Objective and Subjective 'Ought'

Over the years, several philosophers have argued that deontic modals, like ‘ought’ and ‘should’ in English, and their closest equivalents in other languages, are systematically polysemous and context-sensitive. On this view, each of these terms can express a range of related concepts – which in this paper I shall to refer to as “‘ought’-concepts” – and the particular context in which the term is used somehow determines which ‘ought’-concept the term expresses in that context.

More specifically, one way in which these ‘ought’-concepts differ from each other is that some of these concepts are more “objective”, while others are more “subjective” or “information-relative”. When ‘ought’ expresses one of these more objective concepts, what an agent “ought” to do in a given situation may be determined by facts that neither the agent nor any of his friends or advisers either knows or is even in a position to know; when it expresses one of the more “subjective” concepts, what an agent “ought” to do is in some way more sensitive to the informational state that the agent (or his advisers or the like) find themselves in at the conversationally salient time.^¹

In this essay, I shall first present some linguistic evidence in favour of this view of ‘ought’. Then I shall propose a precise account of the truth-conditions of propositions involving these ‘ought’-concepts that will explain more clearly how exactly these concepts are related. Unfortunately, in the available space I shall not be able to do much more than simply to propose this semantic account of these kinds of ‘ought’-propositions. In my opinion, the linguistic evidence makes this account more plausible than any alternative account that metaethicists or semanticists have devised so far; but I shall only be able to gesture in the direction of this evidence here.

The general idea of the kind of account that I shall propose is not new. It is fundamentally similar to the theory of “subjective rightness” that is given by Frank Jackson (1986) – since like Jackson’s theory, it gives a starring role to the notions of probability and of the expected value of a proposition. Nonetheless, my account will have several crucial differentiating features: unlike Jackson’s theory, my account implies that standard deontic logic is valid for every one of these ‘ought’-concepts; it is significantly more general than Jackson’s theory, since it is designed to account for all concepts that can be expressed by ‘ought’ and its equivalents (not just for the concept of subjective moral rightness that Jackson is interested in); and it is also designed to mesh with a quite different account of how terms like ‘ought’ interact with conditionals.

The proposal that I shall give here also has affinities with that of Gunnar Björnsson and Stephen Finlay (2010), according to which the context-sensitivity of ‘ought’ is explained on the basis of the thesis that the occurrences of ‘ought’ are relativized to bodies of information. In a somewhat similar way, I shall propose that occurrences of ‘ought’ are relativized to probability functions; and every probability function determines a body of information – namely, the set of propositions that have probability 1 according to that function. Still, as I shall explain in Section 4 below, my approach differs from theirs in several crucial ways.

In my view, a full account of the semantics of a term in a natural language would have to be a fairly complicated story.^² More precisely, such an account would have to involve the following components:

In this essay, I shall focus chiefly on the last of these components. That is, I shall focus on offering a truth-conditional semantics for the propositions that can be expressed by means of deontic modals like ‘ought’, in terms of the conditions that are necessary and sufficient for such a proposition to be true at a possible world.

However, I shall also aim to make a contribution to the first component that would belong in a full account of these deontic modals, since I shall start by surveying the various ‘ought’-concepts that these terms can express in various contexts. After surveying these ‘ought’-concepts, I shall first present the truth-conditional semantics for these concepts in the form of a general schema; and I shall then explain how different settings of the three main parameters that are involved in this schema will yield an intuitively plausible account of the semantic value of each of these different ‘ought’-concepts.

The general semantic approach that I shall take here is in line with what could be called the classical semantics for deontic logic. According to this approach, ‘ought’ and ‘should’ and their equivalents in other languages are all broadly modal terms, just like ‘must’, ‘may’, ‘can’ and the like. 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).

So, 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’. So 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”.

In general, the conditions under which such an ‘ought’-propositions is true at a given possible world can be specified in the following way. For every one of these propositions, and for every possible world w, there is a relevant domain of possible worlds, and a relevant ordering on these worlds, such that the whole ‘ought’-proposition ‘O (p)’ is true at w if and only if the embedded proposition p is true at all worlds in the relevant domain that are not ranked any lower in this ordering than any other worlds in that domain.

If – as will usually be the case – it is possible to express this ordering by means of words like ‘better’ and ‘worse’, then we can say more simply that the ‘ought’-proposition ‘O (p)’ is true at w 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 at w if and only if the proposition that this room is swept is true at all the relevantly optimal worlds in the relevant domain.^³ So long as there are always some worlds in the relevant domain that count as optimal in the relevant way, then it will turn out that all of the principles of standard deontic logic – in effect, the modal system KD – will be valid for every ‘ought’-concept.

