**Objective and subjective ‘ought’**

Ralph Wedgwood

**Abstract**: This essay offers
an account of the truth conditions of sentences involving deontic modals like
‘ought’, designed to capture the difference between objective and subjective
kinds of ‘ought’ This account resembles the classical semantics for deontic
logic: according to this account, these truths conditions involve a function
from the world of evaluation to a domain of worlds (equivalent to a so-called
“modal base”), and an ordering of the worlds in such domains; this ordering of
the worlds itself arises from two further elements – a probability
function and a value function – since this ordering ranks the worlds in
accordance with the *expected value* of
certain propositions that are true at those worlds. Thus, a proposition of the
form ‘Ought (*p*)’ is true at a world
of evaluation w if and only if *p* is
true at all the top-ranked worlds in the domain assigned to *w*. This domain of worlds consists of *metaphysically* possible worlds, while
the probability function is defined over a space of *epistemically* possible worlds (which may include metaphysically
impossible worlds, such as worlds where Hesperus is not Phosphorus). Evidence
is given that this account assigns the correct truth conditions to a wide range
of sentences involving ‘ought’. Since these truth conditions involve both a
domain of metaphysically possible worlds and a space of epistemically possible
worlds, there are two corresponding kinds of *conditional* involving ‘ought’, depending on which space of worlds
is restricted by the conditional. Finally, some objections that might be raised
against this account are answered.

**Keywords**: Ought, deontic
modality, semantics, expected value, conditionals

**Wordcount**: 12,437

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 sentences involving terms that express 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 by 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 distributions*;
and every probability distribution determines a body of information –
namely, the set of propositions that have probability 1 within that distribution.
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 any 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, according to an account of this sort, we can 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: 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 the nature of each of
these concepts can be explained 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 comment, at least in
passing, on 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 this occurrence
of ‘ought’), to yield a further proposition (the proposition that is expressed
by the sentence in which this occurrence of ‘ought’ has largest scope).

Thus,
for example, the occurrence of ‘ought’ in the English sentence ‘This room ought
to be swept’ expresses an ‘ought’-concept that operates on the proposition that
is expressed by the embedded sentence ‘This room is swept’. 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 a sentence expressing such an
‘ought’-proposition is true at a possible world can be specified as follows.
For every such sentence, 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 sentence expressing the ‘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 sentence
expressing ‘*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 sentence ‘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, 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 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, there is
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 informational state of 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 informational state of the relevant agent 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 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 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 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 sentences
that express ‘ought’-propositions are in line with the classical semantics of
standard deontic logic. The truth conditions of every such sentence involves
the following two crucial elements: first, they involve a function *f* that maps each possible world *w* onto a domain of possible worlds *f** *(*w*); secondly, they
involve an ordering on the worlds in this domain. So, to understand the
semantic value of any ‘ought’-concept, we need to understand these crucial
elements.

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*).

There
are two ways of interpreting this expectational conception of the orderings
that feature in the truth conditions of these sentences. On the first
interpretation, the analysis of each of these orderings as resulting from a
probability function *E* and a value
function *V* is built into the *semantics* of modal terms like ‘ought’.
On the second interpretation, the semantics just involves these orderings
themselves, without itself containing any such analysis of the orderings; and
the analysis is purely a *metaphysical*
thesis about the nature of the orderings in question. In fact, I shall argue in
Section 5 below that there are reasons, concerning the truth conditions of *conditional* sentences involving ‘ought’,
for interpreting this expectational conception in the first way, as built into
the semantics of terms like ‘ought’. For the time being, however, we simply
shall leave it open which interpretation of this expectational conception is
correct.

In
the rest of this section, I shall explain this expectational schema in more
detail, starting with some comments on each of its three elements – the
domain function *f*, the probability
distribution *E*, and the value
function *V*.

**(i)** The first element of any instance of this expectational
schema is familiar: it is a domain function *f*,
which maps every world *w* onto the
relevant domain of possible worlds *f** *(*w*). It is this function that identifies the worlds that are, as we
might put it, “up for assessment” by the ‘ought’-concept in question, relative
to *w*. In effect, this function *f* fixes what Angelika Kratzer (2012,
Chapter 2) called the “modal base” – the set of propositions that are true
throughout the domain of worlds that are up for assessment by the
‘ought’-concept, relative to *w*. We
shall explore some specific examples of such domains of worlds in the next
section.

