1. science
2. social science
3. philosophy

Prospective Contextualism
Matt Mandelkern
January 14, 2015
1
Introduction
The following exchange is totally unremarkable:
(1)
Keys
a.
b.
c.
d.
Jack: The keys might be in the garage.
Ruth: No, they can’t be; Julie had them last, and she never goes in the garage.
Jack: Ok, then I think they must be upstairs.
Ruth: Yes, they must be.
Yet the orthodox contextualist approach to the semantics of epistemic modals1 has struggled
to give an account of how ordinary dialogues like this one can take place, and worries about
the adequacy of the orthodox framework to account for the behavior of epistemic modals
have prompted a number of heterodoxies.2
In this paper I will defend the orthodox framework by giving a theory of epistemic modals
within that framework. According to that theory, prospective contextualism, bare epistemic
modals—epistemic modals that are otherwise unrestricted by features of the context (e.g. by
clauses like ‘for all x knows,’ embedding operators, or tense)—quantify over the set of worlds
compatible with the propositions which are common knowledge after the epistemic modal
claim is accepted or rejected. I will argue that this account gives us an attractive account of
how epistemic modals are used to negotiate about the context set, of what pragmatic norms
govern conversational moves involving epistemic modals, and of how epistemic modals embed
under other operators. If this approach works, it dissolves some of the motivation for rejecting
the orthodox approach to epistemic modals. It also has interest beyond epistemic modals: a
1
An epistemic modal is a natural language modal expressed by terms such as ‘might,’ ‘must,’ ‘may,’ ‘could,’
‘possibly,’ and ‘probably,’ under an epistemic interpretations, in contrast to deontic, circumstantial (or
metaphysical), or dynamic readings. I will use ‘might’ as an exemplar of an epistemic possibility modal,
and ‘must’ as an exemplar of a strong epistemic necessity modal. I will discuss intermediate grades of
epistemic modals later on. I won’t discuss modal adverbs here, but it should be clear how to apply the
strategy of this paper to them.
2
E.g. relativism (e.g. Egan et al. (2005), MacFarlane (2011)), expressivism (e.g. Yalcin (2007, 2012a, 2011)),
dynamic approaches (e.g. Veltman (1996), Willer (2013)), as well as some innovative forms of contextualism
(e.g. von Fintel and Gillies (2011)).
1
similar style of account can be given for a wide range of phenomena that involve negotiation
about the context, including conditionals and deontic modals, as well as performatives which
are prima facie totally unlike epistemic modals.
2
The Orthodoxy and Its Discontents
According to the orthodox, truth-conditional, contextualist approach to epistemic modals,
an epistemic modal quantifies over a set of worlds provided by context.3 More precisely,
context provides a function from centered worlds4 to sets of worlds: call it fc (⋅). For all
centered worlds w, according to orthodoxy, fc (w) represents in some sense the set of worlds
epistemically accessible from w. A bare epistemic modal (assume epistemic modals are bare
unless otherwise noted) evaluated at a context c and centered world w quantifies over fc (w):
‘must’ is a universal quantifier over fc (w); ‘might’ is an existential quantifier over fc (w).
So much for the orthodoxy. There have been a variety of objections to this framework
for epistemic modals. For now I’ll focus on one central objection: that there is no way to
systematically spell out what worlds are treated as epistemically accessible in a context—
what the function fc amounts to—while respecting uncontroversial facts about how epistemic
modals are used in conversation. We can put the objection as a dilemma.5
One horn of the dilemma—solipsistic contextualism—takes the set of epistemically accessible worlds at < c, w > to be the set of worlds compatible with the knowledge of the
speaker of c at w. Then—using ‘φ’ as a sentence variable—⌜Might φ⌝, asserted by S, means
⌜φ is compatible with S’s evidence.⌝ The problem with this approach is that it can’t make
sense of the way we disagree and agree about epistemic possibility claims. When Jack says
‘The keys might be in the garage’ and Ruth disagrees with him, she is not claiming that
Jack knows that the keys aren’t in the garage. She doesn’t dispute that it’s compatible with
Jack’s knowledge that the keys are in the garage. Yet it is still perfectly felicitous for Ruth
to disagree with Jack and to reject his claim.
The data about agreement and disagreement thus push us away from solipsistic contextualism and towards a view on which the epistemically accessible worlds are those compatible
with what the group knows: group contextualism. This is the second horn of the dilemma.
There are two obvious ways of spelling out group contextualism, but new problems arise
3
For early accounts along these lines, see e.g. Hacking (1967), Teller (1972), Kratzer (1977), and DeRose
(1991); G.E. Moore’s Commonplace Book is the earliest formulation I know of a view along these lines
Moore (1962).
4
A triple of a world, time, and individual. The orthodoxy is not always put in terms of centered worlds, and
this feature is unnecessary for the semantics that I ultimately give, but is helpful to give an intuitive feel
for the general approach.
5
Laid out in MacFarlane (2011), von Fintel and Gillies (2011).
2
for each approach. On the first approach, we take the domain of quantification of epistemic
modals to be the weakest proposition the group of interlocutors knows. Where Ki,w is the set
of worlds compatible with i’s knowledge at w, the weakest proposition known by a group I
is ⋃ Ki,w . But this approach is a non-starter, for it predicts that ⌜Must φ⌝ is true at < c, w >
i∈I
just in case all the interlocutors of c know that φ is true at w. But then ⌜Must φ⌝ is true
only if everyone already knows φ is true! This is certainly not right, for ⌜Must φ⌝ can be
used to inform one’s interlocutors of the truth of φ.
We get a more plausible version of group contextualism if we take the domain of quantification of epistemic modals to be the strongest proposition the group knows: ⋂ Ki,w . This
i∈I
approach gives a better account of the meaning of ‘must’: it is sufficient for ⌜Must φ⌝ to be
true, on this account, if some individual in the group knows that φ is true. But it fails to
account for how we can responsibly assert ‘might’-claims in normal circumstances. On this
approach, ⌜Might φ⌝ is true only if no one in my group of interlocutors knows that φ is false.
The standard account of pragmatic norms is that one ought to assert ψ only if one bears
the appropriate attitude—knowledge or justified belief, and in case at least belief—towards
JφK.6 But clearly one may assert ⌜Might φ⌝ while being agnostic about what information
one’s interlocutors have regarding the truth-value of φ: to assert ⌜Might φ⌝, one need only
regard JφK as being a proposition that should be taken seriously. One needn’t know or even
believe that one’s interlocutors do not know that φ is false. Jack can responsibly assert that
the keys might be in the garage even if he has no idea whether Ruth has knowledge that
rules out that possibility.
Whichever way it tries to spell out what worlds count as epistemically accessible, then,
the orthodoxy seems to face problems. There are three possible responses to this. One
response is to take these worries to be decisive, and reject the orthodoxy. Another response
is to maintain the orthodoxy, but give up the ambition of giving a general account of what
worlds count as epistemically accessible. This is a plausible option, but it’s theoretically
disappointing. A third option is to keep digging: to look for a general characterization of
the epistemic accessibility relation that makes sense of agreement and disagreement and of
the pragmatic norms that govern epistemic modals. This is the option I’ll take.
I’ll draw two lessons from the dilemma presented just now. First: the problems of the first
horn of the dilemma are problems about agreement and disagreement. So we must give an
account of what epistemic modals are used to do in a conversation that makes sense of what
6
JσK (where defined) is the intension of ⌜σ⌝ for any string σ. I usually assume for ease of exposition that
σ doesn’t contain context-sensitive terms; where σ does contain context-sensitive terms, then JσK will be
the intension of ⌜σ⌝ in the context in which ⌜σ⌝ is uttered; when considering a sentence embedded within
another sentence, I assume that they are both evaluated at the same context. When the double brackets
are superscripted to a context and world pair, they deliver the extension of ⌜σ⌝ at < c, w >.
