Maria Lasonen-Aarnio argues against unlimited higher-order defeat.¹ Her main argument can be sketched as follows.² Suppose for reductio that some undefeated higher-order negative evidence has a defeating effect on evidence that justifies attitudes, no matter how high in order the negative evidence might be. If so, then rules for justifying attitudes by evidence would have to have unlimited complexity. Such rules could not guide us toward forming justified attitudes. Yet such guidance is an essential function of epistemic rules. So undefeated negative higher-order evidence does not always defeat lower-order justification.³

This is a forceful line of reasoning against its target theories. Here is how Lasonen-Aarnio characterizes the theories.

Rule-driven theories as Lasonen-Aarnio describes them are vulnerable to her main objection. If justification derives from rule following, then the justifying rules have to be followable in order for justification to be available. Lasonen-Aarnio gives excellent reason to think that rules that take into account higher-order negative evidence of every height are too complex to be followable. As a result, it is highly doubtful that unrestricted higher-order defeat can be accommodated by followable rules.

Not all theories of justification are “rule-driven,” in the sense that they state rules aimed to give guidance. Some theories of justification are aimed at explaining its nature by specifying the conditions that constitute having a justified -doxastic attitude. In other words, these “constitutional accounts,” as we can call them, are aimed at telling us what makes attitudes justified. A constitutional account need not guide us to justification any more than a theory of what constitutes knowledge must guide us to knowledge. Thus, constitutional accounts are not threatened by Lasonen-Aarnio’s main line of argument against unlimited higher-order defeat.

Nevertheless Lasonen-Aarnio’s paper contains serious threats to constitutional accounts. The paper raises two concerns that challenge any theory that counts all higher-order negative evidence as potentially defeating justification.⁴ Lasonen-Aarnio does not fully develop these challenges. They are inessential to her main argument. But either could be a conclusive objection to the most plausible constitutional accounts that allow unlimited higher-order defeat. The challenges will be investigated here. The goal is to find their strongest versions and to assess them.

The focus here will be on a class of plausible constitutional accounts of justification that allow unlimited higher-order defeat. We can call the selected class Downward Defeat (DD) theories. It is hereby stipulated that DD theories are those that meet the following conditions. They are about the justification of the doxastic attitudes of belief, disbelief, and withholding judgment.⁵ Their distinctive features are manifested in cases in which S has evidence in support of p and S has either (1) reason to think that S lacks justification for believing p , or (2) reason to think that S is incompetent at rationally assessing S’s evidence regarding p. DD theories imply that having either (1) or (2) as evidence is having a potential defeater of S’s justification for believing pp ⁶ That is, having evidence of sort (1) or (2) renders belief in p less justified or unjustified, unless the justification-reducing effect is neutralized by other evidence that counters it. Additionally, DD theories imply that this defeat has a specific effect on justification. DD theories imply that when evidence that would justify belief in p is wholly defeated by (1) or (2) evidence, the justified attitude toward p is withholding judgment (unless the defeat is accompanied by new evidential support for p or its negation).

Here is an intuitive defense of DD theories. Epistemically justified belief is a sort of reasonable belief. It is the sort that is particularly concerned with the proposition’s truth. Belief by S in p is reasonable in this way only if its justification takes into account all of the information that S has about S’s access to p’s truth. The higher-order evidence cited in DD theories is about S’s access to p’s truth. The evidence indicates either (1) that S does not have justification for regarding p as true or (2) that S is likely to be wrong about what attitude toward p S’s evidence justifies. Again, we are assuming that S has evidence that would support p’s truth to S and thereby justify believing p in the absence of the higher-order negative evidence. When S also has sufficiently powerful negative higher-order evidence of type (1) or type (2), from S’s point of view S’s access to p’s truth is too unreliably related to the fact of the matter for believing p to be reasonable. Cases of type (1) occur when it is credibly denied to S that some evidence that prima facie supports p does give that support. With a sufficiently credible denial, the prima facie evidence for p does not justify believing p. This defeat is like other familiar cases of undermining. It is like the way in which evidence of misleading lighting conditions defeats otherwise supportive color experiences as justification for color judgments. Cases of type (2) occur when S has evidence for S’s being incompetent at assessing evidence that seems to S to support p. Sufficiently credible evidence of this incompetence renders it seriously doubtful to S that seeming support for p is genuine. It ceases to be reasonable for S to believe what the evidence seems to support. When S has good enough evidence of type (1) or type (2), S’s reasons to believe p no longer support p’s truth from S’s perspective. Evidence of type (1) or (2) gives S nothing that favors p’s falsehood. In light of all of the information that S has to go on, it is most reasonable for S to take a noncommittal attitude toward p’s truth. S is justified in withholding judgment on p.

