**Objective and subjective ‘ought’**

Ralph Wedgwood

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 or context-sensitive. On this view, in effect, there
are many different concepts that can be expressed by ‘ought’ – as we might
call them, many different “‘ought’-concepts” – and whenever the term is
used, the particular *context* in which
it is used somehow determines which of these concepts it expresses on that
occasion.

More
specifically, one way in which these ‘ought’-concepts differ from each other is
that some of them 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 at a given time 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 different ‘ought’-concepts. Unfortunately, in
the available space I shall not be able to do much more than simply to propose
this semantic account of these ‘ought’-concepts. 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 basically
akin to the theory of “subjective rightness” that was 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 possible world.
Nonetheless, my account has several crucial differentiating features: unlike
Jackson’s theory, my account implies that *standard
deontic logic* is valid for every kind of ‘ought’; it is much more general
than Jackson’s theory, since it is designed to account for *all* the concepts that can be expressed by ‘ought’ and its
equivalents (not just 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 uses of ‘ought’ are
relativized to bodies of information. In a somewhat similar way, I shall
propose that uses 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
meaning of a term in a natural language would have to be a fairly complicated
story. More precisely, such an account would have to involve the following components:

**a.
**An account of the *syntactic*
role of the term – that is, of how the term can combine with other terms
to form well-formed grammatical sentences;

**b. **An account of what it
is to *understand* the term – that
is, to be *competent* in using the term
and in interpreting its use by other speakers;

**c.
**An account of the range of *semantic values* that the term can have – that is, of the
contributions that the term can make to the *truth
conditions* of sentences in which it appears;

**d.
**An account of the *non-truth
conditional* aspects of meaning that the term can have – for example,
of any conventional implicatures or presuppositions that can be conveyed by the
use of the term;

**e.
**An account of how the *conversational
context* in which the term is used determines its meaning and its semantic
value in the particular context in question.

In this essay, I shall focus
chiefly on the third of these components, (c), the range of semantic values
that deontic modals like ‘ought’ and ‘should’ can have – although I shall
also comment briefly on the fifth component, (e), the question of how the
conversational context in which the term is used determines the meaning that it
has in the context in question.

Otherwise, I shall strive to remain
neutral about all the other components of the story. Thus, with respect to the
first component (a), I shall not commit myself to any detailed claims about the
underlying syntax or logical form of sentences involving ‘ought’ and ‘should’.
In particular, even though I shall claim that ‘ought’ and ‘should’ have
different semantic values in different contexts, I shall not commit myself to any
particular view about how these different semantic values arise from the underlying
syntax. Specifically, I shall not commit myself to any view about whether
sentences containing ‘ought’ contain *hidden
variables* (or hidden terms of some other kind), so that the way in which
the term’s semantic value shifts between contexts results simply from different
items’ being referred to by these hidden terms, or whether some other syntactic
phenomenon underlies these shifts. I shall not even rule out the idea that the
term ‘ought’ is syntactically simple and unstructured, and simply demands
different semantic interpretations in different contexts.

Similarly, with respect to the
second component (b), I shall not here defend any particular view of what it is
to understand or to be a component user of the term. In fact, I am inclined to
favour a certain sort of account of this second component of a term’s meaning.
Specifically, I am tempted to explain what it is to be linguistically competent
with a term by appealing to the range of *concepts*
that the term can be used to express – so that to be linguistically
competent with the term is to have the ability to use the term to express
concepts within that range (in a way that enables competent hearers to
interpret one’s use of the term as expressing the concept within that range
that one intends to express). Then I am tempted to explain the nature of each
of these kinds of concepts in terms of the *conceptual
role* that the concept plays in one’s thinking, and in terms of the way in
which this conceptual role determines the object, property, or relation that
the concept *stands for* or *refers to*.[2]

However, even though I am
attracted to this view of what linguistic competence consists in, I shall not attempt
to defend this view here. Instead, I shall simply give an account of the range
of truth conditions that sentences involving ‘ought’ can have. To bring out the
similarity between the different truth conditions in this range, I shall put my
account in the form of a *schema*
involving three different parameters; as I shall explain, the different truth
conditions that a sentence involving ‘ought’ can have in different contexts all
correspond to different ways of setting these three parameters. So, in effect,
something in the conversational context in which the term ‘ought’ is used must
determine what these parameters are; I shall try to make a few remarks, at
least in passing, about what features of the conversational context could do
this.

