1. The Symmetry Between Practical and Epistemic Rationality

In contrast to Harman, Hieronymi, and Weintraub, the account developed here defends the claim that there is no asymmetry between practical and epistemic rationality in cases such as Buridan's ass. Briefly put, the idea is that when the comparison between practical and epistemic decisions is made at the appropriate level, we see that the alleged asymmetry between the practical and the epistemic is only apparent. We can call this the parity account. This account has three separate but related components. In this section, we discuss these components; in subsequent sections, we address objections aimed at each component.

The first component of the parity account is that the proper practical analog of belief is not action, but intention. Call this the belief-intention analogy. There are two motivations for the belief-intention analogy: First, note that just as beliefs are the mental states that agents (when functioning properly) reason in accordance with, intentions are the mental state that agents (when functioning properly) act in accordance with. Beliefs and intentions are the mental backdrop against which agents reason and act, respectively. Second, beliefs and intentions both have content, whereas actions do not—beliefs and intentions are about something while actions are not in the relevant sense about anything. Unlike actions, both beliefs and intentions are contentful mental states. This strongly suggests that just as the norms of epistemic rationality govern belief in the first instance, the norms of practical rationality govern intentions in the first instance.Footnote ²

The second component of the parity account is that both beliefs and intentions come in degrees; that is, both are gradable states. Call this the gradability thesis. In the case of belief, this thesis is familiar and widely accepted: agents’ doxastic states can be described in terms of their degrees of belief, that is, credences, and these are widely assumed to be governed by probabilistic norms of rationality (see Kyburg Reference Kyburg1961; Jeffrey Reference Jeffrey and Swain1970; Christensen Reference Christensen2004). Of course, it is often convenient to describe agents as believing propositions simpliciter (as opposed to having particular degrees of belief in propositions), but on the current view this should not be taken to indicate that there is some further doxastic attitude—belief simpliciter—that God would have had to create once she had endowed all agents with degrees of belief. Rather, the folk concept of belief simpliciter simply denotes contextually determined sets of degrees of belief—usually if not always to a degree of belief above some contextually determined threshold (see Foley Reference Foley1992; Weatherson Reference Weatherson2005; Ganson Reference Ganson2008; Sturgeon Reference Sturgeon2008).

Taking account of this point, we can restate BSR*—the principle that says it is irrational to believe on the basis of insufficient reason—in a way that applies to graded belief:

BSR says that rationality in (degree of) belief requires support by sufficient reason: one cannot rationally have a higher degree of belief in P than in Q unless the reasons in favor of thinking P is the case are stronger than the reasons in favor of thinking Q is. For our ass, who has no reasons to believe that either of the two bundles has more hay, BSR yields the result that the ass's degree of belief that the left bundle has more hay should match the ass's degree of belief that the right bundle has more hay.

A clarification: BSR imposes a restriction on the rationality of having a higher degree of belief in some proposition P than in another proposition Q. It says that this should occur only when there are stronger reasons to believe P than Q. This implies that when the reasons for believing P and Q are equally strong, one should not have a higher degree of belief in P than in Q. This in turn implies that, if one has any degrees of belief in both P and Q at all, then these should be equally strong. Notice, however, that BSR is compatible with an agent lacking any degree of belief in either or both of P and Q. Thus, for example, BSR does not tell us anything about the rationality of having a degree of belief in P but lacking any degree of belief in Q when there are equally strong reasons to believe each proposition.

Admittedly, there is an issue here about what it is to lack any degree of belief at all in some proposition. We are inclined toward the view that to lack any degree of belief at all is to have a completely mushy or indeterminate degree of belief that stretches over the entire unit interval, i.e., [0,1], instead of being a specific point on that interval (see, e.g., Levi Reference Levi1974; van Fraassen Reference van Fraassen, Dunn and Gupta1990; Joyce Reference Joyce2010; Moss Reference Moss2015). One nice thing about this kind of picture is that it allows for the extent to which you have a degree of belief in a proposition to be a matter of degree as well: it will depend on how mushy your degree of belief is, where ‘how mushy’ is determined by how large the interval is that describes your degree of belief (a larger interval corresponds to a mushier degree of belief), with the limits being (a) the entire unit interval [0,1] and (b) a specific point on that interval, e.g., 0.7. But for all we say here, it may be that some alternative picture of what it is to lack any degree of belief at all is preferable.

