2. THE PROBLEM

We make all sorts of errors: we misremember, we think we see something we didn't, we make fallacious inferences, we misapply good rules of inference, etc. These are epistemic errors because they lead to inaccurate and/or irrational beliefs. Throughout, my reference to our fallibility signifies our proclivity toward epistemic error.

To begin to see the problem our fallibility gives rise to, let's start with an example:

In this example, Andy receives evidence that she has likely made an error in her calculations. Call evidence of epistemic error higher-order evidence.Footnote ⁸ The widespread intuition that Andy should reduce her confidence is typically encoded in the judgment that maintaining her confidence after she receives the higher-order evidence would be epistemically irrational.Footnote ⁹ I will suppose that this judgment is correct, and that it represents the fact that Andy, like the rest of us, must take her fallibility into account when managing her beliefs.

To make the problem more precise, I will replace talk of the Evidentialist Dictum with talk of Evidentialism, the view that believing a proposition is epistemically rational for someone just in case her evidence supports that proposition. On my usage, Evidentialism implies that rational belief supervenes on evidential support, rather than evidence alone: any two people for whom the same propositions are supported (to the same degree) by their respective evidence are justified in believing exactly the same things.Footnote ¹⁰ Evidentialism is a broad view that includes both objective and subjective Bayesianisms, for instance.Footnote ¹¹

One additional claim will be used to generate the problem, Entailment-Support: If a body of evidence entails some empirical (contingent a posteriori) proposition, that body of evidence supports that proposition.Footnote ¹² This claim is controversial. Some will view it as downright implausible, while others will think it is the only objective evidential support principle.Footnote ¹³ I'm not sure it's the only objective evidential support principle, but I'm confident that it's not downright implausible. The principle, for instance, does not say that if your body of evidence entails any proposition (e.g., necessary truths), your body of evidence supports it. Moreover, it should be endorsed by anyone who accepts a probabilistic account of evidential support, which I consider a plausible conception of evidential support. In any case, in §5, I'll discuss challenges Evidentialists face if they reject this principle. Until then, I'll suppose it's true.

The problem is that Evidentialism cannot accommodate the judgment that Andy's belief is irrational once she receives the higher-order evidence. This is because, by Entailment-Support, Andy's evidence supports this belief, since her evidence entails it. More carefully: Andy is in an Entailment Case of higher-order defeat – an Entailment Case for short. In an Entailment Case, at t₁, the subject's evidence entails some proposition, P, and she believes P on the basis of this evidence. Then, at later t₂, she acquires higher-order evidence that renders her belief in P irrational.Footnote ¹⁴ By Evidentialism and Entailment-Support, Andy's belief is rational at t₁, and by Evidentialism and the judgment that Andy's belief is irrational at t₂, Andy's belief is not supported by her evidence at t₂. If it's not supported by her evidence at t₂, then, by Entailment-Support, it's not entailed by her evidence at t₂. But entailment is monotonic: adding evidence to a body of evidence without removing any evidence leaves the entailment intact. Hence, her belief is entailed by her evidence at t₂, hence it is supported, hence it is rational. Thus, the judgment that Andy's belief is irrational when she acquires the higher-order evidence appears to be inconsistent with Evidentialism and Entailment-Support. Since the latter principle spells out when a body of evidence supports a proposition, this appears to be an instance of the conflict: one cannot always simultaneously respect one's evidence and respect one's fallibility. Without a solution to this problem, Evidentialism will be unable to accommodate our judgments about how evidence of fallibility bears on rational belief.Footnote ¹⁵

3. EVIDENCE-LOSS

Abandoning Evidentialism at this point would be hasty, for nothing has been said about whether Andy loses evidence between t₁ and t₂. Some philosophers discussing related problems do address this step. For instance, Kelly (Reference Kelly, Christensen and Lackey2013: 46) writes:

What Kelly says here is true. But he doesn't defend the claim that in the relevant cases the subject does not lose evidence. Yet, the considerations adduced in the last section suggest an argument from Evidentialism to the conclusion that Andy does lose evidence. Call it the Evidence-Loss Argument.

1. 1. Evidentialism: Believing P is rational for S at t just in case S's evidence supports P at t.