3
we agree about or disagree about in using them. Second: the problems of the more plausible
version of the second horn of the dilemma are problems about the norms of assertion. So we
must give an account of the pragmatic norms governing epistemic modal claims that explains
how we are able to responsibly assert them and agree and disagree about them in ordinary
contexts.
3
An Observation
I’ll start by addressing the first of these points. What are epistemic modals used to do in a
conversation? What are we proposing when we assert an epistemic modal claim, and what
are we agreeing or disagreeing about when we accept it or reject it?
When I characterized what one needs to be committed to in order to responsibly assert
⌜Might φ⌝ above, I said that one needs to think only that JφK should be taken seriously as
a live possibility. Likewise it seems that this is all one needs to be committed to in order
to responsibly accept a ‘might’-claim; to reject a ‘might’-claim, one needs to think that we
should not be treating JφK as a live possibility. When Jack says that the keys might be in
the garage, he is proposing that he and Ruth treat this as a live possibility. When Ruth
disagrees, she proposes, by contrast, that they rule this possibility out.
A parallel observation can be made in the case of ‘must’: in order to responsibly assert
⌜Must φ⌝, one needs to think that JφK should be treated as true in a conversation. In order
to responsibly accept the claim, one needs to agree that we should commit ourselves to JφK;
in order to responsibility reject it, one needs to think that we should still leave open the
possibility that ⌜¬φ⌝ is true. When Ruth says that the keys can’t be in the garage, she is
proposing that she and Jack commit themselves to the proposition that the keys aren’t in
the garage, and this is what Jack agrees to when he acquiesces. When Ruth says the keys
must be upstairs, she proposes that she and Jack commit themselves to the proposition that
the keys are upstairs, and this is what Jack agrees to, if he accepts her assertion.
This suggests a general characterization of what epistemic modal claims are used to do:
they are used to negotiate about what entailment and compatibility properties the context
set of the conversation has. The context set is a formal tool that keeps track of what is being
treated as a live possibility at a given juncture in the conversation. Following Stalnaker,7 we
can characterize it as the set of worlds compatible with the propositions that are mutually
accepted in a conversation, where a proposition is mutually accepted by a group just in
7
E.g., Stalnaker (2002, 1999a). I depart from Stalnaker’s presentation in Stalnaker (2002) slightly: Stalnaker
says that JφK is common ground just in case all members accept JφK, believe that they accept it, believe they
believe it, and so on; on the formulation I give, we rather need acceptance all the way down. Acceptance
is any one of a class of propositional attitudes that includes belief, presumption, acceptance for the sake of
conversation, knowledge, etc.; see Stalnaker (1984) for discussion.
4
case everyone in the group accepts it, accepts that they accept it, and so on ad infinitum
(say that a proposition is presupposed or common ground just in case it’s accepted in this
way). On this account, a claim of the form ⌜Might φ⌝ is a proposal which, if asserted and
accepted, ensures that the context set is compatible with JφK; a claim of the form ⌜Must φ⌝
is a proposal which, if asserted and accepted, ensures that the context set entails JφK.8
4
Prospective Contextualism
I will take this observation as the starting point for presenting my own view, prospective
contextualism. In this section and the next, I’ll lay out prospective contextualism and argue
that it captures this observation well. In the subsequent section, I’ll return to the issue of
what pragmatic norms govern the production and acceptance of epistemic modal claims, and
will argue that prospective contextualism has a good answer to this question.
If epistemic modal claims are used to negotiate about the properties of the context set,
then a very natural suggestion about their semantics is that they quantify directly over the
context set of the conversation. Then a ‘might’-claim would be a claim that its prejacent is
compatible with the context set, and a ‘must’-claim would be a claim that its prejacent is
entailed by the context set.9
This view is moving in the right direction, but it makes badly wrong predictions about
truth-values. First, like the first version of group contextualism that we looked at above, it
makes it impossible to truly assert ⌜Must φ⌝ in an informative way. If JφK is not already
common ground, then ⌜Must φ⌝ will be false. So on this account, ⌜Must φ⌝ can be truly
asserted only when JφK is common ground. This is clearly false: as I noted above, one can
assert ⌜Must φ⌝ as a way of advocating that one’s interlocutors accept JφK. Likewise, this
account predicts that it will be impossible to dispute ‘might’-claims. By asserting ⌜Might φ⌝,
one makes clear that one doesn’t accept J¬φK, and thus the context set will be compatible
with JφK at the time at which one evaluates the claim.10 But clearly not all ‘might’-claims
8
This observation was first made in Stalnaker (1999b), I believe. von Fintel and Gillies (2010) has a series
of arguments that show persuasively that asserting a ‘must’-claim commits a speaker to its prejacent; the
arguments can be naturally extended to show that accepting a ‘must’-claim likewise commits a speaker to
its prejacent.
9
Yalcin (2007, p. 1013) mentions a view along these lines, and comments that it is the best possibility for
an orthodox treatment of epistemic modal. It is also closely related to the approach of Veltman (1996).
10
Assuming that we evaluate claims relative to a context set updated with the fact that the claim has been
made; see Stalnaker (1998) and von Fintel (2008) for discussion. Note importantly that this is not the
prospective context set in the sense in which I define it below, but rather an earlier point in the evolution
of the context set. A view according to which epistemic modals quantified over this context set would be
much simpler, insofar as it assimilated the interpretation of epistemic modal claims to the interpretation
of all other assertions; but it won’t work for the reasons given in the text.
5
are true when asserted,11 as evidenced by our ability to disagree about them.
We can avoid both these results by making the domain of quantification the prospective
context set: the context set as it stands after the epistemic modal claim has been accepted
or rejected.12 This lets us avoid the prediction that ⌜Must φ⌝ is true only provided that
JφK is already common ground: rather, ⌜Must φ⌝ is true provided JφK is common ground
after ⌜Must φ⌝ is asserted and accepted or rejected. Likewise, it lets us avoid the prediction
that ⌜Might φ⌝ is always true when asserted: rather, it will be true provided that JφK is
compatible with the common ground after ⌜Might φ⌝ is asserted and accepted or rejected.
I will ultimately adopt something very similar to the view under consideration, and I
think it could work in its present form. But it makes somewhat unsatisfying predictions
about ‘must’-claims. In particular, it predicts that ⌜Must φ⌝ can be true while φ is false
(namely, just in case the conversants mistakenly accept φ). This is a result that von Fintel
and Gillies (2010) have argued is unacceptable: they argue that ⌜Must φ⌝ entails φ. The view
under consideration can capture something very close to the claim that ⌜Must φ⌝ entails φ,
though: namely, it follows from the view under consideration that one cannot accept ⌜Must
φ⌝ in a context without accepting φ. It may be that that is a strong enough prediction. But
in any case, there is a relatively trivial change we can make to the proposed semantics to
predict that ⌜Must φ⌝ entails φ: instead of quantifying over the prospective context set, we
take epistemic modals to quantify over the prospective common knowledge of the group: the
set of worlds compatible with the propositions that are known by everyone, known to be
known, and so on, after the modal claim is accepted or rejected.
From a pragmatic point of view, this account will be identical to an account according
to which epistemic modals quantify over the context set, because the context set perceives
itself as representing common knowledge of a group (even when it doesn’t, and even when
interlocutors recognize that it doesn’t). From within, everything that is accepted in a context
set is being treated as known, and everything that is treated as being known is accepted in the
context—this is part of what it is to accept a proposition for the sake of a conversation.13
And so if it is commonly accepted that JφK is common knowledge, then it is commonly
accepted that φ is true, and if it is commonly accepted that JφK is not common knowledge,
11
Even if it is sometimes very hard to oppose a ‘might’-claim; see Lewis (1979) for discussion.
Stalnaker (2014) makes a similar move, presenting a semantics that is similar to prospective contextualism.