So far we have noted that belief is a gradable state. That intention is a gradable state is a less familiar thesis, and correspondingly, it is a less widely accepted idea. However, once the possibility of gradable intention is raised, it is hard to deny. This is so for at least two reasons. First, the thesis is intuitively plausible as a description of our mental life since we do distinguish between our stronger and weaker intentions. For example, a father may have a very strong intention to buy his daughter a birthday present, a somewhat weaker intention to buy his daughter a book for her birthday, and a yet weaker intention to buy her a book about Winnie-the-Pooh. The most natural and plausible way of modeling these variations is by taking intention, like belief, to be an inherently gradable type of state.Footnote ³

Second, the gradability of intention is needed to avoid analogs of the preface paradox for rational intention (for the classic statement of the preface paradox in the case of belief, see Makinson [Reference Makinson1965]). A nongradable conception of intention yields counterintuitive results according to which combinations of seemingly rational intentions cannot count as rational. Borrowing an example from Goldstein (Reference Goldstein2016): Susan may strongly intend to visit each of 20 different cathedrals on her trip to Europe, and she may also strongly intend to skip visiting one of them (since she can only afford the entrance fee for 19 cathedrals). If we take Susan's intentions to be nongradable, her intentions count as mutually inconsistent and thus irrational. On a gradable conception of intention, by contrast, there is no necessary inconsistency because a strong intention to perform each of 20 actions is compatible with a strong intention not to perform all of them. The upshot is that these preface-like paradoxes are effortlessly resolved in much the same way that a gradable conception of belief solves the preface paradox.Footnote ⁴

Some might find these motivations for accepting the gradability thesis about intention insufficient. Here, our aim is not to argue for the gradability thesis about either belief or intention. Instead, we provide these cases as motivation for accepting that view, at least for the sake of argument. We aim to show what work the view can do for us if we accept it. Readers uncomfortable with the suggestion that intention, like belief, is a gradable state are invited to read the following arguments conditionally: if we accept the gradability thesis about both belief and intention, then we can dissolve the apparent asymmetry between practical and epistemic rationality.

Now, with the belief-intention analogy and the gradability thesis about belief and intention in place, the third component of the parity account is that, as with belief, rationality in intending to do one thing more strongly than another requires the presence of stronger reasons to intend to do that first thing. More precisely:

For our ass, ISR yields the result that the ass's degree of intention to go to the left bundle should match the ass's degree of intention to go to the right bundle. In effect, then, the ass should be, with respect to its degrees of intention regarding the left and right bundles, in equipoise: after all, the ass has neither more reason to intend to go left than right, nor more reason to intend to go right than left. Note, however, that it does not follow that the ass should be, with respect to all its bundle-involving intentions, in equipoise. After all, we have said that the ass is hungry and wants to eat hay: so, the ass will have a very high degree of intention to go to either the right bundle or the left bundle and a correspondingly very low degree of intention to go to neither bundle. Since the ass, by hypothesis, has much stronger practical reasons to go to either bundle than it does to go to neither bundle, ISR happily permits the ass to form a very strong intention to go to either bundle.

As in the case of belief, a clarification is in order. ISR imposes a restriction on the rationality of having a higher degree of intention to ϕ than to ψ; it says that this should occur only when there are stronger reasons to intend to ϕ than to ψ. This implies that when the reasons for intending to ϕ and ψ are equally strong, one should not have a higher degree of intention to ϕ than to ψ. This in turn implies that, if one has degrees of intentions to ϕ and ψ at all, then they should be equally strong. Notice, however, that ISR is compatible with an agent's lacking any degree of intention with regard to either or both of ϕ-ing and ψ-ing. Thus, for example, ISR does not tell us anything about the rationality of having a degree of intention to ϕ but lacking any degree of intention with respect to ψ-ing when there are equally strong reasons to intend each action.Footnote ⁵