**1. ****A semantic framework**

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’-proposition is true at a
possible world can be specified in the following way. For every one of these
propositions, and for every possible world *w*,
there is a *function* that maps
possible worlds onto *domains* 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, out of all worlds in the domain that this function assigns to *w*, the embedded proposition *p* is true at all worlds that are not
ranked any lower down in this ordering than any other worlds in this domain.[3]

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.[4] 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: a function that maps possible worlds onto *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, there
may be some kind of value, and some probability distribution, such that this
ordering of the worlds is equivalent to an ordering in terms of the *expected value* of the worlds, according
to this probability distribution. However, before developing this expectational
conception of the relevant ordering, I shall survey some of different concepts
that the term ‘ought’ can express.

**2.
****The varieties of
‘ought’**

In earlier work, I have surveyed
several of the different concepts that words like ‘ought’ can express.[5] As
I have argued, some of these ‘ought’-concepts are instances of the “practical
‘ought’”; some are instances of the “purpose-relative ‘ought’”, some of the
“‘ought’ of general desirability”, 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:

(1) He has no way of knowing it, but he ought to turn left at this point.

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 that 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 a subjective or
information-relative version. For example, consider 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 of opening the safe; the statement takes no stand on whether the
person in question ought (in the all-things-considered practical sense of
‘ought’), to try to open the safe at all.

It seems clear that 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 fact, it also seems plausible to me that other kinds of ‘ought’, like what I have elsewhere called the “‘ought’ of general desirability” and the “rational ‘ought’”, also have both objective and subjective or information-relative versions. In general, it seems 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 focus 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 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:

(3) Tonight’s performance ought to be a lot of fun.

This seems just to
mean, roughly, that it is *highly probable given the salient body of evidence*
that tonight’s performance will be a lot of fun. If this is indeed at least
roughly what the epistemic ‘ought’ means, then it is clear that the “salient body
of evidence” need not include the total evidence available to the speaker at
the time of utterance, since it seems that even if one knows that the orbit of
Pluto is not elliptical, it might be true for one to say:

(4) The orbit of Pluto ought to be elliptical (although of course it isn’t).

I shall aim to give an account of the semantic value of a range of uses of ‘ought’ that includes these uses of the term.

**3.
****The expectational
schema**

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: the truth conditions of every ‘ought’-proposition
involves the following two crucial elements: first, they involve a function
from possible worlds to *domains* of
possible worlds; secondly, they involve an *ordering*
on these worlds. So, to understand the semantic value of any ‘ought’-concept,
we need to understand these crucial elements.

First,
then, 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*.

Secondly,
within the framework that we are assuming, the semantic value of each use of ‘ought’
will involve an *ordering* on the relevant
possible worlds. In this paper, I shall propose a broadly *expectational* conception of this ordering. For every use of ‘ought’,
the ordering of worlds in the domain is always an ordering in accordance with
the *expected value* of those worlds. If
the ordering of worlds has this expectational structure, it is itself the result
of two more fundamental components: a probability distribution *E*; and a value function *V*, which assigns a value to each of 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 maps every world *w*
onto a corresponding domain of possible worlds *f** *(*w*). This function identifies the worlds that are in some sense
viewed as “available” from *w*: in
effect, it is these worlds that are up for assessment by the ‘ought’-concept in
question, relative to *w*. In effect,
this function *f* fixes what Angelika
Kratzer (2002) called the “modal base” – the set of propositions that are
true throughout this domain of worlds, setting the bounds of the domain of
possible worlds that are up for assessment by the ‘ought’-concept in question.

When
this domain of worlds is in place, the ‘ought’-concept orders these worlds into
at least two subsets – one favoured subset, and at least one less favoured
subset – such that a proposition *p*
“ought” to 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
distribution *E*. Every probability
distribution 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 distribution. 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
distribution.