**(ii)** The
second element of any instance of this expectational schema is a probability distribution
*E*. I shall assume that every probability
distribution is a function that assigns real numbers in the unit interval from
0 to 1 to the propositions in a propositional algebra (that is, a set of
propositions that is closed under Boolean operations like negation, disjunction,
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.

Another
way of thinking of such probability distributions is as defined over a *space of possible worlds*, relative to a
certain “field” of subsets of this space of worlds. This “field” also
constitutes an algebra, in the sense that it is closed under operations like complementation,
union, and the like; the probability function assigns real numbers to the sets
of worlds in this field.[6] This
probability function can be thought of as a *measure*
on the space of worlds: intuitively, it tells us *how much* of the whole space of worlds is taken up by each set in
this field. (This is why the probability measure has to obey a basic additivity
principle: the proportion of the whole space taken up by the union of any two
disjoint sets of worlds is the *sum* of
the proportions taken up by those sets.) This way of thinking of probability
distributions is equivalent to thinking of them as defined over propositions,
so long as for each of the relevant propositions, the field contains a set of
worlds in which that proposition is true. (Indeed, on some views, each of these
propositions is *identical* to the
corresponding set of worlds.)

It
seems clear that for some purposes, we will have to consider probability
distributions in which some propositions that are metaphysically necessary but
knowable only empirically – such as the proposition *that Hesperus = Phosphorus* – have a probability less than 1.
If we think of the probability distribution as defined over a space of worlds,
this means that we will have to allow the space to include worlds where
Hesperus ≠ Phosphorus. Such worlds are not metaphysically possible, but
they may still be *epistemically*
possible. So the space of worlds over which the probability distribution is
defined is a space of epistemically possible worlds, not a space of
metaphysically possible worlds.

Although
we can make sense of probability distributions in which the proposition *that Hesperus *≠* 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 identical
to Phosphorus, if you ought to visit Hesperus, it surely follows that you also
ought to visit Phosphorus. To explain this fact about deontic modals, within
the semantic framework that I am assuming here, the domain of possible worlds *f** *(*w*) must be 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.[7] 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. Metaphysically possible worlds are
individuated by the Russellian propositions that are true at those worlds: a
metaphysically possible world *w*_{1}
is identical to a metaphysically possible world *w*_{2} if and only if exactly the same Russellian
propositions are true at *w*_{1}
and *w*_{2}. 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*. Since the
propositions that in this way individuate a possible world must form a
logically complete and consistent set, this explains why there cannot be
metaphysically possible worlds in which you visit Hesperus but not Phosphorus.

By
contrast, the epistemically possible worlds are individuated by the *Fregean* propositions that are true at
those worlds – where Fregean propositions are 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. An epistemically possible world *w*_{1} is identical to an epistemically possible world *w*_{2} if and only if exactly the
same Fregean propositions are true at *w*_{1}
and *w*_{2}. 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 allows for the existence of an epistemically possible world in which you
visit Hesperus but not Phosphorus.

**(iii)** Finally, the third element of any
instance of this expectational schema is a *value*
function of a certain kind.

In
general, this value function will evaluate 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 of
metaphysically possible worlds. I shall also assume that these propositions are
*jointly exhaustive*: that is, *at least* one of these proposition is
true at every world in this domain. In other words, this set of propositions
forms a *partition* of this domain of
worlds: at every possible world in this domain, exactly one of these
propositions is true.

Since
no more than one of these propositions is true at every world in this domain,
and there is no metaphysically possible world where you visit Hesperus without
also visiting Phosphorus, the proposition that you visit Hesperus cannot be a
distinct member of this set of propositions from the proposition that you visit
Phosphorus. Thus, the propositions in this set must be *Russellian* propositions (indeed, each such proposition might simply
be identified with a *subset* of the
domain of metaphysically possible worlds). In effect, every such value function
provides a set of Russellian propositions {*A*_{1},
… *A _{n}*} that forms a
partition of the relevant domain of worlds, and assigns a value to each of these
propositions.

We
may think of the value that the value function assigns to each Russellian proposition
*A _{i}* in this set as a real
number

**(iv)** In
this way, any instance of this expectational schema involves three items: a
function *f* from each metaphysically possible world to a relevant domain of such worlds; a probability
distribution *E*; and a value function *V* defined over a set of propositions
that constitutes a partition of the relevant domain of metaphysically possible worlds.
To represent the fact that a particular instance of the expectational schema
gives an account of the conditions under which a use of a sentence involving
‘ought’ is true, I shall explicitly index this occurrence of ‘ought’ to this
trio of items: ‘Ought_{<f, E, V>}’.