Thus, the parity account holds, first, that epistemic and practical rationality govern belief and intention respectively (the belief-intention analogy); second, that belief and intention are both gradable mental states (the gradability thesis); and third, that practical rationality requires that one has stronger intentions for one action rather than another only if one has stronger practical reasons for intending the former than one has for intending the latter (Intention Sufficient Reason, ISR). This dissolves the apparent asymmetry between practical and epistemic rationality with respect to Buridan's ass since structurally identical principles—viz., ISR and BSR—govern the practical response it is rational for the ass to have (in terms of its intentions) and the epistemic response it is rational for the ass to have (in terms of its beliefs). The idea, then, is that once the comparison is made at the appropriate level—in terms of graded intention and graded belief—there simply is no difference between what it is rational for the ass to do when the (practical or epistemic) reasons in favor of two alternatives are equally strong. When the practical reasons in favor of two courses of action are equally strong, it is irrational to intend to perform one of them more strongly than the other. And when the epistemic reasons in favor of two propositions are equally strong, it is irrational to believe one of them more strongly than the other.Footnote ⁶

One might wonder how actions enter this picture. After all, there is clearly some relationship between rational actions and rational intentions. Although nothing about the parity account commits it to any particular view about that relationship, it seems clear what a proponent of the parity account should say about this relationship, viz., that in order for it to be rational to perform intentionally some action ϕ rather than perform intentionally some alternative action ψ, it must be rational to have a greater or equal degree of intention to ϕ as to ψ. In the case of Buridan's ass, this condition is met: by ISR, it is not irrational to have the same degree of intention to ϕ as it is to ψ. So, were the ass to go intentionally to the left bundle, its action would be rational according to ISR; the same can be said were it to go to the right bundle.

The upshot is this: if the parity account is correct, what is required for it to be rational for the ass actually to go to (say) the left bundle rather than the right is not that it is rational for the ass to intend to a greater degree to go to the left bundle rather than to the right bundle. All that is necessary is that it be rational for the ass to have a greater or the same degree of intention to go to the left bundle as to go to the right bundle. Thus, it can be rational to perform some action even if there is no overall practical reason to perform that action rather than some other action, despite the fact that rationally intending to a greater degree to perform some action requires that it be rational to have an overall practical reason to perform that action.Footnote ⁷

2. Independent Support for ISR

The parity account, as we have just seen, dissolves the apparent asymmetry between epistemic and practical rationality. ISR is crucial to its ability to do so: it is because intentions to perform one action rather than another should not be arbitrarily strong that, in cases such as Buridan's ass, the epistemic and practical responses it is rational for the ass to have are, mutatis mutandis, the same. Accordingly, one reason for accepting ISR is that it helps us dissolve what would otherwise be a puzzling, unexplained asymmetry between epistemic and practical rationality. But is there any independent reason—that is, independent from its use in this argument—for accepting ISR? Yes: alternatives to ISR, principles that allow for intentions to be arbitrarily strong, all deliver problematic results in a range of cases. Let us explain.

Suppose some alternative to ISR is true. Then there will be cases where, without exhibiting any irrationality, an agent more strongly intends to ϕ than she intends to ψ even when the reasons in favor of intending to ϕ and intending to ψ are equally strong. (Since this is precisely what ISR denies, any alternative to ISR must allow for this possibility.) Perhaps the ass is supposed to be a case in point: we can imagine that the ass more strongly intends to go to the left bundle than the right bundle despite lacking a reason that more strongly favors intending to go left than intending to go right. According to the current idea, there is nothing irrational about doing so.

The problem with this proposal becomes clear if we imagine what happens, in a scenario such as the one we are considering, if the ass were to learn that the right bundle contains one more straw of hay than the left bundle. That fact is, by hypothesis, a reason for the ass to increase the degree of its intention to go right rather than left (or, what amounts to the same thing, a reason to decrease the degree of its intention to go left rather than right). Even the proponent of some alternative to ISR, who thinks it is not irrational to have arbitrarily a stronger intention to do one thing rather than another, should admit that failing to respond to this reason in this way would itself be irrational. Accordingly, let us suppose the ass does respond to it, either by increasing the degree of its intention to go right rather than left or by decreasing the degree of its intention to go left rather than right. What is the result?