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 distribution as corresponding to a space of *epistemically possible worlds*. A
particularly simple example of this is the omniscient probability distribution,
which corresponds to a space containing just one 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 distribution, 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 distribution in question is not this omniscient
function – indeed, even if it assigns non-trivial probabilities to *infinitely* many mutually exclusive
propositions – we can still conceive of this probability distribution 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 distributions 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 distribution in question treats as absolutely certain to be
true. These epistemically possible worlds need not be metaphysically possible. Even
though it is metaphysically necessary that Hesperus is Phosphorus, we can make
sense a probability distribution in which the proposition that you visit
Hesperus has a different probability from the proposition that you visit Phosphorus.
So it seems that there could be some epistemically possible worlds in which you
visit Hesperus but not Phosphorus (or vice versa).

Although
we can make sense of probability distributions in which the proposition that you
visit Hesperus but 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. Since Hesperus is in fact identical
to Phosphorus, if you ought to visit 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 domain
of possible worlds *f** *(*w*) is a domain, not of epistemically possible worlds, but of *metaphysically* possible worlds.

On
this picture, then, we have in effect *two*
different spaces of possible worlds – a domain of metaphysically possible
worlds, and a space of epistemically possible worlds.[6] 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)** Finally, according to this expectational schema,
the semantic value of each use of ‘ought’ must also involve a *value* function of a certain kind.

In
many contexts, it is natural to think of this value function as evaluating a
certain set of *alternatives* –
such as a set of alternative acts, or the like. When we speak of an “act” here,
it seems that what we really mean is a *proposition*
to the effect that the relevant agent performs an act of the relevant type at
the relevant time. So a more general account would involve regarding this value
function as evaluating a certain set of alternative propositions. To say that
these propositions are “alternatives” to each other is to say that they are *mutually exclusive*: no more than one of
these propositions is true at any world in the relevant domain. I shall also
assume that these propositions are *jointly
exhaustive*: that is, *at least* one
of these proposition 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.

Given
these assumptions about the value function, it will in fact do no harm if we
simply think of this value function as evaluating *worlds* (since instead of assuming that the value function evaluates
these “alternative propositions”, we may assume that it evaluates worlds in
such a way that it assigns exactly the same value to all worlds in the domain
where the same member of this set of propositions is true). Intuitively, it
seems that these worlds are metaphysically possible worlds: since visiting
Hesperus just is visiting Phosphorus, there can surely be no difference in
value between the world where you visit Hesperus and the world where you visit
Phosphorus. This value function “measures” the value of the worlds in this
domain in the sense that it maps each world *w*
within the domain onto a real number *V** *(*w*) that represents the value of the world *w*.

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.[7]

**(iv)** According
to my proposal, then, the semantic value of every use of ‘ought’ involves three
items: a function *f* from each metaphysically possible world to a relevant domain of
metaphysically possible worlds; a probability distribution *E* (that is, as we have in effect seen, a structured space of epistemically
possible worlds); and a value function *V*
defined over the metaphysically possible worlds. We may represent this semantic
value by explicitly indexing ‘ought’ to this trio of items: ‘Ought_{< f, E,
V>}’.

I
have proposed that the value function *V*
itself is defined over metaphysically possible worlds. However, the probability
distribution *E* can assign
probabilities to hypotheses *about* the
value that *V* assigns to various
worlds – where each of these hypotheses is, in effect, a Fregean
proposition. For example, such hypotheses might include: ‘The world in which I
visit Hesperus has value *n*’, and ‘The
world in which I visit Phosphorus has value *m*’ –
where these two hypotheses seem intuitively to be different from each other. In
effect, then, these hypotheses refer to metaphysically possible worlds by means
of epistemically possible worlds: the epistemically possible worlds are like
modes of presentation of metaphysically possible worlds.

We
can now give a definition of the *EV*-expected
value of an epistemically possible world *w*,
in the following way. Consider a collection of hypotheses concerning *w* {*h*_{1}, … *h*_{k}}, where each hypothesis *h _{i}* has the form ‘

∑_{i}*n _{i} E*

In
this way, the epistemically possible worlds can be ordered in terms of their *EV*-expected value. This ordering of the
epistemically possible worlds will then provide a corresponding selection
function *S*_{<f, E, V>} over
the metaphysically possible worlds. I have suggested that epistemically
possible worlds are in effect modes of presentation of metaphysically possible
worlds.[9]
Whenever an epistemically possible world *w _{E}*
has maximal

My
central proposal in this paper is that it is this selection function that is crucial
for the truth conditions of sentences of the form ‘Ought_{< f, E,
V>}(*p*)’. Specifically, we can specify these truth conditions as
follows:

‘Ought_{< f,
E, V>}(*p*)’ is true
at *w* if and only if *p* is true at every world *w*′ ϵ
*S*_{<f, E, V> }(*f*(*w*)).