That semantics differs in one significant respect: rather than building the prospectivity into the semantic
content of epistemic modals and preserving an intersective update rule for the assertion of an epistemic
modal claim, Stalnaker takes the prospectivity to come via a special force rule which governs epistemic
modal claims. One benefit of the approach I take is that it lets us maintain a unified approach to assertion
as an update of the context set by intersection.
13
This seems intuitively plausible, and is formally suggested by Stalnaker’s logic for common ground in
Stalnaker (2002) by the fact that models for common ground are quasi-reflexive: if a world is accessible
from some world, then it accesses itself.
12
6
then it is not commonly accepted that φ is true.14 But this account seems to make slightly
more satisfactory predictions of truth-values, and so I’ll adopt it.
Officially, then, the view I will defend, prospective contextualism, is the form of the
orthodox approach to epistemic modals according to which an epistemic modal quantifies
over the prospective common knowledge at the world of evaluation:
Prospective Contextualism:
• JMight φKc,w =1 iff ∃w′ ∈ fc (w) ∶ JφKc,w = 1
′
• JMust φKc,w =1 iff ∀w′ ∈ fc (w) ∶ JφKc,w = 1
′
• fc (⋅) takes each world15 w in its domain to the prospective common knowledge at w of the speakers of c.
Where, again, the prospective common knowledge is the set of worlds compatible with what
is commonly known by a group after a given claim is asserted and accepted or rejected. fc (⋅)
will necessarily be a partial function, defined at all the worlds in the context set but not
necessarily at worlds outside the context set. I take this to be the right prediction: it is
puzzling how to evaluate epistemic modals at worlds outside the context set.16
5
Getting Force From Content
We are looking for an account according to which asserting and accepting a claim of ⌜Might
φ⌝ has the result of ensuring that the context set is compatible with JφK, and asserting and
accepting a claim of ⌜Must φ⌝ has the result of ensuring that the context set entails JφK. In
this section I argue that prospective contextualism gives us such an account.
Let’s consider a ‘might’-claim. According to prospective contextualism, a claim of the
form ⌜Might φ⌝ is a claim that the prospective common knowledge is compatible with JφK.
As I argued above, this will amount to a claim that the prospective context set is compatible
14
To guarantee this condition held, we could add an axiom to a logic that includes an operator ◻ for ‘it is
common ground that,’ an operator ◊ as its dual, an operator ∎ for ‘it is common knowledge that,’ and an
operator ⧫ as the dual of ∎. The axioms we’d need would be ◻ ∎ φ ⊧ ◻φ and ◻⧫φ ⊧ ◊φ. These axioms
seem very plausible: where the attitude of acceptance is belief, as it usually is, they follow from the axioms
BKφ ⊧ Bφ and B¬Kφ ⊧ ¬Bφ, which should be acceptable, at least under the idealizing assumptions of
formal pragmatics.
15
Note that the worlds need not be centered.
16
A fact that may help explain conflicting intuitions about eavesdropper cases: see Knobe and Yalcin (2014).
See also Stalnaker (2014) for discussion.
7
with JφK. According to the standard pragmatic story, due to Stalnaker (1978), accepting an
assertion of ψ updates the context set by intersecting it with JψK (and thus bringing it about
that the context set entails JψK). Thus if a claim of ⌜Might φ⌝ is accepted, the context set
will come to entail that the context set is compatible with JφK.
An epistemic possibility claim, on this view, is thus a proposal which, if accepted, brings
it about that the context set entails that the context set is compatible with its prejacent.
This does not seem to be quite what we were looking for, though. We are looking, rather, for
an account of epistemic possibility claims according to which an epistemic possibility claim,
if accepted, directly brings it about that the context set is compatible with its prejacent. To
see the problem, suppose that we are looking for a certain kind of claim which, if asserted
and accepted, has the result of ensuring that the cat is in its box. ‘The cat is in its box’ is
one candidate. But, barring some extra machinery, this is clearly a bad candidate: if this
claim is asserted and accepted, then it’s ensured that the context set entails that the cat is
in the box, but it’s not ensured that the cat is in the box.
Context sets are special, though. The relationship between a context set and itself is
not like the relationship between a context set and my cat. If the context set entails that
the context set has a certain structural property, then in many cases, the context set will
automatically have that property. This is not magic; rather, it’s because the context set
represents what is mutually accepted. Context sets are structured in a way that assumes
that the underlying attitude of mutual acceptance has a certain degree of transparency. In
particular, given the account of the structure of context sets laid out in Stalnaker (2002),
it follows, first, that if it’s mutually accepted that it’s mutually accepted that JφK, then it
is also mutually accepted that JφK; and, second, that if it is mutually accepted that JφK
is compatible with what’s mutually accepted, then JφK is compatible with what’s mutually
accepted.17
Let’s use ◻ to represent a modal operator which we interpret as ‘it is common ground
that,’ and ◊ to represent its dual, ‘it is compatible with the common ground that.’18 Then
these two claims amount to
17
We can make this claim a bit more general to account for how we interpret epistemic modals embedded
under disjunction and conjunction: in the modal language that includes a modal operator ◻ interpreted
‘S presupposes that,’ then where ψ is any purely modal sentence (any sentence such that all of the atomic
sentences it contains are within the scope of a ◻ operator that is also in ψ) then ◻ψ → ψ will be true at the
designated world of any model for speaker presupposition. This is a property I call self-determination
of speaker presupposition, and argue for and discuss in Mandelkern (MSc). Note, however, that we
do not have the corresponding property if we interpret ◻ as ‘it is common ground that.’ For in that case
◻(◻ρ ∨ ◻ξ)⊭ ◻ρ ∨ ◻ξ. However, the switch to speaker presupposition ultimately suffices for an account of
how we interpret epistemic modals.
18
As is standard, I’ll let the terms and sentences of the formal language name themselves.
8
Positive Collapse:
◻ ◻ φ ⊧ ◻φ
and
Negative Collapse:
◻◊φ ⊧ ◊φ.
Both claims are fairly intuitive. The common ground is typically constituted by belief.
In that case, the first of these principles amounts to the claim that if we believe that we
believe JφK, then we believe JφK. The second amounts to the claim that if we believe that JφK
is compatible with our beliefs, then JφK is compatible with our beliefs.19 And both claims
are theorems of the logic of common ground given in Stalnaker (2002).20
Neither of these claims is uncontroversial as a claim about propositional attitudes in
general. There are certainly psychological phenomena that are naturally described as cases
in which someone believes she believes something, but in fact believes the opposite. These
19
Some caution is needed here. As I discuss below, there are cases in which derived or local contexts coexist
alongside global contexts. It is not plausible that derived contexts obey the same structural constraints as
global contexts; for instance, in counterfactual derived contexts, the speakers themselves need not exist at
the worlds in question, and therefore obviously acceptance does not have the iterated structure required
for these collapse principles to hold. But all we need is for these principles to hold for the global context.
Suppose that the global context is constituted by an attitude represented by ◻ (e.g. common belief), and
the derived context by an attitude represented by ∎ (e.g. counterfactual supposition), with ⧫ its dual.
Then if an epistemic modal is asserted and understood to be updating the local context, it will do so by
updating the global context with the the proposition expressed by ◻ ∎ φ or ◻⧫φ, depending whether the
modal in question is a necessity or possibility modal. But the derived context is simply defined to be the
set of worlds that has the properties attributed to it by the global context. So we can immediately conclude
∎φ, or ⧫φ, respectively, from these two claims. These inference patterns should be carefully distinguished
from the inferences from ◻ ∎ φ to ◻φ, and from ◻⧫φ to ◊φ: those inferences are not in general valid.
