1 Introduction

According to proponents of pragmatic encroachment (PE), practical factors such as the stakes in a given situation can have a bearing on the epistemic propriety of a subject’s belief formation. In this paper, I explore one way to explain PE in terms of zetetic or inquiry-related factors. Defenders of what I call zetetic encroachment maintain that the mechanism that gives rise to PE rests on normative reasons in favour of so-called inquisitive attitudes.Footnote 1 The subject in a high-stakes situation has a special zetetic reason to be curious about the question at hand, and this reason must be taken into consideration when assessing the subject’s epistemic rationality. I argue, however, that such an approach to PE cannot be successful. The fact that some topic is more interesting than another does not entail that there are additional reasons against believing propositions concerning the former topic.

I start by outlining the general idea behind explaining PE in terms of zetetic encroachment (Sect. 2) before introducing the inquisitive attitude view of suspension and how, exactly, it facilitates zetetic encroachment (Sect. 3). In an intermediate step before articulating my objections to zetetic encroachment, I discuss anti-inquisitive attitudes, which yield further promising instances of zetetic encroachment (Sect. 4). However, I maintain that, as soon as one accepts contrastivism about epistemic reasons, the motivation for zetetic encroachment fades away. The reasons in question are reasons to suspend judgement in one way rather than another, but they are not reasons to suspend rather than believe (Sect. 5). Finally, I argue that one can reach a similar conclusion without adopting contrastivism: as soon as one attends to graded inquisitive attitudes, one can again demonstrate that zetetic factors do not encroach on the epistemic rationality of one’s belief formation (Sect. 6).

2 From pragmatic to zetetic encroachment

Consider the following paradigmatic example, which proponents of PE frequently allude to (DeRose, 1992; Stanley, 2005):

Low stakes

Hannah is driving home on a Friday afternoon and intends to deposit a paycheck at the bank just because it would be convenient. But upon noticing long lines at the bank, she considers driving straight home and returning Saturday morning instead. She remembers that the bank has been open on a Saturday in the past, and although she things to herself that it’s possible the bank changed its hours, she believes that it will be open tomorrow and drives home.

High stakes

Hannah is driving home on a Friday afternoon and intends to deposit an important paycheck. If she does not have enough money to pay her mortgage by Sunday in her bank account, Hannah’s very livelihood is on the line. But upon noticing long lines at the bank, she considers driving straight home and returning the next morning instead. She remembers that the bank has been open on a Saturday in the past, and although she things to herself that it’s possible the bank changed its hours, she believes that it will be open tomorrow and drives home.

According to the intuition of proponents of PE, there is a significant epistemic difference between Hannah’s belief formation in Low Stakes and High Stakes. For this paper, I will restrict my attention to the following PE-thesis: the stakes involved in cases like the above can make a difference regarding the epistemic rationality of the subject, where ‘epistemic rationality’ is understood substantively.Footnote 2 A subject is epistemically rational in this sense iff they are properly responsive to their set of epistemic reasons.Footnote 3 Thus, under this perspective, PE takes the following form: while Hannah has sufficient epistemic reasons to believe that the bank will be open tomorrow in Low Stakes, she ceases to possess such sufficient reasons in High Stakes.Footnote 4

Before proceeding, some clarifications regarding the concept of an epistemic reason are necessary. Again, following the authors who defend zetetic encroachment, I will treat epistemic reasons as the right kind of reasons for doxastic attitudes. The distinction between the right kind of reasons (RKRs) and the wrong kind of reasons (WKRs) is a long-standing idea in the literature on the normativity of attitudes.Footnote 5 An RKR R of some attitude φ is characterised by (1) how R is related to the correctness conditions of φ-ing; (2) the distinct motivating force for the subject to φ for the motivating reason that R; and (3) R’s bearing on the attitude-specific form of rationality of the subject. Consider, for instance, admiration. That a person has some admirable features is a reason in favour of admiring that person, which (1) is related to the correctness conditions of admiring and (2) can be a motivating reason for me to admire said person. Moreover, (3) there will be an admiration-specific failure in being insensitive to the admirability of the person in question. In contrast, a monetary incentive to admire the person seems to lack these features: (1) gaining a monetary reward is not related to the correctness conditions of admiration; (2) in normal circumstances, it seems very difficult to admire someone based on such a monetary incentive; and (3) not being responsive to such prudential reasons might make the attitude practically irrational, but it is not an admiration-specific kind of rational failing. Thus, monetary incentives are WKRs for admiring someone. A similar story can be told about beliefs. Evidence that p is an RKR in favour of believing p. After all, (1) it is related to the correctness condition of believing; (2) it is a prime motivating reason to believe p; and (3) being sensitive to evidence clearly plays a role in a belief-specific form of rationality or what I have called epistemic rationality above. Monetary incentives lack those three features.

