2. Zetetic accounts

Staffel (Reference Staffel2023) holds that higher-order uncertainty can defeat the doxastic justification of what she calls “terminal” attitudes, which are the types of attitudes adopted as the conclusion of one’s deliberation. Those terminal attitudes that are actually supported by the first-order evidence keep counting as propositionally justified for agents under higher-order uncertainty. But these agents are not in a position to base such attitudes on the evidence in a way that makes them doxastically justified (see Silva Reference Silva2017; Smithies Reference Smithies, Silva and Oliveira2022; Van Wietmarschen Reference Van Wietmarschen2013). For instance, given her uncertainty about the reliability of the test she employed, Amy, the coroner, is no longer doxastically justified in arriving at conclusions about the crime scene on the basis of the results of that test (even if the conclusion that there was O-negative blood at the crime scene remains propositionally justified). In this way, Staffel accounts for the Negative Intuition in terms of defeat of doxastic (but not propositional) justification.

On the assumption that doxastic justification requires propositional justification, Staffel’s view entails that cautious terminal attitudes such as suspending judgment (terminally) are not doxastically justified either. These attitudes are not supported by the original first-order evidence, so, on Staffel’s view, they are not propositionally justified – which means that they are not doxastically justified. Indeed, under sufficiently higher-order uncertainty, it may be that no terminal attitude is doxastically justified (Staffel Reference Staffel2023: 242; also Silva Reference Silva2017).

How can Staffel account for the Positive Intuition that cautious attitudes are often permissible under higher-order uncertainty? Staffel’s answer begins by noting that higher-order uncertainty may call for reopening one’s deliberation, in order to reassess the evidence. While redeliberating, the agent may adopt provisional, transitional attitudes, which reflect their temporary assessment of the evidence at different stages of their reasoning process. These transitional attitudes are different from terminal attitudes constituting the conclusion of one’s reasoning, and can be doxastically justified under higher-order uncertainty, insofar as they properly track the progress of a permissible reasoning process. For example, an agent under higher-order uncertainty may be doxastically justified in adopting a transitional conciliatory attitude that manifests their doubts about what the evidence supports. So, Amy may provisionally reduce her credence that O-negative blood was present at the crime scene.

I will think of reopening one’s deliberation as an inquiring activity. In this way, Staffel resorts to inquiring activities (redeliberating) to explain what attitudes can be doxastically justified for agents under higher-order uncertainty. While no nontransitional attitude can be doxastically justified as long as sufficient higher-order uncertainty remains, agents may be doxastically justified to adopt transitional attitudes. Therefore, Staffel offers a zetetic explanation of the Positive Intuition by appeal to transitional attitudes characteristic of redeliberation.

Palmira (Reference Palmira2024), in turn, has proposed that higher-order uncertainty can require agents to engage in double-checking, which he takes to be rationally incompatible with believing a conclusive answer to the question under investigation. On Palmira’s account, agents under sufficient higher-order uncertainty ought to double-check, and this is why they ought not to take the question at issue to be settled, and therefore should not retain their (conclusive, terminal) beliefs about the answer to that question. Given that double-checking is an inquiring activity, Palmira’s is a zetetic account of the Negative Intuition.

Palmira’s proposal can also accommodate the Positive Intuition, insofar as double-checking is rationally compatible with cautious attitudes like suspension or reducing one’s initial confidence. On top of this, double-checkers can adopt other inquiry-related attitudes, such as hypothesizing or endorsing some answer, which are also compatible with double-checking (Palmira Reference Palmira2020).

Thus, both Staffel and Palmira offer attractive accounts of higher-order uncertainty in terms of inquiry-related attitudes, vindicating what I have called the Negative and the Positive Intuitions. The problem with these views, however, is that these intuitions persist in cases in which no further inquiring activities, be it double-checking or redeliberating, are called for. I will argue that these cases are problematic for zetetic accounts of higher-order uncertainty.

3. The end of inquiry

I grant that zetetic views highlight important connections between higher-order uncertainty and inquiry. However, they do not provide a complete account of the epistemic impact of higher-order uncertainty. This is so because engaging in inquiring activities is not guaranteed to resolve the agent’s higher-order uncertainty – and, indeed, further inquiring is not always epistemically required for agents under higher-order uncertainty. There are cases in which higher uncertainty persists despite the fact that the agent is epistemically permitted to put an end to (or not engage in) the relevant inquiring activities. I call these cases higher-order uncertainty at the end of inquiry. My claim is that zetetic views are unable to offer a satisfactory account of the epistemic impact of higher-order uncertainty at the end of the inquiry, that is, when no inquiring activity is called for.