20
Proof: That framework takes as an axiom ◻(◻φ → φ). This axiom corresponds to the semantic constraint
of quasi-reflexivity in a Kripke model for common ground: where R is our accessibility relation, ∀w∃w′ ∶
w′ Rw → wRw. This constraint corresponds to the intuitive idea, adverted to in discussing the relationship
between common ground and common knowledge above, that the attitude that underlies common ground
views itself as knowledge-like: it takes itself to accurately portray the world. I assume our logic is normal;
then ◻(◻φ → φ)⊧ ◻ ◻ φ → ◻φ. Since ◻(◻φ → φ) is an axiom, ◻ ◻ φ → ◻φ will be a theorem of our system,
and thus Positive Collapse will be true for every substitution instance.
Likewise the logic in question will validate Negative Collapse, thanks to the serial and transitive constraints on our model. The serial constraint says that ∀w∃w′ ∶ wRw′ : that is, at every world, the common
ground propositions are consistent. The transitive constraint says that ∀w∀w′ ∀w′′ ∶(wRw′ ∧ w′ Rw′′ )→
wRw′′ , and corresponds to positive introspection for acceptance. Suppose that Negative Collapse is
not a theorem; then we will have a countermodel, and so for some proposition p, world w, and valuation
function v: v(◻◊p, w)=1 and v(◊p, w)=0. Since the model is serial, it follows from the first of these assumptions that there is some w′ such that wRw′ and such that there is some w′′ such that w′ Rw′′ and
v(p, w′′ )=1. But by transitivity wRw′′ , and thus v(◊p, w)=1, contradicting our second assumption. So
Negative Collapse will be true for every substitution instance.
9
should be captured by a semantics for ‘believes.’21 and so the two collapse principles should
not be taken for granted as axioms of the logic of belief. But we should accept them as
describing the attitude that underlies common ground under the idealizing assumptions we
make when doing formal pragmatics: the transparency of the attitudes in question is a
crucial assumption of the framework.22
It follows, then, that prospective contextualism does indeed give us an account of epistemic modals according to which they are used to negotiate about whether the context set
entails (is compatible with) their prejacent. Suppose a claim of the form ⌜Must φ⌝ is asserted
at t1 and accepted at t2 . Then at t2 , it is common ground that φ is common ground in the
prospective context. In this case, the prospective context is the context at t2 , so at t2 , it
is common ground that φ is common ground. It follows from Positive Collapse that φ is
entailed by the context set. So an epistemic necessity claim is a claim which, if asserted and
accepted, ensures that the context set entails its prejacent. Likewise, suppose a claim of the
form ⌜Might φ⌝ is asserted at t1 and accepted at t2 . Then at t2 , it is common ground that
φ is compatible with the prospective context set. Since the prospective context set is the
context set at t2 , at t2 it is common ground that φ is compatible with the context set. It
follows from Negative Collapse that φ is compatible with the context set. So an epistemic
possibility claim is a claim which, if asserted and accepted, ensures that the context set is
compatible with its prejacent.
This gives us an account of the content of epistemic modals which lets us explain why
people agree and disagree about them. To assert an epistemic modal claim is to make a
proposal to make context set entail (be compatible with) its prejacent; when interlocutors
discuss and dispute epistemic modal claims, they are agreeing and disagreeing about this
proposal.
The possibility of giving a contextualist account according to which epistemic modal
claims are used directly to negotiate about the context set is important, because it shows that
the orthodox pragmatic framework is substantially more flexible than it might first appear.
On that framework, an assertion with content JφK is a proposal to intersect the context set
with JφK. Prima facie, it thus looks like the only semantic affect an assertion can have on
the context set (ignoring pragmatic effects like conversational implicature, etc.) is to bring
it about that the context set entails the assertion’s content. But some assertions have more
21
One way of doing this while still validating these principles is to appeal to fragmentation; see Stalnaker
(1984).
22
In any case, I will make this assumption for this paper. If we end up with a logic for common ground that
fails to validate the principles in question, then this account of epistemic modals won’t work as it stands;
in that case Stalnaker’s implementation with a special force rule for epistemic modals in Stalnaker (2014)
would be preferable.
10
structurally complex semantic effects on the context set: namely, epistemic possibility claims
bring it about that the context set is compatible with their prejacent (without bringing it
about that they entail their prejacent). We do not, however, need a new pragmatic framework
to account for this:23 rather, the argument of this section shows that it’s possible to achieve
this kind of structural change to a context set via ordinary intersective updating.
The rule to update by intersection is not always sufficient to describe how context sets
evolve. Suppose a group presupposes JφK and then comes to presuppose JφK: the rule to
update by intersection wrongly predicts that in this case the context set becomes the empty
set. Likewise, consider a case in which J¬φK is common ground at t1 . An assertion of ⌜Might
φ⌝ at t1 , if accepted at t2 , will have the effect, by intersective updating, of ensuring that the
context set at t2 is compatible with JφK: for as we have seen, it’s impossible for JMight φK to
be common ground while the context set entails J¬φK. But the update is not as mechanical as
in other cases, since it involves some kind of context repair mechanism. By accepting JMight
φK at t2 , the interlocutors come to presuppose something inconsistent with something else
they presuppose, namely J¬φK. Both these cases are resolved by some general context repair
principle, something of the form: ‘When speakers come to presuppose something in conflict
with something they earlier presupposed, revise the context set in a minimal way to maintain
the later presupposition.’ So updating a context set with an assertion of ⌜Might φ⌝ requires
two rules: first, a rule to update the context set with new content by intersection; and,
second, a rule about how to resolve potential conflicts in the common ground.24 This is still,
however, well within the scope of the orthodox pragmatic framework: both rules are quite
general and apply to all assertions, not just those containing epistemic modals.25
6
Norms of Epistemic Modal Claims
I proposed above that the dilemma we started with left us with two lessons. The first was
that we need to find an account of what epistemic modals are used to do in a conversation
that makes sense of what we agree about or disagree about in debating them. Prospective
contextualism gives us such an account. It makes sense of what we are negotiating about
23
E.g., a dynamic semantic framework (Veltman, 1996), (von Fintel and Gillies, 2007), an expressivist framework (Yalcin, 2007), or a special force rule for epistemic modals (Stalnaker, 2014).
24
See Yablo (2011) for discussion of this latter issue.
25
This is a point where Stalnaker (2014)’s approach of positing a special force rule for epistemic modals may
appear simpler than my approach, since that force rule already encodes that the context set is to modified
in a minimal way to make the epistemic modal claim true, and thus that account does not need to advert
to a separate rule about context set revision in cases of inconsistency. But it’s important to note that,
although my account has to advert to two rules where Stalnaker’s has to advert to only one, on my account
both those rules are fully general, whereas Stalnaker needs both those rules—for assertion generally—as
well as a special force rule for epistemic modals. The difference is, again, relatively minor, but I think
there is some reason to stick with the more uniform approach I’m advocating.
11
when we negotiate about epistemic modal claims: we are negotiating about what propositions
we should treat as open possibilities for the sake of the conversation, and what propositions
we should treat as true for the sake of the conversation.
The second lesson of the dilemma that we started with was that we must give an account
of the pragmatic norms governing epistemic modal claims that explains how we are able to
responsibly assert, agree, and disagree about them in ordinary contexts. This is the task
that I turn to now.
On first glance, it might seem like prospective contextualism does worse than any of
the competitors on this front. We rejected an account of epistemic modals on which they
quantify over the stronger proposition known by a group on the grounds that it was too
difficult for any individual speaker to know what that proposition was to explain how it is
that speakers responsibly assert epistemic modal claims in perfectly ordinary circumstances.
According to prospective contextualism, epistemic modals quantify over the prospective
common knowledge of a conversation. But surely it’s even harder to know what will be
common knowledge in a conversation at some point in the future than it is to know what
the strongest proposition known by the group is.