I
have proposed that the value function *V*
is defined over a set of Russellian propositions that forms a partition of the domain
of metaphysically possible worlds. However, the probability distribution *E* can assign probabilities to hypotheses
*about* the value that *V* assigns to various propositions –
where each of these hypotheses is, in effect, a *Fregean* proposition. For example, such hypotheses might include:
‘The proposition that I visit Hesperus has value *n*’, and ‘The proposition that I visit Phosphorus has value *m*’ – where these two hypotheses are
distinct from each other.

In
this way, the hypotheses to which *E *assigns
probability refer to Russellian propositions by means of modes of
presentation – where these modes of presentation of Russellian
propositions are, in effect, Fregean propositions. It seems that just as the
relevant set of Russellian propositions forms a partition of the domain of
metaphysically possible worlds, the corresponding Fregean propositions forms a
partition of the space of epistemically possible worlds. Since each of these
hypotheses involves a Fregean proposition *A _{E}*
(as a mode of presentation of a Russellian proposition

We
can now give a definition of the *EV*-expected
value of a Fregean proposition *A _{E}*,
in the following way. Consider a collection of hypotheses {

∑_{i}*n _{i} E*

Since
the set of Fregean propositions that feature in these hypotheses forms a
partition of the epistemically possible worlds, the epistemically possible
worlds themselves can be ordered in terms of the *EV*-expected value of the proposition in this set that is true at
each world. Let us say that the epistemically possible worlds that are not
ranked lower down in this ordering than any other such worlds have “maximal *EV* value”.

For
each of these epistemically possible worlds, we need to find the metaphysically
possible worlds that in the relevant way “correspond to” that epistemically
possible world. In the simple cases, a metaphysically possible world* w _{M}* corresponds to an
epistemically possible world

We
can now define a selection function *S*_{<f, E, V>} over
the metaphysically possible worlds that will pick out the metaphysically
possible worlds that correspond to the epistemically possible worlds with
maximal *EV*-value: for any
metaphysically possible world *w _{M}*,

The
truth conditions of sentences of the form ‘Ought_{< f, E, V>}(*p*)’ can be specified in terms of this selection function *S*_{<f, E, V> }:

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

Let
us illustrate this proposal by considering the example of Frank Jackson’s (1991)
“three drug” case. In this case, the
speakers using ‘ought’ are focusing on the practical situation of a certain
agent *x* at a time *t*; in this situation, there are three
options available to *x* at *t* – giving the patient drug 1,
giving the patient drug 2, and giving the patient drug 3. The agent *x* knows that drug 3 is second-best.
Unfortunately, although *x* knows that
either drug 1 is best or drug 2 is best, *x*
does not know which – and *x*
knows that if drug 1 is best, drug 2 will be disastrous, while if drug 2 is
best, drug 1 will be disastrous. The speakers are considering what *x* ought to do at *t* given the informational state that *x* is in at *t*. Then the
three parameters *f*, *E*, and *V* will be something like the following:

·
*f*(*w**) is the set of metaphysically possible worlds that are
practically available to *x* at *t* (so in these worlds, everything that *x* cannot change by *x*’s actions at *t* is
exactly as it is in *w**).

·
*E* is a probability
distribution that in the appropriate way corresponds to *x*’s informational state at *t*.

·
*V* is a value function
that assigns values to the three Russellian propositions, *A*_{1}, *A*_{2},
and *A*_{3} – the
propositions that at *t*,* x* gives the patient drug 1, drug 2, and
drug 3, respectively – where these three propositions form a partition of
the domain of worlds *f*(*w**).