In this way, this classical approach to the semantics of ‘ought’ involves two parameters: something that determining a domain of possible worlds, and the relevant ordering on these worlds. As I shall explain in the third section of this paper, this ordering of worlds can itself be regarded as having an expectational structure – that is, as generated by two separate underlying factors, a value function and a probability function. However, before developing this expectational conception of the relevant ordering of worlds, I shall survey some of different concepts that the term ‘ought’ can express.

In earlier work, I have surveyed several of the different concepts that words like ‘ought’ can express.^⁴ As I have argued, some of these ‘ought’-concepts are instances of the “practical ‘ought’”; some are instances of the “‘ought’ of general desirability”, some of the “purpose-relative ‘ought’”, some of the “rational ‘ought’”, and so on.

For our purposes, the most important point is that each of these kinds of ‘ought’ can be used in a more or less “objective” or “subjective” way. For example, let us start with instances of the “practical ‘ought’”. Suppose that you are on top of a tower, watching someone trying to escape from a maze on the ground below. Then you might say:

Here what an agent “ought” to do does not depend purely on the information that is possessed by the agent at the relevant time; so this first example involves the “objective” ‘ought’, rather than the “information-relative” ought.

On the other hand, sometimes we use ‘ought’ in such a way that it does depend purely on the information that is available to the relevant agent at the relevant time. Thus, we might say about the man who is making his way through the maze:

(2) All the evidence that he has suggests turning right at this point would be the best way to escape from the maze, and so that is what he ought to do now.

Here what the agent “ought” to do depends only on the information that the agent actually possesses at the relevant time. So this second example involves a “subjective” or “information-relative” ‘ought’, not an objective ‘ought’.

In general, many different kinds of ‘ought’ seem to have both an objective and an information-relative version. For example, there is both an objective and an information-relative version of the purpose-relative ‘ought’, such as ‘He ought to use a Phillips screwdriver to open that safe’. What makes this the “purpose-relative ‘ought’” is that the truth value of this statement simply depends on whether or not using a Phillips screwdriver is part of the best way to open the safe; the statement takes no stand on whether the person in question ought, all things considered, to try to open the safe at all.

This purpose-relative ‘ought’ also comes in both objective and subjective versions. An objective version of this sort of ‘ought’ might be: ‘He has no way of knowing it, but he ought to use a Phillips screwdriver to open that safe’. A subjective or information-relative version of this ‘ought’ might be: ‘Since he doesn’t know what sort of safe it is, he ought to start with the ordinary screwdriver first’.

In general, it seems clear that for each of these kinds of ‘ought’, there must be some systematic connection between the more objective and the more subjective versions of that kind of ‘ought’. Moreover, it seems that it must be broadly speaking the same kind of systematic connection in each case. The next two sections of this paper will be focused on exploring the nature of this connection.

In addition to giving an account of the relationship between the subjective and objective versions of each of these four kinds of ‘ought’, I shall also aim to unify my account of these phenomena with yet another kind of ‘ought’ – specifically, with the so-called epistemic ‘ought’, as in:

This seems just to mean, roughly, that it is highly probable given the evidence that tonight’s performance will be a lot of fun. But there are also yet other uses of the epistemic ‘ought’ that are slightly less straightforward, such as:

This just appears to mean that there are some facts that should lead one to expect the orbit of Pluto to be elliptical (not that it is highly probable given all one’s evidence that the orbit is elliptical). I shall aim to give an account of ‘ought’ that also includes these concepts as well.

As I explained in Section 1 above, I am assuming that the truth conditions of every kind of ‘ought’-proposition are in line with the classical semantics of standard deontic logic. So, the truth conditions of every ‘ought’-proposition involves the following two crucial elements: first, they involve a certain domain of possible worlds; secondly, they involve a certain ordering on the worlds in this domain. So, to understand the semantic value of any ‘ought’-concept, we need to understand what fixes the relevant domain of worlds, and the relevant ordering on these worlds.

I shall propose here that the domain of possible worlds relevant to whether or not a given ‘ought’-proposition is true at a given world w is itself a function of w. So, it seems that for every ‘ought’-concept, there will be some function f that maps each possible world w onto a set of possible worlds f (w) – where this set of worlds is the domain that is relevant to whether or not propositions involving this concept are true at that world w.