The desired result, the result we can all agree would be the rational result in terms of the ass's intentions, is that the ass now more strongly intends to go right than left. After all, the ass just learned that the right bundle has more hay in it, and, by hypothesis, the ass wants as much hay as possible. But if the proposal we are considering here is correct, this result does not follow. For notice that if any alternative to ISR is correct, there is no reason why the ass, even after increasing its degree of intention to go right, would not end up in a state in which it still has a stronger intention to go left or in a state in which its intentions to go left and to go right are equally strong. Of course, whether this sort of case materializes will depend on how much stronger the intention to go left was initially and on how strong a reason for going right is provided by the information that the right bundle contains slightly more hay. However, the point remains that no alternative to ISR will guarantee that gaining a practical reason to intend to ϕ rather than to intend to ψ, in a situation where you had no such reasons before, will make it rational to have a stronger intention to ϕ than to ψ.

So, independently of its use by the parity account in dissolving the asymmetry in cases such as Buridan's ass, ISR is made plausible by the fact that it guarantees that gaining a reason to ϕ rather than to ψ ‘tips the balance’ in favor of ϕ-ing if the scales were equally balanced before. However, one might think that ISR is not the only principle that guarantees this. In particular, consider a principle such as this:

If true, SR would explain why, in the sorts of cases outlined above, it would be irrational for the ass to end up in a state where its intention to go left and its intention to go right are equally strong, and it would do so without appeal to ISR. Thus, it might appear that ISR is otiose, and opponents of it can simply accept SR, which is plausible in its own right, and go on to reject ISR, while continuing to deliver the required result.

However, there are at least two problems with this response. First, supposing that SR is true, we can ask what explains why it is true. And we suggest the most plausible explanation of SR is provided by:

RIP is very plausible on its own. (So, too, is the corresponding principle for belief, which claims that an agent's degree of belief in a proposition P, if she has one, should be proportional to the strength of her epistemic reasons to believe P.) Moreover, RIP explains why SR is true in an elegant way. Why is it irrational, given stronger reasons to intend to ϕ, to have an equally strong or even stronger intention to ψ? Because the strength of one's intentions ought to be spread across actions proportional to the strength of the reasons there are for those intentions. But notice that the opponent of ISR cannot appeal to RIP in order to explain SR. For note that RIP does not just entail SR, it also entails ISR. While we are happy to accept SR, doing so will not do away with the argument for ISR because the best explanation of why SR is true appeals to a principle, viz., RIP, a principle that itself entails ISR.

A second problem with using SR to handle the cases discussed above while rejecting ISR emerges when we consider how degrees of intention should rationally change when one gains reasons for or against intending something. Consider the following very plausible principle:

Anyone who accepts SR but rejects ISR will have to deny RIG. To see why, consider an agent A who, at t₁ , has equally strong reasons to intend to ϕ as she has to intend to ψ and yet intends to ϕ more strongly than she intends to ψ (in violation of ISR but not SR). Now suppose that, at a later time t₂ , A gains a reason to intend to ϕ (but does not gain a reason to intend to ψ) and so, by the lights of SR, all that is required is that A should continue to intend to ϕ more strongly than she intends to ψ. Indeed, for all SR tells us, we can suppose that the rationally required state of comparative intentions at t₂ is exactly the same as the state A was in before, that is, at t₁ . In that case, A would have gained a reason to intend to ϕ (and no other reason) and yet according to someone who accepts SR but rejects ISR, A should not increase her degree of intention to ϕ. This is so despite the fact that, as we have described the case, it is possible that the original intention to ϕ is not maximal. Hence, a proponent of SR who rejects ISR must also reject RIG. And, again, that seems to be the wrong result.

3. The Intentional Action Objection

We have just seen an argument against alternatives to ISR (and thus in favor of ISR itself) to the effect that those alternatives deliver unacceptable results in terms of the rationality of particular intentions. But it might appear that accepting ISR has its own unacceptable results. In particular, it might appear that accepting ISR delivers unacceptable results regarding the rationality of particular intentional actions. We will call this the intentional action objection to ISR.

