1. ‘Ought’ and possibility

In this essay, I shall assume the account of the semantics of ‘ought’ that I have defended elsewhere.¹ The term ‘ought’ is a broadly modal term, just like ‘should’, ‘must’, ‘may’, ‘can’ and the like. (In English these terms are auxiliary verbs, while in many other languages they are impersonal verbs taking a noun clause as their complement.) I shall suppose that every occurrence of ‘ought’ expresses a concept that functions as a propositional operator – that is, as a concept that operates on a proposition (the proposition that is expressed by the sentence that is embedded within the scope of the modal term), to yield a further proposition (the proposition that is expressed by the whole sentence).

Thus, for example, the occurrence of ‘ought’ in the English sentence ‘This room ought to be swept’ expresses an ‘ought’-concept that operates on the proposition that is expressed by the embedded sentence ‘This room is swept’. In this way, the proposition expressed by the sentence ‘This room ought to be swept’ has the logical form ‘O (This room is swept)’, where ‘O (…)’ is the relevant ‘ought’-concept. In a proposition of the form ‘O (p)’, I shall call the proposition p on which the relevant ‘ought’-concept operates the “embedded proposition”.

The truth conditions of these ‘ought’-propositions can be explained using the device of possible-worlds semantics, in the following way. For every one of these propositions, there is a relevant domain of possible worlds, and a relevant ranking on these worlds, such that the whole ‘ought’-proposition ‘O (p)’ is true if and only if the embedded proposition p is true at all worlds within the relevant domain that do not come lower down in this ranking than any other worlds in that domain. If – as will often be the case – it is possible to express this ranking by means of words like ‘better’ and ‘worse’, then we can say more simply that ‘ought’-proposition ‘O (p)’ is true if and only if the embedded proposition p is true at all the optimal worlds in the relevant domain. So, for example, the proposition that this room ought to be swept is true if and only if the proposition that this room is swept is true at all the relevantly optimal worlds in the relevant domain.²

Now, according to my account, for every concept that can be expressed by ‘ought’, the relevant domain must always be a domain of at least logically possible worlds, and the relevant ranking on that domain must be such that there are always some worlds in the domain that are not ranked lower down than any others. So it follows that whenever an ‘ought’-proposition ‘O (p)’ is true, there is an at least logically possible world in which the embedded proposition p is true. For example, if the proposition that this room ought to be swept is true, then there must be an at least logically possible world in which the proposition that this room is swept is true. In that sense, ‘ought’ always implies at least logical possibility.

There may be some ‘ought’-concepts that do not entail any stronger kind of possibility than bare logical possibility. This may be the case with what I have elsewhere called the “‘ought’ of general desirability”. This kind of ‘ought’ is expressed by the word ‘shouldst’ in the first line of Wordsworth’s poem England 1802:

Milton! Thou shouldst be living at this hour:

England hath need of thee….

The first line of Wordsworth’s poem may imply only that it is barely logically possible for Milton (who actually died in 1674) to be alive in 1802. It is not necessary that it should be physically possible in any sense, and still less that any agent should have the power to ensure that Milton is alive in 1802.

However, many other kinds of ‘ought’ are quite different from this. In particular, some kinds of ‘ought’ are clearly indexed to the situation of a particular agent x at a particular time t. To make this aspect of the concept explicit, these propositions could be thought of as having the logical form ‘O_{<x  t>} (p)’. Here, it seems, it is necessary for the truth of the proposition ‘O_<x, t> (p)’ that this particular agent x should have the power or ability, at this particular time t, to realize the embedded proposition p.

For example, suppose that at some university, the Dean remarks to the Chair of the Philosophy Department, which is aiming to appoint a new Professor of Moral Philosophy:

We ought to hire that man Bernard Williams.

This statement can clearly be refuted by pointing out that the university in question simply cannot now hire Bernard Williams, since (sadly) he is now dead. So, for this statement to be true, the relevant agent (here, presumably, the particular university referred to in this context by ‘we’) must have the power, at the time of utterance, to hire Bernard Williams. Otherwise, the sentence is false. In general, the kinds of ‘ought’ that are indexed to the situation of a particular agent at a particular time all seem to imply this more dynamic kind of possibility: a proposition p counts as “possible” in this dynamic sense if and only if the relevant agent has the power at the relevant time to realize this proposition p.

This point can be modelled within the sort of semantics that I am assuming, in the following way. With every kind of ‘ought’ that is indexed to the situation of a particular agent at a particular time in this way, the relevant domain of possible worlds consists of the worlds that it is in the relevant way within the power of that agent to realize at that time. This will guarantee that every ‘ought’ of these kinds implies the dynamic kind of ‘can’ that expresses what the relevant agent at the relevant time has the relevant sort of power or ability to realize.

These agent- and time-relative kinds of ‘ought’ seem to include both what I have elsewhere called the “practical ‘ought’” (the kind of ‘ought’ that is concerned with the courses of action that are available to an agent at a particular time) and also what I am here calling the “rational ‘ought’” (which is focused not on the courses of action that the agent might choose between, but on the various beliefs or intentions that the agent might have, or on the various processes of reasoning that the agent might go through, at the relevant time).³ When we talk about what plans or intentions an agent ought to have at a given time, it seems that this kind of ‘ought’ is also indexed to the situation that the agent is in at the relevant time. While it certainly is plausible that there are important differences between the practical ‘ought’ and the rational ‘ought’, they seem to be similar in at least this respect. In general, every occurrence of either the practical or the rational ‘ought’ implies that the relevant agent has the power to act or think as she ought to at the relevant time.