Within the framework that we are assuming, the second crucial element in the semantic value of each ‘ought’-concept is an ordering on the worlds in the relevant domain. In this paper, I shall propose a broadly expectational conception of this ordering. For every ‘ought’-concept, the ordering of worlds in the domain is always an ordering in accordance with the expected value of certain propositions that are true at these worlds.

If the ordering of worlds has this expectational structure, it is itself the result of two more fundamental components: a probability function E; and a value function V, which assigns a value to each member of a set of propositions which are true at the worlds within the domain f (w). In the rest of this section, I shall comment on each of these three components in turn.

(i) First, let me comment on the function f that for every world w yields the relevant domain of possible worlds f (w). This function identifies the worlds that are in some sense viewed as “available”: in effect, it is these worlds that are up for assessment by any judgment involving the ‘ought’-concept in question. The ‘ought’-judgment looks at these worlds, before ordering them into at least two subsets – the favoured subset, and the less favoured subsets – such that a proposition p “ought” be (in the relevant sense) if and only if p is true throughout this favoured subset of the domain. We shall explore some specific examples of such domains of worlds in the next section.

(ii) The second element involved in the semantic value of each ought-concept is a probability function E. Every probability function is a function that assigns real numbers in the unit interval from 0 to 1 to the propositions in a certain propositional algebra (that is, a set of propositions that is closed under Boolean operations like negation, conjunction, and so on); any function of this sort that obeys the fundamental axioms of probability theory counts as a probability function. So, in particular, the omniscient probability function – the function that assigns 1 to every true proposition and 0 to every false proposition in the relevant algebra – is itself a probability function.

As we shall see, it will be convenient for various purposes – and especially for explaining the interaction of modals like ‘ought’ and ‘should’ with conditionals – to think of each such probability function as corresponding to a space of epistemically possible worlds. A particularly simple example of this is the omniscient probability function, which corresponds to a space containing just a single epistemically possible world – specifically, the epistemically possible world that corresponds to the actual world, the world that implies the true answer to every question that it speaks to, and no false answer to any question. This space of epistemically possible worlds clearly corresponds to the omniscient probability function, because every true proposition in the algebra holds at all of the worlds in this space, and no false proposition holds at any of the worlds in this space.

However, even if the probability function in question is not this omniscient function – indeed, even if it assigns probabilities to infinitely many atomic propositions – it would still be possible to conceive of this probability function as corresponding to a certain space of possible worlds, where the probability of a proposition p corresponds to the proportion of the total space occupied by the sub-region of the space where p is true.

I said above that each of these probability functions corresponds to a space of “epistemically possible” worlds. These worlds are epistemically possible because they are all compatible with every proposition that has probability 1 – that is, with everything that the probability function in question treats as known with certainty. Moreover, it is at least arguable that these epistemically possible worlds are not required to be compatible with all metaphysical necessities. For example, it seems that we can make sense of a probability function in which the proposition that Hesperus exists and is not identical to Phosphorus has a non-zero probability; so it seems that we must allow for an epistemically possible world in which Hesperus exists but is not identical to Phosphorus – even though it is metaphysically necessary that if Hesperus exists, it is identical to Phosphorus.

Although we can make sense of probability functions in which the proposition that Hesperus is not Phosphorus has a non-zero probability, the sentence embedded inside a deontic modal term like ‘ought’ seems to permit the substitution of necessarily co-referring terms. Given that Hesperus is in fact identical to Phosphorus, if you ought to visit the planet Hesperus, it surely follows that you also ought to visit Phosphorus. To explain this fact about these deontic modals, within the semantic framework that I am assuming here, it seems that the “possible worlds” that I discussed in my account of the semantics of ‘ought’ in Section 1 are not epistemically possible worlds, but metaphysically possible worlds.

On this picture, then, we have in effect two different spaces of possible worlds – a space of metaphysically possible worlds, and a space of epistemically possible worlds. Many different interpretations of these two spaces of possible worlds are possible, but to fix ideas, I shall propose one such interpretation here. According to this interpretation, these two spaces of possible worlds correspond to two different kinds of propositions.

The metaphysically possible worlds correspond to propositions of the “Russellian” kind – structured entities that are composed, by means of operations like predication, negation, conjunction and the like, out of entities like individuals, properties and relations. (Indeed, these metaphysically possible worlds can be viewed as consisting in big sets of such Russellian propositions.) Thus, the Russellian proposition that you visit Hesperus is composed out of you, the visiting relation, and the planet Hesperus itself. This proposition is therefore identical to the Russellian proposition that you visit Phosphorus. In this way, this conception of metaphysically possible worlds can explain why there cannot be any metaphysically possible worlds in which you visit Hesperus but do not visit Phosphorus.