The objection starts with what is perhaps a natural principle connecting intentions and intentional actions:

For example, if an agent raises her hand intentionally at 1:15 p.m., then at 1:15 p.m. the agent's intention to raise her hand is stronger than each of her competing intentions at 1:15 p.m., such as, the intention to shake her hand or to keep it where it was. The objection proceeds: it certainly does not seem irrational for the ass to go intentionally to the left bundle at some particular time t. Indeed, we have already granted this claim. Thus, given SIP, the ass's intention to go to the left bundle at t must be stronger than each of the ass's competing intentions at t. Now, ISR says that it would be irrational for the ass's intention to go to the left bundle to be stronger than each of the ass's other intentions at t, and in particular that it would be irrational for the ass's intention to go to the left bundle to be stronger at t than the ass's intention to go to the right bundle. But then ISR says that the ass is necessarily subject to some irrationality: after all, the ass will (if SIP is correct) necessarily intend to a greater degree to go to the left bundle at t than it will intend to go to the right bundle at t, and doing so is (according to ISR) irrational. Hence, ISR must be mistaken, since it involves agents in unavoidable irrationality in cases such as Buridan's ass.

The correct response to this objection is to reject the principle connecting intention and intentional action—that is, to reject SIP. It is not true that if one ϕs intentionally at some time t, then at t one's intention to ϕ is stronger than each of one's other intentions at t. A simple counterexample shows this: An agent can simultaneously intend to finish her book manuscript to a very high degree, intend to finish watching the last season of The Wire to a somewhat lower degree, and intentionally do the latter rather than the former (perhaps through weakness of will). To put the point differently, SIP wrongly entails that if an agent has a stronger intention to finish her book manuscript than to watch The Wire tonight, then her watching of The Wire could not be something she does intentionally.Footnote ⁹

Thus, SIP is subject to straightforward counterexamples. Why, then, might it seem so plausible at first sight? The answer, we submit, is that SIP is easily confused with a true principle in its vicinity, namely:

SMP states a truism about the connection between the degree to which agents are motivated to do certain things and what, as a matter of fact, they do. (indeed, it may well be plausible to define ‘motivation’ such that SMP becomes a conceptual truth; for discussion, see McCann [Reference McCann1995]). However, the objection considered above does not go through given this principle, because the fact that an agent is most motivated to do something clearly does not imply that she most strongly intends it. To illustrate, an addict may have a stronger intention to resist her addiction and yet be more strongly motivated to sate her addiction, which causes her to relapse. Of course, things could happen otherwise: it may be that the addict in fact more strongly—perhaps because of some irrationality—intends to sate her addiction. The point here is simply that it need not be like this: sometimes, agents do otherwise than what they most strongly intend to do. But something clearly causes them to act in the particular way they do act, namely, their motivations. It is the possibility of the latter sort of cases—failures to do what one most strongly intends to do, because one's motivations do not line up with one's intentions—that militates in favor of keeping motivation and intention separate in theorizing about agents’ cognitive economies. Indeed, the literature on intention and motivation appears to reflect this, for the claim that motivations and intentions are distinct and separable mental states is a familiar and uncontroversial point.Footnote ¹⁰

In sum, then, we should reject the principle connecting intention and intentional action, viz., SIP, regardless of our acceptance of ISR. SIP is subject to clear and straightforward counterexamples, and its apparent plausibility is due to a confusion between the degree of one's intention to perform an action and the degree to which one is motivated to perform that action.

4. Remaining Asymmetries? First Pass: Full Belief and Full Intention

In the remaining three sections, we consider three final objections to the parity account. Rather than rejecting ISR, these objections grant the symmetry between rational belief and rational intention, but argue that this symmetry does not eliminate the asymmetry between epistemic and practical rationality. The first objection claims that while BSR and ISR establish a symmetry between rational degrees of belief and intention, respectively, there remains an asymmetry between full belief and full intention. The idea is that if one has equally strong reasons for believing P and for believing a competing proposition Q, it will always be irrational to believe fully P. By contrast, the objection goes, if one has equally strong reasons for intending to ϕ and for intending a competing action ψ, it is not always irrational to intend fully to ϕ.