2. 2. Entailment-Support: If S's evidence entails (empirical) P at t, then S's evidence supports P at t.

3. 3. Entailment Case: At t₁, S's evidence entails P, and S believes P on the basis of this evidence. At t₂, S acquires higher-order evidence that renders S's belief irrational.

4. 4. Entailment-Loss principle: S's evidence entails P at t₁ and not at t₂ only if S loses evidence between t₁ and t₂.

5. 5. S's evidence doesn't support P at t₂. (By (1) and (3))

6. 6. S's evidence doesn't entail P at t₂. (By (2) and (5))

7. 7. Therefore, S loses evidence between t₁ and t₂. (By (3), (4), and (6))

The Entailment-Loss principle is the only premise not discussed so far. It follows from the monotonicity of entailment and a plausible understanding of evidence. Entailment relations between sets of propositions cannot change, but which set of propositions constitutes one's evidence can change. Thus, this argument suggests the Evidence-Loss Account of higher-order defeat, that acquiring higher-order evidence that one has improperly assessed or is not in a position to accurately assess one's evidence sometimes causes one to lose some of that evidence.Footnote ¹⁷

In addition to the Evidence-Loss Argument, there are two reasons to believe the Evidence-Loss Account. First, it has a precedent in the literature. Williamson (Reference Williamson2000: 219) describes an example of evidence-loss occasioned by acquiring evidence that one misassessed one's original evidence:

Williamson concludes, “Thus e will no longer form part of my evidence.” In this case, something very improbable occurs, given the subject's assessment of his evidence. So, upon making the observation, he loses evidence as a result of becoming reasonably worried that he misassessed this evidence. Thus, acquiring evidence of misassessment can result in evidence-loss.

Second, the Evidence-Loss Account explains the illegitimacy of dogmatically dismissing higher-order evidence in a way that parallels the standard account of the illegitimacy of the reasoning involved in the Dogmatism Paradox for knowledge,Footnote ¹⁸ and its two main competitors on this front are incompatible with Evidentialism. Suppose Andy were to reason as follows:

Several philosophers have cautioned against such dogmatic responses to higher-order evidence.Footnote ¹⁹ Since the hypoxia warning calls into question Andy's evidence assessment, appealing to that assessment to conclude she's not suffering from hypoxia seems illegitimate. A similar form of dogmatic reasoning in response to misleading evidence against knowledge has been widely discussed. Consider Harman's (Reference Harman1973: 148) statement of this reasoning:

What explains why these sorts of reasoning are illegitimate?

In the knowledge case, the standard criticism is that the reasoning incorrectly presupposes that once one has knowledge, one may always thereafter use it in one's reasoning. But acquiring misleading evidence can cause one to lose the knowledge one might have used to dismiss that evidence.Footnote ²⁰ Evidentialists can claim something similar about Andy's reasoning. It's illegitimate because although her evidence previously entailed that she had enough fuel, this doesn't warrant her in disregarding further evidence. Getting that further evidence may change what her evidence entails by causing her to lose evidence. This is just what the Evidence-Loss Account implies.

Evidentialists cannot accept two alternative explanations found in the literature. First, there is Christensen's (Reference Christensen2010, Reference Christensen2011) Bracketing Explanation, on which accounting for her higher-order evidence requires Andy to bracket her original reasons. This is a “virtual” rather than “genuine” evidence-loss account: Andy doesn't actually lose evidence, but what she is justified in believing after she acquires the higher-order evidence depends only on the evidence remaining after she brackets her original evidence. While discussing disagreement, Kelly (Reference Kelly, Christensen and Lackey2013: 45) discusses the parallel between dogmatic reasoning involving higher-order evidence and the Dogmatism Paradox, and proposes what I'll call the Non-Monotonic Explanation of why this reasoning is illegitimate:

The idea is that the support enjoyed by a subject's belief before she was aware of the disagreement is lost, in the standard way, once she learns of the disagreement. As a result, subsequently appealing to that belief to dismiss her peer's belief is irrational.