There is right. But prospective contextualism has the resources to account for why, in
spite of the difficulty of knowing what the prospective common knowledge in a conversation
will amount to, epistemic modals can be responsibly asserted and accepted in ordinary
circumstances. I will argue that there is no norm of the form: assert (accept) an epistemic
modal claim only if you know (justifiably believe, believe) its content. Rather than being an
ad hoc fix, I will argue that this follows directly from the form of the prospective contextualist
semantics.
On the account I have given, in paradigm cases, the truth of an epistemic modal claim
depends on whether it is accepted. Suppose that at a context c and time t1 , JφK is not
common ground. ⌜Must φ⌝ is true as asserted at < c, t1 > only if JφK is common ground at
the prospective context set, < c, t2 >, which happens just in case ⌜Must φ⌝ is asserted and
accepted by all the interlocutors of c. So ⌜Must φ⌝ is true as asserted at c at t1 only if ⌜Must
φ⌝ is asserted at t1 and accepted at t2 . The truth of ⌜Must φ⌝ thus entails that ⌜Must φ⌝ is
asserted and accepted.
Likewise, suppose that at < c, t1 >, J¬φK is common ground. ⌜Might φ⌝ is true as asserted
at < c, t1 > only if JφK is compatible with the context at < c, t2 >, which happens just in case
⌜Might φ⌝ is asserted and is accepted by all the interlocutors of c. So ⌜Might φ⌝ is true as
asserted at c at t1 only if ⌜Might φ⌝ is asserted at t1 and accepted at t2 . The truth of ⌜Might
φ⌝ in this case thus entails that ⌜Might φ⌝ is asserted and accepted.
There will be different permutations of these cases, depending on the prior status of the
12
epistemic modal’s prejacent, but the basic idea is robust: according to prospective contextualism, an epistemic modal claim’s truth depends in part on whether it is asserted and
subsequently accepted.
But it is a general principle of action theory that, for propositions ρ and ξ, if ρ entails
ξ, then in deciding whether to bring about ξ, one cannot take into account the truth of ρ.26
One cannot deliberate about whether to do ξ on the basis of a premise that entails that one
in fact does ξ. In deliberating about whether to assert (or accept) a sentence ψ, then, one
cannot take into account anything that entails that one in fact asserts (or accepts) ψ.
In particular, where ψ has the form of an epistemic modal claim, then, one cannot take
into account the truth of that claim itself in deciding to assert or accept the claim. To do so
would, in paradigm cases at least, be to take for granted that the claim will be asserted and
accepted: in other words, to take for granted the very thing that one is deliberating about.
If epistemic modals have the content ascribed to them by prospective contextualism,
then, there can be no norm of the form: assert (accept) an epistemic modal claim only if
you know (justifiably believe, believe) its content. And so it won’t matter that the content
of epistemic modal claims, on this account, is very hard to know (or justifiably believe, or
even believe).27
What do we have instead? There are, of course, many moves in a language game whose
truth-value play no role in determining the norms relevant to the move. Consider in particular
proposals like ‘Let’s go to the beach!’ A proposal like this is governed by a norm along
the lines of: propose φ only if you reasonably believe (or perhaps know) φ makes a good
proposal.28
In the last two sections, I argued that epistemic modal claims are proposals about how
the context set should evolve. They are proposals about how to proceed with respect to a
certain problem—what should count as agreed upon for the sake of the conversation. And
so we expect that the norm for asserting and accepting epistemic modal claims should be
exactly the norm that’s in place for proposals in general: assert an epistemic modal claim
26
See discussion in Ninan (2005).
There is some subtlety here: I am certainly not claiming that, in considering whether to assert ⌜Might φ⌝
(⌜Must φ⌝), one cannot or should not take into account the fact that one knows that φ might (must) be
true. Indeed, that might be necessary condition on responsible assertions of epistemic modal claims. But
it could be that JS knows might φKc,w is true, while at S’s context of utterance, k, JMight φKk,w =0, since
as I discuss below, the truth conditions of the former depend just on S’s knowledge state, while the truth
conditions of the latter depend also on what is common knowledge at k (though note, of course, that due
to the factivity of knowledge, if JS knows might φKc,w =1, then JMight φKc,w =1; see Mandelkern (MSb) for
discussion).
28
There are also various more objective versions of the norm: ‘just in case you know that φ makes a good
proposal,’ or ‘just in case φ makes a good proposal’. I don’t mean to commit to any particular stance on
those questions here.
27
13
only if you reasonably believe (know) it is a good proposal for how to proceed with the
problem of coordinating the context set; likewise, accept an epistemic modal claim only if
you reasonably believe (know) it is a good proposal about how to update the context set.
Since none of these norms adverts to the truth of an epistemic modal claim, it will not be a
problem that according to prospective contextualism, the truth of an epistemic modal claim
is very hard to know: the only special doxastic relationship one needs to have towards the
content of an epistemic modal claim is to reasonably believe that it describes a way the world
should be, not necessarily a way that the world is or will be.
In claiming that epistemic modals are governed by the norms of proposals, I am not
claiming that epistemic modal claims have a different norm than the norm of assertions in
general. According to the orthodox pragmatic framework, all assertions are proposals. And
so all assertions are governed by the same norm: make the assertion only if you reasonably
believe (know) that the proposal it makes is a good one.
Generally speaking, the aim of the conversation will be to make the context set maximally
informative regarding the issues that the conversants evince interest in. The conversants will
thus generally aim to make the context set accurately represent the maximal information
accessible to them. This consideration dictates that broadly epistemological considerations
will guide the making and acceptance of claims of all sorts. When a proposal is an update
whose felicity depends only on certain facts that are settled independently of whether the
update is made, then perhaps there is (in some cases) a specific norm that comes into play,
something like: assert φ only if you know JφK.29 But that is just a special case of a more
general norm governing assertions, and follows, if at all, from facts about when an assertion of
this kind makes a good proposal. But when, for whatever reasons, the proposal’s felicity does
not depend (only) on certain facts that are settled independently of whether the proposal
is made and accepted, then one will have to advert to other considerations to determine
its felicity. This is the case for a large class of proposals, epistemic modal claims among
them. But epistemic considerations will still in general guide the production and acceptance
of epistemic modal claims: typically, one should assert (accept) an epistemic modal claim
just in case one has reason to believe that the proposal the claim makes will put the group
in the best epistemic situation.
So, for instance, in Keys, when Jack says that the keys might be in the garage, his
proposal is presumably motivated by a reasonable belief that the group should not yet commit
itself to ruling out that option. When Ruth disputes Jack’s statement, she is proposing the
opposite: that the group should, in fact, rule out that option. If she gives adequate reasons
for this, Jack will acquiesce. And in general,
29
As argued in Williamson (2001).
14
Not every conversational move is made with the goal of maximizing mutually accessible
information, though. Take this case:30
(2)
a.
b.
Steve: So, are you voting for Kucinich?
Erin: I might be, I might not be.
Erin knows who she’s voting for; she just thinks it’s none of Steve’s business. Here, Erin
simply does not want the context set to reflect all the knowledge available to her; so she
has (non-epistemological) reason to leave it open in the context set who she is voting for,
and thus to assert her epistemic modal claim. This is a perfectly acceptable move: we have
many reasons to make and accept assertions, not all of them epistemological. As long as
these motivations are reasonably easy to infer, interlocutors will not have trouble interpreting
why their interlocutors have made an epistemic modal claim, or what their interlocutors are
trying to do with it. It’s a major benefit of prospective contextualism that it treats cases
like this as perfectly ordinary; epistemic modal claims, like claims of all sorts, vary in their
aims, and thus in the very local norms that govern them, but they are all proposals about
how the context set ought to evolve, and thus all governed by a general norm which governs
proposals of that kind.31
This completes my response to the dilemma we began with. Epistemic modal claims are
proposals about how the context set should evolve, and as such their production and uptake
are governed by the norms which govern all proposals—norms which make it easy to see how
epistemic modal claims can be responsibly asserted and accepted in ordinary situations.