These justification verdicts are what DD theories imply. The plausibility of this view makes such theories worth defending.

Lasonen-Aarnio poses an argument against the possibility of an “Über-rule”. An Über-rule is “a function from epistemic circumstances to whatever the correct epistemic response is (or whatever the permitted doxastic responses are) in those circumstances” (2014: 330). There are two further features of Über-rules. First, an Über-rule is complete: “for any circumstances in which there is some epistemically rational doxastic state in the first place, the Über-rule codifies what that state (or range of states) is” (2014: 331). Second, “the following kind of situation can never arise: a subject does exactly as the rule recommends, but she has evidence that the resulting doxastic state is flawed” (2014: 331).

Lasonen-Aarnio’s argument against the possibility of an Über-rule is explicitly given against theories that are committed to this thesis:

Higher-order defeat says that the higher-order evidence “has defeating force” with respect to a doxastic state. Presumably this means that the evidence is a typical sort of defeater of justification for the state—the higher-order evidence reduces or nullifies the justification that the person has for being in the state, unless the higher-order evidence is itself defeated.

Not all DD theories are committed to Higher-order defeat. Unlike Higher--order defeat, the stipulated characterization of DD theories says nothing about the defeasibility of justification for withholding judgment. DD theories do share implications of Higher-order defeat concerning the justification of belief. DD theories imply that sufficiently strong higher-order evidence of the sorts that they cite is always a defeater of justification for belief, unless the potentially defeating higher-order evidence is itself defeated. This is implication concerning defeat for belief is enough for the argument to apply to DD theories.

Here is Lasonen-Aarnio’s presentation of the argument against the existence of an Über-rule:

This argument unjustifiably assumes that it is possible for a proposition that is specified as an Über-rule implication also to be a proposition against which S receives the oracular testimony. The argument does not derive this possibility from DD theories together with some plain facts. If it did, then the source of the implied contradiction would be rightly assigned to the DD theories. There is no prospect of that derivation, however. DD theories imply that certain propositions attributing justification are defeated by certain testimony. The theories and the plain facts do not so much as suggest that the justification also survives the receipt of the testimony.

An analogy will highlight the problem for the argument. The objectionable assumption of a joint possibility is plain to see in the following relevantly similar argument.

Preliminaries: S might have considered any simple proposition—say, an attribution of a familiar color to a familiar object. There are always some simple propositions that S is not considering. Let’s call “NC” a theory that identifies, for some possible situations, some simple proposition that S can consider but is not considering. Clearly some such theories are true. It could not refute all NC theories to argue as follows:

First we assume that some proposition, PNC, is a proposition that NC implies that S is not considering in a possible situation PS. Next we note that any simple proposition can be expressed and S can see and understand an expression of it and thereby consider it. Now we assume that in PS an expression of PNC is something that S sees and understands. The expression is displayed and S is looking at it and comprehending it. Finally we infer that NC is incorrect, since by hypothesis NC implies that S is not considering PNC in PS, yet that is what S is doing in PS.

This anti-NC argument clearly fails. Its flaw is first to assume that an implication of NC for PS is that S is not considering PNC, and then just to assume that in the same PS situation things happen that make S consider PNC. The argument does not derive the possibility of S considering PNC in PS from what NC requires of its implications. The argument does not give any good reason to think that both the implication and the consideration can happen together. No such reason exists. Granted, any proposition that NC implies S not to be considering is one that S can consider. But no tenable basis exists for thinking that a true NC would imply the possibility of a case in which S does consider an NC implication.

