1. Introduction
It is often said that epistemology is normative.Footnote 1 One way to spell out this normativity is to take epistemology to be (at least among other things) about what we should believe.Footnote 2 That there are obligations to have certain beliefs seems plausible, because there are particular cases that suggest that much. For instance, Lewis Carroll’s Tortoise, in a chat with Achilles about geometry, professes to believe a couple of premises and to believe that a certain conclusion follows from the premises.Footnote 3 To make the case particularly vivid, let us stipulate that the premises are in fact true, that the conclusion in fact follows from the premises, and that the Tortoise knows all of this. Nothing stands in the way of the Tortoise’s believing the conclusion, yet the Tortoise refuses to believe it. The Tortoise has an obligation to believe the conclusion, it seems, but does not comply with this obligation. More specifically, it seems that the Tortoise has a narrow-scope obligation that pertains to believing the conclusion and not merely a wide scope obligation that pertains to the conditional of (believing the conclusion if certain conditions, such as believing the premises, are satisfied). For suppose that the Tortoise had falsified the conditions, say by giving up his belief in the premises. In this case, he would have avoided the obligation, it seems, not complied with it, which speaks in favour of the narrow-scope reading of the original obligation. A wide-scope obligation, by contrast, would have been complied with, not avoided, had the Tortoise given up his belief in the premises.Footnote 4
It would be good if we could not merely point to particular cases but say something systematic about obligations to believe. An interesting type of systematic statement would be a norm that specifies a sufficient condition for being obligated to believe a proposition. The most promising candidate for such a norm is a norm which says that one ought to believe a proposition if one is in a position to know it. In this paper, I raise two problems for this norm (and for variants thereof). I argue that the norm makes demands that exceed our cognitive capacity and that it has normative consequences that are irrational.
2. Being-in-a-position-to-know norms
The norms I focus on in this paper are a species of a kind of norm that has the following form:
Following Ichikawa (Reference Ichikawa2022: 1), I will call norms of this form positive epistemic norms.Footnote 5 On the face of it, it seems promising to spell out a positive epistemic norm whose triggering condition is that the thinker in question is in a position to know the proposition:
(In the symbolism, ‘Ʞφ’ stands for ‘One is in a position to know φ’, ‘Bφ’ stands for ‘One believes φ’, and ‘Oψ’ stands for ‘ψ is obligatory for one’.) Norm (Ʞ) is endorsed (eventually with a slight modification, to be discussed below) by Jonathan Ichikawa (Reference Ichikawa2022).Footnote 6
There are several aspects of the being-in-a-position-to-know norm, (Ʞ), that make it prima facie attractive. One aspect is that (Ʞ) is a promising way of fitting positive epistemic norms into the popular framework of knowledge-first epistemology, where knowledge is taken to be a key primitive notion which frequently plays a role in positive epistemic appraisals.Footnote 7 Admittedly, the fit between (Ʞ) and the knowledge-first approach would be even better for a norm that had ‘One knows p’ as its triggering condition. Such a norm would be trivial, however, because it would be impossible to violate it given that knowledge entails belief (see Ichikawa Reference Ichikawa2022: 2). Thus, a norm that has ‘One knows p’ as its triggering condition would be much like a norm which says that if one does at least three good deeds a day, one should do at least one good deed a day. Unlike knowing, being in a position to know does not entail belief and hence avoids the triviality problem while still being in the spirit of the knowledge-first programme (see Ichikawa Reference Ichikawa2022: 13).
Another attraction of (Ʞ) is that it has advantages vis-à-vis other positive epistemic norms of form (N) that have as their triggering condition the mere truth of the proposition in question or the condition that the proposition is sufficiently likely on one’s evidence. These other positive epistemic norms are beset by problems that (Ʞ) stands a chance of avoiding. There are such a vast number of truths that it seems implausible that we are obligated to believe all of them (see Boghossian Reference Boghossian2003; Bykvist and Hattiangadi Reference Bykvist and Hattiangadi2007). A proposition can be true without its being the case that we are in a position to know it, so this problem does not immediately carry over to (Ʞ). (We will see, however, that (Ʞ) still generates too many obligations to believe, which are problematic in combination, though not because of their sheer numerosity.) Lottery propositions which say that ticket number so-and-so in a large and fair lottery (whose draw has not taken place yet) will lose are sufficiently likely on the evidence. Lottery propositions pose problems for a formulation of norm (N) in terms of evidential probability, because it seems that we are not obligated to believe all of the lottery propositions.Footnote 8 , Footnote 9 This is no problem for (Ʞ), because we are not in a position to know lottery propositions.