Hence, the version of PE under investigation in this paper states that the stakes of a given situation can alter the sufficiency of a subject’s RKRs in favour of their believing some proposition. Now, a set of reasons in favour of an option φ counts as sufficient iff they are at least as weighty as the reasons against φ-ing. Thus, a natural place to look for the mechanism that is supposed to explain PE is in the reasons against φ-ing.Footnote 6 For this paper, I will again assume for the sake of argument that reasons against an option can be reduced to reasons in favour of competing options.Footnote 7 In the case of believing p, there appear to be two competing options: disbelieving p and being doxastically neutral – or what one might call suspending judgement as to whether p.Footnote 8 Assuming that the stakes involved in situations of PE could add additional RKRs in favour of disbelieving p, is an extremely contentious premise. After all, similar to believing p, the paradigmatic RKRs of disbelieving p are evidence against p, while practical considerations such as monetary incentives are WKRs. Therefore, the only viable option left to explain PE in terms of an alteration of RKRs seems to be the third doxastic option of suspension. If there is an additional RKR in favour of suspension in High Stakes that can outweigh the RKRs in favour of belief, one would be able to accommodate PE in such a reasons-centred framework.Footnote 9

Therefore, the RKRs of suspension are a critical juncture in this line of reasoning.Footnote 10 It seems plausible – and here, I agree with proponents of zetetic encroachment – that monetary incentives are WKRs for doxastic neutrality. The fact that I will receive a million pounds if I suspend as to whether p does not seem like a consideration that is (1) connected to the correctness conditions of suspension in the appropriate way;Footnote 11 (2) something I could base my suspension on as a motivating reason; or (3) related to the epistemic rationality of my suspension. Therefore, even if Low Stakes and High Stakes differ regarding the practical value or usefulness of Hannah suspending her judgement, this consideration would not be an RKR in favour of suspension and, thus, not what defenders of PE are looking for.

At this point, proponents of zetetic encroachment can make their argument: the relevant difference between Low Stakes and High Stakes does not concern the utility of Hannah suspending her judgement, but it concerns certain zetetic or inquiry-related features of the situation. The fact that Hannah’s livelihood is on the line makes the question ‘Has the bank changed its opening hours?’ much more interesting to Hannah than in Low Stakes. The question becomes a topic that is much more worthy of inquiry.Footnote 12 Now, if suspension were an attitude that is sensitive to these kinds of differences, one could explain the PE phenomenon in terms of zetetic encroachment. In High Stakes, Hannah has an additional or stronger RKR in favour of suspension, which explains why she is irrational in believing that the bank did not change its opening hours.

3 Suspension as an inquisitive attitude

One of the most prominent analyses of suspension in the literature provides a straightforward case in favour of the above take on the RKRs of the third doxastic option. According to Friedman’s analysis, suspension is an inquisitive attitude and, therefore, tightly linked to inquiry and zetetic factors.Footnote 13 In this section, I introduce Friedman’s account of the relationship between inquiry, inquisitive attitudes, and belief. Thereafter, I demonstrate that RKRs in favour of inquisitive attitudes could explain PE. Finally, before moving on to the discussion of the limits of Friedman’s account, I defend zetetic encroachers from an objection that one might raise at this point.

In her seminal work on the relationship of inquiry and belief, Friedman (2017b), 2019) argues for the following position: in order to engage properly in an inquiry into some question Q, a subject has to have an inquisitive mindset concerning Q. Inquiry is not the mere performance of certain bodily motions or mental actions; rather, it is goal-directed activity. Hence, inquiry proper consists of a subject putting Q on their research agenda and adopting the aim of finding an answer to Q. Now, Friedman continues, this inquisitive mindset can be further analysed. It amounts to the subject taking up an inquisitive attitude towards Q – an attitude that is:

  1. (1)

    directed at the question Q rather than at some proposition (question-directedness);

  2. (2)

    amounts to having Q open or unanswered in one’s thought (doxastic openness); and.

  3. (3)

    includes the aim of answering Q (motivational element).

Consider, for instance, curiosity, which is the paradigmatic example of such an inquisitive attitude (Whitcomb, 2010). First, while one might sometimes talk about being curious about certain objects or subject matters, a distinct form of curiosity seems to be directed at puzzling questions (cf. Dover, 2023). Second, it seems strange to be properly curious about some question while already having a firm belief in one of the answers to said question. If I am curious about whether the butler is the murderer, it would be odd if I already believed that the gardener did it. Finally, being curious about a question involves asking it, so to speak. Curiosity includes having a positive stance on whether to inquire into the issue further. One might spell this motivational element out in conative or affective terms, either as amounting to a form of desire towards answering Q or as merely a pro-attitude towards being in a position to answer Q.Footnote 14

Due to the first two of the above characteristic features, Friedman maintains that inquisitive attitudes such as curiosity are intimately linked to the third doxastic option of suspension. First, suspension is also directed at questions rather than propositions.Footnote 15 Second, having Q open in one’s thought is nothing but the sort of doxastic neutrality that authors wish to refer to when using ‘suspension’. Suspension, then, can be seen as the most general inquisitive attitude. Thus, Friedman’s position culminates in the following biconditional claim: a subject puts a question Q on her research agenda iff she suspends judgement about Q.

In order to see how such a take on suspension could be the basis for zetetic encroachment, one must turn towards the RKRs of inquisitive attitudes. I maintain that the RKRs of inquisitive attitudes, such as curiosity, are precisely the kind of considerations zetetic encroachers are looking for, namely facts about the extent to which a question is interesting. Such facts are (1) clearly related to the correctness conditions of curiosity. Questions merit or call for curiosity by some subject to the degree that they are interesting to that subject. Furthermore, (2) one can clearly become curious about a subject matter for the reason that it is interesting. Finally, (3) there appears to be a special sort of rational failing if one is curious about a boring topic or lacks an adequate amount of curiosity towards interesting ones. Therefore, given that High Stakes contains an additional RKR in favour of inquisitive attitudes, Hannah has an additional RKR in favour of suspension. This additional reason to be curious about the bank’s opening hours explains the PE-specific shift between Low Stakes and High Stakes.