Consider cases of what I will call ineffective inquiring. These are situations in which the agent knows they are not in a position to reduce their higher-order uncertainty through further inquiring activities. Redeliberation and double-checking are not all-powerful, and at some point, they may give out: it can become clear that further engagement in these activities will not improve one’s higher-order uncertainty. An agent may realize that she cannot gain access to the information (or skills) needed to overcome their higher-order uncertainty. For instance, Amy, the coroner, may know that the information required to solve her (higher-order) doubts has been lost forever. If this is so, further redeliberating or double-checking seems pointless, and it is hard to see why there would be an epistemic requirement to engage in them. In particular, it is difficult to vindicate this requirement from the perspective of the consequentialist view about epistemic norms adopted by Palmira (Reference Palmira2024). After all, in these cases, the agent knows that further inquiring will not bring additional epistemic value. Therefore, in this type of situation, the agent will not be subject to consequentialist (epistemic) requirements to keep inquiring.

Arguably, it can also happen that agents are required, for epistemic reasons, to put an end to the relevant inquiring activities before their higher-order uncertainty is resolved (these are cases of inadvisable inquiring). Sometimes, prolonging the relevant inquiring activities may become detrimental to the agent’s epistemic goals – for example, because it would take up cognitive and material resources that would be better allocated to other tasks in order to promote the agent’s overall epistemic goals. That is, further inquiring into a certain question can have epistemic opportunity costs that make it (epistemically) inadvisable. For instance, it could be that redeliberating about the blood tests is inadvisable given Amy’s epistemic goals (say, identifying the culprit), because these goals are better served by focusing instead on other forensic evidence (e.g., fingerprints). Again, from a consequentialist perspective, it seems clear that agents in these situations are epistemically required to put an end to the relevant inquiring activities. Note that this requirement is not practical, but epistemic, in the sense that it is derived from the agent’s epistemic goals.

Moreover, for questions of minor interest, it is surely epistemically permissible not to engage in further inquiry and just adopt whatever (nontransitional) attitude is fitting given one’s limited epistemic position. It is implausible that we are epistemically required to try to improve our epistemic position regarding all questions about which we have higher-order uncertainty, no matter how trivial they are.

I think that these are all cases in which there can be higher-order uncertainty at the end of inquiry. I will focus, however, on what I have called situations of ineffective inquiring, since the case I want to make is particularly strong in relation to them.Footnote ³

4. Persistent higher-order uncertainty

Persistent higher-order uncertainty can remain, as we have seen, at the end of inquiry. The Negative Intuition retains its pull in these cases. It still seems problematic to stick to one’s guns under higher-order uncertainty at the end of inquiry. After all, the agent will still be uncertain about whether their original attitude is actually supported by the evidence. However, at the end of the inquiry, this intuition cannot be explained in terms of requirements to engage in further inquiry, given that in these cases, there are no such requirements. In particular, at the end of the inquiry, there is no requirement to double-check, so in these cases, the problem with retaining one’s original belief cannot be that this conflicts with a requirement to double-check. Thus, Palmira’s (Reference Palmira2024) strategy is not effective here.

Imagine, for instance, that Amy stops double-checking because she realizes that she will never be in a position to solve her uncertainty about the reliability of the test. Since this (higher-order) uncertainty persists, it would be problematic for Amy to insist that there was O-negative blood at the crime scene, relying on the evidence provided by the test. This is a case at the end of the inquiry, in which there are no epistemic requirements to engage in inquiring activities like double-checking. Therefore, one cannot appeal to rational incompatibilities with such requirements in order to explain why Amy’s attitude would be epistemically problematic.

5. Nontransitional attitudes at the end of inquiry

Is any attitude at all doxastically justified under persistent higher-order uncertainty at the end of inquiry? On Staffel’s (Reference Staffel2023) view, such an attitude would have to be transitional. For, on her view, higher-order uncertainty defeats the agent’s doxastic justification to adopt nontransitional attitudes. Remember, however, that agents at the end of inquiry can permissibly put an end to their redeliberation (or perhaps they were not even required to reopen it in the first place). If they do so, the attitudes they form towards the question at issue will be nontransitional. Staffel seems committed to taking any such attitude to lack doxastic justification, as long as sufficient higher-order uncertainty remains.