As
I explained above, this proposal is simply an account of the truth conditions
of ‘ought’-sentences. I am not proposing that there are hidden variables
referring to these parameters *f*, *E*, and *V* in the actual *syntax* of
these sentences; my proposal is simply that we can analyse the semantic value
of each occurrence of ‘ought’ – the contribution that this occurrence of
‘ought’ makes to the truth conditions of the sentence in which it appears –
in terms of these three parameters. Similarly, I am also not claiming that *linguistic competence* with ‘ought’
involves some kind of implicit knowledge or grasp of this semantic account;
this semantic account does not by itself settle the question of how best to
account for our competence with ‘ought’.

However,
I shall assume that in normal contexts when ‘ought’ is used, something must
determine what these three parameters are. Presumably, this will involve the
speakers in the context actually focusing on or thinking of something that
somehow determines these parameters. I shall not take a definite stand on what
exactly the speakers in the context must be focusing on in this way. (No doubt,
few actual speakers typically think of a probability distribution by means of
the formal mathematical concept of probability!) It might be, for example, that
the probability distribution *E* is determined
by the speakers’ in some way thinking of or imagining a certain *epistemic perspective* – where as a
matter of fact, this perspective can be modelled by means of the probability
distribution *E*.

As I shall put it, in the
context in question, each of these three parameters *f*, *E*, and *V* is “contextually salient”
(although – as I have said – I shall remain neutral about what
exactly is involved in these parameters’ being contextually salient in this
way). In the next section, I shall show how different settings of these three
parameters *f*, *E*, and *V* can yield
intuitively plausible truth conditions for each of the kinds of ‘ought’ that we
considered in the previous section.

**4.
****Instances of the
expectational schema**

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 distribution – 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 distribution 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 semantic values of various objective kinds of ‘ought’
are reflected, not in the probability distribution *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 the worlds
in each domain.

It seems plausible that the semantic value
of every instance of the *practical*
‘ought’ is focused on the situation of a particular agent *x* at a
particular time *t*. (It is this that has tempted many philosophers –
like Mark Schroeder (2011) – to argue that the practical ‘ought’ actually stands
for a relation between an agent and act-type.) So it seems that the semantic
value of this use of ‘ought’ 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
worlds within the relevant domain of possible worlds. Presumably, *V* will evaluate these worlds purely on
the basis of how the relevant agent acts in the relevant situation. For
example, more specifically,
*V* might be a measure of the value of
these worlds that is based purely on degree of *choiceworthiness* of the *act*
that the agent performs in this situation within each of these worlds. On
this view, then, if the relevant ‘ought’ is the objective practical ‘ought’, focused
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 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 distribution (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 distribution 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,
however, is 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
distribution that reflects this information. Moreover, if the agent herself
also thinks that there is some available information that she has not yet acquired,
it will be very natural for the agent to use an ‘ought’-concept that in this
way involves a probability distribution that reflects that information that the
agent hopes to acquire.[10]

In
general, a probability distribution is in effect a way of representing a
certain epistemic perspective; and an epistemic perspective can become conversationally
salient for many reasons. For example, as we have noted, many probability
distributions 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 the corresponding epistemic
perspective will be salient in the conversational context in question. There
are 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 or observer of the agent to whom the occurrence of
‘ought’ is indexed, rather than that agent herself.