Are there any other RKRs in favour of inquisitive attitudes? One might be concerned, for instance, that monetary incentives can be RKRs in favour of inquisitive attitudes. After all, many scientists and explorers seem to become curious about a subject matter (at least in part) due to the fact that there is a monetary incentive to do so, such as my employer instructing me to investigate some topic. Since, as I argued in Sect. 2, monetary incentives are no RKRs of the third doxastic stance, one might argue that Friedman’s account must be rejected from the start. However, even in the above cases, one does not receive a monetary incentive simply for becoming curious. Instead, one gets rewarded for inquiring into the topic. This latter fact, I maintain, makes the research field more interesting, that is, the degree to which a subject matter is interesting to the subject can be altered by monetary incentives. Hence, even in such cases, it is the degree to which a question is interesting that works as an RKR, not the monetary incentives themselves.Footnote 16 The same thesis seems to hold true for moral reasons to inquire: if I owe it to another person to engage in an inquiry into some question, that question becomes more interesting to me and, thus, calls for an inquisitive attitude.Footnote 17 Therefore, zetetic encroachment does also explain certain forms of moral encroachment in that moral considerations can alter the RKRs in favour of the third doxastic stance.Footnote 18 Finally, one might argue that the prospect of succeeding in one’s inquiry also counts as an RKR in favour of inquisitive attitudes: that one’s inquiry will be fruitful and yield epistemic gains for the subject is an RKR in favour of inquisitive attitudes.Footnote 19 Thus, zetetic encroachment could also explain the puzzling effects of learning about forthcoming or easily available evidence from Schroder (2012b). Learning about such evidence, Schroder argues, is a normative reason against believing. However, it is also indicative of the fact that further inquiry into the matter will produce more epistemic goods. Hence, the zetetic encroacher can explain Schroder’s observation in terms of an RKR in favour of inquisitive attitudes.Footnote 20 In going forward, I will restrict my attention to facts about the interestingness of a topic. However, my arguments against zetetic encroachment extend to these other reasons as well.

Before moving on, I defend zetetic encroachers from a potential concern.Footnote 21 One central assumption of explaining PE in terms of RKRs in favour of suspension is that whatever ‘suspension’ denotes must be in the right sort of conflict with belief and disbelief. Consider, for instance, accounts according to which ‘suspension’ denotes a mental action that occurs prior to making up one’s mind about a subject matter (McGrath, 2021a, b; Crawford, 2022) or afterwards (Wagner, 2022). Such a mental action can, at least sometimes, be performed intentionally and it should be sensitive to practical considerations. In High Stakes, Hannah might have an RKR in favour of postponing her judgement regarding whether the bank has changed its opening hours. It might be beneficial for her to wait before making up her mind on that question until she receives further evidence. This phenomenon, however, is distinct from PE. As McGrath (2021a, 474 f.) has already noted, the epistemic justification of one’s beliefs seems to be unaltered, even if they are the product of an unwise lack of suspension in the sense of waiting. If I receive a monetary incentive to postpone my deliberation about a subject matter, and I still go through with making up my mind about that subject matter, the epistemic rationality of the resulting beliefs should not be altered. The reward is an RKR in favour of one mental action, namely waiting, and an RKR against another mental action, namely engaging in judging whether something is the case. Yet, it does not count as an RKR against believing itself.Footnote 22 Now, one might argue that the inquisitive attitude view of suspension is in the very same spot. In contrast to settled attitudes, such as beliefs and disbeliefs, inquisitive attitudes are unsettled and, therefore, pertain to a different stage of deliberation.Footnote 23

I maintain that zetetic encroachers have some resources to withstand this objection. While waiting or postponing must happen before one enters into doxastic deliberation, the same does not hold for inquisitive attitudes. The questions ‘Is Q interesting?’ and ‘Is p the case?’, where p is an answer to Q, can be asked simultaneously. Hence, in contrast to prior mental actions, inquisitive attitudes can prima facie rival belief and disbelief as deliberative options. While it does not make sense to regard an RKR in favour of believing as an RKR against the mental action of postponing, it might be perfectly acceptable to treat it as an RKR against being or, rather, staying curious. The mere fact that the former are settled attitudes, while the latter are unsettled ones, does not strike me as sufficient to rule out such a weighing of reasons.Footnote 24 Thus, there is an important disanalogy between McGrath’s view and Friedman’s, and, without further argument, one cannot extend the case against a postponing or waiting explanation of PE to zetetic encroachment.

4 Inquiry-ending suspension and anti-inquisitive attitudes

Ever since being proposed, Friedman’s biconditional claim has faced a lot of criticism in the literature, and scholars have envisaged objections to both of its directions. For this paper, the claim that one can suspend judgement on an issue only by putting that issue on one’s research agenda is more important.Footnote 25 As many scholars have observed, there are many cases in which one suspends judgement on a question without putting it on one’s research agenda.Footnote 26 Sometimes suspension works as an inquiry-ending attitude. For instance, in cases wherein I learn that finding an answer to my original question is beyond my epistemic capabilities, it would be odd to react with anything but the third option of doxastic neutrality. However, this doxastic openness does not seem to be accompanied by any sort of pro-attitude towards further investigating the question. For instance, it would have been odd for Kant to proceed by writing essays on speculative metaphysics after articulating the bounds of sense and the limits of human cognition which block that very research project from bearing fruits. In this section, I present the upshots of such an anti-inquisitive form of suspension for the thesis of zetetic encroachment. As Lord (2020) and Lord and Sylvan (2021) anticipate, there might be even more ways in which the degree to which a question is interesting can encroach on the epistemic. Furthermore, by considering these cases of zetetic encroachment, my diagnosis of what is going wrong in zetetic encroachment should become much more apparent.