Quite similarly, S can consider any proposition attributing to S a justified attitude. S can see a displayed expression of it and have it in mind. S can receive trustworthy testimony against any proposition that S can consider. But nothing indicates it to be possible that any proposition is at once both an Über-rule implication and the subject of the testimony. Clearly the Über-rule does not imply this possibility on its own. When the testimony to S denies that S is justified in believing p, for instance, the Über-rule counts the testimony as a defeater of S’s evidence for p. So the Über-rule does not imply that S is justified in believing p. Thus, the subject of the testimony, the proposition that S is justified in believing p, is not an Über-rule implication. The argument needs good reason to think that if there is an Über-rule, then it is possible that some proposition is at once both an Über-rule implication and the subject of the testimony. No such reason exists.

Here is an objection to the criticism of the oracle argument.

Whatever is an Über-rule implication is something against which S can get the testimony, and possibly S does get testimony against whatever is an Über-rule implication about a possible case. It does not follow that is possible that S does get the testimony against what is an Über-rule implication. Again, the argument needs good reason to think that those things can happen together. No such reason is available. Compare again the counterpart reasoning about NC theories: Whatever proposition NC implies that S is not considering, S can consider it, and possibly S is considering whatever proposition NC implies not to be considered in some possible case. It does not follow that it is possible that a proposition that an NC theory implies that S is not considering is also a proposition that S is considering. Instead, for S to consider a proposition makes it not an implication of a correct NC theory. In the same way, when S considers a proposition attributing to S justified belief in p, the oracle’s testifying against it makes the considered proposition not an implication of an Über-rule. Thus, the oracle argument makes an unjustifiable assumption of a joint possibility.

The denial of this possibility does not imply any mysterious limit on what can happen. The higher-order defeat implications of Über-rules do not limit what propositions about justification can be considered while they are reliably denied. The implications just limit what propositions about justification can be true while they are reliably denied. Any Über-rule implication about any oracle case can be stated while the case occurs. The implication can be understood, believed with justification, and even known by anyone who does not have the oracular testimony or any other defeater for believing what the proposition says. DD theories even allow S to be considering an Über-rule implication while receiving the testimony, if S takes the oracle to be denying something else.

It remains highly plausible that certain evidence, such as the oracular denial to S that believing p is justified, does defeat at least modest justification for believing p. The justification is undercut. The testimony raises questions for S: “What am I missing about this evidence, or about p, or about justification? How does this evidence for p not justify belief?” S has available no support for answers that resolve S’s access to p’s truth. It is most reasonable for S to respond by withholding judgment, as the DD theories imply.¹⁰

The second problem for DD theories that is presented in Lasonen-Aarnio’s paper is stated briefly in a footnote:

This passage describes evidence that it suggests to be universally defeating. In order to make the possibility of such evidence maximally credible we can add a believable source for the evidence. To jeopardize DD theories more directly we can replace “cognitive error” with an error concerning the justified attitude. We can assume that the evidence is testimony from someone whom S knows to be trustworthy. We can assume that S is told that S has taken a drug with the effect that whatever attitude S adopts toward some particular proposition is almost certainly unjustified. Let’s call this evidence No Justified Attitude (NJA).

The cited passage says that Higher-order defeat theories apparently imply that there is no rational response to having the NJA evidence. Again, DD theories are not committed to the full thesis of Higher-order defeat, since they are not specified to imply anything about the defeat of justification for withholding. But it would refute DD theories for there to be no justified response to the NJA evidence when belief was justified. DD theories imply that there is always a justified response to defeated justification for believing, namely, withholding judgment.

A justified doxastic attitude remains available after receiving the NJA evidence. The previously justified attitude remains justified. The NJA evidence is too indiscriminate to defeat the justification for the previously justified attitude. If the NJA evidence were testimony against the justification of only some of the available doxastic attitudes, then the NJA evidence would leave it open that a mistake or a cognitive malfunction is making trouble. But evidence that uniformly opposes the justification of all attitudes, while giving no reason, is just mysterious. The NJA evidence has no intelligible bearing on either the truth of the proposition or what might be faulty about each doxastic response to it. When evidence is like that, the attitude that is justified given the rest of the evidence remains justified.