7
Truth-Conditional Performatives
On the account I’m advocating, an assertion of an epistemic modal is a proposal about how
the context set should evolve that is made by asserting a claim about how the context set
will evolve. This may seem implausibly roundabout, excessively byzantine to be a plausible
proposal about the meaning of a natural language expression. It particular, it may look
as though the truth conditions in my account are idle wheels, and that a more perspicuous
formulation would not give ordinary truth conditions to epistemic modal claims at all, instead
finding another, more direct way to predict that they are proposals about how the context
30
31
From Yablo (2011); cf. similar cases in von Fintel and Gillies (2008).
The openness and variety of norms that can be relevant in deciding whether a proposal was a good one
makes sense of the range of intuitions in the range of cases explored in papers like Hacking (1967), Teller
(1972), and DeRose (1991). We know that if the ship’s mate in Hacking’s case had just looked through
the log, he would have gotten more information about where the treasure was, and so we are inclined to
judge his proposal about what possibilities to treat as live as a bad proposal. We are more forgiving if the
relevant information is out of the mates’ reach.
15
should evolve.
But in fact the method which I argue epistemic modals exploit—making a proposal by
making a truth-conditional claim about the future—is natural and widespread in natural
language. In this section, I’ll briefly explore some of these other constructions. The local
point of doing so is to show that this phenomenon is widespread, and so it is not implausible
to suggest that epistemic modals function this way, too. These constructions also strike me
as interesting and worthy of investigation in their own right.
I’ll call the class of constructions in question—the class to which I’m proposing epistemic
modals belong—‘truth-conditional performatives.’ These constructions share with epistemic
modals that they are about a future state of affairs, but a future state of affairs that depends,
in part or in whole, on whether the construction in question is asserted and accepted. It
follows, reasoning as in the last section, that the norms that govern these constructions are
not the specific epistemic norms that govern typical factual assertions, but rather the more
general norms that govern proposals in general.
Here’s an example of a pair of truth-conditional performatives (suppose that John is
supposed to be doing his homework, that Mark is partly in charge of John):
(3)
a.
b.
c.
Mark: What are you doing this afternoon?
John: I’ll be playing outside.
Mark: Oh no you won’t be! You will finish your homework first.
When John says, ‘I’ll be playing outside,’ he makes a claim that has straightforward truthconditions: his claim is true in every scenario in which he is playing outside in a (contextually
specified) future time. But John’s main aim in making this claim is not to inform Mark about
the future, but rather to make a proposal. Mark is partly in charge of determining what’s
permissible for John. If Mark accepts that John will be playing outside, then he implicitly
makes it permissible for John to be playing outside. John’s main aim in asserting that he is
going to be playing outside is an attempt to change the permissibility facts, not to inform
Mark about his location. And John’s assertion is perfectly responsible, perfectly within the
norms of assertion, even if he doesn’t know that he’s going to go outside—indeed, even if he
thinks that his bid will probably fail.
Mark’s response, likewise, is a statement about the future, with straightforward truthconditions. But, again, it might be a reasonable thing to say even if Mark is unsure if it is
true. Suppose that John is under the normative sway not only of Mark, but also of another,
higher authority, Jake. Mark knows that John might appeal his decision to Jake, and that
Jake might well overturn it. What Mark seeks to do in asserting (3-c) is not to inform John
about the future, but rather to establish certain norms. And again, whether or not this is
16
a responsible, permissible move in the conversation depends not on whether Mark knows
that John won’t go outside, but rather on whether Mark thinks that John ought not to go
outside.
Compare the following similar case:
(4)
You are going to open that door.
given as an order. The structure here is, again, that of a statement whose truth-value
is settled in part by whether it is made and accepted, and thus whose assertability and
acceptability depend on considerations other than its truth-value (in this case, partly on
considerations of who has the appropriate normative authority in this case, and whether she
is using it well).
Claims with the structure of truth-conditional performatives are widespread in natural
language, in varying guises. That suggests that a similar structure may obtain in other
cases, even when the structure is not as manifest as in cases like this. For instance, we can
apply this framework to performatives of the sort J.L. Austin discussed in Austin (1979):
‘I hereby name you. . . ,’ ‘It is hereby agreed that. . . ,‘I hereby promise you. . . ,’ and so on.
Let’s say, for instance, that the context set keeps track of what promises are made: so JS
promises x to φKc,w =1 just in case it is common knowledge at the prospective context set
that S is committed to bring about JφK, and x is one of the interlocutors at c. On that
account, ⌜I hereby promise x to φ⌝ is an assertion that has truth-conditions—it’s true just in
case I am publicly committed to φ at the time at which it’s accepted—but it is an assertion
whose content is made true just by being asserted and acknowledged.32 So, again, it is
not an assertion with a content whose truth can figure in determining whether to assert it,
but rather a proposal which, if asserted and accepted, does come out true. I take it that
the norms that govern performatives of this kind, then, are again the norms of proposals
in general, and not norms that require knowing or reasonably believing the content of the
claims.
Note that all these examples vary with respect to certain normative facts: for instance,
whether my proposal that you be married, or that you close the door, is accepted depends
partly on whether I am invested with the right normative power to marry you, or get you
to close the door. But those are separable features of the examples, and parallels to the
32
Performatives of this kind seem to require less acceptance on the part of one’s interlocutors than do
performatives of the kind considered above, though it certainly requires minimal acknowledgement, and it
does seem possible for me to make a claim like this false by retorting that you do not have the authority
to make a promise in this case, or name the child, or whatever. These seem to be separable features of
the cases, though, features having to do with the specific, varying normative structures of the cases: the
underlying structure is analogous to the cases considered above.
17
case of epistemic modal claims are easy to draw. Indeed, we could think of epistemic modal
claims as proposals that, if accepted, change the context set of the conversation thanks to
the normative power invested in the conversants to determine the nature of the context set.
On the account I have given, epistemic modals have truth conditions: they are claims
about the way the context set will be. But epistemic modals have the force of proposals
to make the context set have that property. This is not a unique structure, though: it
is recapitulated throughout a wide variety of constructions that have truth conditions and
also have performative force. The existence of the class of truth-conditional performatives
suggests that epistemic modal claims are not an anomaly, nor are their truth conditions idle
wheels: rather, conversants use the truth-conditions of claims of this sort to make proposals
about what the world should be like vis-`a-vis the claim’s subject matter.
8
Further Extensions
We can extend the prospective contextualist framework that I’ve proposed for truth-conditional
performatives to other claims that similarly have an intimate connection to what is common ground. Because of the close interplay between context and modality, the framework is
particularly useful for giving accounts of other kinds of modals.
First, we can extend the framework to other epistemic modals. It has been a simplifying
assumption to treat epistemic modals as all of the form ⌜Might φ⌝ or ⌜Must φ⌝. Epistemic
modals also come in intermediate grades: ⌜Probably φ⌝, ⌜Ought φ⌝, and so on. Extending
our framework to capture this is straightforward. We need, first, a measure structure33
on the context set which is jointly accessible in the same way the context set itself is. It
doesn’t matter for our purposes what form the structure takes;34 as long as this measure
structure obeys an analogous collapse mechanism to the one we discussed above for common
ground, we can give an analogous semantics to the one we gave for ‘might’ and ‘must.’ Say
that JProbably φKc,w =1 just in case the measure structure of the prospective context makes
JφKc,w sufficiently likely. Provided that ‘the measure structure of the context set makes
JφKc,w likely’ follows from ‘it is common ground that the measure structure of the context
set makes JφKc,w likely,’ an assertion of ⌜Probably φ⌝ will have the force of a proposal to
adopt a contextual measure structure that makes JφKc,w likely. I take it this is exactly the
force we should expect for an epistemic modal of this form: this account makes sense of
the phenomena and norms of production and uptake of claims of this form in precisely the
same way the parallel account made sense of this for ‘might’ and ‘must.’ And a collapse
33
34
Or measure structures—I assume for simplicity there’s just one.