It does not yet follow that any occurrence of the practical or rational ‘ought’ implies that the agent also has the power at the relevant time to think or act otherwise than as she ought to. Indeed, in the sort of semantics that I am assuming, if a proposition p is true in all the worlds that it is within the power of the agent x to realize at the relevant time t – that is, in effect, if p is simply bound to be true no matter how the agent x exercises her various capacities and abilities at t – then ‘O_{<x, t>} (p)’ is also bound to be true. However, such ‘ought’-truths are, in a sense, degenerate or trivial truths. An ‘ought’-truth of the form ‘O_{<x, t>} (p)’ will only count as a non-trivial or non-degenerate truth if the embedded proposition p is true at the optimal worlds in the relevant domain but not at all the worlds in that domain.

So the claim that an ‘ought’-proposition ‘O_{<x, t>} (p)’ is a non-trivial truth of this sort implies not only that the embedded proposition p is within the relevant agent’s power to realize at the relevant time, but also that certain other propositions that are incompatible with p are also within the agent’s power to realize at that time.

In this way, whenever an agent is subject to a non-trivial ‘ought’, there are at least two incompatible propositions such that the agent has the power to make each proposition true. This is a two-way power: a power to φ and not to φ – the sort of power that the sixteenth-century theologian Luis Molina called the “liberty of indifference.”⁴ If you have this sort of two-way power over whether or not you φ, we could say that your φ-ing is in your control.

In short, this conception of the relevant sort of ‘ought’ supports the following conclusions: whenever an agent responds to her situation as she ought not to have done, she had the power to respond as she ought to have done; and whenever an agent is subject to a non-trivial ‘ought’, she also had control over whether or not she responded as she ought to.

In the next two sections, I shall consider some objections that philosophers may raise against these conclusions. Answering these objections will help us to give an analysis of the relevant sort of ‘can’ – that is, of the relevant concept of what is within the agent’s “power” at a given time.

2. Objections to “‘Ought’ implies ‘can’”

Harry Frankfurt (1969) has argued that an agent can be morally responsible – and even blameworthy – for a certain action even if there were no “alternate possibilities” in which the agent could have acted otherwise. Here is Frankfurt’s (1969, 835) famous example:

Suppose someone – Black, let us say – wants Jones to perform a certain action. Black is prepared to go to considerable lengths to get his way, but he prefers to avoid showing his hand unnecessarily. So he waits until Jones is about to make up his mind what to do, and he does nothing unless it is clear to him (Black is an excellent judge of such things) that Jones is going to decide to do something other than what he wants him to do. If it does become clear that Jones is going to decide to do something else, Black takes effective steps to ensure that Jones decides to do, and that he does do, what he wants him to do. Whatever Jones’s initial preferences and inclinations, then, Black will have his way. …

Suppose, for example, that what Black wants Jones to do is to kill Smith. But as things turn out, Black never has to intervene because “Jones, for reasons of his own, decides to perform and does perform the very action Black wants him to perform.” Frankfurt (1969, 836) concludes that in this case, Jones is blameworthy for his action – even though Black has ensured that Jones could not have acted otherwise.

Intuitively, if one is blameworthy for acting in a certain manner, then it must have been in some way wrong of one to act in that manner. After all, how could one be blameworthy for the manner in which one acted if the manner in which one acted was not wrong in any way, but utterly impeccable instead? But if it was in some way wrong of one to φ, then it must also have been true in some sense that one ought not to have φ-ed. So, if Frankfurt is right to conclude that Jones is blameworthy for the way in which he acted, we can surely also conclude that Jones ought not to have acted in that way – even though Frankfurt also claims that in this case, Jones “could not have done otherwise”. Thus, if Frankfurt’s conclusion is correct, it can also be used to show that the proposition that one ought not to have φ-ed does not entail the existence of any “alternate possibility” in which one did φ. If Frankfurt’s arguments are successful, they can be used to attack the principle that ‘ought’ implies ‘can’.⁵

Moreover, it seems that we can easily extend Frankfurt’s argument so that it applies to the rational ‘ought’ as well as to the practical ‘ought’. Suppose that Black would even prevent Jones from choosing not to kill Smith: for example, perhaps, if it seems to Black that Jones is about to choose any course of action which involves not killing Smith, Black would ensure that Jones does not choose that course of action (perhaps Black has implanted a chip in Jones’s brain which will result in Jones’s instant death before Jones can choose not to kill Smith). Still, some philosophers might be tempted to say that Jones ought to choose not to kill Smith, even though Black has ensured that there is no possibility of Jones’s making any such choice.

In fact, however, this Frankfurt-inspired argument fails. In this case, there is indeed no available possibility in which Jones chooses not to kill Smith – in other words, Jones cannot choose not to kill Smith. Given the principle that ‘ought’ implies ‘can’, it follows that it is not true that Jones ought to choose not to kill Smith. But even if it is not true that Jones ought to have chosen not to kill Smith, it could still be true that Jones ought not to have chosen to kill Smith. So even though Black has deprived Jones of the opportunity of choosing not to kill Smith, he has not deprived Jones of the opportunity of not choosing to kill Smith. So Jones still has an opportunity of choosing differently from how he actually chooses.

What if the chip that Black has implanted in Jones’s brain can somehow zap a choice to kill Smith directly into Jones’s mind? In this case, Jones would not even have the opportunity of not choosing to kill Smith. But he would still have the opportunity of not choosing to kill Smith entirely of his own accord, “for reasons of his own”. That is, Jones could still have made the choice in a different way from the precise way in which he actually did; and so it could still be true that Jones ought not to have chosen to kill Smith in the precise way in which he does.⁶

In general, it is clear every Frankfurt-style case involves a counterfactual manipulator who removes some of the agents’ opportunities, by standing ready to intervene if the agents exercise some of their thinking or reasoning capacities in a certain way. It follows that the counterfactual manipulator cannot remove the agents’ thinking or reasoning capacities. Moreover, it also follows that the counterfactual manipulator cannot remove all opportunities for the agents to exercise those thinking or reasoning capacities otherwise than as they actually do. If the manipulator had intervened, his intervention would have been triggered by the agents’ thinking or reasoning differently from how they actually did. If there was no possibility of the agent’s thinking or reasoning differently from how they actually did, there is also no possibility of the manipulator’s intervening. So these cases presuppose that it is possible for the agents to think and reason differently from how they actually did. So even if ‘ought’ implies ‘can’, it could still be true that the agents ought not to have exercised their thinking or reasoning capacities in the precise way in which they actually did.