If one wants to remain aligned with Friedman’s thesis that one can understand the form of doxastic neutrality which is in proper competition with belief and disbelief in terms of inquisitive attitudes, one must qualify her theory to account for the cases of anti-inquisitive suspension. The most straightforward way to do so is by distinguishing between two kinds of suspension, namely a pro-inquisitive and an anti-inquisitive suspension (Lord, 2020; Lord & Sylvan, 2021). Friedman’s theory is only true for the former. The latter, on the other hand, can be understood in terms of an inquiry-opposed analogue to Friedman’s inquisitive attitudes. These anti-inquisitive attitudes towards some question Q can, thus, be understood as:

  1. (1)

    being directed at Q rather than at some proposition (question-directedness);

  2. (2)

    amounting to having Q open or unanswered in one’s thought (doxastic openness); and.

  3. (3)

    inhibiting the inclusion of the aim of answering Q (motivational element).

The first two characteristic features work just like in the case of inquisitive attitudes. Anti-inquisitive attitudes only differ in their last feature: instead of coming with a conative or affective pro-attitude towards inquiring into Q, they amount to a con-attitude towards doing so. Thus, one might describe the form of suspension under investigation as closed-minded, in that it is a form of agnosticism in which the subject does not aim to improve their epistemic standing concerning Q.Footnote 27

On this picture, instead of three competing options in one’s theoretical deliberation, there are actually four options: one can believe p, disbelieve p, pro-inquisitively suspend judgement as to whether p, and anti-inquisitively suspend judgement as to whether p. Now, if the RKRs in favour of anti-inquisitive attitudes do not completely align with the RKRs in favour of inquisitive ones, one should expect even more zetetic encroachment phenomena. After all, analogous to the analysis of High Stakes, the RKRs in favour of the last of the above options might be sufficient to outweigh the RKRs in favour of belief, thereby making an otherwise epistemically rational belief irrational.

The question remains as to what the RKRs in favour of anti-inquisitive attitudes are. Presumably, they mirror the RKRs in favour of inquisitive attitudes discussed in the previous section. Hence, the first set of RKRs that comes to mind is the degree to which a topic is uninteresting or unimportant to the subject. For instance, the question of what kind of breakfast Julius Caesar had on the ides of March 44 BC calls for an anti-inquisitive attitude (Snedegar, 2017, p. 119). Furthermore, there might be moral considerations which make a topic uninteresting in this sense. For instance, intimate social relationships might call for an anti-inquisitive attitude towards certain questions about my partner.Footnote 28 Similarly, one could maintain that a right to privacy can make it the case that certain topics are off limit to one’s inquiry.Footnote 29 Finally, as demonstrated by the example of Kant above, negative prospects of a successful inquiry might also be RKRs in favour of an anti-inquisitive attitude.Footnote 30 Again, my arguments in the subsequent sections also extend to these kinds of cases.

Lord and Sylvan (2022) maintain that one prominent puzzle in the literature on the relation of epistemic and zetetic normativity can be understood as a case of zetetic encroachment via RKRs in favour of anti-inquisitive attitudes. Consider the following case presented by Friedman (2020).

4.1 Chrysler count

Martha is in the window business, and it has become important to her to know how many windows the Chrysler Building has. Given her close proximity to the building, she decides the best method of finding out is [by] going to Grand Central Station and counting. This task takes a full 90 min of her time and concentration, during which she fails to extend her knowledge about other matters. (Lord & Sylvan, 2022, p. 158).

According to Friedman, there is tension between epistemic and zetetic norms in cases such as Chrysler Count. Zetetic norms seem to require Martha not to come to believe all sorts of facts that her evidence would also support, such as the fact that the car in front of her is blue. However, when it comes to epistemic norms, Martha seems permitted to come to believe that the car in front of her is blue. Now, Lord and Sylvan maintain that, given their theory, this last assessment turns out to be mistaken: Chrysler Count is a case of zetetic encroachment in which the RKRs in favour of anti-inquisitive suspension outweigh the reasons in favour of belief. Therefore, although Martha may be in a position to know that the car in front of her is blue, the fact that this issue is much more uninteresting or unimportant to her than the number of windows can encroach on the epistemic evaluation of her belief by being an RKR in favour of an anti-inquisitive attitude that outweighs the evidence-based RKR in favour of belief. Hence, pace Friedman’s assessment, Martha is not epistemically permitted to believe that the car in front of her is blue.Footnote 31

To conclude, by attending to the limits of Friedman’s original account of suspension, one can find further ways in which the thesis of zetetic encroachment could work. For this paper, it does not matter whether Lord and Sylvan’s analysis of Chrysler Count is a good solution to Friedman’s puzzle.Footnote 32 The main takeaways from this section are: (1) given an inquisitive attitude account of suspension, we should expect there to be different ways to suspend judgement; moreover, (2) if anti-inquisitive attitudes work in parallel with inquisitive ones, there should be further instances of zetetic encroachment aside from cases of PE.