By contrast, the epistemically possible worlds seem to correspond to Fregean propositions – structured entities that are composed, by means of operations like predication and the like, out of concepts, which are modes of presentation of such entities as individuals, properties and relations. (Indeed, we could identify these epistemically possible worlds with big sets of such Fregean propositions.) Since one and the same planet may have several different modes of presentation – including a “Hesperus” mode-of-presentation and a “Phosphorus” mode-of-presentation – this conception of epistemically possible worlds can explain why there can be an epistemically possible world in which you visit Hesperus but not Phosphorus (and vice versa).

(iii) According to this expectational schema, the semantic value of each ‘ought’-concept must also involve a value function of a certain kind.

I shall propose here that every such value function assigns a value to each proposition in a set of propositions, relative to a given domain of worlds. More specifically, I shall assume that all the propositions in this set are alternatives to each other – that is, no more than one of these propositions is true at any world in the relevant domain. Moreover, I shall also assume that this set of propositions is exhaustive – that is, at least one proposition in this set is true at every world in the domain. In other words, this set of propositions forms a partition: at every possible world in this domain, exactly one of these propositions is true. For every relevant domain, there will be a suitable partition of this sort such that this value function measures the value of the propositions in this partition relative to that domain.

To say that this value function “measures” the value of each of these propositions within this domain is to say that this value function maps this proposition and domain of worlds onto a real number that represents the value of the proposition within the domain. This measure is presumably not unique: the choice of unit will obviously be arbitrary (just as it is arbitrary whether we measure distance in miles or kilometres), and the choice of zero point may also be arbitrary as well (just as it is arbitrary whether we take the zero point on a thermometer to be 0 Fahrenheit or 0 Celsius). But to fix ideas, let us suppose that except in these two ways, this value function is not arbitrary. Given an arbitrary choice of a unit and a zero point, this function gives the true measure of the relevant value. (In more technical terms, we are supposing that the structure of the value being measured fixes a value function that is unique up positive affine transformation; the value in question can be measured on an interval scale.)

(iv) According to my proposals, then, the semantic value of every ‘ought’-concept involves three items: a function f from each metaphysically possible world to a relevant domain of such worlds; a probability function E (that is, as we have in effect seen, a space of epistemically possible worlds); and a value function V defined over propositions and domains of worlds. We may represent this concept by explicitly indexing the deontic operator to this trio of items: ‘Ought_<_f_,_E_,_V_>’.

We can now give a more precise definition of the EV-expected value of a proposition p in a certain domain D, in the following way. Consider a collection of hypotheses {h₁, … h_n}, where each hypothesis h_i has the form ‘V (p, D) = n_i’. Suppose that this collection of hypotheses forms a partition, in the sense that it is epistemically certain that exactly one of these hypotheses is true; and suppose also that E assigns a probability to each of these hypotheses. Then the EV-expected value of p in D is the probability-weighted sum of the value of p in D according to each of these hypotheses, where the value of p in D according each hypothesis is weighted by the probability of that hypothesis. In symbols, the EV-expected value of p in D is:

Since at every possible world in this domain D, exactly one of the propositions that are measured by V in D is true, we can also order the worlds in D by the EV-expected value of the proposition in this set that is true at each of those worlds. My central proposal in this paper is that it is this ordering on the worlds that is relevant to the truth-conditions of the ‘ought’-proposition in question.

‘Ought_<_f_,_E_,_V_>(p)’ is true at w if and only if p is true at every world w′ ϵ f(w) such that none of the propositions that are measured by V in f(w) has greater EV-expected value in f(w) than the proposition that is true at w′.

In the following section, I shall show how we set each of these three parameters f, E, and V in such a way that we can obtain intuitively plausible truth-conditions for each of the kinds of ‘ought’ that we considered in the previous section.

The schema set out in the previous offers a simple way of understanding the maximally objective kinds of ‘ought’. With these kinds of ‘ought’, E is the omniscient probability function – the function that assigns probability 1 to every truth and probability 0 to every falsehood; as I explained in the previous section, this omniscient probability function in effect corresponds to the epistemic space containing just one epistemically possible world – namely, the world that corresponds to the actual world.