In this way, these Frankfurt-inspired cases help us to understand the kind of ‘can’ that is implied by the rational ‘ought’. For it to be true that an agent “can” think or reason in a certain way, the agent must have both the capacity and the opportunity for thinking in that way. Moreover, to capture the truth about the ways in which the agent ought to think and reason at a particular time, the relevant “ways” of thinking may have to be individuated quite finely: for example, it may be that the relevant way of thinking is not as simple and general as not choosing to kill Smith; it may be more specific and detailed than that, such as not choosing to kill Smith of one’s accord, for reasons of one’s own.

A second objection to “‘Ought’ implies ‘can’” is due to Peter A. Graham (2011). Graham focuses on a case in which a surgeon cuts up two healthy patients in order to save ten other patients who would otherwise die. Graham claims that the surgeon is acting wrongly even if she is acting from a “compulsion” that she cannot resist. He defends this claim by arguing for the following two theses: first, it would be permissible for another agent – such as a janitor, for example – to shoot the surgeon in order to stop her from cutting up the two healthy patients; and secondly, every adequate explanation of why it would be permissible for the janitor to shoot the surgeon implies that if the janitor did not shoot the surgeon, the surgeon would be acting wrongly in cutting up the two healthy patients.

If the surgeon is acting wrongly in cutting up the two patients, it is surely true that the surgeon ought not to cut up these two patients – even though her “compulsion” allegedly ensures that she could not have done otherwise. Again, we can adapt this argument so that it focuses on the rational ‘ought’ instead of the notion of “acting wrongly”, since it also seems intuitively plausible to say that the surgeon ought not to have chosen to cut up the patients, even if her compulsion made it impossible for her not to make that choice.

Thus, to defend the principle that ‘ought’ implies ‘can’, I shall have to argue for at least one of the following two propositions: either (a) it is really true that the surgeon is incapable of not choosing to cut up the patients, and so it is not true that she ought not to have chosen to do so; or (b) it is true that she ought not to have chosen to cut up the patients, and so, despite her “compulsion”, she must have been capable of not making that choice.

As a matter of fact, it seems that the nature of “compulsions”, at least in the actual world, supports this second claim (b). This is because such compulsions seem broadly similar to powerful addictions, which are certainly at least partial excuses or mitigating factors, significantly reducing the extent to which the agent is blameworthy for her choices, but do not completely remove the agent’s capacity for choosing otherwise.⁷ In some sense, the compulsion may “diminish” the surgeon’s capacity to think and reason as she ought to; this explains why the compulsion will normally at least mitigate the extent to which the agent is blameworthy for making that choice. But so long as the surgeon’s capacity to think and reason as she ought to has not been diminished all the way to zero, it will still be true to say that she “can” think and reason as she ought to.

We might wonder: Why couldn’t there be a “super-compulsion”, which completely removes the agent’s capacity to reason in any way otherwise than as she actually does? However, it seems doubtful whether such a “super-compulsion” is compatible with genuine reasoning at all. Every case of genuine reasoning involves the thinker’s exercising his or her reasoning capacities. Moreover, it is arguable that these reasoning capacities essentially involve the kind of two-way powers that I mentioned at the end of the previous section. For example, if a reasoner exercises the capacity to deliberate about a certain proposition p at a certain time t, the reasoner surely also has the capacity not to deliberate about p at that time, but to deliberate about some alternative proposition q instead. If that is correct, then it is impossible for any genuine reasoner to be incapable of reasoning in any way other than as she actually does. Without the capacity to reason in more than one alternative way, the agent is not in fact reasoning at all.

In this way, Graham fails to refute “‘Ought’ implies ‘can’”: he does not produce any case in which it is clear that the agent ought not to have made the choice that she actually made, even though she could not have refrained from making that choice. Nonetheless, his objection has also helped us to understand the kind of ‘can’ that is implied by the rational ‘ought’. For it to be true that one “can” think or reason in a certain way, one must have a capacity for reasoning in that way; these capacities come in degrees, and so may be diminished without being totally removed; and all reasoning of any kind involves the exercise of capacities of this kind.

3. Voluntary control vs. deliberative control

I have argued that every non-trivial proposition involving the rational ‘ought’, of the form ‘O_{<x, t>} (p)’, implies that at the relevant time t, the agent x has control over whether or not p is true – that is, the agent has the power to realize p, and also has the power to realize some other incompatible proposition as well.

Some philosophers will claim that such “control” can only be exercised voluntarily, or by executing a choice or intention to exercise such control. Given what I have argued about ‘ought’, this claim implies that the idea that there are non-trivial truths about the beliefs that an agent ought to form presupposes a kind of doxastic voluntarism – that is, the thesis that it is possible to form beliefs voluntarily or at will.⁸

Many philosophers reject such doxastic voluntarism, arguing that it impossible to form a belief voluntarily, or by executing a choice or intention to do so. It certainly seems that, even if one can form a belief in a proposition p voluntarily, forming this belief cannot be a “basic action”, something that one can do simply by executing an intention to do it: the only way in which one could execute an intention to form a belief in p would be by engaging in some complicated activities of self-manipulation, and even then one’s forming the belief in p would be the causal effect of one’s executing this intention, and would not itself consist in one’s execution of any intention.

Moreover, whether or not one believes a proposition often seems to be determined directly by the evidence, without one’s having any choice in the matter at all. Suppose that one is standing in the driving rain, soaked to the skin, with one’s face constantly battered by raindrops. It seems impossible in this case for one to believe that it is not raining: in this way, one seems to have no control whatsoever over whether one believes that it is not raining; and it may seem tempting to generalize from this that one has no control over one’s beliefs at all.