5 Objection I: Epistemic contrastivism

As witnessed in the previous section, an inquisitive attitude account of suspension is forced to accept some form of plurality of ways to suspend judgement. In contrast to traditional epistemology, the doxastic option space does not contain three options but four ({believe; disbelieve; pro-inquisitively suspend; anti-inquisitively suspend}). In this section, I argue that the motivation of zetetic encroachment can be undermined, given an independently motivated thesis about the nature of epistemic reasons. Under the assumption of contrastivism about epistemic reasons, it strikes me as very apparent that the degree to which a topic is interesting is only a reason to inquisitively suspend rather than anti-inquisitively suspend. It is not a reason to inquisitively suspend rather than believe, and, therefore, there is no zetetic encroachment. I start by outlining and shortly motivating contrastivism before turning to my assessment of RKRs of inquisitive and anti-inquisitive attitudes in such a theory of normative reasons.

Reasons contrastivism is the thesis that normative reasons do not speak in favour of an option tout court, but only relative to a specific competing option.Footnote 33 Thus, a reason might support an option φ in comparison to an option ψ, but it might not do so in comparison to another option χ. Given that the weight of reasons is, therefore, relativized to these pairwise comparisons, one has to qualify one’s definition of a sufficient reason as well: an option counts as being supported by sufficient reasons iff it is not outweighed in any of the pairwise comparisons with competing options. Epistemic normativity and the weighing of epistemic reasons are seen as one prime application of this conception of normative reasons. After all, to explain the phenomenon of prohibitive balancing – the fact that, in the case of evidential ties, neither believing nor disbelieving are rational options – contrastivism about epistemic reasons is a very promising position.Footnote 34 Thus far, however, it has only been formulated regarding an option space containing three members. As Snedegar (2017) and Tucker (forthcoming) argue, accepting that evidence that p can be both a reason in favour of believing p rather than disbelieving p or suspending judgement on p, as well as a reason in favour of suspending rather than disbelieving can help circumvent the many puzzles of evidential ties. Or, as I recently proposed, one can achieve the same results by arguing that evidence is a reason to believe p rather than disbelieve p, but not a reason to believe p rather than suspend as to whether p (Vollmer, 2024). Both ways of construing epistemic reasons are independently motivated.

The question remains as to what happens to the contrastivist pictures if one distinguishes between two ways to suspend as to whether p is the case. First, I assume that the general method of weighing epistemic reasons above does not change dramatically by distinguishing the two kinds of suspension. That is, in Snedegar’s and Tucker’s view, evidence will still count as a reason to suspend as to whether p, be it inquisitively or anti-inquisitively, rather than disbelieve p. Similarly, in my view, evidence that p will not count as a reason in favour of belief rather than suspend, either way. Second, and more importantly for my argument, the RKRs of inquisitive attitudes I have discussed up to this point naturally fall into either of the contrastivist proposals as the reasons to suspend one way rather than the other. The fact that some questions under investigation are extremely interesting is clearly a reason to suspend in an open-minded, pro-inquisitive manner rather than in a closed-minded, anti-inquisitive one. Hence, one can do justice to the basic motivations driving zetetic encroachment by treating the interestingness of a topic as an RKR in favour of one way to suspend judgement rather than another.

However, the degree to which a topic is interesting no longer looks like a plausible reason to suspend inquisitively rather than to believe. Hence, despite allowing for these additional RKRs to make some difference in the outcome of one’s theoretical deliberation, they do not come with the upshots envisaged by zetetic encroachers. In High Stakes, Hannah has an additional RKR in favour of inquisitively suspending judgement on the question rather than doing so anti-inquisitively. Yet, since this RKR does not amount to a reason against believing, the zetetic factor at play is incapable of explaining PE. The same result occurs concerning the cases from the previous section, such as the uninteresting proposition about Ceasar’s meal plan. The fact that this topic is unimportant to me is an RKR in favour of anti-inquisitive suspension rather than inquisitive suspension; however, it is not an RKR in favour of anti-inquisitively suspending rather than believing. This latter pairwise comparison will be determined by other factors, such as my epistemic standing concerning answering the respective question.

To conclude, as soon as one adds some contrastivist resolution to zetetic encroachment, any intuitive motivation that this position seems to have fades away. The claim that the interestingness of a topic can be an RKR in favour of an attitude that is in the right sort of competition with belief and disbelief is not false but imprecise, and this impreciseness leads some scholars to endorse zetetic encroachment. As soon as one realises that one is only confronted with an RKR to suspend one way rather than the other, one should drop this claim.

6 Objection II: Graded inquisitive attitude

In this section, I present an argument that establishes a similar conclusion to the line of thought from the previous section without relying on the assumption of contrastivism. Instead, I base my reasoning on the observation that inquisitive attitudes, such as curiosity, typically come in degrees. Here are the outlines of my rationale:

  1. 1.

    Inquisitive attitudes come in a gradable form.

  2. 2.

    Any degree of inquisitive attitude counts as a form of suspension.

  3. 3.

    What differs between PE cases, such as Low Stakes and High Stakes, is the degree of inquisitive attitude which is fitting towards the question of the bank’s opening hours.

  4. 4.

    The weight of RKRs in favour of the fitting degree of inquisitive attitude stays the same across cases.