The differences between the various objective kinds of ‘ought’ are reflected, not in the probability function E, but in the different settings of the other two parameters – the function f that fixes the relevant domain of metaphysically possible worlds, and the value function V that measures the value of various propositions in each domain.

It seems plausible that every instance of the practical ‘ought’ is in a sense indexed to the situation of a particular agent x at a particular time t. (It is this that has tempted many philosophers to argue that the practical ‘ought’ actually expresses a relation between an act-type, an agent, and a time.) So it seems that the semantic value of this ‘ought’-concept will involve a function f that maps each world w onto the worlds that are “practically available” from the situation that the agent x is in at the time t in w – in effect, the worlds that the agent x can realize through the acts that he or she performs at t in w.

This concept will also involve a value function V that measures the value of the various acts available to x at t, within the relevant domain of possible worlds. Formally, we can follow certain decision theorists like Richard Jeffrey (1980) in identifying each of these acts with a proposition – in effect, the proposition that the agent x does an act of the act-type in question at the time t. This set of propositions forms a partition in the sense that the agent does one of these acts, and no more than one of these acts, at t in each world in this domain. Specifically, then, V might be a measure of these available acts in terms of how choiceworthy those acts are in this domain of worlds.

On this view, then, if the relevant ‘ought’ is the objective practical ‘ought’, indexed to the situation of an agent x at a time t, then ‘Ought (p)’ is true at a world w if and only if p is true in all the worlds that are practically available from the situation that x is in at t in w where x does one of the maximally choiceworthy acts that available at that time t.

With the more subjective kinds of the practical ‘ought’, V and f are exactly as they are with the objective practical ‘ought’, and E is some less omniscient probability function (that is, a space of epistemically possible worlds containing more than one world). For example, in many contexts we might use the term ‘ought’ to express a practical ‘ought’-concept whose semantic value involves a probability function that corresponds to the system of credences that would be ideally rational for a thinker to come to have if their experiences, background beliefs, and other mental states were exactly like those of the agent x at t.

This is, however, not the only concept that a subjective practical ‘ought’ can express. If the speakers have pertinent information that is not yet available to the agent who is under discussion, it will often be natural for the speakers to use an ‘ought’-concept whose semantic value involves a probability function that reflects this information. Moreover, if the agent herself also thinks that there is some available information that she has not acquired yet, it will be very natural for the agent to use an ‘ought’-concept that in this way involves a probability function that reflects that information that the agent hopes to acquire.^⁶

In general, there is no shortage of probability functions, and in many different contexts it will be natural to use an ‘ought’-concept whose semantic value involves a probability function that is conversationally salient for one reason or another. As we have noted, many probability functions correspond to the systems of credences that a perfectly rational thinker would come to have in response to certain experiences, given a certain set of background beliefs and other mental states. If this collection of experiences and other mental states is precisely the collection of experiences and states that a certain conversationally salient agent has at a certain conversationally salient time, this can explain why this probability function will be salient in the conversational context in question. But many factors can explain why a certain agent and time are salient in a conversational context. For example, in many contexts, the salient time will often be the time of action, rather than the time of utterance; and the salient agent may be an adviser of the agent to whom the occurrence of ‘ought’ is indexed, rather than that agent herself.

This idea of relativizing ‘ought’-concepts to probability functions is clearly akin to the idea of Björnsson and Finlay (2010) that occurrences of ‘ought’ are relativized to bodies of information. However, there are a number of crucial differences. First, although every probability function determines a body of information (consisting of the propositions to which the function assigns probability 1), the converse does not hold: there are many probability functions corresponding to each body of information. In this way, probability functions contain more structure than mere bodies of information. Secondly, my proposal is not committed to their view that every occurrence of ‘ought’ is relativized to an “end” or “standard” that can be understood in wholly non-normative terms. Finally, my proposal is easier to reconcile with some of the classical theories in this area: unlike their account, my proposal entails standard deontic logic; and it is clearly much easier to integrate with the classical view of rational choice as maximizing some kind of expected value.

In general, we can make sense of objective and subjective versions of many kinds of ‘ought’. For example, this point seems to hold, not just of the practical ‘ought’, but of the purpose-relative ‘ought’, the ‘ought’ of general desirability, and the rational ‘ought’ as well. In each case, the objective and the subjective ‘ought’ differ only with respect to the relevant probability function E: the objective ‘ought’ is indexed to the omniscient probability function, whereas the more subjective ‘ought’ is indexed to a more subjective probability function that corresponds to the credence function of a thinker who (although perfectly rational) is significantly more ignorant about the world.