In fact, if this objection really tells against the idea that there are non-trivial truths (involving the rational ‘ought’) about what one ought to believe, it would also tell against the idea that there are non-trivial truths about what one ought to choose as well. To choose a course of action is precisely to form an intention to pursue that course of action. For example, to choose to tell a certain joke is in effect to form an intention to tell that joke. So if you executed an intention to choose to tell the joke, you would in effect be executing an intention to form an intention to tell the joke. While it may sometimes be possible to execute an intention to engage in some complicated form of self-manipulation that will result in your forming an intention to tell the joke, it still seems that your forming the intention to tell the joke is at most the causal effect of your executing your intention to engage in that self-manipulation; it does not itself consist in your executing the intention to engage in that self-manipulation. Thus, executing an intention to form an intention to tell the joke could not be a “basic action”: in this sense, one cannot directly execute an intention to form the intention; we cannot form intentions voluntarily or at will.⁹

Admittedly, it is true that with respect to choices, we are often in the situation of “Buridan’s Ass”, where it is evident that we have to make a completely arbitrary choice (whereas it is doubtful whether we are ever in a comparable situation with respect to beliefs, in which it is clear that we have to form a completely arbitrary belief). But even in these cases, we typically just directly make an arbitrary choice for one of the available options; we do not normally make the arbitrary choice by executing an intention to make the choice. Moreover, whether or not we form a certain choice or intention often seems to be determined directly by compelling reasons that bear on what to do. For example, if you are close to the edge of an immensely high cliff, with no reasons of any kind to jump off the edge, it may simply be impossible for you to choose to jump. So there also seem to be severe limits on what it is possible for you to choose, as well as on what it is possible for you believe. In general, broadly similar considerations seem to tell against a voluntarist view of intention as against a voluntarist view of belief.

One response to these considerations would be to deny that there are any non-trivial truths either about what one ought to believe or about what one ought to choose. But this response seems too drastic to be plausible. A better response would be to recognize that in addition to the “voluntary control” that we sometimes have over how we act, there is also a different kind of control that we have over our intentions and beliefs.

One way to articulate a more general notion of “control” is by deploying the notion of a capacity. We have voluntary control over how we act because we can (i) form intentions about how to act, by exercising our intention-forming capacities in various ways, and then (ii) by exercising our intention-executing capacities, we can carry out those intentions. But these intention-forming capacities belong to the larger category of reasoning capacities. So we can also make sense of the suggestion that we have control over our beliefs and intentions because we can exercise our reasoning capacities, and the way in which we exercise those reasoning capacities will determine what we believe and intend. We could call the latter sort of control “deliberative control”. Our voluntary control over how we act involves both our intention-forming capacities and our intention-executing capacities; our deliberative control over what beliefs or intentions we have involves our reasoning capacities alone.

This distinction points to the basic difference between the practical ‘ought’ and the rational ‘ought’. The role of the practical ‘ought’ is to guide us to form and execute our intentions to act in accordance with the evidence that bears on how we ought to act. By contrast, the rational ‘ought’ guides us more directly: under favourable circumstances, we can form and revise our beliefs and intentions, by exercising our reasoning capacities, directly in response to the evidence that bears on how we ought to form and revise those beliefs and intentions.

This notion of deliberative control involves the notion of our having capacities that we can exercise. To say that we “can” exercise these capacities is to say more than just that we possess these capacities; we must also have a suitable opportunity for exercising these capacities. In short, the kind of ‘can’ implied by the rational ‘ought’ involves both opportunities and capacities. In the following three sections, I shall first explain how we can use the notions of opportunities and capacities to analyse this kind of ‘can’, and then –somewhat more tentatively – I shall suggest an analysis of what these opportunities and capacities amount to.

4. Possibility, opportunity and capacity

The orthodox view among formal semanticists – such as, most notably, Angelika Kratzer (1977) – is that ‘can’ always expresses some kind of possibility. So, whenever the word ‘can’ is used, the context must somehow fix on a relevant domain of possible worlds (often a fairly restricted domain, which has something to do with the practical or epistemic situation of certain salient agents at a certain time). Then a proposition of the form ‘Can (p)’ is true if and only if there is a possible world w within the relevant domain such that the embedded proposition p is true at w.

Some discussions of ‘can’ distinguish between the uses of ‘can’ that ascribe specific abilities and those that ascribe general abilities.¹⁰ It is undeniable that just like many other present-tensed statements – such as ‘Ruth goes to church on Sundays’ – a statement of the form ‘I can speak German’ can be used to make a generic quantification over all normal situations of a certain kind. For our purposes, however, these generic uses of ‘can’ are less important than statements about how a thinker can exercise her capacities in the particular situation under consideration. (As we shall shortly see, the notion of “possessing a capacity” always involves a certain kind of generality; but as I pointed out at the end of the previous section, we are aiming here to give an account, not of what it is for a thinker to possess a capacity, but of what makes it true that the thinker can exercise her capacities in the particular situation at hand.) So, I shall aim to ensure that my account of the relevant sort of ‘can’ conforms to this orthodox approach within formal semantics. At the same time, my account will also invoke the notions of opportunities and capacities that were introduced in the previous sections.

Within the framework of this orthodox semantics, the crucial task for analysing any kind of ‘can’ is to specify the relevant domain of possible worlds. I propose that the relevant domain of possible worlds can be defined in terms of opportunities and capacities, in something like the following way.

Consider an occurrence of ‘can’ that is indexed to the situation of a certain agent x at a certain time t in the actual world w*. The agent x will have a certain set of reasoning capacities C in this situation – that is, x’s reasoning capacities at t in w* are all and only the capacities in C.