This
idea of relativizing ‘ought’-concepts to probability distributions 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 distributions
corresponding to each body of information. In this way, probability
distributions 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 integrate with some of
the classical theories in this area: unlike their account, my proposal entails
standard deontic logic; and it clearly yields the right verdicts in contexts
where it is assumed that the agent ought to maximize some kind of expectation
of some kind of 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
distribution *E*: the objective ‘ought’
is indexed to the omniscient probability distribution, whereas the more
subjective ‘ought’ is indexed to a more subjective probability distribution
that corresponds to the credence function of a possible thinker who (although
perfectly rational) is significantly more ignorant and uncertain 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 focused on 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 worlds
that are available to the agent at the time in question, not in terms of the overall
choiceworthiness of the act that the agent performs in those worlds, but purely
in terms of how good what the agent does in those worlds is as a means to
accomplishing that purpose *P*.
Otherwise, the two kinds of ‘ought’ work in more or less the same way.

As
I remarked 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 roughly equivalent to saying that
the embedded proposition ‘Tonight’s performance will be a lot of fun’ is *highly probable* given the salient 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 the epistemic ‘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 epistemic
perspective. (Again, this could be pretty well any perspective; the
participants in a conversation will just have to interpret the contextual clues
in order to discern which perspective is contextually salient in the relevant
way.)

Finally,
*V* could simply be a function that
ranks worlds according to the worlds’ answers to a certain question, by ranking
the *true* answer above the *false* answer – say, by assigning a
value of 1 to worlds that give the true answer and 0 to worlds that 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 these answers’ probability according to *E*; and this ranking determines a
corresponding ordering of worlds in accordance with the probability of each
world’s 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 distribution 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 of the world 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). A proposition *p*
that follows 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
distributions (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 distribution *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 distribution.

So,
for example, even if the speaker knows perfectly well that the orbit of Pluto
is not elliptical, the relevant probability distribution *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 distribution
that corresponds to the credences that it would be rational to have given a
body of information that is different from the speaker’s actual total evidence
but contextually salient for other reason. So this approach has no difficulty
handling such puzzling instances of the epistemic ‘ought’ as ‘The orbit of
Pluto ought to be elliptical (though of course it isn’t)’.[11]

**5.
****‘Ought’ and
conditionals**

Finally, I should like
to comment on what this expectational model of ‘ought’ implies about how
‘ought’ interacts with conditionals. The general idea is familiar from such
classic discussions of conditionals as that of Angelika Kratzer (1986). According
to Kratzer, quite generally, the effect of conditionals is to restrict some
domain of possible worlds that is involved in the semantics of a modal operator
that appears (at least implicitly) as the dominant operator of the consequent
of the conditional – by restricting this domain of worlds to that subset
of the domain where the antecedent of the conditional is true.

Once we have the idea
of a *space* of possible worlds –
as opposed to a mere domain or set of possible worlds – it is natural to reinterpret
this “restricting” function of conditionals. Instead of simply replacing the
domain of possible worlds with the subset of the original domain where the
conditional’s antecedent is true, we may conceive of the conditional as
replacing the original space of possible worlds with the *sub-region* of the space where the conditional antecedent is true.

Where the space of
worlds has no more structure than a simple set of worlds, the sub-region of the
original space will simply be the subset where the antecedent is true –
just as on Kratzer’s original proposal. However, where the space of worlds has
the structure of a probability distribution, replacing the space with the
sub-region where the antecedent is true is equivalent to replacing the original
probability distribution by the result of *conditionalizing*
it on the antecedent.

According the account
that I have proposed here, the semantics of ‘ought’ involves *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*. The
antecedent of the conditional will restrict one of these spaces of worlds; but
it may be up to the particular conversational context to determine which of
these two spaces is restricted in this way.

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 of 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:

1.
Metaphysical: For any
two propositions *p* and *q*: ‘[If *p*] *q*’ is true at *w* iff *q* [*f*/ *f′*] is true at *w* –
where *q* [*f*/ *f′*] is the result of uniformly replacing *f* in *q*
with *f′*, which is the function
from any possible world *w*′ to
the subset of *f* (*w*′) where *p* is true.

2.
Epistemic: For any two
propositions *p* and *q*: ‘[If *p*] *q*’ is true at *w* iff *q* [*E*/ *E′*] is true at *w* –
where *q*
[*E*/ *E′*] is the result of uniformly
replacing *E* in *q* with *E′*, which is
the sub-region of *E* where *p* is true.