It would be intrinsically interesting to explore exactly how this schema can be worked out in detail for each of these other kinds of ‘ought’; but to save space, I shall here only explain how it would work for the purpose-relative ‘ought’. So far as I can see, the purpose-relative ‘ought’ resembles the practical ‘ought’ in that they are both implicitly indexed to the situation of a particular agent x at a particular time t. So the relevant function f from worlds to domains of worlds is again the function that maps each world w onto the worlds that are “practically available” from the situation that the agent x is in at the time t in w.

The only respect in which the purpose-relative ‘ought’ differs from the practical ‘ought’ is in involving a different value function V. For the purpose-relative ‘ought’, there is some purpose P that is contextually salient, and the value function V ranks the alternative acts that are available to the agent at the time in question, not in terms of their overall choiceworthiness, but purely in terms of how good they are as means to accomplishing that purpose P. Otherwise, the two kinds of ‘ought’ work in more or less the same way.

As I said in Section 2 above, it would be preferable if our account of ‘ought’ could also encompass the other kinds of ‘ought’ that I considered in that section – including the epistemic ‘ought’ (as in ‘Tonight’s performance ought to be a lot of fun’, which as I said seems mainly just to indicate that the embedded proposition ‘Tonight’s performance will be a lot of fun’ is highly probable given the relevant evidence).

The schema that I proposed in the previous section may be able to capture the epistemic ‘ought’, in something like the following way. For this kind of ‘ought’, the three parameters may be the following. First, f can simply be the function that maps each world onto the universal set of all possible worlds. Secondly, E can be a space of epistemically possibilities modelling some possible state of information. (Again, this could be pretty well any state of information; the participants in a conversation will just have to interpret the contextual clues in order to discern which state of information is involved in the semantic value of an occurrence of the term ‘ought’ in that context.)

Finally, V could simply be a simple function that ranks the rival answers to a certain question by ranking the true answer above the false answer – say, by assigning a value of 1 to the true answer and 0 to the false answer. Now, as is well known, probabilities are themselves simply expectations of truth-values. So the ranking of answers to this question in terms of their EV-expected value is identical to the ranking in terms of their probability according to E; and this ranking determines a corresponding ordering of worlds in accordance with the probability of those worlds’ answer to the question. So, for example, if the rival answers to the question are simply p and ‘¬p’, then the proposition ‘It ought to be that p’, involving this epistemic ‘ought’, will be true just in case p is more than probable than ‘¬p’ (according to the probability function that corresponds to E).

One might wonder whether p’s being barely more probable than ‘¬p’ is enough to make it true to say ‘It ought to be that p’, using this epistemic ‘ought’. At least, if we were considering a fair lottery with 100 numbered tickets, we would not typically say such things as ‘The winning ticket ought to be one of the tickets numbered between 50 and 100’.

However, the reason for this may be that the question that we normally have in mind is not simply whether or not the embedded proposition is true, but whether or not some more comprehensive explanatory picture is true. If this comprehensive explanatory picture is more than 50% probable, and the proposition p follows from this explanatory picture, then it will be true to say ‘It ought to be that p’ (since p will be true in all the worlds within the domain where this explanatory picture is true). The propositions that follow from a comprehensive explanatory picture of this sort will typically be significantly more probable than that comprehensive picture itself.

This simple account of the value function V, in terms of the truth-value of answers to a certain question, may turn out not to be completely defensible in the end; a more complicated of this value function may be required. But at all events, to capture the range of ways in which we use the epistemic ‘ought’, we have to allow that many different probability functions (or spaces of epistemically possible worlds) can be involved. In particular, when a speaker asserts a proposition involving an epistemic ‘ought’-concept of this sort, the probability function E involved in this concept’s semantic value does not have to correspond to the information that is actually available to the speaker. It may be a different probability function.

So, for example, even if the speaker knows perfectly well that the orbit of Pluto is not elliptical, the relevant probability function E does not have to assign a probability of 0 to the proposition that the orbit of Pluto is elliptical; it may be a probability function that corresponds to the credences that it would be rational to have on the basis of a different body of information of some kind. So this approach has no difficulty handling such puzzling instances of the epistemic ‘ought’ as ‘The orbit of Pluto ought to be elliptical’.

Finally, I should like to comment on what this expectational model of ‘ought’ implies about how ‘ought’ interacts with conditionals. In effect, this model will allow for two kinds of conditional ‘ought’ – effectively, a subjunctive or metaphysical conditional ‘ought’, and an indicative or epistemic conditional ‘ought’.