Inevitably, there will be a variety of different ways of exercising these capacities. For every way W of exercising some members of this set of capacities C, if the agent has an opportunity of exercising these capacities in way W in this situation, then there will a set of possible worlds in the relevant domain in which the agent exercises those capacities in that way W. Specifically, this set of worlds will be the subset of the worlds in which the agent x exercises these capacities in way W at t which are (i) nearest to the actual world w*, and (ii) normal with respect to the operation of those capacities.

Since the agent has an opportunity to exercise her capacities in way W, we may stipulate that the relevant “nearness” and “normality” conditions will ensure that this subset of the domain is never empty. The whole domain of worlds will contain such a subset for every such way of exercising these capacities, but otherwise it will contain no other worlds. A statement of the form ‘Can (p)’, indexed to the situation of the agent x at time t, will be true in w* just in case there is a world in this domain in which p is true.

This appeal to the “nearest” worlds in which the agent exercises these capacities in the relevant way W is modelled on David Lewis’s (1973) semantics for counterfactual conditionals. According to Lewis’s semantics, a counterfactual of the form ‘If x had exercised her capacities in way W, it would have been the case that p’ is true if and only if p is true in all the nearest worlds in which x exercises her capacities in way W; and a counterfactual of the form ‘If x had exercised her capacities in way W, it might have been the case that p’ is true if and only if p is true in some of the nearest worlds in which x exercises her capacities in that way.

My proposal about the semantics of the relevant sort of ‘can’ is designed to ensure that a statement of the form ‘Can (p)’, indexed to the situation of the agent x at time t, logically implies that x has the opportunity at t of exercising her capacities in some way W such that if x exercised her capacities in way W at t, then p might be true. If p is true in that (non-empty) subset of the worlds in which x exercises her capacities in way W that are (i) nearest to the actual world and (ii) normal with respect to the operation of the relevant capacities, then p will obviously also be true in some of the nearest worlds in which x exercises his capacities in way W.

According to my proposal, ‘Can (p)’ does not imply that there is a way W in which x can exercise her capacities at t such that p is true in all the nearest worlds in which x exercises her capacities in way W, since some of those worlds might fail to meet condition (ii) – that is, some of these worlds may not be normal with respect to the operation of the relevant capacities. Thus, ‘Can (p)’ does not imply that there is a way W of exercising these capacities such that if x exercised these capacities in way W, p would be true. Instead, what ‘Can (p)’ implies is something stronger than the ‘might’-counterfactual but weaker than the ‘would’-counterfactual – namely, that there is a way W in which x can exercise the relevant capacities such that one of the normal consequences that x’s exercising these capacities in way W might have is p’s being true.

We need to appeal to a counterfactual of intermediate strength, stronger than the ‘might’-counterfactual but weaker than the ‘would’-counterfactual, in order to capture our intuitions about ‘can’. Suppose that I have a rudimentary level of skill at playing darts. Even if there is a possible world in which when I exercise my darts-playing capacities, I intentionally hit the bull’s-eye, it does not seem true to say that I “can intentionally hit the bull’s-eye”, since the possible world in which I intentionally hit the bull’s-eye is not sufficiently normal for the operation of my darts-playing capacities. Indeed, even if, once in a lifetime, I actually hit the bull’s-eye, the actual world would then fail to count as sufficiently normal for the operation of my darts-playing capacities, and so it still would not follow that I can intentionally hit the bull’s-eye.¹¹

On the other hand, I can intentionally hit the top half of the darts board. Nonetheless, it does not follow that in absolutely every one of the nearest worlds in which I exercise my darts-playing capacities in the relevant way, I hit the top of half of the board. For it to be true that I can intentionally hit the top half of the darts board, my darts-playing capacities do not have to be quite as super-reliable as that. Even if there are some worlds where I aim slightly too low, and so fail to hit the top half of the darts board, this does not imply that I cannot intentionally hit the top half of the board. Indeed, in those worlds, I will kick myself for missing the top half of the darts board precisely because I know that I could have hit it.¹²

So far, this account of the truth-conditions of the relevant sort of ‘can’ has taken the notion of exercising a capacity, and the notion of an opportunity for exercising a capacity, as primitive. In the next two sections, I shall propose an analysis of these two notions. My analysis will be broadly reductive in spirit: according to this analysis, capacities can be identified with dispositions of a certain sort, and opportunities can be identified with a certain sort of chances.

5. Capacities and dispositions

Several philosophers – perhaps most notably Michael Fara (2008) – have recently suggested identifying capacities with dispositions. Some other philosophers – such as Randolph Clarke (2009) – have objected to this identification. I shall argue here that with some careful amendments, this dispositionalist theory of capacities is not vulnerable to those objections.

Some objections to the dispositionalist theory of capacities stem from the assumption that this theory is designed to explain not just what it is for an agent to have a certain capacity (and what it is for the agent to exercise this capacity), but also to explain what it is for the agent to have an opportunity for exercising the capacity as well. In my view, we should not accept this assumption. Your dispositions are grounded in relatively intrinsic features of you, whereas your opportunities also depend on more remote features of your environment. So we should not expect to be able to analyse your opportunities in terms of your dispositions. However, your capacities differ from your opportunities in precisely this respect: your capacities are grounded in relatively intrinsic features of you, rather than in more remote features of your environment, and so it is much more plausible to identify your capacities with some of your dispositions.

Fara’s dispositionalist theory focuses on the kinds of capacities that I would call our “intention-executing dispositions”. This is why he identifies the capacity to φ with the disposition to φ when one tries to φ. More precisely, the nature of each disposition is given by a function that maps stimulus conditions onto response conditions. Fara’s proposal in effect identifies the capacity to φ with the disposition that, for every time t, maps the stimulus condition tries to φ at t onto the response condition φ-s at (or shortly after) t.