*E* assigns probabilities to various hypotheses –
including hypotheses *about* the value
that *V* assigns to *A*_{1}, *A*_{2}, and *A*_{3}.
In referring to these Russellian propositions *A*_{1}, *A*_{2},
and *A*_{3}, these hypotheses
use modes of presentation of these propositions – and we are assuming that
these modes of presentation of Russellian propositions are themselves Fregean
propositions. To keep things simple, however, let us suppose that *E* puts the relevant Fregean propositions
into a one-to-one correspondence with the Russellian propositions. (That is, for
each of these Russellian propositions, there is exactly one Fregean proposition
that is a mode of presentation of* *that
Russellian proposition such that *E*
attaches non-zero probability to any hypotheses involving that Fregean
proposition.) Thus, there is also a corresponding set of Fregean propositions
forming a partition of the epistemically possible worlds – *A _{E}*

Assume
that for each of these Fregean propositions *A _{E}*

·
*h*_{1.1} is ‘*V*(*A _{E}*

·
*h*_{2.1} is ‘*V*(*A _{E}*

·
*h*_{3.1} is ‘*V*(*A _{E}*

Suppose that for all *i*, *E*(*h _{i}*

·
*EV*(*A _{E}*

·
*EV*(*A _{E}*

·
*EV*(*A _{E}*

Thus, the epistemically
possible worlds that have maximal *EV*-value
are all and only the worlds at which *A _{E}*

As
I explained above, this proposal is simply an account of conditions under which
‘ought’-sentences are true. I am not proposing that there are hidden variables
referring to these parameters *f*, *E*, and *V* in the actual *syntax* of
these sentences. 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 argue in Section 5 that all of these three parameters – *f*, *E*,
and *V* – are part of the *semantics* of ‘ought’, in the sense that
they must be included in any systematic account of the truth conditions of the
full range of sentences involving ‘ought’. So, 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 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 think of a probability distribution by means of the
formal mathematical concept of probability!) For example, the probability
distribution *E* might be 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 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 Section 2.

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

The
schema set out in the previous section 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.

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
semantic value will also involve a function *V* that measures the value of the various
acts that the agent performs at any of these available possible worlds. For
example, more specifically,
*V* might be a measure of the *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 forms 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,
it is a probability distribution that encodes a significant degree of ignorance
and uncertainty about the world. For example, in many contexts we might use a
practical ‘ought’ in such a way that its semantic value involves a probability
distribution that corresponds to the system of credences that would be *ideally rational* for a thinker 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 incorporates this 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 an ideally 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 conversationally salient agent has at a 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 on whom this occurrence of the practical ‘ought’
is focused, 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, conceived of simply as sets of
propositions. 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 different probability distributions in
which the same propositions have probability 1. 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.

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*: with the objective ‘ought’, *E* is the omniscient probability
distribution, whereas with the more subjective ‘ought’, *E* is indexed to a 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 various
acts that the agent performs at any of the worlds that are practically available
to the agent at the time in question, not in terms of their overall choiceworthiness,
but purely in terms of how good these acts are 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 *that 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 set of all
possible worlds that are compatible with everything that is known for certain
in the context. Secondly, *E* can be a probability
distribution 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 answers to a certain *question*,
which we can think of as a partition of alternative answers to the question, by
ranking the *true* answer to the
question above all the *false* answers –
say, by assigning a value of 1 to the true answer and 0 to false answers. 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 sentence ‘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 51 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 general explanatory picture of the world is true. If this general
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 general
explanatory picture of this sort will typically be significantly more probable
than that general 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.

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 reasons. 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**

In this section, I shall
comment on what this expectational model of ‘ought’ implies about how ‘ought’
interacts with conditionals. It is here that we shall see why the probability
distribution *E* needs to be part of
the semantics of ‘ought’.

The general idea is
familiar from such classic discussions of conditionals as that of Angelika Kratzer
(2012, Chapter 4). 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.

As I mentioned in the
previous section, we can think of the probability distribution as itself a *space* of possible worlds – where a
“space” of worlds is more than a mere set of worlds. A space of worlds involves
not just a set of worlds but also a *measure*
on subsets of this space. That is, there is a certain “field” of subsets of the
space such that we can make sense of ratios between the proportions of the
whole space that are taken up by these subsets. For example, we can make sense
of the idea that one subset takes up *twice
as large* a proportion of the whole space as another. So we can in effect
view the probability distribution *E*
as a structured measureable space of worlds of this sort.

Once we have the idea
of a *space* of possible worlds –
as opposed to a mere domain or set of 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’s 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 I shall call the second sort of conditional the “epistemic
conditional”.

The truth conditions
of these two kinds of conditionals can be specified 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 clause for this second epistemic conditional requires that
the space of possible worlds *E* must
itself be part of the *semantics* of
the sentence that expresses the proposition *q*.
It is only if *E* is part of the
semantics that the effect of embedding this sentence within a conditional can
be to restrict this space *E* to the
sub-region of the space where the antecedent proposition *p* is true.