This is an unpalatable result. The Positive Intuition remains attractive at the end of the inquiry. It seems that agents under higher-order uncertainty at the end of inquiry may still adopt (propositionally and doxastically) justified attitudes concerning the question at issue. These will be nontransitional, conclusive attitudes that reflect the agent’s current grasp of the evidence available, which will be incomplete or limited. For instance, Amy may close her (re)deliberation about the tests by suspending judgment about whether there was O-negative blood at the crime scene.

Perhaps it could be replied that, as long as sufficiently higher-order uncertainty remains, one cannot be epistemically permitted to put an end to redeliberation or double-checking, but only to leave them on stand-by or interrupted. And it could be further argued that, insofar as these inquiring activities cannot be permissibly closed, nontransitional attitudes about the answer to the question at issue will be doxastically unjustified. At most, one would be justified to adopt transitional attitudes regarding such a question.

I think, however, that this reply is unmotivated. Think of cases of ineffective inquiry. Here, it is clear that there are no epistemic reasons or obligations to continue redeliberating, even if the agent keeps being interested in the question at issue (in the sense that it is still included in their intellectual agenda). True, as long as the agent’s higher-order uncertainty remains unresolved, their evidential situation will be limited and imperfect. Yet this does not mean that the agent is not permitted to close their deliberation and form a nontransitional attitude regarding the question investigated. Being in an imperfect epistemic position with respect to some question is not incompatible with being (doxastically) justified to adopt nontransitional attitudes towards that question.Footnote ⁴ We often adopt nontransitional attitudes concerning questions we are uncertain about. In particular, one may suspend judgment or reduce one’s confidence in the answer to questions one is uncertain about. Note that Staffel (Reference Staffel2019) grants that there are nontransitional forms of suspension. This is the type of attitude I have in mind here: it is a conclusive, nontransitional attitude that closes one’s deliberation by reflecting one’s uncertainty about the matter at hand.Footnote ⁵

Consider cases of first-order uncertainty, in which an agent has incomplete (first-order) evidence regarding some question. It can be perfectly fine (epistemically) for this agent to adopt a nontransitional attitude toward that question, for instance, to suspend judgment about its answer. This may be so even if the agent knows that they could get further relevant evidence, say, by visiting the local library. In some cases, the agent is just not epistemically required to keep gathering evidence: they can simply suspend judgment (nontransitionally).

Something analogous happens with higher-order uncertainty. It is often epistemically permissible for agents not to engage in further inquiring activities aimed at resolving their higher-order uncertainty. When this is so, agents may be (both propositionally and doxastically) justified to adopt an attitude that fits properly their imperfect grasp of the evidence. This attitude does not need to be provisional and fluctuating, capturing an intermediate stage of one’s ongoing deliberation, or a preliminary take on the evidence. That is, the relevant attitude does not need to be transitional, but it can rather reflect one’s stable, conclusive (albeit imperfect and limited) grasp of the evidence available. In particular, in cases of ineffective inquiring, the agent knows that their higher-order uncertainty will not be resolved through further inquiring, and that their take on their evidence is not bound to change in the foreseeable future. The agent’s uncertainty about what the evidence supports, may be in these cases, stable and conclusive, and it can, therefore, be properly expressed by a (nontransitional) attitude with which the agent closes their (re)deliberation.

At the end of the inquiry, therefore, agents will not just interrupt their redeliberation, but they may bring it to a close with an attitude properly fitting their persistent uncertainty. Arguably, such attitudes can be doxastically justified. Given that these attitudes are nontransitional, we cannot explain their justification by appealing to the norms of transitional attitudes. In this way, Staffel’s (Reference Staffel2023) zetetic account cannot vindicate the Positive Intuition in cases at the end of inquiry.

6. Responding to imperfectly grasped evidence

I have argued that there are cases, which I have called at the end of inquiry, in which we cannot explain the epistemic impact of higher-order uncertainty in terms of inquiring activities like double-checking or redeliberating. The reason is that, in these cases, higher-order uncertainty persists despite the fact that further inquiry is not required (and perhaps is even inadvisable). Thus, zetetic accounts of higher-order uncertainty, like Staffel’s (Reference Staffel2023) and Palmira’s (Reference Palmira2024), are incomplete.

Is there a more general way of dealing with higher-order uncertainty, which applies as well to cases at the end of inquiry? The view I want to put forward is that higher-order uncertainty can undermine one’s access to the evidence available (González de Prado Reference González de Prado2020). Propositional justification is understood, on this view, as supported by those evidential reasonsFootnote ⁶ one has access to.Footnote ⁷ Thus, higher-order uncertainty can defeat not only doxastic, but also propositional justification, by undermining the agent’s access to some of their original first-order evidence.