Fara (2005), like Alexander Bird (1998) before him, insists that it is a mistake to analyse dispositions in terms of conditionals (including counterfactual conditionals). Fara suggests instead that we can analyse dispositions by quantifying over normal cases: if each of these “cases” involves a time as well as a possible world, then to say that an agent x is disposed to φ when x tries to φ is to say that in every normal case in which x tries to φ at the time of the case t, x φ-s at or shortly after t.

A potentially different approach would view dispositions as closely akin to ceteris paribus laws of nature. According to this second approach, to say that an object has a disposition is to say that it has intrinsic features in virtue of which it falls under a ceteris paribus law of a certain kind. This second approach will in fact be equivalent to Fara’s so long as (i) a case counts as “normal” if and only if cetera are paria in the relevant way, and (ii) the law in question is the law that ceteris paribus, for any time t, if x tries to φ at t, x φ-s at or shortly after t. But this law-based approach may have some advantages over Fara’s approach, since it can allow that the relevant ceteris paribus law is a probabilistic law (like the laws of classical statistical mechanics or Mendelian genetics), rather than a simple universal quantification over times or the like.

However, for present purposes, I shall remain neutral about the nature of dispositions. Whatever the best account of dispositions turns out to be, it seems plausible to identify capacities with dispositions of a certain sort. Possessing a capacity can be identified with having the corresponding disposition, and exercising a capacity with manifesting the corresponding disposition. I shall also not commit myself to a definite account of what it is to “manifest” a disposition; but it seems that for x to manifest this disposition to φ whenever x tries to φ will involve its being the case that in virtue of this disposition, x’s trying to φ is in a suitable way a proximate cause of x’s actually φ-ing.

Since we are interested in understanding reasoning capacities, rather than intention-executing capacities, the relevant capacity to φ will not be a disposition to φ whenever one tries to φ. Instead, we should follow a suggestion that is due to Donald Davidson (1980, 68). The capacity will be a disposition that responds to one’s having a set of mental states and events that counts as a reason for one to form or revise one’s attitudes in a certain way W.¹³ The disposition will respond to this set of mental states and events precisely by forming or revising one’s attitudes in that way W (or perhaps by having a certain chance of forming or revising one’s attitudes in that way). For example, suppose that the set of mental states and events that one is going through at a certain time counts as a reason for one to form the belief that one’s train is late. Then one might manifest a reasoning disposition of this kind if one responded to this set of mental states and events by forming the belief that one’s train is late.¹⁴

In general, each of these reasoning dispositions corresponds to a function of the following kind: the domain of the function is a set of stimulus conditions each of which consists in the reasoner’s undergoing a set of mental states and events that counts as a reason for forming or revising one’s attitudes in some way W; and the function maps this stimulus condition onto the response condition that consists in forming or revising one’s attitudes precisely in that way W (or by having a certain chance of forming or revising one’s attitudes in that way).

This dispositionalist view of capacities can make sense of a point that we noted in Section 2, that capacities come in degrees, and can be “diminished” without being totally removed. Especially if the dispositions in question are probabilistic in nature, we can distinguish between more and less reliable dispositions. At least one way for one agent’s capacity to be greater than another agent’s is for the first agent to have a more reliable disposition; and for someone’s capacity to be “diminished” is for the reliability of the corresponding disposition to be reduced in some way.

I am assuming here that every disposition is defined by a function that has a domain of stimulus conditions and a corresponding range of response conditions. In this way, the identification of capacities with dispositions of a certain kind supports the following claim of Anthony Kenny (1975, 135) – at least if we take Kenny’s use of the term ‘ability’ as coextensive with my use of the term ‘capacity’:

Abilities are inherently general; there no genuine abilities which are abilities to do things only on one particular occasion. This is true even of abilities, such as the ability to kill oneself, which of their nature can be exercised only once.

This view of capacities also explains the attractions of the well-known conditional analysis of what it is to have the power to φ – according to which to have the power to φ is to be such that one would φ if one chose to. Although I have not endorsed the analysis of dispositions in terms of counterfactual conditionals, it is clear that a disposition ascription is at least very close to a cluster of counterfactual conditionals.¹⁵ So if capacities are dispositions, this would explain the appeal of the conditional analysis.

At the same time, I have not analysed this sort of ‘can’ simply in terms of the agent’s possession of these capacities. As I have emphasized above, for it to be true that one can exercise one’s capacities in a certain way on a particular occasion, it is not enough that one simply possesses these capacities on that occasion; one must also have the opportunity to exercise those capacities in that way on that occasion. In the next section, I shall turn to the question of how to understand these opportunities.

6. Opportunities and chances

For an agent x to have an opportunity to exercise certain capacities in a certain way at a time t in a world w, a crucial necessary condition must be met: there must have been a non-zero chance in w, up to shortly before t, that x will exercise those capacities in that way at t.¹⁶

The way in which I am thinking of “chances” here is inspired by some recent work of Luke Glynn (2010). Strictly speaking, according to Glynn’s account, chances are relative not just to worlds and times, but also to what Glynn calls “levels”. These “levels” are in effect levels of causal structure in the world. Different scientific theories may be concerned with different levels: microphysics is concerned with the microphysical level, while thermodynamics and Mendelian genetics are concerned with different, less fundamental levels.

Probabilistic laws of nature can be thought of as assigning chances to various propositions in relation to each world and time, relative to the level of causal structure to which those laws of nature belong. These chances can be thought of as measuring sub-regions of a space of possibilities: specifically, for the chances that are relative to time t, world w, and causal level l, the relevant space of possibilities consists entirely of possibilities in which all l-level facts about times before t, and all l-level laws of nature, are held fixed – but the l-level facts about times after t are not in general held fixed. The chance of a proposition p, in relation to t, w, and l, corresponds to the proportion of this space of possibilities in which p is true.

For the opportunities of an agent, the relevant level of causal structure is presumably the broadly folk-psychological level, which deals with the explanation of the agent’s actions and attitudes in terms of the agent’s motivating reasons for those actions and attitudes. The reason for this is that what is at issue is a distinctively agential kind of ‘can’; so it seems that the relevant level of causal structure will have to be the broadly folk-psychological level, since it is at this level that the central agential notions have their home, in the explanation of actions in terms of the agent’s motivating reasons.