It is not clear to us that we should accept the objection's last claim, viz., that it could be rational to intend fully something when one's reasons are equally strong for a competing intention. Nevertheless, we grant that claim for the sake of the argument and more generally grant that there is an asymmetry between rational full belief and rational full intention in this respect. However, we deny that this asymmetry amounts to an asymmetry between epistemic and practical rationality. Let us explain.

The parity account involves a commitment to the gradability thesis, according to which belief and intention are both inherently gradable states. On this view, full beliefs and full intentions are both wholly reducible to contextually determined sets of degrees of belief and intention, respectively. Put differently, full beliefs and full intentions are nothing over and above (contextually determined) sets of graded states. Accordingly, there can be no normative principles governing such states over and above those that govern the underlying graded states. Once we have fixed the principles governing degrees of belief and intention, there are simply no further demands of rationality to be found. It follows that if there is symmetry in the rational demands on degrees of belief and intention (which is what the current objection grants), there can be no remaining asymmetry between the normative principles governing belief and intention, respectively.

How then would the alleged asymmetry between rational full belief and rational full intention arise in the first place? The answer must be that, for whatever reason, our folk concepts of full belief and full intention refer to somewhat different sets of degrees of belief and intention. For example, perhaps our folk concept of full belief tends to refer to a relatively small interval of degrees of belief at the upper end of the belief spectrum, whereas our folk concept of full intention tends to refer to a somewhat larger interval at the upper end of the intention spectrum. While we doubt that there is any such robust difference between these two folk concepts, our point now is that such a difference in our folk concepts would have no bearing on the issue of whether there is any asymmetry in the normative principles governing belief and intention. This is because the underlying mental states—the states to which our folk concepts would refer in their crude and contextually determined manner—would still be governed by perfectly symmetric normative principles: BSR and ISR.

5. Remaining Asymmetries? Second Pass: Belief and Action

Let us turn then to a second objection alleging that there is a remaining asymmetry between epistemic and practical rationality. This objection claims that since the view on offer here grants that BSR is true and ASR is false, it still entails an asymmetry between rational belief and rational action. Thus, the objection goes, the asymmetry between epistemic and practical rationality has not been eliminated but instead merely relocated.

In response to this objection, note first that although the parity account entails an asymmetry between rational belief and rational action (in that BSR is true while ASR is false), it entails precisely the same asymmetry between rational intention and rational action (in that ISR is true while ASR is false). This latter asymmetry cannot be explained by an asymmetry between epistemic and practical rationality as such because intentions and actions both fall within the domain of practical rationality. Indeed, there is a plausible explanation of the asymmetry between rational belief and rational action that applies equally to the asymmetry between rational intention and rational action.

This explanation begins by noting that actions are not the sort of things that can be distributed among a set of mutually exclusive options in proportion to the strength of one's reasons. One simply cannot perform one action to some (nonzero) extent and simultaneously perform another, incompatible action to some (nonzero) extent. By contrast, both beliefs and intentions can be distributed among mutually exclusive options in this way, in that one can have a (nonzero) degree of belief in two incompatible propositions P and Q and a (nonzero) degree of intention to perform two incompatible courses of actions ϕ and ψ.

This is important since the case of Buridan's ass and other cases like it are precisely the sorts of cases in which it is rational to place a (nonzero) degree of belief and intention in two incompatible options.Footnote ¹¹ In particular, we have argued that it is rational to place an equal degree of belief and intention in each option in the case of Buridan's ass (and other cases in which the reasons for two or more mutually exclusive options, whether epistemic or practical, are equally strong). But there is simply no such thing as performing two mutually exclusive actions to an equal (nonzero) degree. In the case of Buridan's ass, for example, the ass cannot simultaneously go to both bundles of hay; furthermore, the ass cannot ‘split the difference’ and somehow go to both bundles equally, that is, move toward both of them to the same degree. In short, the logic of action itself precludes any possibility of one's actions reflecting the weight of reasons in the way one's beliefs and one's intentions can reflect the weight of reasons.