My proposal is that the relevant form of access amounts to being in a position to respond competently to the evidence in question.Footnote ⁸ An agent has access to some evidential consideration just in case they are in a position to rely on it competently. Thus, if an agent is only in a position to rely on some evidence in an incompetent, risky way, they do not have access to that the evidence – in the sense that the (propositional) justification of their attitudes is not determined by that evidence, which counts as inaccessible. Agents under higher-order uncertainty may not be in a position to respond to the evidence competently, but only in unduly risky ways. This is how higher-order uncertainty can compromise an agent’s access to the evidence.

I will flesh out the notion of competence in terms of good dispositions, resorting to Lasonen-Aarnio’s (Reference Lasonen-Aarnio2020, Reference Lasonen-Aarnio, Brown and Simion2021, Reference Lasonen-Aarnio2024) analysis of dispositional evaluations. In the view I want to put forward, responding competently to the evidence involves the manifestation of a good, feasible disposition to respond to the evidence. This is a feasible disposition by virtue of which the agent tends to treat considerations as evidential reasons for attitudes only when they actually constitute such evidential reasons. My proposal, therefore, is that an agent has access to some evidence if and only if they are in a position to rely on it by manifesting a good disposition to respond to evidence.Footnote ⁹ Only such accessible evidence contributes to the (propositional) justification of the agent’s attitudes.

When assessing whether an agent has access to some evidence, we are interested in whether it would be possible for the agent to rely on the evidence by means of a good disposition. Thus, the type of evaluation I will focus on is restricted to dispositions that are available in the type of circumstances the agent is in. Lasonen-Aarnio calls these feasible dispositions (2021: 102–105). What counts as feasible depends on the type of agent we take as a reference for competence. There is room for flexibility here. For instance, for some purposes we may be interested in treating as a reference idealized perfect reasoners, while on other occasions we may want to focus on more realistic agents with certain cognitive limitations. Here, I will assume that feasibility is sensitive at least to the informational limitations of the agent.

Evaluations of dispositions assess their performance across relevant counterfactual cases. Whether a disposition is good depends on how it would perform in different relevant instances of the type of situation the agent is in. I will think of relevance in terms of their degree of normalcy, in line with Lasonen-Aarnio (2020; Reference Lasonen-Aarnio, Brown and Simion2021: 100).Footnote ¹⁰ More specifically, I will take relevant cases to include normal cases among which the agent cannot feasibly discriminate, given the type of evidence available.

My view is that a disposition to respond to evidence is good if and only if it is a feasible disposition by virtue of which the agent would tend to treat as evidential reasons, across relevant, normal cases, only considerations that constitute such reasons. An agent has access to some evidence if and only if they are in a position to rely on it by manifesting a good disposition to respond to evidence. I will show now how this form of access can be undermined by higher-order uncertainty.

Let us go back to CORONER. Remember that in that example, Amy is uncertain about whether the test she performed was contaminated. If it were, the test would fail to provide actual evidence supporting Amy’s belief about the crime scene – the evidence apparently offered by the test would be undercut. Should Amy keep trusting the test, she would manifest a disposition to ignore this higher-order uncertainty. In cases in which the test was actually contaminated, this disposition would fail to make Amy rely on actual evidence supporting her attitudes (she would rely on undercut evidence).

Note that, given Amy’s current higher-order uncertainty, situations in which the test was contaminated would be normal enough (Lasonen-Aarnio Reference Lasonen-Aarnio, Brown and Simion2021: 107). In light of Amy’s knowledge that most instruments in the laboratory were contaminated, it would not be surprising if the test she performed was contaminated too: this possibility would not call for a special explanation. Moreover, it is not feasible for Amy, given the type of information she has, to discriminate cases in which her uncertainty is misleading, and the test is reliable from cases in which it is not. I am assuming that relevant cases include normal cases among which the agent’s feasible dispositions cannot discriminate. Therefore, normal cases where the test is contaminated should count as relevant for assessing Amy’s dispositions. These will be relevant, non-marginal cases in which the disposition to keep trusting the test would lead Amy to rely on considerations that do not constitute actual evidence (but merely undercut evidence). In my view, this means that this is not a good disposition to respond to the evidence, insofar as it would not tend to make Amy rely only on actual evidence across relevant cases.