The general idea is familiar from such classic discussions of conditionals as that of Angelika Kratzer (1986). Quite generally, the effect of conditionals is to restrict some space or domain of possible worlds that is involved in the modal operator that appears (at least implicitly) as the dominant operator of the consequent of the conditional – by restricting this space or domain of worlds to that sub-region of the space where the antecedent of the conditional is true.

With the approach to ‘ought’ that I have proposed here, however, there are two spaces or domains of possible worlds – the domain of metaphysically possible worlds that is fixed by the function f, and the space of epistemically possible worlds E. So some conditionals will restrict the domain of metaphysically possible worlds f (w) to the subset of that domain where the antecedent is true; but other conditionals will restrict the space of epistemically possible worlds E to that sub-region the space where the antecedent is true. Just to give them labels, I shall call the first sort of conditional ‘ought’ the “metaphysical conditional”, and the second sort of conditional I shall call the “epistemic conditional”.

In short, the truth conditions of these two kinds of conditionals can be formulated as follows.

It is clear that the truth conditions that I have assigned here to the metaphysical conditionals involving ‘ought’ are in effect the same as those that were assigned to the so-called dyadic ‘ought’-operator by the classical deontic logicians such as Åqvist (1967) and Lewis (1973).

On the other hand, the truth conditions that I have assigned to the epistemic conditionals involving ‘ought’ have the effect of replacing the probability function E that would be involved in the semantic value of the consequent of the conditional if it appeared alone with the result of conditionalizing that probability function on the antecedent.

For example, consider the familiar examples that have been used to illustrate the dyadic ‘ought’-operator. Suppose that an adviser is remonstrating with a recalcitrant advisee. First, the adviser says ‘You ought not to shoot up heroin’, and then when the advisee indicates that he may not follow this advice, the adviser continues, ‘And if you do shoot up heroin, you ought to shoot up with clean needles’.

If these statements involve the practical ‘ought’, indexed to the advisee’s situation at the time of the utterance, then the adviser’s first statement is true because out of all the worlds that are practically available to the advisee at the relevant time, the worlds where the advisee acts in a maximally choiceworthy way are all ones where he does not shoot up heroin. The second statement is true because out of all the worlds that are practically available to the advisee at the relevant time and the advisee does shoot up heroin, the worlds where the advisee acts in a maximally choiceworthy way are all worlds where he shoots up with clean needles.

For an example of the epistemic conditional, consider the following variant of Frank Jackson’s (1991) three-drug case – specifically, a four-drug case. There are two drugs, A and B, such that it is known for certain that one of these two drugs will completely cure the patient while the other drug will kill him, but unfortunately it is impossible to tell which of the two drugs will cure the patient and which will kill him. In addition, there are two other drugs, C and D, each of which will effect a partial cure, but one of which will have an extremely unpleasant side-effect – and again, it is not known for certain which of these two partial cures will have that side-effect. Now, suppose that the patient is about to have a test: if the test is negative, it is drug C that will have the unpleasant side-effect, while if the test is positive, drug D will have the unpleasant side-effect. Then it will be true to say ‘If the test result is positive, we should give the patient drug C.’ This statement is true because we give drug C in all possible worlds (in the relevant domain) in which we take the course of action that maximizes expected choiceworthiness, according to the probability function that results from our current system of credences by conditionalizing on the proposition that the test result is positive.

There are two main things that I have done in this paper. First, I have set out a related group of truth-conditions – in effect, the truth-conditions that a family of concepts might have. These truth conditions naturally divide into those that belong to more “objective” concepts and those that belong to more “subjective” concepts, depending on whether the probability function involved in these truth-conditions is the omniscient probability function, or a function that in some way reflects the ignorance and uncertainty of certain relevant agents.

Secondly, I have suggested that these are in fact the truth-conditions of the concepts that are expressed in English by a range of uses of deontic modals like ‘ought’ and ‘should’. In the space available, this suggestion could not be defended in any detail. The suggestion seems plausible to me, but I confess that much more empirical evidence about the semantic intuitions of competent speakers of English would have to be considered to give a full defence of this suggestion. If this suggestion seems less plausible to some readers than it does to me, then the concepts that I have highlighted may at least seem to be theoretically useful concepts for philosophers to use in their investigations of the normative part of philosophy.