All three explanations imply that the dogmatic reasoning is unreasonable because some of the premises of the dogmatic reasoning are unjustified. However, Evidentialists can accept neither the Bracketing Explanation nor the Non-Monotonic Explanation. The problem cases are Entailment Cases: the original evidence entails the relevant beliefs, hence the Evidentialist must say that the original evidence supports the beliefs. No matter how much evidence one brackets, and no matter how much additional evidence gets added to one's body of evidence, if one does not lose any evidence, then according to Evidentialism the premises of the problematic reasoning remain justified. Indeed, Christensen argues that Andy's evidence does still support her beliefs because, on his non-Evidentialist account, higher-order evidence defeats while leaving evidential support relations intact.Footnote ²¹ Although Kelly wants to provide an Evidentialist account, he admits that Entailment Cases give rise to a genuine puzzle.Footnote ²² The Evidence-Loss Account allows Evidentialists to solve that puzzle.

4. AGAINST THE EVIDENCE-LOSS ACCOUNT

The Evidence-Loss Account should strike Evidentialists and non-Evidentialists alike as a serious hypothesis. In spite of its attractions, however, it is open to at least three objections. The first shouldn't worry Evidentialists much. The second and third strike me as strong objections.

First, the Evidence-Loss Account says when Andy acquires the higher-order evidence she thereby loses evidence. But which evidence does she lose? No principled answer seems available. Given the description of the case, there are four main options, but picking one rather than the other is arbitrary.

This objection should be addressed if the Evidence-Loss Account is defended further. However, lacking a precise, general answer is not a major embarrassment, since the main alternative faces a similar question, and also lacks a precise, general answer. This alternative is Christensen's Bracketing Account, according to which, accommodating higher-order evidence requires bracketing some of one's original evidence.Footnote ²³ But which evidence, or how much of it, must Andy bracket?Footnote ²⁴ It's unlikely that any principled answer will be forthcoming. Thus, the Evidence-Loss Account can adopt a companions-in-guilt strategy. It's not off the hook. But this is a challenge rather than a strong objection.

According to the second objection, the Evidence-Loss Account requires an implausible “purpose-relative” conception of evidence possession. Consider a case of peer disagreement. Suppose that while out to dinner, you and your friend discover that you disagree about your shares of the bill. Even if, in some sense, you thereby lose evidence, you can still legitimately appeal to this evidence for some purposes. Suppose it's part of your original evidence that the bill, before tip, is $60. You can reasonably reject your friend's claim that your share is $400, since the bill itself is only $60.Footnote ²⁵ But, to avoid condoning dogmatism, the Evidence-Loss Account prohibits appealing to this evidence to dismiss the more plausible position that, with tip, your shares are $35, rather than $36, say. Now suppose you're out to dinner with two people: one claims your shares are $400 and the other claims $35. Arguably, you can reasonably dismiss the $400 verdict, but not the $35 verdict. What explains this? The natural answer is that for the purposes of ruling out the ridiculous response you can reasonably appeal to your original evidence, but for the purposes of ruling out the sensible response you cannot.Footnote ²⁶ The Evidence-Loss Account explains the former fact by positing evidential support, hence evidence possession, and it explains the latter fact by positing evidence-loss. Thus, if the proponent of the Evidence-Loss Account wants to capture all of these facts, she seems committed to a purpose-relative account of evidence possession: you possess the evidence about the bill for the purpose of dismissing the ridiculous response, but not for the purpose of answering the sensible one.

While the claim that evidence possession is purpose-relative is not obviously incoherent, it seems implausible. It's not as if considerations available to you for the purpose of answering one question vanish when you attend to another. But on the Evidence-Loss Account they do lose their status as evidence depending on your purposes or the questions you're addressing. This means if you were aware of the Evidence-Loss Account's truth, things would end up looking very strange from your perspective. You might think: “I previously possessed evidence E, which supported belief in P and in Q. Now that I have this higher-order evidence, I still possess E for the purpose of answering whether P, E still bears on the question whether Q, but I do not possess E for the purpose of answering whether Q.” This doesn't seem right. The Evidence-Loss Account introduces relativity into evidence possession where there appears to be none.