  5. 5.

    Thus, the reasons to suspend based on degrees of inquisitive attitudes stay the same across these cases as well. Therefore, there is no zetetic encroachment.Footnote 35

I start by outlining my view of graded inquisitive attitudes, which incorporates a defence of the first two premises of this reasoning (6.1). Afterwards, I go through the remaining three steps to make my case against zetetic encroachment (6.2). Finally, I turn towards one possible rejoinder on the side of zetetic encroachment, i.e., the idea that there are flat-out inquisitive attitudes besides the graded ones. I maintain that this defensive manoeuvre has little prospect of succeeding (6.3).

6.1 Graded inquisitive attitudes

So far, inquisitive attitudes have been conceived of as an all-or-nothing matter: either one is curious towards some question, or one is not. However, such a treatment strikes me as distorting the phenomenon under discussion: paradigmatic inquisitive attitudes, such as curiosity, are gradable in that one can speak of them in a comparative fashion. For instance, I am more curious about many philosophical questions than I am about the question of the number of pencils on my desk. I presume that any satisfactory theory of inquisitive attitudes should provide an account of how this comparative talk works and how degrees of inquisitive attitudes must be understood. In this subsection, I posit my preferred account of graded inquisitive attitudes. Afterwards, I identify some of the downsides of its main rival. At the very least, opting for an alternative conception of graded inquisitive attitudes does not seem to be a promising proposition for the defenders of zetetic encroachment.

How can one square graded forms of inquisitive attitudes with Friedman’s conception of them? As a short reminder, I listed three characteristic features (Sect. 3). These attitudes are (1) question-directed, (2) doxastically open, and (3) have a certain pro-inquisitive motivational profile. I maintain that the most plausible way to extend such a perspective on inquisitive attitudes to graded ones is by keeping the first two elements fixed while allowing the third to come in degrees. At least for the most paradigmatic inquisitive attitude – curiosity – only this way of construing the matter achieves appropriate results. First, the question-directedness of inquisitive attitudes is clearly not the feature one should focus on at this point. An attitude is either directed at a question or it is not; there is no way to introduce degrees into this aspect of inquisitive attitudes. Second, doxastic openness might come in a gradable form. However, the degree to which a question is open in my deliberation does not seem to track the semantics of ‘more curious’. Consider the example from above: I do not want to say that the question of pencils on my desk is less open in my mind than certain philosophical questions. Whatever degrees of doxastic openness might amount to (see below), I might even have a higher degree of doxastic openness concerning the former. Instead, through comparative usages of ‘curiosity’, one wants to express a divergence concerning the third feature: I am much more disposed to inquire into some philosophical questions than to count the number of pencils on my desk right now. The affective or conative dimension of inquisitive attitudes is the most promising route to extend Friedman’s conception to degrees: if I am more curious about some question Q than about some other question Q*, the aim of answering Q ranks higher on my research agenda than answering Q*. Put differently, my desire to answer Q is stronger than my desire to answer Q*.

If this account of graded inquisitive attitudes is correct, one can deduce the following implication for my argument in the next subsection: Given Friedman’s original motivation to view suspension as the most general inquisitive attitude, one should also regard degrees of inquisitive attitudes as ways of suspending judgement. After all, the aspect of inquisitive attitudes that puts them on the table as being related to suspension is their requirement of doxastic openness. Since the flat-out conception of inquisitive attitudes that I have discussed up to this point does not differ in this regard from graded ones, any non-zero degree of inquisitive attitude towards some question Q should amount to suspending judgement about Q. If p is an answer to Q, it is just as odd to believe p and to be curious about Q than it is to believe p and be somewhat curious about Q. Correspondingly, by the very reasoning posited by zetetic encroachers, any RKR in favour of a degree of inquisitive attitude should be an RKR in favour of suspension. This result will become important during the subsequent steps of my argument.

Before advancing to these further stages of my reasoning, however, I turn towards an objection that is repeatedly levelled at my line of thought. Even if it does not track the comparative ‘curiosity’ talk, one might still want to adopt a conception of inquisitive attitudes according to which the second dimension of doxastic openness comes in a gradable fashion as well.Footnote 36 Although it is certainly conceivable, I maintain that such a position has several problematic aspects, especially if it is posited by a defender of zetetic encroachment. First, note that all I need for my argument to work is that any degree of inquisitive attitude counts as a way of suspending judgement. Therefore, to avoid my conclusion, one must construe doxastic openness in a belief-compatible fashion. If every degree of doxastic openness concerning a question Q is incompatible with having a flat-out belief in an answer to Q, then the current worry does not affect my strategy in this section. After all, it would still be the case that any degrees of inquisitive attitude should count as a way to suspend judgement based on the very same reasoning Friedman posited in the first place. Thus, to drive a wedge in my reasoning against zetetic encroachment, at least some degrees of doxastic openness have to be compatible with belief.