I have said that the existence of such a non-zero chance of the agent x’s exercising their capacities in the relevant way at time t is a necessary condition of x’s have the opportunity of exercising their capacities in that way at t. We can see that it is not a sufficient condition by reflecting on the Frankfurt-style cases. Suppose that there is a non-zero chance that Black’s intervention will fail to prevent Jones from choosing not to kill Smith. This is not enough to make it true that Jones has a genuine opportunity of choosing not to kill Smith, if in all the nearest worlds in which Jones does not choose to kill Smith of his own accord, Black intervenes successfully and prevents Jones from choosing not to kill Smith.

In this case, Jones lacks any opportunity at time t of choosing not to kill Smith because the fact that Black would intervene and prevent Jones from making such a choice is causally independent of the way in which Jones exercises his capacities at t. In that sense, the fact that Black would intervene successfully in this way is a fact at the folk-psychological agential level that is causally independent of how Jones exercises his capacities at the relevant time. More precisely, then, I propose that the genuine opportunities for the agent x at the time t are precisely the non-zero chances that are consistent with all the causally independent folk-psychological truths of this sort.

In one sense, the approach that I am advocating here is reductive: it seeks to reduce facts about an agent’s powers and abilities to facts about chances, dispositions, and causal relations between mental events, mental states, and actions. In another sense, however, it is not reductive, since it is compatible with the view that the core folk-psychological properties and relations are themselves completely irreducible, and cannot be reduced to any physical or functional properties whose nature could be explained in non-psychological terms.

One notable advantage of this approach, at least when conjoined with Luke Glynn’s idea that all chances are relative to some level of causal structure, is that it can explain how the proposition that the agent “can” exercise her capacities otherwise than as she actually does is compatible with the thesis that the world is deterministic, at least at the microphysical level. Suppose that at time t, I actually exercise my capacities in way W₁ rather than in an alternative way W₂. Then if the causal structure of the world is deterministic at the microphysical level, it seems plausible that the proposition that I will exercise my capacities in way W₂ at t has a micro-level chance of 0 at all times in the actual world w*. However, the proposition that I will exercise my capacities in W₂ may still have a chance greater than 0 at the folk-psychological level. According to the picture that I have sketched here, it is this sort of chance that is necessary for me to have had an opportunity for exercising my capacities otherwise than how I actually exercised them.

According to the semantics that I proposed in Section 4, a proposition of the form ‘Can (p)’, indexed to the situation of an agent x at a time t, is true at a world w if and only if there is a possible world in the relevant domain at which p is true. Suppose that w’s laws of nature are deterministic at the microphysical level. Then if the relevant domain consisted only of worlds in which the laws of nature are exactly as they are in w, and in which all past events prior to t were exactly as they were in w, then the relevant domain could not contain any worlds in which any microphysical facts were different from what they are in w. If all the mental and agential facts supervene on the microphysical facts, then the relevant domain cannot contain any worlds in which the relevant agent exercises her capacities otherwise than as she actually does.

As we have seen, however, if there are any non-trivial truths involving the rational ‘ought’, it must be true that the agent could have exercised her capacities otherwise than as she did – and so the relevant domain must contain some possible worlds in which the relevant agent exercises these capacities differently. However, we should not take this point to show that the existence in the actual world of non-trivial truths involving rational ‘ought’ is incompatible with the world’s being deterministic at the microphysical level. It far from obvious that the relevant domain must contain only worlds where all microphysical events prior to time t are exactly as they actually are, and where the microphysical laws of nature are exactly as they actually are. The relevant domain must presumably contain only worlds where the psychological laws and mental events and states prior to t are as they actually are. But so long as the laws of psychology are indeterministic – as they surely are – this point creates no problem for the existence of non-trivial truths involving ‘ought’. If the relevant domain may contain worlds where either the past microphysical events or the laws of microphysics are different from how they are in the actual world, then a kind of compatibilism will be true: even in a deterministic world, it will still be true, in the relevant sense, that the agent could have exercised her capacities otherwise.

7. ‘Can’ in context

Up to this point, I have been overlooking a crucial point about the analysis that I have presented – namely, the fact that several of the crucial terms appearing in this analysis are not perfectly precise. For example, my allusions to the “nearest” worlds in which the agent x exercises the relevant capacities in a certain way, and to worlds that are “normal” with respect to the operation of those capacities or dispositions, are clearly less than completely precise.

The justification for this sort of imprecision is familiar: it is that the word ‘can’ itself is imprecise. There is a range of different precise concepts that the term can be taken as expressing. Sometimes the context in which the term is used will narrow down this range of concepts in some way; and different contexts may narrow down this range in rather different ways, depending on the interests and purposes of the participants in the conversation.

For example, the context in which the term ‘can’ is used can obviously make a difference to which agent and which time an occurrence of this sort of ‘can’ is indexed to. Moreover, the “time” that I have alluded to is probably better thought of as a period or stretch of time, rather than as an instant or point in time. So the context in which the word ‘can’ is used can also make a difference to how long this time period is. In some contexts, we may focus on how the agent exercises her capacities over an extended period of time. In other contexts, however, we focus only on how the agent exercises her capacities during a much shorter period, and we may even treat the way in which the agent would exercise her capacities after that period as causally independent of how the agent exercises these capacities during the short period in question.¹⁷

Moreover, in the previous section, I identified opportunities with chances – suggesting that there is an opportunity for you to exercise your capacities in a certain way only if there is a non-zero chance of your exercising your capacities in that way. But in some contexts, a genuine “opportunity” may be taken to require more than just any non-zero chance, however small. In these contexts, the proposition that there is an opportunity for you to exercise your capacities in a certain way implies that there is a significant chance of your exercising your capacities in that way.