Of course, proponents of the Evidence-Loss Account can insist that this mischaracterizes which evidence has been lost and any trace of purpose-relativity will vanish once the proper characterization is in place. However, this response invites the question: Why does the subject lose that evidence rather than this evidence? The more heavily the account relies on particular judgments about which evidence one loses in response to higher-order evidence, the more urgent the need to answer the first objection begins to look. I think placing much theoretical weight here would be unwise.

The purpose-relativity of evidence possession might be defended by appealing to the idea that epistemic notions are ‘interest-relative,’ in the sense that, for instance, whether a subject knows or is justified in believing something depends partly on her interests or what is at stake for her.Footnote ²⁷ Indeed, Stanley (Reference Stanley2005: 182) suggests that all epistemic notions are interest-relative, including evidence. Inspired by Stanley's position – Strong Interest-Relativism – a proponent of the Evidence-Loss Account may double down and defend the purpose-relativity of evidence possession.

Certainly by some people's lights we needn't take the Evidence-Loss Account seriously if it relies on Strong Interest-Relativism. But even if Strong Interest-Relativism is defensible, the claim that evidence possession is purpose-relative is even more radical. First, the Evidence-Loss Account is primarily concerned with evidence possession, rather than support strength. Some of Stanley's remarks seem to suggest that what is relative to one's interests is support strength, not possession. But that won't justify the purpose-relativity of evidence possession. Stanley also sympathetically discusses Williamson's E = K account of evidence, according to which, one's evidence is just what one knows. If E = K and Strong Interest-Relativism are true, then whether a proposition is part of one's evidence will depend on one's interests. Yet, this doesn't guarantee purpose-relativity. The Evidence-Loss Account allows evidence possession to vary while interests are held fixed, since interests and purposes are distinct. There may be much or little at stake for you, but once we hold fixed your interests, Strong Interest-Relativism will have fixed what evidence you possess, whereas the Evidence-Loss Account will still leave this purpose-relative. So, in this respect the Evidence-Loss Account is more radical than Strong Interest-Relativism.

According to the third objection, the Evidence-Loss Account gives the wrong sort of response to Evidentialism's problem with accommodating higher-order defeat. On the Evidence-Loss Account, Andy's belief turns out to be irrational because she loses evidence. But a common concern that arises when we consider our fallibility is that we make “performance” errors while attempting to properly form beliefs. Hume (Reference Hume and Nidditch1978: 180), for instance, insists that although deductive rules of inference are certain and infallible, our application of them is not.Footnote ²⁸ Likewise, when Andy gets the hypoxia warning, this is worrisome because it makes it likely that she made a faulty inference. And, it seems, this sort of worry leaves an agent's evidence untouched.

Compare Williamson's ball example (§3) with the Hypoxia example. In Williamson's case, the subject should abandon belief in his evidence because what he observes is incredibly unlikely if his evidence is true. Since incredibly unlikely things are probably false, his evidence is probably false, too. This is why claiming evidence-loss is plausible. But nothing like this occurs in Hypoxia. Andy takes her evidence to support a proposition, while having strong evidence that her take on the evidence is flawed. Unlike the subject in Williamson's case, what Andy observes is not incredibly unlikely if her evidence is true. Putting the comparison slightly differently: in contrast to the subject in Williamson's example who acquires reason to think he has misassessed what his evidence is, Andy only acquires reason to think she has misassessed what her evidence supports. Whereas continuing to accept what she took her evidence to support when she gets the hypoxia warning is unreasonable, relying on her judgments about what evidence she possesses seems unproblematic. Thus, while it's true that Williamson's example sets a precedent for the Evidence-Loss Account, this account doesn't properly explain all problematic Entailment Cases.

Since the Evidence-Loss Account arguably leads to an implausible, purpose-relative conception of evidence possession, and it provides the wrong sort of response to the problem raised by Entailment Cases insofar as that problem is about performance errors, I think we have good reason to reject the account as implausible and/or ultimately unmotivated.

5. EVIDENTIAL SUPPORT

The most natural move for Evidentialists to make at this point is to reject Entailment-Support.Footnote ²⁹ By itself, rejecting this principle wouldn't show that Evidentialism can capture higher-order defeat, but it would allow Evidentialists to avoid the argument based in Entailment Cases that Evidentialism can't capture higher-order defeat.

