-ideal case, one might overlook or misinterpret the higher-order evidence and come believe that one's belief about p is rational after all. In that case, it does not follow from the Subjective Higher-order Defeat Explanation that one's belief about p fails to be rational. It is easy to see how one could end up overlook or misinterpret one's evidence in this way. For example, the evidence might be complex, or one might be misled by wishful thinking, deluded by bias, and so on. For instance, in controversial areas of disagreement like morality, politics, and economy, it is seems likely that people are reluctant to give up their cherished beliefs despite ample evidence of disagreement as a result it seems that one could easily fail to believe that one's belief about p fails to be rational, even if one has sufficiently strong higher-order evidence to indicate that this is the case. 17 However, the Subjective Higher-order Defeat Explanation face some problems of its own (Klenk, 2019). First, it might be objected that believing that one's belief about p fails to be rational (in response to higher-order evidence about p) cannot be necessary for higher-order defeat. If believing that one's belief about p fails to be rational is necessary for higher-order defeat it seems to follow that unreflective subjects would be immune to higher-order defeat (Casullo, 2018). Second, it might be argued that believing that one's belief about p fails to be rational (in response to higher-order evidence about p) cannot be sufficient for higher-order defeat. If one accepts that an irrational belief to the effect that one's belief about p fails to be rational is sufficient for higher-order defeat, it seems that one also has to accept that an irrational belief might serve as a justifier in order to be consistent. But as Alexander (2017) argues, this is highly counterintuitive.
In response to these objections, it is important to have in mind that the Subjective Higher-order Defeat Explanation is motivated by a structural conception of rationality. Epistemic Enkrasia is s structural requirement of rationality that tells us what combinations of attitudes are permissible from a perspective of coherence. From this perspective, it is neither surprising that unreflective subjects can be immune to defeat nor that irrational beliefs can serve as justifiers. First, a subject that is unreflective in the sense that she does not reflect on the sources of her beliefs, and as a consequence neither forms beliefs about the sources of her beliefs, seems to be able to avoid higher-order defeat. For instance, if one ignores higher-order evidence to indicate that one lacks important evidence regarding p or that one's beliefs about p is the result of an unreliable belief-forming process, one will probably not come to believe that one's belief about p fails to be rational. But this is how structural rationality works. Given that one is able to make one's attitudes cohere, one will also be able to preserve their structural rationality. For example, my belief that everyone is set out to kill me seems to stand in conflict with the evidence that people I meet do not attempt to do so. However, if I form the belief that I carry an invisible shield that prevents them from realizing that I am the one they are after, it seems that I can preserve the coherence among my attitudes. This also explains how an irrational belief can serve as a justifier according to the structural view of epistemic rationality. My belief that I carry an invisible shield is irrational in a certain sense, i.e., have no good reason to think so, but it helps justify my belief that people would try to kill me if they only knew the truth about my identity.
A final worry about the Subjective Higher-order Defeat Explanation is that it implies that higher-order defeat is a contingent matter. Whether or not one's belief about p suffers higher-order defeat is contingent on what one comes to believe in response to the higher-order evidence. But even if one could manage to avoid higherorder defeat in this way, it still seems to be something epistemically bad about ignoring higher-order evidence in this way. However, the Subjective Higher-order Defeat Explanation is unable to account for this.
In response, one might argue that a failure to correctly respond to one's higherorder evidence represents a rational failure of another type. Given a substantive view of epistemic rationality one has reason to believe in accordance with one's evidence. Failing to correctly respond to one's higher-order evidence is therefore a failure to believe in accordance with one's evidence. For instance, given that Watson ignores Holmes testimony he fails to correctly respond to the higher-order evidence. As a result, his belief that the evidence supports believing that the butler did fails to be rational, at least on the substantive view of epistemic rationality. However, this does not prevent his belief that the butler did it from being rational in the structural sense. This also explains why he is able to avoid higher-order defeat according to the Subjective Higher-order Defeat Explanation. Given that structural epistemic rationality and substantive epistemic rationality represent different areas of normative evaluation as some philosophers have suggested (e.g., Worsnip, 2018), this seems to be a possibility. But this is neither the time, nor the place to discuss the prospects of such a pluralistic view on rationality.

Concluding Remarks
This paper argues that, believing that one's belief about p fails to be rational (in response to higher-order evidence about p) is necessary and sufficient for higherorder defeat. The result is interesting and has many applications. To finish, let me just make two brief comments on the result. First, those who do not accept Epistemic Enkrasia as a constraint on epistemic rationality are not likely to be convinced by the Subjective Higher-order Defeat Explanation. For example, according to some versions of evidentialism what one ought to believe is strictly regulated by one's evidence and does not depend on considerations which have to do with the coherence 1 3 of one's present doxastic attitudes. 18 An alternative could be to bite the bullet and reject that higher-order evidence is evidence, or to claim that higher-order defeat is impossible (e.g., Titelbaum, 2015). Secondly, It might be worthwhile to examine other types of explanations as well, beside the two we have considered here. For example, it is possible that other versions of the Objective Higher-order Defeat Explanation might fare better than the ones discussed in this paper. An alternative that recently has come to the fore is to accept that higher-order evidence does not affect the evidential support of the target belief, but argue that higher-order evidence nonetheless might provide one with a reason to suspend judgment about the relevant matter at issue (Lord, 2018). 19 Funding Open access funding provided by University of Gothenburg.

Conflict of Interest
The author declare no competing interests.
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