Amy, therefore, is not in a position to trust her test by manifesting a good disposition to respond to the evidence. That is, Amy is no longer in a position to rely competently on the evidence provided by the test she performed. In this way, Amy has lost access to this evidence. Thus, Amy’s grip on the evidence has become more precarious or impoverished. Moreover, Amy has no access to other evidence supporting her initial belief that there was O-negative blood at the crime scene. Propositional justification is, on my view, determined by support from accessible evidence. Therefore, Amy is no longer propositionally justified to retain her original belief, because she has lost access to the evidence that supports it. Higher-order uncertainty has defeated the propositional justification of Amy’s original belief by undermining her access to the evidence supporting it: we can say that her higher-order uncertainty has acted as a dispossessing defeater (González de Prado Reference González de Prado2020). This accounts for the Negative Intuition – the intuition that higher-order uncertainty can make it impermissible to retain the attitude supported by the agent’s original evidence.

What attitude is justified for Amy, given her evidential situation once she loses access to the evidence provided by the test? Amy no longer has access to evidence supporting conclusive beliefs about the presence of O-negative blood in the crime scene. But there are other evidential considerations supporting more cautious attitudes. For instance, she can suspend judgment on the basis of the facts that she is uncertain about the reliability of the test and that she lacks further evidence regarding the matter at issue. These facts constitute evidential reasons for suspension. Amy can suspend on the basis of these reasons by manifesting a good, feasible disposition to respond to evidential considerations. In normal cases in which Amy has this kind of higher-order uncertainty, this disposition would lead her to rely only on considerations that are actually reasons for her attitudes. So, Amy is in a position to rely competently on these reasons for suspension. This means that these evidential considerations are accessible to Amy as reasons for suspending. Moreover, Amy has no stronger accessible reasons against suspending (remember, in particular, that she has no access to evidential reasons for belief). Therefore, these considerations justify (propositionally) a cautious attitude like suspending. This vindicates the Positive Intuition: suspension becomes justified after Amy loses access to the evidence supporting her original belief.Footnote ¹¹

The view I am proposing manages, therefore, to account both for the Negative and Positive Intuitions. This account does not depend on any requirement to engage in further inquiry activities. Thus, it has no problem dealing with cases at the end of the inquiry. My proposal offers, in this way, a more general account of higher-order uncertainty cases than that provided by zetetic views like Staffel’s or Palmira’s. Moreover, as I show in the next section, my view can incorporate the insights about the connections between higher-order uncertainty and inquiry highlighted by zetetic accounts.

7. Inquiry and access to the evidence

Higher-order uncertainty, I have argued, can defeat one’s access to the evidence. But, in many cases, there are things one can do to try to defeat the defeating power of higher-order uncertainty and (re)gain access to the evidence. In particular, one can engage in inquiring activities aimed at reducing higher-order uncertainty, for instance, double-checking or redeliberating. If such an inquiry is successful, and one gets rid of higher-order uncertainty, one may then manage to place oneself in a suitable position to respond competently to one’s original evidence.

When assessing whether an agent can rely competently on some evidence, it is important to be clear about the time at which the agent is to make up their mind, exercising the relevant competences. In order to be in a position to manifest competence, one needs to find oneself in appropriate circumstances. It may happen that an agent is not in a position to respond competently to the evidence at some time t₀ but could get to be in such a position at a later time t₁, if they improve their epistemic position in the meantime by engaging in certain courses of action. More specifically, inquiring activities may be needed for agents to get to a position from which they can rely on some evidence competently.

We can see now how my proposal explains the links between higher-order uncertainty and inquiry discussed by zetetic accounts. Under higher-order uncertainty, gaining access to certain evidence may require engaging in inquiring activities like double-checking or redeliberating, in order for agents to dispel their higher-order uncertainty and place themselves in a position to rely competently on the evidence. Thus, agents under higher-order uncertainty will often, although not always, have reasons to further inquire, as a way of securing access to the evidence available.

I agree with zetetic accounts, therefore, that inquiring activities like double-checking or redeliberating are often the appropriate response to higher-order uncertainty. But I do not take these inquiring activities to explain the primary epistemic impact of higher-order uncertainty. Rather, it is because of the defeating effects of higher-order uncertainty that further inquiry is often the right reaction to this sort of uncertainty. In my view, the fact that agents under higher-order uncertainty may lose access to some of their evidence explains why agents in this type of situation are often required to further inquire. This constitutes, I think, a more fundamental account of higher-order uncertainty and its links with inquiry, which can deal adequately with cases at the end of inquiry.