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
an example of the metaphysical conditional, 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, 1 and 2, 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 unknown which of the two
drugs will cure the patient and which will kill him. In addition, there are two
other drugs, 3 and 4, each of which will effect a partial cure, but one of
which will have an unpleasant side-effect – though it is not yet known
which drug will have that side-effect. Suppose that the patient is about to
have a test: it is known that if the test is negative, it is drug 3 that will
have the unpleasant side-effect, while if the test is positive, drug 4 will
have the unpleasant side-effect. Then it is true to say ‘If the test result is
positive, we should give the patient drug 3.’

This
statement is true because we give drug 3 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 seems to be the intuitively correct truth conditions for this
sentence – which supports the semantic proposal that I am making here.

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 family of truth conditions – in effect, the truth conditions that the
sentences expressing 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 uses
of the English 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 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 proposition, 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 proposition
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 him John – who harbours grave doubts about all views
according to which one should choose options that maximize some kind of
probabilistic expectation of some kind of value. Instead, John is attracted to
a rival theory of rationality, such as the *maximin*
theory – according to which in every choice situation, one should choose one of
the options whose worst possible outcomes are at least no worse than the worst
possible outcomes of the available alternatives. Suppose that the most
plausible version of the expected-value theory would favour John’s choosing act
*A*, and the maximin theory would favour
her choosing act *B*. It would seem
true to say ‘For all John knows, he ought to choose *B*’. Can we really handle cases of this sort in a satisfactory
manner if the notion of maximizing expected value is built into the semantics
of ‘ought’ 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 the maximin 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 John knows, *p*’ are hard to interpret. In some contexts, it seems that it could
be true to say such things as ‘For all Pythagoras knew, there are only finitely
many prime numbers’. To explain why this sentence is true, it is surely not
necessary to argue that there are some possible worlds where there are only
finitely many prime numbers! In a similar way, it should be possible to explain
why the sentence ‘For all John knows, he ought to choose *B*’ without supposing that there is any context such that the notion
of maximizing expected value plays no role in the correct account of the truth
conditions that an ‘ought’-sentence has in that context.

A
similar objection is raised by Fabrizio Cariani (this volume, §2.2), who focuses
on cases where a sentence involving ‘ought’ is embedded inside a larger
sentence, like ‘John believes that he ought to choose *B*’, which ascribes a belief to a heterodox theorist like John.
Cariani argues that an account like mine will have difficulties explaining why
this belief-ascription is true.

In
fact, however, my account has no difficulty providing such an explanation. It
seems most promising to link my account of the semantics of ‘ought’ with a *relational analysis* of
belief-ascriptions. According to this relation analysis, the belief-ascription
is true because John stands in the *belief-relation*
to a *content* of the appropriate kind that
can be expressed in this context by the embedded sentence ‘he ought to choose *B*’.

According to Cariani
(ibid.), “the appeal to
the relational analysis is merely evasive, unless it is complemented by an
account of what content is expressed by a deontic sentence in a given context”.
But it is surely not obvious that in order to defend my account of the
semantics of ‘ought’, I need to commit myself to a full account of the
semantics of belief-ascriptions here. It is enough if I can make it plausible
that it is possible in principle to give an illuminating analysis of
belief-ascriptions that harmonizes with my account of ‘ought’.

So, to fix ideas, I
shall suggest a possible analysis of this sort. I am not firmly committed to
all the details of this suggestion; the suggestion is included here only to
respond to Cariani’s objection. According to this suggestion, in this context
the embedded sentence ‘he ought to choose *B*’
express a Fregean proposition – presumably, a Fregean proposition that
John could express in an appropriate context by uttering the sentence ‘I ought
to choose *B*’.

It seems clear that
this Fregean proposition is capable of being true or false; in that sense, this
proposition has truth conditions. Presumably, to make this suggestion
compatible with my account, this Fregean proposition must have has the same
(extensional) truth-conditions that my account assigns to the ‘ought’-sentence
in this context. However, there is no reason to think that John himself must entertain
this Fregean proposition by means of explicitly thinking of these truth
conditions. John must latch onto this proposition somehow, but it is not
necessary for him to latch onto the proposition by means of an implicit grasp
of the most systematic account of the truth conditions of sentences that express
this proposition. Instead, I suggest, John latches onto this proposition by deploying
some mode of presentation of the property that, according to my account, the embedded
proposition *that John chooses B* would
have to possess for the whole ‘ought’-proposition to be true. The content of
John’s belief is a Fregean proposition that applies this mode of presentation
to this embedded proposition. Exactly how John grasps this mode of presentation
of this property is a delicate question, but it seems possible that he could grasp
this mode of presentation without having any awareness of how the property is
analysable in terms of a domain function *f*,
a probability distribution *E*, and a
value function *V*.