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
distribution *E* that would be involved
in the semantic value of the consequent of the conditional if it appeared unembedded
with the result of *conditionalizing*
that probability distribution 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’, focused on 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 – though
it is not yet known which of these two partial cures will have that
side-effect. Now, suppose that the patient is about to have a test: it is known
that 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
distribution that results from our current system of credences by
conditionalizing on the proposition that the test result is positive.[12]

This
is not to say that every conditional with an ‘ought’ in the consequent conforms
to one of these two patterns. Suppose for
example that we are considering another agent – call her Alice – and
wondering which of two courses of action, *A* and *B*, it is most rational
for her to take. Then we might say: ‘I’m not sure which of these two courses of action* *Alice regards as preferable. But if she
thinks that *A* is preferable to *B*, she should do *A*’.[13]
This seems to me to be an ordinary indicative conditional – to be
explained in the same way as all other indicative conditionals (whatever that
way is). In this case, the local context in which this occurrence of ‘should’
occurs makes a certain possible epistemic perspective *E* salient – specifically, the perspective that Alice would
have if she thinks that *A* is
preferable to *B*. The semantic value
of this occurrence of ‘ought’ is to be analysed in terms of this epistemic
perspective *E*.

**6.
****Objections and
replies**

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 distribution
involved in these truth conditions is the omniscient probability distribution,
or a probability distribution that in some way reflects a greater degree of ignorance
and uncertainty.

Secondly,
I have suggested that these truth conditions capture the semantic values of the
concepts that are expressed in English by uses of deontic modals like ‘ought’
and ‘should’. In the space available, this suggestion could not be defended in
detail. The suggestion seems plausible to me, but I concede 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 – even if they are not expressed
in English by deontic modals like ‘ought’ and ‘should’ – may at least turn
out to be useful concepts for various theoretical purposes.

In
this final section, I shall offer a brief reply to an objection that might be
raised against my suggestion that this family of truth conditions really
captures the semantic values of uses of ‘ought’. Some readers may worry that my
account seems to build in some controversial assumptions about rational choice
into the very semantics of ‘ought’. In some unpublished notes quoted by Kai von
Fintel (2012: 25), Kratzer objects to accounts that do this, asking
rhetorically: “Why pack information about rational decision making into the
meaning of modals?”

Strictly
speaking, however, I have not in fact said anything about rational decision
making here. Admittedly, my account makes use of the general idea of the
expected value of a possible world, which is an idea that is also invoked in
many theories of rational choice – for example, by those theories that imply
that a rational choice must maximize *expected
utility*. My account has in fact made absolutely no mention of utility at
all. (There may be contexts where the value function *V* involved in the semantic value of an occurrence of ‘ought’ is a
utility function; I take no stand on the issue.) Still, it may seem that the
mere fact that I have made use of the general idea of the expected value of a world
brings my account too close to “packing information about rational decision
making into the meaning of modals”.

There
are two main problems that might be alleged to affect accounts of the semantics
of ‘ought’ that appeal to the idea of the expected value of a world. First, one
might think that this idea is too controversial and too technical to be
implicit in the linguistic competence of ordinary speakers. Secondly, one might
think that there are some specific cases that cannot be handled in an
intuitively acceptable way by any such account.

My
account is not vulnerable to the first problem, since I have explicitly
distanced myself from any attempt to explain linguistic competence in terms of
an implicit grasp of the truth conditions that I have described. It is undeniably
an important question what linguistic competence consist in, but unfortunately
I cannot address that question here. At all events, it is far from obvious that
the truth conditions that I have described are incompatible with any plausible
account of linguistic competence.

The
second problem is potentially more serious. For example, consider an
agent – call her Barbara – who harbours grave doubts about the theory that
rational choices must maximize any kind of probabilistic expectation of any
kind of value. Instead, Barbara takes very seriously a rival theory of
rationality, which is some kind of non-maximizing theory. Suppose that the
maximizing theory would favour Barbara’s choosing act *A*, and the non-maximizing theory would favour her choosing act *B*. It would seem true to say ‘For all Barbara
knows, she ought to choose *B*’. Can we
really handle cases of this sort in a satisfactory manner if maximization is
actually built into the semantics of ‘ought’ and ‘should’ as I propose?