This fundamental difference between the structure of belief and intention, on the one hand and action on the other by itself suggests that action will not be governed by the same sorts of norms as belief and intention. Here we have at least the beginning of an explanation of the fact that ASR is false while BSR and ISR are both true. But let us push further. Given a set of mutually exclusive and jointly exhaustive possible actions, an agent cannot but perform exactly one of those actions while leaving all other possible actions unperformed. As we have noted, it is also impossible for the agent somehow to ‘split the difference’ with regard to action by performing two or more mutually exclusive actions to an equal extent. Given the principle that it must be possible to do what one is rationally required to do (i.e., that ‘rationally required’ implies ‘can’), an agent cannot be rationally required to achieve such an impossible feat.Footnote ¹² That is, it cannot be a requirement of rationality that an agent's action be equally distributed among two incompatible options when reasons for each are equally strong in the way it can be a requirement that her beliefs and intentions should be so distributed, as BSR and ISR say they must.

Let us spell out the reasoning here by returning to the case of Buridan's ass. The ass can be described as facing a choice between three mutually exclusive and jointly exhaustive possible actions: going to the bundle on the left, going to the bundle on the right, and going to neither bundle. Formally (in what follows, we are assuming a standard KD deontic logic):

(1) ¬Can[¬Left ∧ ¬Right ∧ ¬Neither]

We now invoke the principle that ‘rationally required’ implies ‘can’:

(2) RR[ϕ] → Can[ϕ]

From these, we can derive:

(3) ¬RR[¬Left ∧ ¬Right ∧ ¬Neither]

In other words, it is not rationally required that [the ass not go left and not go right and not go to neither]. By DeMorgan's law, we now get:

¬RR¬[Left ∨ Right ∨ Neither]

Now, ‘rationally required’ and ‘rationally permitted’ are interdefinable. In particular, if you are not rationally required to do something, then you are rationally permitted not to do it. Thus, we have (where ‘RP’ stands for ‘rationally permitted,’ and eliminating negation):

(4) RP[Left ∨ Right ∨ Neither]

Rational permission distributes over disjunction, so that if you are rationally permitted to do a disjunction of things, you are rationally permitted to do each of those things:

(5) RP[Left] ∨ RP[Right] ∨ RP[Neither]

Of course, it would not be rational for the hungry ass to go to neither bundle —that is, ¬RP[Neither] —because it would thus eventually starve to death. Assuming that these actions exhaust the ass's options, it must be rational for the ass to go to one of the two bundles—that is, RP[Left] ∨ RP[Right]. This suffices to explain why ASR is false in this case, implying as it does that the ass is not rationally permitted to go to either bundle. When it comes to belief and intention, by contrast, the ass has the option of distributing its beliefs and intentions equally over the options available to it. For this reason, there is no true analogue of premise (1) for either belief or intention. As a consequence, BSR and ISR are not similarly ruled out by the principle that ‘rationally required’ implies ‘can’. Since the ass can distribute its beliefs and intentions equally over options that are supported by equally strong reasons, the ass need not be rationally permitted to discriminate in favor of one of these options in its beliefs and intentions.

In sum, then, the explanation for the fact that ASR is false given that BSR and ISR are both true is that since there is no such thing as performing two actions equally, rationality cannot require that we do any such thing. By contrast, since both beliefs and intentions can be equally distributed in the relevant sense, rationality may require that we do so in some cases. Importantly, this explains the asymmetry between rational action and rational belief not in terms of an asymmetry between epistemic and practical rationality as such, but rather in terms of a difference between the nature of beliefs and actions, viz., that the former can be equally distributed whereas the latter cannot. Of course, exactly the same difference holds between the nature of intentions and actions, which explains the corresponding asymmetry between rational intentions and rational actions. Thus, we have a unified explanation of the two asymmetries between rational actions and rational beliefs/intentions.

6. Remaining Asymmetries? Third Pass: Requirements of Rationality

Finally, we now turn to a third objection to the parity account, one that is based on an alleged remaining asymmetry between practical and epistemic rationality in cases such as Buridan's ass. Above we assumed that it would be irrational for the hungry ass to go to neither of the two bundles. But what makes this course of action irrational? Presumably, this should be explained in terms of some further requirement of rationality. Since that requirement would then apply to something that is clearly in the domain of practical rationality, viz., action, it seems we must accept a requirement of practical rationality with no obvious parallel in the epistemic domain. Thus, the objection concludes, there is an important structural difference between practical and epistemic rationality after all.