A straightforward way to spell out gradable doxastic openness while avoiding the pitfalls of belief incompatibility is in terms of credences. The degree of doxastic openness featured in a degree of inquisitive attitude is the degree to which the subject’s credences on the issue approximate 0.5. If I am slightly wondering whether it will rain today, my credences towards a positive and a negative answer to said question can come quite far apart from 0.5, say, 0.8 and 0.2, respectively. If I am deeply invested in the question, however, my degree of doxastic openness amounts to credences that are closer to neutrality, say, 0.6. and 0.4. Now, in order to transition from this view of credences to Friedman’s view of suspension as a flat-out attitude, one can simply follow the Lockean idea of thresholds: a credence X above a certain threshold TB counts as believing, and a credence below a threshold TDB counts as disbelieving. Any credence in between amounts to suspending judgement. If one combines this theory with the above account of graded inquisitive attitudes, one can achieve the desired result: high degrees of doxastic openness above a threshold TS are incompatible with belief and do count as a form of suspension, while low degrees of doxastic openness are compatible with belief and, thus, do not count as suspension. Therefore, only RKRs in favour of degrees of inquisitive attitudes above TS would be RKRs in favour of suspension.

I see several problems with such a view on graded inquisitive attitudes. First, the assumption of Lockeanism is at least controversial. Many scholars oppose such a strict connection between flat-out doxastic attitudes and graded ones.Footnote 37 Second, while being a less-discussed issue, the literature on the RKRs of credences seems to converge on evidentialism concerning credences.Footnote 38 However, according to the above account, at least some RKRs in favour of credences will be based on zetetic considerations. Third, and relatedly, the above account commits a proponent of zetetic encroachment to the idea that there is a PE phenomenon concerning credences. However, credal PE is a much more controversial position than PE regarding flat-out belief.Footnote 39 Thus, any defender of zetetic encroachment along these lines must buy into another controversial assumption.

Finally, one has to keep the following in mind: any degree of doxastic openness above TS still counts as a form of suspension. Thus, my argument in the next subsection still applies to any degree of inquisitive attitude that requires openness above TS. As I demonstrate at the end of the next subsection, this position comes with the odd conclusion that zetetic encroachment does not itself come in degrees but that it is an on-and-off mechanism. Hence, even if one is willing to buy into all these downsides of such a conception of graded inquisitive attitudes, one will not end up with the envisaged version of zetetic encroachment that could explain PE.

6.2 Reasons in favour of graded inquisitive attitudes

To recapitulate, up to this point, I have argued for the first two premises of my contention: (1) one can and should conceive of inquisitive attitudes in a gradable manner, and (2) each of these attitudes counts as a way of suspending judgement. In this subsection, I introduce the remaining pieces of my case against zetetic encroachment. The focal point of this reasoning is the insight that Low Stakes and High Stakes only differ in the fitting degree of inquisitive attitude and not in the weight of RKRs favouring the fitting degree.

To make this point explicit, it makes sense to start from the plausible insight that graded inquisitive attitudes are sensitive to the same kinds of considerations as the flat-out variant, which came up in Sect. 3. These were, primarily, facts about the interestingness of the question at hand. Thus, the RKRs of graded inquisitive attitudes should also be those kinds of considerations. Now, given that these are the RKRs of inquisitive attitudes and that the RKRs of attitudes are related to their conditions of fittingness or correctness (Sect. 2), one can deduce some insights about the fittingness conditions of these attitudes as well. A degree of inquisitive attitude towards some question Q is fitting iff it matches the degree to which Q is interesting. Thus, in Low Stakes, the question of whether the bank changed its opening hours merits a minor degree of inquisitive attitude, say X. In High Stakes, the same question calls for a higher degree, say Y.

Now, I turn to the – perhabs surprising – implication of this consideration.Footnote 40 According to any plausible theory about the way RKRs and fittingness conditions are connected, Hannah has stronger RKRs to take up an inquisitive attitude of degree X in Low Stakes than she has to take up an attitude of degree Y. After all, ceteris paribus, X would be the rational degree to take up, while having an inquisitive attitude of degree Y would be irrational. Conversely, in High Stakes, Hannah has a stronger RKR to adopt an inquisitive attitude of degree Y than to adopt an attitude of degree X. However, and this is crucial, the RKRs for assuming an inquisitive attitude of degree X in Low Stakes do not seem to differ from the RKRs for assuming an attitude of degree Y in High Stakes. Both are the fitting degrees of inquisitive attitudes, and, thus, the RKRs in favour of each of them should not differ.

However, following the result from the previous subsection, each of these degrees of inquisitive attitudes counts as a way to suspend judgement. Furthermore, given the idea at the centre of zetetic encroachment, an RKR in favour of either of these inquisitive attitudes counts as an RKR to suspend judgement. In that case, Hannah’s RKRs in favour of suspension, which are based on her RKRs for having an inquisitive attitude of degree X in Low Stakes, should be just as weighty as her RKRs in favour of suspension, which are based on her RKRs for having an attitude of degree Y in High Stakes. Therefore, the zetetic considerations in paradigmatic cases of PE do not influence the epistemic rationality of the subject’s belief formation. To conclude, as soon as one turns towards a graded conception of inquisitive attitudes, zetetic encroachment ceases to be a plausible thesis.