These
cases seem hardly typical of the normal use of deontic modals, since they
concern the use of these terms by theorists or philosophers in talking about
other theorists. It is questionable whether such esoteric uses are the most
reliable evidence for a theory of the meaning of words in a natural language.
Nonetheless, a number of recent writers seem to have been moved by cases of
this sort. For example, Jennifer Carr (2013) has proposed that there should be
a separate parameter in the semantics of deontic modals for a *decision rule*: in some contexts, this
decision rule might be maximizing expected utility, but in other contexts, it
might be some other decision rule, such as a non-maximizing rule.

In
my view, however, this manoeuvre greatly complicates the semantic account of
deontic modals, in a way that is far from obviously warranted by the linguistic
evidence. Statements of the form ‘For all Barbara knows, *p*’ are hard to interpret: indeed, in some contexts, it seems that
it could be true to say such things as ‘For all Pythagoras knew, there were
only finitely many prime numbers’. On the face of it, it should be possible to
give a theory of what such sentences mean without supposing that there is any
context such that the notion of maximization plays no role in any correct
account of the truth conditions that an ‘ought’-sentence has in that context.

So
far as I can see, there is no clear case where we have the intuition that a
sentence that has ‘ought’ as the dominant operator – for example, a
sentence of the form ‘Barbara ought to choose *B*’ – is true, in a way that clearly cannot be handled by a
maximizing account such as the account that I have proposed. I have already
briefly mentioned the “purpose-relative ‘ought’” in Sections 2 and 4 above; one
kind of purpose-relative ‘ought’ can be used to speak about what agents ought
to do *in order to* *conform* to a certain normative theory.
It could be that in any case where we are tempted to assert a sentence of the
form ‘Barbara ought to choose act *B*’,
on the grounds that *B* is what is
recommended by a certain non-maximizing theory, our assertion is either false
or else true only when the relevant occurrence of ‘ought’ is understood as the
purpose-relative ‘ought’, relativized to the goal of conforming to the theory
in question. At all events, the linguistic evidence does not clearly support
the conclusion that the semantics of ‘ought’ needs to be complicated in this
way in order to handle these rather recherché cases.

Even
though my account is unified in that the notion of maximization plays a role in
my account of the semantic value every kind of ‘ought’, it is in other ways an
immensely broad and flexible account of the term. Many other philosophers of
language and metaethicists have proposed much narrower interpretations of
‘ought’, which dramatically *under-predict*
many of the readings of ‘ought’ that seem genuinely available.[14] By
contrast, 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 this wide 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 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’.[15]

**References**

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).

Carr,
Jennifer (2012). “Deontic modals without decision theory”, *Proceedings of
Sinn und Bedeutung* 17: 167–182.

Charlow,
Nate (2013). “What we know and what we do”, *Synthese*
190: 2291–2323.

Ewing,
A. C. (1947). *The Definition of Good* (New York: MacMillan).

von
Fintel, Kai (2012). “The best we can (expect to) get? Challenges to the classic
semantics for deontic modals” <http://mit.edu/fintel/fintel-2012-apa-ought.pdf>

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, Niko, and
MacFarlane, John (2010). “Ifs and Oughts”, *Journal
of Philosophy* 105: 571–590.

Kratzer, Angelika (2002).
“The Notional Category of Modality”, in Paul Portner and Barbara Partee, ed., *Formal Semantics: The Essential Readings*
(Oxford: Blackwell), 289–323.

———— (1986).
“Conditionals”, *Chicago Linguistics Society* 22: 1–15 <http://semanticsarchive.net/Archive/ThkMjYxN/Conditionals.pdf>

Lewis, David K.
(1973). *Counterfactuals* (Oxford:
Blackwell).

Parfit, Derek (1984). *Reasons and Persons* (Oxford: Clarendon
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Schroeder, Mark
(2011). “*Ought*, Agents, and Actions”,
*Philosophical Review* 120 (1): 1–41.

Sidgwick, Henry
(1907). *The Methods of Ethics*, 7^{th}
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Swanson, Eric (forthcoming).
“Ordering Supervaluationism, Counterpart Theory, and Ersatz Fundamentality”, *Journal of Philosophy*.