A
further concern that Cariani raises is whether my account will make it the case
that John’s beliefs are “logically inconsistent”. In principle, there are many
views that philosophers have defended that are inconsistent with the correct
semantics for some natural-language expressions. For example, some philosophers
have defended the view that there are *deontic
dilemmas* – cases in which it is simultaneously true that you ought to
do *A* and also that you ought not to
do *A*. According to almost all the
accounts of ‘ought’ that semanticists have proposed, these philosophers’ views
are inconsistent with the correct semantics for ‘ought’. In principle, I accept
that cases could be devised in which the beliefs of John the maximin theorist
would be similarly “inconsistent”. However, since beliefs can be in this sense
“inconsistent” in highly non-obvious ways, I do not see how this counts as any
sort of objection to my account.

In
general, cases where an ‘ought’-sentence of this kind is embedded within a
hyperintensional context like ‘John believes that…’ or ‘For all Barbara knows…’
raise so many problems of their own that they seem not to provide firm grounds
for objecting to my account. Moreover, 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 do
*A*’ – is true, in a way that
clearly cannot be handled by the account that I have proposed.[14] In
short, the linguistic evidence does not clearly undermine my account of the
semantics of ‘ought’.

Even
though my account is unified in that the notion of maximization features in my
account of the semantic value every occurrence 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.[15] 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’.[16]

**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).

Cariani,
Fabrizio (this volume). “Deontic modals and probabilities: One theory to rule
them all?”

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.

Easwaran,
Kenny (2014). “Regularity and Hyperreal Credences”, *Philosophical Review*
123 (1): 1– 41.

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.

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

Kratzer, Angelika (2012).
*Modals and Conditionals: New and Revised
Perspectives* (Oxford: Oxford University Press).

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

Parfit, Derek (1984). *Reasons and Persons* (Oxford: Clarendon
Press).

Schroeder, Mark
(2011). “*Ought*, Agents, and Actions”,
*Philosophical Review* 120 (1): 1–41.

Sidgwick, Henry
(1907). *The Methods of Ethics*, 7^{th}
edition (London: Macmillan).

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,
IL: Open Court).

Wedgwood,
Ralph (2007). *The Nature of Normativity* (Oxford: Clarendon Press).

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

[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] For technical reasons (see
Easwaran 2014), if the space contains *indenumerably*
many worlds, it may not be possible assign a probability to *every* set of worlds in the space –
it may be that only certain sets of worlds can have a probability assigned to
them. This is why the probability distribution is defined over the worlds only
relative to a “field” of sets of worlds – where this field contains all
and only those sets of worlds that correspond to propositions in the relevant
algebra. Fortunately, this complication will not matter for present purposes.

[7] 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.)

[8] 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.

[9] An alternative
approach would be to understand the “expected value” of a Fregean proposition *A _{E}* as defined in terms of the

[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). Those
rival accounts all represent the relevant body of information by means of the
“modal base” – that is, the propositions that are true throughout the
relevant domain of worlds *f*(*w*); my account represents this body of
information in a fundamentally different way – by means of the probability
distribution *E* that, together with
the relevant value *V*, determines the
ordering of the worlds in this domain. In this way, my account agrees with
Charlow’s central point, that a good semantic account must make provision for
conditionalizing, not only the modal base, but also the relevant ordering of
the worlds. It is precisely for this reason that I propose that there are two
different kinds of deontic conditionals.

[13] I owe this example to Alex Silk.

[14] Indeed, I suspect that in any
case where we are tempted to assert a sentence of the form ‘Barbara ought to do
*A*’, on the grounds that *A* is what is recommended by Barbara’s
non-maximizing theory, our assertion is either *false*, or else true only when this occurrence of ‘ought’ is
understood as the *purpose-relative*
‘ought’, relativized to the goal of *conforming
to* the non-maximizing theory in question.

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

[16] 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 in 2014, I benefited greatly
from some highly illuminating comments from Nate Charlow, Matthew Chrisman,
Alex Silk, and Malte Willer.