The two most prominent contenders are: a preorder on worlds, following Kratzer (e.g. ?); or a probability
measure on a σ-algebra of the set of worlds under consideration, following Yalcin (especially Yalcin (2012a)).
18
principle of this kind is very plausible: part of what it means for a measure structure to be
the measure structure of a context is for it to be the case that if it’s commonly accepted that
that’s the measure structure of the context, then that is indeed the measure structure of the
context. The same pragmatic norms will apply to intermediate grades of epistemic modals
as apply to epistemic possibility and necessity modals, and for the same reasons.
We can make very similar moves for deontic modals.35 According to the orthodox framework, a deontic modal claim says that some proposition JφK is required by (or compatible
with) some salient set of deontic commitments.36 Intuitively, deontic modal claims are used
to negotiate what those commitments are, just as epistemic modal claims are used to negotiate what is compatible with (or entailed by) the context set. But it’s not obvious how
to get this result on the orthodox approach. We face a similar dilemma: whose deontic
commitments are in question? If it’s the speaker ’s deontic commitments, we can’t account
for the way we argue and disagree about deontic modal claims. If it’s the group’s deontic commitments, it’s hard to see how we can know enough to responsibly assert deontic
modal claims. Prospective contextualism resolves this dilemma in the same way it resolves
the dilemma for epistemic modals. Deontic modal claims are proposals about what deontic
commitments the group ought to treat as commonly accepted.37 A deontic necessity claim
of the form ⌜Mustd φ⌝ is true just in case, at the prospective context, φ will be entailed by
the deontic commitments of the group. A deontic possibility claim of the form ⌜Mayd φ⌝ is
true just in case, at the prospective context, φ will be compatible with the deontic commitments of the group. Provided that we have collapse principles of the form ⌜if it’s common
ground that our deontic commitments require φ, then our deontic commitments require φ⌝,
and ⌜If it’s common ground that φ is compatible with our deontic commitments, then φ is
compatible with our deontic commitments⌝, deontic modal claims will be claims about what
deontic commitments we ought to adopt as a group. These principles are very plausible:
joint deontic commitment should have roughly analogous structure to joint acceptance. And
again, the same pragmatic norms will govern deontic modal claims: norms which require
that assertion and uptake be well-advised, but not necessarily that the claims’ content be
known.
This strategy is general, and can be further applied in fairly straightforward ways. Where
the truth of a claim depends in part on whether it is asserted and accepted, we find truth35
Following Stalnaker (2014), though again, Stalnaker makes the move by positing a special prospective force
rule for deontic modals, rather than by making their content prospective.
36
I’ll again leave it open just what a set of deontic commitments amounts to; most simply we could think of
it as a set of propositions, though that may not be satisfactory ultimately.
37
In the case of epistemic modals, we built in some objectivity to the semantics by making the domain
of quantification the prospective common knowledge, rather than the prospective context set. It’s an
interesting question whether a similar move could be made in this case by a moral realist.
19
conditional performative structures recapitulated. This is a fruitful framework for understanding various kinds of modal claims; more obviously performative claims of the kind
I discussed in the last section; and, perhaps, for understanding further phenomena that
have to do with negotiating contextual parameters, like resolving vagueness38 or local lexical
questions.
9
Embeddings
I’ve defended a semantics—and a companion pragmatics—for bare epistemic modals. I’ll
close by briefly addressing the question of what predictions this semantics makes about
embedded epistemic modals.
I have argued that bare epistemic modals are used to make claims about what structural
features the context set should have. Embedded epistemic modals are clearly not used in
the same way. Consider:
(5)
Either Bob is in his office, or else he must be in the pub.
‘He must be in the pub’ as used in (5) is clearly not a proposal to make the context set entail
that Bob is in the pub. It rather seems to be a proposal to conclude that Bob is in the pub
provided we learn that he is not in his office.
We can predict this by maintaining that, as in unembedded uses, embedded epistemic
modals are used to negotiate about what properties the context set should have: not the
global context set, though, but the derived 39 context set introduced by the embedding environment. For instance, ⌜φ or ψ⌝ as asserted at c introduces a derived context set for the
evaluation of ψ as follows: where Kc is the context set of c, the derived context for ψ is
Kc ∩ J¬φK. An epistemic modal embedded to the right of ‘or,’ then, is a proposal about
how to update the derived context introduced by ‘or.’ ⌜φ or must ψ⌝ is a proposal to make
Kc ∩ J¬φK entail JψK. This seems like the right result, if we posit that derived contexts can
be used to keep track of admissible evolutions of the context set: to accept Jφ or must ψK is
to commit to accepting JψK conditional on learning J¬φK.
This result follows naturally (though not immediately) from prospective contextualism.
If bare epistemic modals are evaluated relative to a function that takes each world to the
prospective common knowledge at that world, embedded epistemic modals are evaluated
relative to a function shifted by the embedding operator40 so that it takes each world to
38
Cf. Barker (2002, 2013).
Or local or subordinate context: the notion comes from Stalnaker, and has been developed in particular in
the dynamic tradition, e.g. by Heim. See Stalnaker (2014) for a recent discussion.
40
I leave this rule as a pragmatic rule, a rule about how to select the modal base for epistemic modals,
39
20
the prospective derived context at that world.41 Since derived contexts are dependent on
mutual acceptance in a parallel way to global contexts,42 it will follow that if it is common
ground that the local context has a certain entailment, compatibility, or measure theoretic
property, then the derived context set has that property. So embedded epistemic modals
can be used to change the properties of their derived context sets in just the same way that
bare epistemic modals can be used to change the properties of their global context sets.
Let’s look at how this works for indicative conditionals. Some indicative conditionals have
overt epistemic modals in the consequent; following Kratzer, I assume that other conditionals
have covert epistemic modals in the consequent.43 and that, in either case, the modal in
the consequent is evaluated relative to the derived context which results by intersecting the
global context set with the proposition expressed by the antecedent. Consider:
(6)
If Bob isn’t in his office, he must be in the pub.
On the proposed account, this is a proposal to make the derived context set—the intersection
of the global context set with the proposition in the antecedent—entail the consequent. In
other words, it is a proposal to conclude that Bob is in the pub, assuming he isn’t in his office.
If accepted, it encodes, again, a constraint on the evolution of context sets: we agree that,
should we come to presuppose that Bob isn’t in his office, we will also come to presuppose
that he is in the pub. This seems like a good prediction, one which makes sense of what we
negotiate about with indicative conditionals and how we can responsibly produce them.
This account is a form of a strict conditional account of indicatives, an account according
to which an indicative conditional of the form ⌜If φ then ψ⌝ is true just in case all the accessible
JφK-worlds are JψK-worlds.44 My account builds in two further assumptions: first, that a
world counts as accessible just in case it is compatible with what is common knowledge;45
second, that the common knowledge in question is the prospective common knowledge. The
latter constraint accounts for the fact that we can assert indicative conditionals of the form
⌜If φ then ψ⌝ even when the prior context includes Jφ ∧ ¬ψK-worlds: the conditional is a
proposal to exclude those worlds, not a statement that they are already excluded.
The first constraint—that a world counts as accessible just in case it’s compatible with
what is common knowledge—accounts for the fact that certain inferences that are strictly
though it could easily be encoded semantically instead.
Stalnaker (2014) makes the same proposal; the approach is also similar to that of Yalcin (2007).
42
See Footnote 19 for discussion.
43
Kratzer (1986), following Lewis (1975). Some conditionals instead have generic modals in the consequent;
I ignore those here.
44
Assuming an implicit ‘must’; mutatis mutandis for other epistemic modals in the consequent of conditionals.