For several reasons, I think we shouldn't find this satisfying. First, Evidentialists who reject Entailment-Support must abandon a plausible conception of evidential support because something like Entailment-Support should be endorsed by anyone who thinks of evidential support probabilistically. Given certain Evidentialists’ (e.g., Bayesians’) other theoretical commitments, rejecting Entailment-Support and/or a probabilistic conception of evidential support won't be a plausible option. More than this, though, the probabilistic conception strikes me as plausible. One of the main reasons it's plausible to think, as Evidentialists do, that rational belief is based in evidential support is that typically the more epistemically rational a belief is, the more likely it is to be true, and, likewise, typically the greater evidential support one has for a belief, the more likely it is to be true.Footnote ³⁰ When we ask about the strength of the evidence we are asking how probable a hypothesis is given that evidence. This suggests that evidential support should be understood probabilistically.Footnote ³¹

Evidentialists might reject the probabilistic conception in general, and Entailment-Support in particular, by appealing to human limitations. If Evidentialism is wedded to Entailment-Support, Evidentialism implies that we are rational in believing infinitely many propositions.Footnote ³² But some think of rationality deontologically, that is, in terms of epistemic obligation, oughts, or requirements.Footnote ³³ Moreover, many endorse an ought-implies-can principle in epistemology.Footnote ³⁴ Since humans are finite, we cannot believe infinitely many propositions. So, the argument might go, we are not obligated to do this, so Entailment-Support and probabilistic conceptions of evidential support aren't true.Footnote ³⁵

There's plenty to question in this argument. One response, of course, is to insist that since Entailment-Support is true, Evidentialism is false. Setting that aside, though, it's not clear that Evidentialists should rely on this argument. Not only does nothing require the combination of views the argument relies on, it may also be true that this combination should be avoided. Alston (Reference Alston1988) argues against deontological conceptions of justification by appealing to ought-implies-can, whereas Feldman (Reference Feldman2000) – himself, an Evidentialist – defends a deontological conception by arguing against ought-implies-can. One plausible conclusion to draw from these arguments, independently of your stance on Evidentialism, is that ought-implies-can shouldn't be paired with the deontological approach.Footnote ³⁶ If that's right, then the argument relies on a conjunction that should be eschewed, and Evidentialists cannot reasonably defend their rejection of Entailment-Support in this way.

The second reason we shouldn't be satisfied with a simple rejection of Entailment-Support is that Evidentialists may be unable to capture higher-order defeat even if Entailment-Support is false. Christensen (Reference Christensen2010: 197) argues that even in non-Entailment Cases higher-order evidence defeats while leaving evidential support intact. Suppose my evidence strongly supports, but does not entail, some hypothesis, and I adopt belief in that hypothesis on the basis of an inference to the best explanation, only to learn from a trustworthy source that I was slipped a reason-distorting drug before I made the inference. Christensen argues that I cannot rationally maintain my belief even though my evidence still supports it. Why does my evidence still support the belief? Because the evidence is not in question (as in Williamson's case). And the explanatory connection between that evidence and my belief remain incredibly strong, since these connections don't depend on any claims about me or my current reasoning abilities.

Christensen's argument depends on the conjunction of (1) H is the best explanation of E ₁ and (2) H is the best explanation of E ₁&E₂. He can stipulate (1), but whether (2) is true depends on the case. Since some instances of this conjunction are false, Evidentialists might reasonably claim that Christensen's case – where E ₂ is the evidence about the reason-distorting drug – is one such instance. Evidentialists, like Conee and Feldman (Reference Conee, Feldman and Smith2008), who think evidential support relations are explanatory relations may insist that the higher-order evidence shifts evidential support by changing the best explanation.

For what it's worth, it doesn't seem that this will always be true. Imagine Darwin adopting belief in the theory of evolution after surveying all of his data, only to be told that he'd just ingested a reason-distorting drug right before he had reasoned to this conclusion. Is it really plausible to say that the theory of evolution is no longer the best explanation of his data? If we set the case up right, it will certainly seem irrational for him to maintain his belief. But it's not obvious to me that evolution will no longer be the best explanation.