Many other philosophers of language and metaethicists have proposed very narrow interpretations of ‘ought’, which dramatically under-predict many of the readings of ‘ought’ that seem genuinely available.^⁷ On the other hand, the range of truth-conditions that I have identified in Sections 3–4 above is much wider. So my suggestion – that all the truth-conditions identified here belong to concepts that can be expressed by ‘ought’ in ordinary English – implies that these deontic modals, like ‘ought’ and ‘should’, are capable of expressing a far wider range of concepts, depending on the particular context in which they are used.

In this way, my suggestion clearly runs the opposite danger – that of over-predicting the readings of ‘ought’ that are available. For example, the schema that I outlined in Section 3 seems to predict that there is a practical ‘ought’-concept that is indexed to the situation that I am in right now, and to the space of epistemically possible worlds that corresponds to Julius Caesar’s state of information on that fateful morning of 15 March 44 BC. It is doubtful, to say the least, whether there is any way of using terms like ‘ought’ in English that will express this concept.

It does not seem clear to me that this point grounds any decisive objection to my approach. We should concede, it seems to me, that this concept really exists, but that we have no natural way of expressing it in English (or in Latin, or in any natural human language), largely because of the very limited interest that this concept would have for us. Admittedly, the suggestions that I have made in this paper would need to be supplemented in order to explain why there is no natural way of using our natural-language terms to express many of these concepts. But I see no reason to think that such supplementation will prove impossible.

In general, of the two dangers that face such interpretations of natural-language expressions, the danger of over-predicting the readings that are available seem less grave than the danger of under-predicting such readings, since it will often be possible to supplement an account that looks likely to over-predict the available readings of a given term with some further account that explain why those readings will not in fact be available in any real conversational context. An account that under-estimates the range of concepts that a term can express, on the other hand, seems to have no way of being supplemented in order to rectify this deficiency. So there are some general reasons to be optimistic that the sort of approach that I have sketched here will help us to achieve a better understanding of these deontic modals like ‘ought’ and ‘should’.

Notes

1 For some philosophers who have advocated distinguishing between the objective and the subjective ‘ought’, see Brandt (1959, 360–67), Ewing (1947), Parfit (1984, 25), Jackson (1986), Jackson and Pargetter (1986, 236), and Gibbard (2005).

2 I have attempted to sketch some parts of this story elsewhere; see especially Wedgwood (2007, chaps. 4–5).

3 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).

4 See especially Wedgwood (2007, Section 5.2, and 2009, Section 2).

5 For some purposes, it may be preferable to understand the “expected value” of a proposition p as defined in terms of the conditional probability of these hypotheses – conditional on the proposition p that is in question. To put it symbolically, the appropriate expectation might be: ∑_i n_i E (V (p, D) = n_i| p); but unfortunately I cannot explore these issues here.

6 This is how I would aim to answer the objections of Kolodny and MacFarlane (unpublished).

7 For an example of an interpretation of ‘ought’ that is dramatically narrower than mine, see Judith Thomson (2008).

Åqvist, Lennart (1984). “Deontic Logic”, in Dov Gabbay, ed., Handbook of Philosophical Logic (Dordrecht: Reidel), 605–714.

Björnsson, G., and Finlay, S. (2010). “Metaethical Contextualism Defended”, Ethics 121 (1): 7–36.

Brandt, R. B. (1959). Ethical Theory (Englewood Cliffs, New Jersey: Prentice Hall).

Gibbard, Allan (2005). “Truth and Correct Belief”, Philosophical Issues 15: 338–350.

Jackson, Frank, and Pargetter, Robert (1986). “Oughts, options, and actualism”, Philosophical Review 95: 233–255.

Jackson, Frank (1986). “A probabilistic approach to moral responsibility”, in Ruth Barcan Marcus, Georg J. W. Dorn, and Paul Weingartner, eds., Logic, Methodology, and Philosophy of Science VII (Amsterdam: North-Holland): 351–365.

———— (1991). “Decision-Theoretic Consequentialism and the Nearest and Dearest Objection”, Ethics 101 (3): 461–482.

Jeffrey, Richard C. (1981). The Logic of Decision, revised edition (Chicago: University of Chicago Press).

Kolodny and MacFarlane (unpublished). “Ought: Between Objective and Subjective” (draft of 2 December 2007).

Kratzer, Angelika (1986). “Conditionals” <http://semanticsarchive.net/Archive/ThkMjYxN/Conditionals.pdf>

———— (2009). “The ‘Good’ and the ‘Right’ Revisited”, Philosophical Perspectives 23: 499-519.