Despite its prima facie attraction, norm (Ʞ) faces serious problems. The first problem is that (Ʞ) makes demands on us that exceed our capacity. We can be in a position to know certain individual propositions while lacking the capacity to believe all of them. Suppose that p and q are different propositions. Suppose that I am in a position to know p and I am in a position to know q (Ʞp ∧ Ʞq). It follows from (Ʞ) that I ought to believe p and that I ought to believe q (O Bp ∧ O Bq). Obligation agglomerates:
By the agglomeration of obligation, it follows that I ought to both believe p and believe q (O(Bp ∧ Bq)).
It might happen, however, that I cannot have both beliefs at once because I lack the capacity. The following grossly simplified case illustrates the idea: my belief box is all but full and has room for only one further belief. I can add proposition p to the box, and I can add proposition q to the box, but I cannot add them both.
We can give more realistic examples if we assume that norm (Ʞ) is implicitly about a certain time interval, say about the beliefs that I ought to form in the next few moments. If I am in a position to know a given proposition but do not believe it yet, I need to engage in some mental activity to come to believe it. Whatever the required activity is, there are only so many propositions that I can subject to this activity in the next few moments. Thus, there will be cases where I am in a position to know a number of propositions individually over the next few moments but cannot come to believe all of them over the next few moments because I cannot carry out the required activity for all of them in this limited amount of time.Footnote 10
Cases where I cannot carry out the required activity in time can also arise without there being a temporal qualification of the norm. Suppose that I was at a party on Saturday and at a different party on Sunday. I am in a position to know how many people attended the Saturday party, because I can access my memory of the Saturday party. I am also in a position to know how many people attended the Sunday party, because I can access my memory of the Sunday party. Unfortunately, I took a memory-destroying drug that will wipe out all my memories of the weekend soon, leaving me time to access at most one of my party memories.Footnote 11
In cases where I lack the capacity to form both required beliefs at once, the obligation to believe both p and believe q conflicts with the principle that ‘ought’ implies ‘can’:
Given (OiC) and the agglomeration of obligation, (Agg), we have to reject norm (Ʞ).
The second problem with (Ʞ) is that it has consequences that seem irrational.Footnote 12 Suppose that p is true, but agent S does not know p. It can be that S is in a position to know p and is also in a position to know that they do not know p (in symbols, Ʞp ∧ Ʞ¬Kp, where Kφ symbolises that S knows φ). It follows from (Ʞ) that S ought to believe p and that S ought to believe that S does not know p (O Bp ∧ O B¬Kp).Footnote 13 By the agglomeration of obligation, it follows that S ought to believe p and believe that S does not know p (O(Bp ∧ B¬Kp)). This looks like a fairly irrational obligation already: we have a knowable proposition and a requirement to believe it as well as to believe that one does not know it.Footnote 14
Things get worse for norm (Ʞ) if we apply a moderate quasi-closure principle for obligatory belief. This principle can be derived as follows. Being obligated to do something implies being permitted to do it, in the epistemic domain as well as elsewhere:Footnote 15
(‘Pφ’ stands for ‘φ is permissible for one’.) It seems very plausible that being permitted to have a conjunction of beliefs entails being permitted to have a single belief whose content is the conjunction of the original contents (see Kroedel Reference Kroedel2012: 59):
Principles (OiP) and (CP) together give us our moderate quasi-closure principle, according to which an obligation to have a conjunction of beliefs entails a permission to believe the conjunction of the original contents:
Applying (QC) to S’s obligation to believe p and believe that S does not know p (O(Bp ∧ B¬Kp)) yields that S is permitted to believe the conjunction of p and the proposition that S does not know p (P(B(p ∧ ¬Kp))). But such a permission seems highly implausible. Perhaps there are some propositions for which it is acceptable that one is permitted to believe that one ignorantly believes them. Propositions about lottery tickets might belong to this category as long as one merely has statistical evidence about whether or not a certain ticket lost; given merely this evidence, one is not in a position to know that the ticket lost (even if in fact it did lose).Footnote 17 Proposition p from our present example is different, however. We assumed that one was in a position to know p. Applying (Ʞ) yields that one ought to believe p. Thus, one ought to believe p because one is in a position to know p. It seems strange that on top of this, one should be allowed to believe p and that one does not know p.