In any case, without principles specifying the circumstances in which a hypothesis is the best explanation of some body of evidence, this disagreement will boil down to a clash of judgments about particular cases. Christensen thinks, at least in a range of cases, acquiring higher-order evidence doesn't change the fact that the relevant hypothesis is the best explanation. Conee and Feldman, and other Evidentialists, might disagree.Footnote ³⁷ It's true that Evidentialists can avoid the problem by altogether abstaining from providing principles of evidential support, so that no determinate, principled judgments can be made about whether, on their view, acquiring some evidence leaves evidential support intact. But Evidentialism would be much more secure – i.e., we could be more confident that Evidentialism can capture higher-order defeat – if Evidentialists addressed the problem by presenting an account of evidential support that rendered the right verdicts without running into additional problems.

Evidentialists might look to their opponents for help on this front. Presumably, non-Evidentialists think there's some principled way to explain why Andy should revise her belief. Depending on the explanation, Evidentialists may be able to convert this principle about rational belief into a plausible principle of evidential support.Footnote ³⁸ For example, suppose the following principle were advanced by non-Evidentialists to explain why Andy should revise her belief:

The Evidentialist might convert Levels into a principle of evidential support:

More generally, it might seem that most stories the non-Evidentialist would tell about higher-order defeat could just as plausibly be told by Evidentialists in terms of evidential support.Footnote ⁴⁰ We can call this the Conversion Strategy.Footnote ⁴¹

The Conversion Strategy faces at least two challenges. First, if applied indiscriminately, the Conversion Strategy runs the risk of trivializing Evidentialism, a substantive thesis. To see this concern, first note that some argue evidential support and coherence – more generally, reasons-based normativity and wide-scope rationality-based normativity – are distinct. Accordingly, some argue that coherence, not evidential support, is the source of higher-order evidence's normative force.Footnote ⁴² Now consider Levels and Levels-Support. Levels appears to be a coherence principle, whereas Levels-Support is, by design, an evidential support principle. By converting Levels into Levels-Support, Evidentialists blur the distinction between these two possible sources of normativity. Maybe Evidentialists are right to do this in this case. But in order to avoid trivializing Evidentialism, Evidentialists had better recognize some alleged source of normativity that cannot be converted into evidential support.

Even if the Conversion Strategy can be applied without trivializing Evidentialism, it still faces a second challenge. Recall from the introduction that several philosophers object to conciliationism on the grounds that it recommends ignoring first-order evidence. Nothing is special about conciliationism here. To respect our fallibility, prominent non-Evidentialist accounts require us to downplay, one way or another, the significance of our first-order evidence. Non-Evidentialists can live with this because their focus is directly on rational belief, rather than evidential support. But if Evidentialists convert non-Evidentialist accounts into principles of evidential support, Evidentialists will thereby transfer this feature (or bug) into their account of evidential support. This might make them susceptible to the sort of objection often leveled against their opponents. For instance, if part of the complaint against conciliationism is that it fails to give the first-order evidence its proper weight, and Evidentialists convert conciliationism's principles of rational belief into principles of evidential support, then Evidentialists will have thereby adopted principles of evidential support that conflict with common judgments about first-order evidence's proper role in evidential support. This would be bad. One would have thought if any view could give the first-order evidence its due, Evidentialism could. If that's right and Evidentialism must ultimately abandon certain claims about first-order evidence's role in determining total evidential support, then a standard argument against non-Evidentialist positions, and in favor of Evidentialism will be undermined.

Thus, the challenge for Evidentialists who want to pursue the Conversion Strategy is to find principles of rational belief (1) that accommodate higher-order defeat, (2) that can be converted into plausible principles of evidential support, and (3) that give the first-order evidence its due. Although I have no knockdown argument that this challenge cannot be met, I'll consider two implementations of the Conversion Strategy to illustrate the difficulty of the challenge.