In general, some contexts, the term ‘can’ may be used fairly strictly – so that in those contexts, relatively few sentences of the form ‘Can (p)’ are true – while in other contexts, the term may be used more loosely – so that in those more relaxed contexts, a larger number of sentences of the form ‘Can (p)’ are true.

Since ‘ought’ implies ‘can’, these different ways of using ‘can’ correspond to analogously different ways of using ‘ought’. When we use ‘can’ more loosely, the relevant domain of possible worlds is more extensive, and includes more possibilities than in some other contexts. In these contexts, the corresponding ‘ought’ is more idealized, since the optimal worlds in this larger domain may not even be viewed as possible in more restricted domains. By contrast, when we use ‘can’ more strictly, the relevant domain of possible worlds is more restricted, and the corresponding ‘ought’ may be less idealized or more “realistic”, since the optimal worlds in this more restricted domain may be definitely inferior to the worlds that would count as optimal in a larger domain.

It does not seem plausible to me that there is a good question about which of these many slightly different ways of understanding ‘can’ and ‘ought’ is the one true notion that is of central importance to philosophy. All of the different notions that can be expressed by these terms in different contexts are equally legitimate, and there is no reason for regarding any of them as more important than the others.

Some moral philosophers seem to wish for a perfect language, with a small number of primitive terms, each of which univocally expresses a philosophically central concept. The languages that we actually speak are profoundly different from that imagined perfection. Moreover, we need to understand the wide range of concepts that we actually use, before we can even begin to identify which concepts are of greatest philosophical importance. The account that I have been proposing here is focused on that preliminary task.

8. Conclusion

In the first three sections of this paper, I argued (against Harry Frankfurt and Peter Graham among others) that the existence of non-trivial truths involving the rational ‘ought’, indexed to the situation of a particular agent at a particular time, implies that in a fairly robust sense the agent had the power or ability to exercise her abilities as she ought to, and also the power to exercise those abilities otherwise than as she ought to. I then offered an analysis of this kind of ‘could have done otherwise’. My analysis was in a way a synthesis of a number of insights that several philosophers have had over the years: Anthony Kenny’s emphasis on the distinction between opportunity and capacity; Angelika Kratzer’s classic analysis of ‘can’; Michael Fara’s dispositionalist theory of capacities; and Luke Glynn’s compatibilist conception of chances. A synthesis of these perceptive insights yields a credible view of the kind of ‘can’ that is implied by the rational ‘ought, and a vindication of the fundamental truth behind the traditional slogan ultra posse nemo obligatur – that is, “‘Ought’ implies ‘can’”.

References

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1 For my earlier discussions of the semantics of ‘ought’, see especially Wedgwood (2007, Chap. 4–5, and 2009).

2 This is in a sense the “classical” semantics for deontic operators, which was defended by such pioneering deontic logicians as Åqvist (1967) and Lewis (1973). My defence of this classical semantics is given in Wedgwood (2007, Chap. 5).

3 For my account of this distinction between the essential conceptual roles of the practical ‘ought’ and the rational ‘ought’, see Wedgwood (2007, 121).

4 See especially the discussion of the liberty of indifference in Kenny (1975, chap. 7).

5 This point is due, that any attack on the principle of alternate possibilities will also undermine “‘Ought’ implies ‘can’”, is due to David Copp (1997).

6 Compare the response to Frankfurt that is given by Otsuka (1999).

7 For an illuminating discussion of addiction, see Yaffe (forthcoming).

8 For a discussion of doxastic voluntarism, see especially Alston (1989) and Williams (1973).

9 For this point about how beliefs and choices are parallel in this respect, see Hieronymi (2006).

10 See e.g. Mele (2002) and Maier (2010) for some discussion of this distinction.

11 For this point, see Kenny (1975, 136). Even though I share Kenny’s intuitions about the darts case, I do not accept his objections to the orthodox possible-worlds semantics for ‘can’. Kenny (1975, 137) objects that in every normal modal logic ‘◊ (p ˅ q)’ entails ‘◊p ˅ ◊q’, but the premise ‘I can pick either a red card or a black card’ does not intuitively entail the conclusion ‘I can pick a red card or I can pick a black card’. However, Kenny’s objection is plausible only if we hear the premise as meaning, in effect, ‘I can execute an intention to bring it about that I pick either a red card or a black card’, and hear the conclusion as meaning ‘I can execute an intention to bring it about that I pick a red card or I can execute an intention to bring it about that I pick a black card’. But then the logical form of the premise is not ‘◊ (p ˅ q)’: it has the more complicated form ‘◊ (Intentionally-bring-about: (p ˅ q))’ instead. So Kenny’s objections do not undermine the orthodox possible-worlds semantics for ‘can’.

12 For this point, see Austin (1961, 166) and response of Kenny (1975, 142).

13 Compare the appeal to “reason-responsiveness” that is due to Fischer and Ravizza (1998).

14 For further discussion of dispositions of this sort, see Wedgwood (2007, chap. 8).

15 For a recent example of an account of our rational capacities in terms of a cluster of such conditionals, see Smith (2003).

16 Peacocke (1999) in effect sees the need for a notion that of an “opportunity” for exercising one’s capacities in the way, but he analyses this notion, not in terms of chances, but in terms what happens in the “close” or “nearby” possible worlds. But to analyse the notion of an agent’s having opportunity at a particular time, it seems preferable to appeal a concept like that of a “chance”, which is explicitly relativized to a particular time as well as to a world, rather than the concept of a close possible world, which is only relativized to a world.

17 I believe that this point is relevant to some of the debates between “actualist” and “possibilist” theories of ‘ought’. The intuitions that seem to support actualist theories may in fact reflect contexts in which the attention is on what the agent should do during a short time period, and facts about what the agent would do after that time period is treated as causally independent. But this point requires a more extended discussion than I can give it here.