We get especially drastic examples of irrationalFootnote 18 consequences of norm (Ʞ) in cases where the agent fails to know the proposition in question by virtue of failing to believe it. Suppose that p is true, but S does not believe p (and hence does not know p). Suppose further that S is in a position to know p and that S is in a position to know that S does not believe p. (in symbols, Ʞp ∧ Ʞ¬Bp). Applied to this case, norm (Ʞ) yields that S ought to believe p and that S ought to believe that S does not believe p (O Bp ∧ O B¬Bp). By the agglomeration of obligation, (Agg), it follows that S ought to believe p and believe that S does not believe p (O(Bp ∧ B¬Bp)). Applying the quasi-closure principle, (QC), yields that S is permitted to believe the conjunction of p and the proposition that S does not believe p (P(B(p ∧ ¬Bp))). A permission to have such a Moore-paradoxical belief seems highly irrational.Footnote 19
3. Responses
In the previous section, we considered two problems for norm (Ʞ), the capacity problem and the rationality problem. In this section, we will look at possible responses.
Let us consider the capacity problem first. The problem was that there are cases where one is in a position to know different propositions individually but is not able to believe them jointly for want of cognitive capacity. In response, one could try to strengthen the triggering condition of (Ʞ), hoping that, with the strengthened condition, the obligation to believe a proposition is triggered only when no capacity limits stand in the way of believing it. We can conceive of this response as endorsing a norm that fits the following schema:
Friends of the schema (ꞰR) face a dilemma, however. The strengthened triggering condition (Ʞp ∧ Rp) either suffices for the agent’s believing p or it does not. If it suffices for belief, the resulting norm is trivial, because it would be impossible to violate it, as was the case for a norm whose triggering condition is knowledge (see Ichikawa Reference Ichikawa2022: 10).Footnote 20 If the strengthened triggering condition does not suffice for belief, some additional mental activity is required of the agent before they believe p. But then the capacity problem re-emerges, because the agent might have the capacity to carry out this extra activity with respect to p and with respect to a different proposition q without having the capacity to carry out the extra activity with respect to both propositions.
To illustrate the dilemma by way of specific norms, take the relation that one has to p if and only if one considers p and competently judges p. If we substitute this relation for relation R in (ꞰR), the resulting norm is trivial, because anyone who considers and competently judges a proposition they are in a position to know thereby believes the proposition. On the other hand, let relation R be the weaker relation in which one stands to p if and only if one considers p.Footnote 21 If one merely considers p, more cognitive effort is needed before one comes to believe p. One might have the capacity for such an effort for each of two (or more) propositions individually but not for both (or all) of them. (If one does not merely consider p, but considers p and already believes p, we land on the triviality horn of the dilemma again.)
Jonathan Ichikawa (Reference Ichikawa2022: 18) ultimately favours a norm that has the following triggering condition: S considers or should consider the question whether p, and S is in a position to know p. This norm also fits the schema (ꞰR), with R being the relation that S considers or should consider the question whether p. Ichikawa’s norm is threatened by the capacity horn of the dilemma at least to the same degree as the norm discussed at the end of the previous paragraph. For instance, it can be that (i) S in fact considers the question whether p; (ii) S should consider the question whether q; (iii) S is in a position to know each of p and q; but (iv) S does not have the capacity to both believe p and believe q.Footnote 22
A different response to the capacity problem is due to Mona Simion (Reference Simion2024). Simion holds that obligations to believe arise from being in a position to know via the notion of proper epistemic functioning (see Reference Simion2024: 209). Simion is aware that there are capacity limitations that could drive a wedge between what we are in a position to know and obligations to believe. The solution she suggests is the following. Suppose that there are sets of propositions s 1, s 2, … s n , such that, for each set s i , the following is true: (i) I am in a position to know each of the propositions in s i ; (ii) I have the capacity to believe all of the propositions in s i ; (iii) I do not have the capacity to believe a set of propositions that is a proper superset of s i . Put less technically, the sets in question are maximal sets of propositions that I am in a position to individually know and to simultaneously believe (I will refer to these sets as ‘maximal sets’ for brevity). Simion holds that one has a prima facie disjunctive obligation to believe all the propositions from one of the maximal sets and an ultima facie obligation to believe all the propositions from the set that is most easily available to me.Footnote 23 The collection of candidate sets can be narrowed down by “normative constraints” (Reference Simion2024: 209 footnote 16) to avoid ties in availability between the sets. In a nutshell, according to Simion, I ought to believe the propositions from the maximal set that is most easily available, given a normative preselection.
The problem with Simion’s suggestion is that there is no guarantee that the normative constraints she invokes avoid ties between the maximal sets. Whatever the normative constraints, on the face of it, they may well allow for maximal sets that are tied for being most easily available. If we narrow down the timeframe and the agent’s capacity enough, we might get a simple case of this sort where the normative constraints select the singletons {p} and {q} (with p ≠ q) as maximal sets that are ranked equally and where p and q are equally easily available for the agent. By their nature as maximal sets, the agent does not have the capacity to both believe p and believe q, so the capacity problem makes a comeback.