Begin with Levels-Support. Recall, it says an agent's evidence doesn't support a proposition if she thinks it doesn't. It's based on Levels, which says rationality forbids you from believing a proposition when you believe your evidence doesn't support that proposition. According to an Evidentialism that includes Levels-Support, Andy should revise her belief because having acknowledged that her evidence probably doesn't support her belief that she has enough fuel, her evidence therefore no longer supports this conclusion. That is, her evidence no longer supports this conclusion because she thinks it doesn't. But this makes evidential support far too subjective. The first-order evidence seems to drop out of the picture completely. Moreover, it implies that anyone can rationally resist counterevidence simply by being dogmatic or pigheaded about what their evidence supports. Of course, Evidentialists might question whether Levels-Support is any worse off than Levels here. But I think it is. Levels might be paired with a more objective account of evidential support, in which case even if the pigheaded person's beliefs satisfy Levels, his beliefs might be rationally criticizable for totally failing to be sensitive to evidence. If Evidentialism and Levels-Support are both true, the pigheaded person's beliefs will be rationally uncriticizable.

A more sophisticated approach faces a related problem. Sliwa and Horowitz (Reference Sliwa and Horowitz2015) argue that accounts of higher-order evidence typically fail to respect all of the evidence, by failing to give proper weight either to first-order evidence or to higher-order evidence.Footnote ⁴³ They explicitly set out to defend a view that avoids this failure. Here's their view:

Applying Evidential Calibration requires three steps. First, determine which proposition your first-order evidence favors, where evidence favors P over ~P just in case the degree of support it provides to P is higher than the degree of support it provides to ~P. Second, determine your expected reliability, r, in making an educated guess about that proposition. Finally, assign r to the favored proposition. If your evidence favors P and your expected reliability is .73, then according to Evidential Calibration, if you have a credence of .73 in P, your belief is rational and you have accounted for all of your evidence.

First-order evidence doesn't completely drop out of Evidential Calibration's picture, but if we interpret it as a principle of evidential support, we do get some odd results. Suppose at t₀, your rational credences are 50/50 in P and ~P, at t₁ you get evidence that slightly confirms P, and then at t₂ you get slightly disconfirming evidence. Suppose your expected reliability about P remains .99 across these times, while the degree of support P receives from your first-order evidence, given the slightly confirming and disconfirming evidence, is .51 and .49 at t₁ and t₂, respectively. Understood as a principle of evidential support, Evidential Calibration implies that the total degree of your evidential support for P goes from .5 to .99 to .01 as you receive what appears to be nearly negligible first-order evidence. Consider a second case. Suppose your expected reliability remains .89 from t₁ to t₃, but you receive first-order evidence that shifts the first-order degree of support for P from .51 up to .99 back down to .51. According to Evidential Calibration, your total degree of evidential support remains at .89 throughout this interval. On this view, then, slight shifts in first-order evidential support lead to huge swings in total evidential support whereas large shifts in first-order evidential support lead to no changes in total evidential support. This doesn't look like a view that takes first-order evidence seriously.

As Sliwa and Horowitz (Reference Sliwa and Horowitz2015: 2854) explain, Evidential Calibration “takes the valence of our first-order evidence into account – whether the evidence favors P or ~P – [but] it ignores the strength of that evidence.” Thus, Evidentialists who apply the Conversion Strategy to Evidential Calibration will be forced to say that when agents have higher-order evidence, the only role first-order evidence plays in determining evidential support is setting valence. Given the two cases just described, this role seems at once too significant and not significant enough. And it's worth emphasizing that Sliwa and Horowitz crafted Evidential Calibration with the explicit intention of giving first-order evidence its due. Yet, when it's converted into a principle of evidential support, it leads to questionable results, at best.

Let's sum up. If Evidentialists want to capture higher-order defeat, they'll need to reject Entailment-Support, and a probabilistic conception of evidential support along with it. But to ensure that they can accommodate higher-order defeat, rather than simply avoid the argument that they can't, they need to do more than deny Entailment-Support. Refusing to provide principles of evidential support leaves Evidentialism on shaky grounds. The Conversion Strategy may be a promising way forward for Evidentialism. But two implementations of this strategy have implausible implications about evidential support because they both fail to give first-order evidence its due. While diminishing the impact of first-order evidence in the ways these theories do may be appropriate for a theory of rational belief, it seems inappropriate for a theory of evidential support. Going forward, the task for Evidentialists is to defend one of these implementations or offer a distinct theory of evidential support that provides both the right verdicts about evidential support and about higher-order defeat. Either way, Evidentialists have their work cut out for them.