To test this out we can consider an example. Suppose that S has heard a weather forecaster predict rain in two days. S has found the forecaster to be pretty reliable. Suppose that S also has the NJA evidence concerning the proposition that it will rain in two days. In this situation S has good reason to think the following.

This thinking is quite reasonable. Relevantly similar thinking is available to -anyone with the NJA evidence. In the presence of NJA evidence the otherwise justified attitudes remain justified.¹¹

What has just been argued about the NJA evidence is not crucial to a defense of DD theories. Suppose that, contrary to what has just been argued, at least sometimes having the NJA evidence defeats the justification for believing a proposition. Whether or not the NJA evidence itself ever does that, the evidence can be enhanced to make it highly credible that it defeats the justification for belief. Suppose that, as in the previous example, S has the reliable forecaster evidence that it will rain in two days. As before, S is told that S is almost certain to fail to form a justified attitude toward the proposition that it will rain in two days, no matter which attitude S adopts. But now the testifier adds that S is especially likely to fail to have a justified attitude if S believes the proposition. We can call this the NJA* evidence.

When we replace the NJA evidence with the NJA* evidence, the forecast supporting the proposition that it will rain in two days seems to be neutralized by S’s higher-order evidence that belief in the proposition is especially likely to be unjustified. No reason is given for that, but it suggests that S’s inclination to believe is particularly rationally defective. This in turn suggests that another doxastic attitude is rationally better. Yet disbelief and withholding judgment are opposed by the testimony too. Additionally, they are out of keeping with S’s forecast evidence. In this version of the example DD theories seem not allow S to have any justified attitude toward the proposition.

S does have available a justified attitude toward the proposition. Withholding judgment is justified. The reason is that quite generally, withholding judgment on a proposition is epistemically justified in the absence of undefeated evidence for or against its truth.¹² The NJA* evidence denies that withholding judgment on the proposition is justified. But that denial is not a defeater of justification for withholding judgment. Justification for withholding is distinctively negative. Neither evidential support nor any other positive epistemic factor justifies it. What makes withholding judgment the justified attitude toward a considered proposition is the absence of good enough epistemic reason to believe it or to disbelieve it.¹³ In other words, withholding judgment on a proposition is rendered unjustified only by having justification for believing it or for disbelieving it.¹⁴ Having a balance of evidence that sufficiently supports the proposition or its negation would provide this justification. In the NJA* version of our example, S has no such balance of evidence.

S has the NJA* evidence for the proposition that withholding is not justified. That is support for this proposition about withholding. It does not support either that it will rain in two days or that it will not. Only such support is justification for belief or disbelief. Only such justification could prevent withholding from being justified.

A new problem might seem to arise by strengthening S’s evidence against the justification of withholding judgment. Suppose that S receives tremendously trustworthy testimony that there is very nearly no chance that S is justified in either believing or withholding judgment on the proposition that it will rain in two days. The testimony asserts that S has taken a drug making S particularly prone to form those attitudes without justification, and that disbelief is unjustified too. We can call this evidence NJA**. S’s having the NJA** evidence gives S extremely good reason to think that withholding judgment on the rain proposition is unjustified. This fact might seem to be a defeater of any justification for withholding that S might have, thus making withholding judgment unjustified for S.

The justification for withholding judgment is not subject to defeat.¹⁵ Defeaters defeat support for a proposition. Withholding judgment is not justified by support for any proposition. Evidence that withholding is unjustified does not justify not withholding. Not withholding requires believing or disbelieving the proposition. Justification for taking either attitude requires epistemic reason pro or con. S lacks that. S still has no undefeated evidence favoring either that it will rain in two days or that it will not. The forecast evidence is defeated by the NJA** evidence, with its trustworthy emphatic denial of the justification of belief. S still has no support for the proposition that it will not rain in two days (we can assume that rain in two days is as likely as not, given the rest of S’s rain evidence). The absence of undefeated support justifies withholding judgment.¹⁶ This bears out the implication of DD theories that defeated justification for belief with no new evidence about the proposition’s truth justifies withholding judgment.

Attractive DD theories avoid the two problems that we have investigated. The sort of defeat that DD theories imply remains quite credibly regarded as a factor in epistemic justification.