Before moving on, I revisit the objection from the previous subsection. Assume that doxastic openness comes in degrees, and only degrees of inquisitive attitudes above a certain threshold TS count as suspension. Assume further that X < TS and Y > TS. Then, the RKRs in favour of the fitting degree of inquisitive attitudes in Low Stakes do not speak in favour of suspension, while they do so in High Stakes. Thus, one might argue that, given that one introduces such a threshold, one can retain zetetic encroachment despite my shift to graded inquisitive attitudes. Nevertheless, as I have already indicated, this manoeuvre is incapable of doing justice to the phenomenon of PE in its entirety. After all, if one compares High Stakes with an even more dire situation in which someone threatens to kill Hannah’s family if she does not have enough money in her bank account, one would expect it to be even harder for her to come to a rational belief. The stakes are higher; thus, she will require even more evidence to count as rational. To put it in terms of zetetic encroachers, the issue of the bank’s opening hours becomes even more interesting, meriting a degree of inquisitive attitude Z with Z > Y. Yet, by the threshold mechanism introduced above, there should not be any difference concerning these two situations: both merit a degree of curiosity above TS; thus, both inquisitive attitudes count as ways of suspending judgement. I maintain that this shortcoming is an undesirable theoretical outcome. In combination with the list of downsides from the previous subsection, I regard this appeal to belief-compatible inquisitive attitudes as a purely evasive manoeuvre by zetetic encroachers, which leaves their position in a very rough spot.Footnote 41

6.3 Inquisitive dualism to the rescue?

Even if degrees of doxastic openness are not a promising line of response on the zetetic encroachers’ side, there might be another strategy of response on their behalf. After all, although there is a strong argument against zetetic encroachment via graded inquisitive attitudes, there might nonetheless be an encroachment phenomenon that works via flat-out inquisitive attitudes. In other words, if one becomes an inquisitive dualist and endorses the idea that there are both graded and flat-out inquisitive attitudes, one might be able to rescue zetetic encroachment. Since many scholars defend a form of doxastic dualism according to which credences and beliefs are irreducible to each other, one might opt for a similar position concerning inquisitive attitudes.Footnote 42 In this case, as long as the RKRs in favour of flat-out inquisitive attitudes are weightier than the RKRs in favour of graded inquisitive attitudes, the encroachment mechanism from Sect. 3 still works since there will be weightier RKRs in favour of suspension in High Stakes than in Low Stakes. However, I regard both aspects of this rejoinder as problematic: inquisitive dualism is on a much worse footing than its doxastic cousin, and the claim about the relative weight of RKRs is purely ad hoc.

A common objection to doxastic dualism centres around redundancy: if flat-out doxastic attitudes and credences perform the very same cognitive function, why do individuals have both of them? In response to this redundancy challenge, defenders of dualism attempt to highlight some differences between the function of the respective attitudes. For instance, one might argue that flat-out beliefs are special in that one relies upon them in practical deliberation. An upshot of this divergence in functions between flat-out and graded doxastic attitudes concerns their RKRs: if they perform different functions, they should also be sensitive to different kinds of considerations. Statistical evidence is often cited as such a factor; it counts as a perfectly acceptable epistemic reason to adjust one’s credences, yet it does not suffice to rationalise beliefs.Footnote 43 Inquisitive dualists, on the other hand, do not seem to have such a principled way to demarcate the role of graded and flat-out inquisitive attitudes. At the very least, the burden of proof lies with them to come up with a functional difference between these two varieties of inquisitive attitudes to avoid a redundancy objection. Furthermore, in contrast to doxastic dualists, an inquisitive dualist does not think that these attitudes are sensitive to different kinds of considerations. Instead, as far as the preceding rejoinder of zetetic encroachment goes, those attitudes are sensitive to the very same kinds of reasons and only differ regarding the weight of those reasons. However, besides making zetetic encroachment work, there does not seem to be any functional difference between those attitudes that would be accompanied by this shift in weight. Hence, I content that the case for inquisitive dualism is much worse than the case for doxastic dualism.

Furthermore, and somewhat relatedly, even if one buys into the idea of a duality of inquisitive attitudes, there does not seem to be any positive motivation for the second claim above, namely the thesis that the reasons in favour of flat-out inquisitive attitudes are weightier than the ones in favour of graded ones. One might even argue that such a comparison does not make sense since flat-out and graded attitudes of the same kind are usually not in the right sort of competition with each other. After all, scholars usually refrain from weighing the reasons in favour of credences and flat-out beliefs against each other. At the very least, the thesis is completely ad hoc. Besides retaining zetetic encroachment, I cannot think of any other application this claim should have.

7 Conclusion

Although it is an interesting and prima facie straightforward way to approach PE, the preceding discussion brought many problematic aspects of zetetic encroachment to light. First, as soon as one becomes aware of the need to add different ways of suspending judgement to one’s theories to make sense of anti-inquisitive instances of suspension, contrastivism about epistemic reasons sheds light on the shortcomings of zetetic encroachment. The reasons in question seem to speak in favour of suspending in one way rather than another, but there is no reason to believe that they speak in favour of suspending rather than believing at all. Second, if one attends to the fact that inquisitive attitudes typically come in degrees, any plausible theory of reasons in favour of graded attitudes should provide an equivalent result as in the contrastivist case. Zetetic considerations might decide which degree of inquisitive attitude I ought to form, yet, they do not alter the reasons in favour of suspension. Therefore, I conclude that one should abandon zetetic encroachment. That said, there might be other ways of explaining PE in a similar fashion, i.e., in terms of RKRs in favour of suspension. While suspension itself is not directly sensitive to practical considerations such as monetary incentives nor to zetetic reasons, as established in this paper, one might still find a difference between Low Stakes and High Stakes which could be relevant for the RKRs of suspension. For instance, as I argued elsewhere, there could be a difference in the salient error possibilities between these situations, and unexcluded salient possibilities of error might very well be RKRs in favour of the third doxastic option (Vollmer, 2024).