One might resign to the fact that ties in maximal sets cannot always be avoided and yet hold on to Simion’s overall framework by claiming that, in cases of ties between maximal sets, all we have are disjunctive obligations to believe the maximal sets. One might even give up on norms of form (N) altogether and claim that all we ever have are disjunctive obligations to believe some maximal set or other, not obligations to believe specific propositions. Such moves would avoid the capacity problem, albeit at the cost of making epistemic norms less specific. The moves would not solve the rationality problem, however. Presumably, a maximal set that contains both a proposition p and the proposition that one does not believe p should never be a candidate to feature even in a disjunctive obligation. But nothing in the disjunctive framework rules out such maximal sets. One could try to exclude such sets by stipulation, but this would seem ad hoc. Thus, in trying to solve the capacity problem, we have opened the door for the rationality problem.
As a last resort, friends of the disjunctive obligations strategy could abandon maximal sets altogether and endorse the following norm, which merely enjoins one to believe some proposition or other that one is in a position to know:
There are no obvious counterexamples to (ꞰD), but the norm is extremely weak and, in consequence, does not seem very interesting.
So far, we have mostly considered responses that modify the triggering condition of norm (Ʞ) somehow. The problems for (Ʞ) arose not for (Ʞ) in isolation, however, but for (Ʞ) in combination with certain general principles, most importantly the ‘ought’-implies-‘can’ principle, (OiC), in the case of the capacity problem and the agglomeration of obligation, (Agg), in the case of the capacity problem and the rationality problem. Thus, one could respond to the problems with (Ʞ) by rejecting that ‘ought’ implies ‘can’ or by rejecting that obligation agglomerates. Indeed, that ‘ought’ implies ‘can’ is often rejected for obligations to believe on the basis of the assumption that ‘can’ implies voluntary control, which we do not have over our beliefs, or at most in very limited ways (see Alston Reference Alston1988).
I do not have much to add to the debates about these principles and will therefore confine myself to some brief remarks. As for ‘“ought” implies “can”’ in the context of obligations to believe, there is the reply – which, in my view, is convincing – that ‘can’ need not be understood in a sense that implies voluntary control (see Bykvist and Hattiangadi Reference Bykvist and Hattiangadi2007; Chuard and Southwood Reference Chuard and Southwood2009). The agglomeration of obligation seems compelling in a great number of cases involving practical obligation: if I ought to help my aunt and I ought to help my uncle, how could it fail to be the case that I ought to help both?Footnote 24 The agglomeration principle strikes me as more plausible than norm (Ʞ), so giving up agglomeration merely to hold on to (Ʞ) does not seem to be a good idea to me.Footnote 25 If agglomeration were to fail, however, one could substitute the principle of Joint Satisfiability, at least for those arguments from this paper that involved an inability to form certain attitudes:
In the case of the parties, for instance, (JS) would get us from the obligation to form a belief about Saturday’s party and the obligation to form a belief about Sunday’s party straight to the claim that I am able to form both beliefs (which, by assumption, is false).
Thus, there is some room for manoeuvre regarding the general principles that feature in the arguments from this paper. Readers who are less sympathetic to ‘“ought” implies “can”’, the agglomeration of obligation, or joint satisfiability can, however, reinterpret the arguments I have presented: they can read them merely as arguments against the conjunction of an epistemic norm and the relevant general principles.
4. Conclusion
There are significant problems with positive epistemic norms whose triggering conditions are, or contain, that one is in a position to know. Such norms make demands that exceed our capacity and that are at odds with the requirements of rationality. One can make some headway by modifying the norms, but it seems that one cannot solve both problems at once, or only at the price of watering down the norms.
To end on a conciliatory note, I should say that even if general positive epistemic norms in terms of being in a position to know are doomed, it does not follow that there are no obligations to believe. That there are such obligations, for instance, for Lewis Carroll’s Tortoise, still seems plausible. But perhaps obligations to believe are too messy or ‘particularist’ to be squeezed into a neat schema.
Acknowledgements
For helpful comments and suggestions, I would like to thank Corine Besson, Alexander Geddes, Benjamin Kiesewetter, Beau Madison Mount, Moritz Schulz, Timothy Williamson, audiences in Hamburg, Oxford, Gothenburg, and Dresden, an anonymous reviewer, and an associate editor of Episteme.
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