45
Stalnaker (1975) proposes a parallel constraint in a variably strict framework, and Williams (2008) proposes
a parallel constraint in a strict restrictor framework.
41
21
speaking semantically valid46 on this account are not in general valid conversational moves.
For instance, the inference from ⌜If φ then ψ⌝ to ⌜If φ and ρ then ψ⌝ is valid on this account,
assuming we hold fixed the context and under the assumption that both conditionals are
well-defined. But if the accessible worlds are just those compatible with the context set—
and assuming that conditionals presuppose that their antecedents are true in some accessible
worlds—it will often be the case that one can truly assert ⌜If φ then ψ⌝ but not ⌜If φ and
ρ then ψ⌝. Suppose that the global context set includes no Jφ ∧ ρK-worlds, and the speakers
are willing to accept that, among Jφ ∧ ¬ρK-worlds, they ought to take seriously for the sake
of conversation only JψK-worlds. Then they will accept the first conditional. But the second
conditional will expand the global context to include Jφ ∧ ρK-worlds. And the speakers may
not be willing to accept that, among all the JφK-worlds now under consideration, they ought
to take seriously for the sake of conversation only JψK-worlds.47
Subjunctive conditionals obviously are not restricted epistemic modals; the modal in
a subjunctive has a very different flavor from the modal in an indicative. But whatever
account of counterfactuals we choose, we should implement it in a prospective framework:
like indicatives, counterfactuals depend on a contextual parameter that determines their
domain of quantification (or selection function). A claim of the form ⌜If φ would ψ⌝ should
not be interpreted as a claim about the prior value of that contextual parameter, but rather
a claim about its prospective value—a claim that is, therefore, interpreted as a proposal to
set the contextual parameter in a way that makes the conditional come out true.
The last case of embedded epistemic modals that I’ll consider is the case of epistemic
modals embedded under propositional attitude operators. When epistemic modals embed
under attitude operators, the derived context at a world w will simply be the set of worlds
accessible at w under the attitude and for the agent in question. There are two important
differences between the derived contexts introduced by attitude operators versus those introduced by operators like ‘or’ and ‘if. . . then. . . .’ First, the derived contexts introduced by
attitude operators are much more robust at worlds outside the context set than the derived
contexts introduced by operators like ‘or.’ At a world outside the context set, there will
only be a derived context for ‘or’ if there is a natural counterpart of the actual conversation
in question. Whereas worlds will have derived contexts for attitude operators as long as
46
I.e., Strawson-valid in the sense of von Fintel (1999b): valid assuming that context is held fixed and that
the conditionals are well-defined.
47
This style of strict-conditional account follows the strategy of von Fintel (1999b), von Fintel (1999a),
and Gillies (2007), applied there to counterfactuals, and spelled out by Williams (2008) for indicatives.
Even if we don’t end up following Kratzer, and instead take the modal in the consequent of an indicative
conditional to differ from an ordinary epistemic necessity modal, we still should implement that strategy
in a prospective framework to account for facts about (dis)agreement and assertion. See Stalnaker (2014)
for one such approach.
22
the agent in question exists at that world. This rightly captures the sense in which the
truth of, say, ‘Sylvie believes it might be raining’ seems to depend more directly on features
of the world, and less on what goes on in our conversation, than does the truth of, say,
‘If Sylvie’s hat is wet, then it might be raining.’ Second, and closely connected to this,
the prospective feature of the content of embedded epistemic modals will be idle in these
cases. Since assertions of epistemic modals embedded under attitude operators will typically
have no effect on the derived context provided by the attitude operator, it won’t make a
difference whether we evaluate the modal relative to the prospective derived context or the
prior derived context: the claim’s truth conditions have to do straightforwardly with the
way the world is, and not the way our context set is, and thus the prospectivity that we
built in to explain how epistemic modal claims could be used to change the context set will
no longer have a role to play. In cases like this, then, epistemic modals will be evaluated
relative to a function that delivers the derived context at a world, not the prospective derived
context. The existence of variation like this suggests that the prospective interpretation of
the constructions in question arises pragmatically due to the intimate connection between
the assertion and acceptance of the claim and the facts that the claim describes; when that
connection is severed, the prospectivity drops out.48
This approach seems to make the right predictions. For instance, it predicts JS believes
might φKc,w =1 just in case JφK is compatible with the derived context at w just in case JφK
is compatible with S’s beliefs at w. It also rightly predicts the infelicity, pointed out by
Yalcin (2007), of sentences of the form ⌜Suppose (φ and might not φ)⌝. The derived context
at a world w is the set of worlds compatible with our suppositions at w. Sentences of this
form make incompatible proposals about that set of worlds: that it entail JφK and that it be
compatible with J¬φK.49
10
Conclusion
I have proposed that epistemic modals quantify over prospective common knowledge. This
approach lets us explain how epistemic modal claims are responsibly produced and debated.
It makes the right predictions about how epistemic modals are embedded. And it provides a
48
This possibility is needed for bare epistemic modals to make sense of exchanges like this, from von Fintel
and Gillies (2008): ‘The keys might be upstairs.’ ‘No, I looked up there.’ ‘Well, all I said was they might
be.’ Since the function which provides the domain of quantification is, on this view, provided as a feature
of context, this kind of variability does not point to a lack of systematicity in the view, provided we can
make sense of it within a systematic pragmatic framework.
49
This account doesn’t obviously make the right prediction about how epistemic modals embed under factive
attitude operators, as noted in Yalcin (2012b). This is an issue I explore in Mandelkern (MSb); following
Yalcin, I argue there that the account does make the right prediction, provided that we adopt a semantics for
factive attitude operators that’s somewhat more structurally complex than the Kratzer/Hintikka semantics.
23
general framework for analyzing the language that we use to negotiate matters that depend,
in part or in whole, on parameters of the context.
I have not made explicit comparisons to other recent approaches to epistemic modals.
From a predictive point of view, I don’t have any general argument that prospective contextualism does better than all the alternatives, and in some cases it won’t: in particular,
prospective contextualism makes almost identical predictions to Yalcin’s expressivist semantics in Yalcin (2007). Even where its competitors are empirically equivalent, though, if
prospective contextualism works, then there is some reason to prefer it on the grounds of
conservatism: many of the alternative approaches proffered in recent years start by arguing
that, for various reasons, the orthodox truth-conditional contextualist semantic and pragmatic frameworks are insufficient for explaining the phenomena of epistemic modals. If this
is wrong, it substantially reduces the motivation for those alternative approaches. There
is also some reason to prefer prospective contextualism on the grounds that it implements
a strategy for explaining epistemic modals that can easily and fruitfully be extended to a
wide variety of other natural language constructions, some of which, like truth-conditional
performatives, are clearly best explained within the orthodox framework.
If Yalcin’s view is expressivist, then mine is one of its descriptivist cousins. Rather than
expressing the way the context set ought to be, on my view, epistemic modal claims describe
the way the context set will be. This is a view that, on the face of it, is wrong: epistemic
modal claims do not seem to play the role simply of describing context sets. But I have
shown that combined with a standard story about assertion and common ground, this view
actually gets things right. On this view, epistemic modal claims make proposals about the
way context sets should be by describing the way they will come to be if the proposal in
question is accepted. The reason the descriptivist strategy works in this case is because the
way things will be in this case depends directly on how we agree to describe them. And
what makes this case special is shared by many others. There are many cases in which we
use assertions to coordinate facts about the context, and the kind of account I have offered
can be extended to those phenomena.
Prospective contextualism preserves an orthodox semantic and pragmatic framework: on
this approach, the content of an epistemic modal claim is a set of truth conditions, determined
by the context of utterance, and an assertion of an epistemic modal claim, if accepted, has
the effect of intersecting the context set with its content. If the approach works, then it
vindicates the adequacy of this framework for a troubling fragment of natural language.
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