Silk, Alex (2013).
“Evidence-Sensitivity in Deontic Modals”, *Journal
of Philosophical Logic* 1–33. DOI: 10.1007/s10992-013-9286-2

Thomson, J. J.
(2008). *Normativity* (Chicago,
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Wedgwood,
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————
(2009). “The ‘Good’ and the ‘Right’ Revisited”, *Philosophical Perspectives*
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[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). In
a somewhat similar way, Sidgwick (1907, 207) distinguished between objective
and subjective rightness and wrongness.

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

[3] So, if the proposition ‘*O*(*p*)’ is not to be
trivial, there must be some worlds that are not ranked any lower in this ordering than any other worlds in the
domain. That is, what David Lewis (1973) called the “Limit Assumption” must
hold. Some philosophers – such as Eric Swanson (forthcoming) – have
denied that the Limit Assumption must hold for all ‘ought’-concepts. But in my
view, there are independent reasons for thinking that it must hold.
Specifically, if ‘ought’ agglomerates over conjunction – including
infinite conjunction – and ‘ought’ implies logical possibility, then it
seems that the Limit Assumption must indeed hold: that is, in effect, there
must be a possible world where everything is as it ought to be.

[4] This “classical” semantics for deontic operators 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).

[5] See especially Wedgwood (2007, Section 5.2, and 2009,
Section 2).

[6] Invoking two spaces of possible worlds – a space
of epistemically possible worlds and a domain of metaphysically possible
worlds – in this way sets my account apart from most previous accounts of
deontic modals, which have typically sought to explain the semantic value of
these modals purely in terms of a single domain of possible worlds. Thus, for
example, the account of Silk (2013) resembles mine to the extent that it allows
the ordering on the worlds to vary with an “information state”, but for Silk
this information state is simply a kind of modal base, and so is nothing more
than a “set of worlds” (15). The main exception is Jennifer Carr (2012, 13) who
proposes that the semantic value of deontic modals involves a modal background,
a probability function, and a value parameter (although confusingly she
describes the modal background and the probability function as together
constituting an “informational parameter”). The main difference between my
account and Carr’s is that her account involves yet another parameter, a
“decision rule parameter”, which seems unnecessary to me; she also does not
distinguish between metaphysically and epistemically possible worlds in the way
that I regard as important. (For further discussion of Carr’s proposal, see
Section 6 below.)

[7] Strictly speaking, to accommodate
incommensurability, we need to consider a *set*
of such value functions, rather than a unique value function. But I shall
ignore this complication for the purposes of the present discussion.

[8] An alternative
approach would be to understand the “expected value” of an epistemically
possible world *w* as defined in terms
of the conditional probability of such hypotheses – conditional on the
world w that is in question. To put it symbolically, the appropriate
expectation might be: ∑* _{i} n_{i} E* (

[9] In principle,
there could be epistemically possible worlds that are like empty names –
in that
there is in fact no metaphysically possible world that they are a
mode of presentation of. (Perhaps the epistemically possible world in which you
visit Hesperus but not Phosphorus is like this – since there is presumably
no metaphysically possible world where you visit Hesperus but not Phosphorus.)
If an epistemically possible world *w** _{E}* is like an
empty name in this way, then we would have to identify the metaphysically
possible worlds that correspond to

[10] This is how I would aim to answer the objections of Kolodny and MacFarlane (2011).

[11] This
view of the epistemic ‘ought’ also helps to explain why it has such different
truth conditions from the epistemic ‘must’ – even though both modals are
broadly speaking necessity operators. For ‘must’, the ordering on the possible
worlds makes no difference to the sentence’s truth conditions; and according to
my proposal, the only relevance of the probability distribution *E* is to generate the ordering of
possible worlds in terms of their *EV*-expected
value. So the truth conditions of ‘Must (*p*)’ depend purely on whether *p*
is true throughout *f* (*w*), and is unaffected by what *E*
and *V* are in the relevant context.

[12] This
interpretation of these epistemic deontic conditionals seems to me to avoid the
problems for rival accounts that are canvassed by Nate Charlow (2013).

[13] I owe this example to Alex Silk.

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

[15] This paper was originally written and posted on my web site in the
summer of 2011. In the spring and summer of 2012, it was presented as talks at
Berkley and at Edinburgh; I am grateful to the members of those audiences for
helpful comments. Finally, in revising the paper around the beginning of 2014,
I benefited greatly from some highly illuminating comments from Alex Silk.