Our response is to reject the idea that the requirement that explains the irrationality of the ass's going to neither bundle is specific to practical rationality. As we noted above, the immediate practical reason why it would be irrational for the ass to go to neither bundle is that it would starve to death, which is clearly worse for the ass than eating either of the two bundles of hay. The requirement of (practical) rationality at work here is thus simply that it is always irrational to perform an action ϕ when it is possible to perform a strictly better alternative action ψ —that is, when one has stronger practical reasons to ψ than to ϕ. This requirement, which mirrors familiar dominance principles from decision theory and which we may call the practical domination principle, is so plausible that it may seem utterly trivial. However, note that nothing more is required to explain the irrationality of the ass's standing halfway between the two bundles without going to either one because just as going to either bundle constitutes a possible course of action for the ass, so too does remaining motionless constitute a possible course of action.

Although this practical domination principle is indeed a requirement of practical rationality, there is an analogous requirement of epistemic rationality. Namely, that it is always irrational to have an epistemic attitude D (to some proposition P) when it is possible to have a strictly better alternative attitude D* (to P) —that is, when one has stronger epistemic reasons to have D* than D (to P). For example, if one has strictly stronger epistemic reasons to have a credence of .7 rather than .6 in a proposition P, then one should not have a .6 credence in P. Call this the epistemic domination principle. Again, the principle is so plausible that it runs the risk of being considered trivial, but its truth (together with that of the practical domination principle) shows that there is no asymmetry between practical and epistemic rationality in the relevant respect. Specifically, the only requirement of practical rationality needed to explain the irrationality of the ass's inactivity in cases such as Buridan's ass is one that has a clear analogue in the domain of epistemic rationality.Footnote ¹³

One final remark before concluding. Suppose one does not accept this line of argument and is still inclined to think that there is a sense in which something in the practical domain, viz., action, is governed by a different kind of requirement than something in the epistemic domain, viz., belief. What follows? We still do not think it follows that there would be an asymmetry between epistemic and practical rationality per se. For, as we discussed in section 5, action is a very different kind of thing than belief. In order to show that practical rationality and epistemic rationality per se are different, one would need to point to similar kinds of things in each domain and show that these very things were governed by different kinds of rational requirements.

An analogy might help make the point. Suppose in conversation a friend, Kim, claims that the requirements of ‘sportsmanship’ are asymmetric in, say, track and field and in soccer. Suppose that as evidence for this claim Kim points out that only in soccer is it considered sportsmanlike to kick the ball out of bounds when a player of the opposing team is injured, and that there is no corresponding conduct considered sportsmanlike to be found in track and field. This would clearly not be good evidence for Kim's claim that the requirements of sportsmanship are asymmetric between the two sports. Why not? Because, in the case of track and field, there are no balls that can be kicked out of bounds; it is not at all surprising that there is a difference when it comes to what sportsmanship in each domain amounts to. But this fact, that sportsmanship manifests itself differently in each domain depending on the materials it has to work on, does not tell us anything about whether sportsmanship per se is fundamentally different in each domain.

In our view, we find ourselves in a similar situation with respect to action and belief. We have just argued that, as a matter of fact, action and belief are governed by symmetrical rational requirements in the case at issue, viz., the practical and epistemic dominance principles. But even if one does not accept this argument, the symmetry between epistemic and practical rationality is not undermined by the point that what counts as rationality in action sometimes differs in interesting ways from what counts as rationality in belief. As we saw in the preceding section, the two are structurally quite different kinds of things—for instance, one can be distributed between mutually exclusive options, the other cannot. One is soccer, the other track. What would undermine our argument for symmetry in cases such as that of Buridan's ass is evidence that there are structural differences between those requirements of practical and epistemic rationality that govern corresponding or analogous phenomena within each domain. While we cannot rule out that evidence of such structural differences will eventually be found, we have not yet seen anything that suggests such evidence will be forthcoming.