Nat Lang Semantics (2006) 14:235–255
DOI 10.1007/s11050-006-9001-8
ORIGINAL PAPER
Future and non-future modal sentences
Tom Werner
Published online: 5 December 2006
Springer Science+Business Media B.V. 2006
Abstract In this paper, I argue for two principles to determine the temporal
interpretation of modal sentences in English, given a theory in which modals are
interpreted against double conversational backgrounds and an ontology in which
possible worlds branch towards the future. The Disparity Principle requires that a
modal sentence makes distinctions between worlds in the modal base. The NonDisparity Principle requires that a modal sentence does not make distinctions on the
basis of facts settled at speech time. Selection of the modal base will set these principles
against each other, or allow for their cooperative interaction. For a root modal base,
there is a conflict and disparity wins. The resulting interpretation is future. For a
non-root modal base, the principles cooperate. Non-disparity determines a non-future
interpretation and disparity requires the sentence to go beyond what is known by the
speaker.
Keywords
Future interpretation of modals Æ Branching worlds
1 Introduction
In this paper, I attempt to derive the apparent temporal ambiguity of a class of
modals in English from their meanings as modals, expanding on work in Werner
(2003a, b). This ambiguity is illustrated in following sentences.
(1)
Jim might be late.
(2)
That will be Jack.
(3)
Jill may be seated.
T. Werner (&)
Department of Philosophy,
Schenley Park, Carnegie Mellon University,
Pittsburgh, PA 15213-3890, USA
e-mail: [email protected]
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(4)
Janet must live in student housing.
(5)
John can’t be our representative.
Each of these sentences can be construed as being either about a current state of
affairs or about some future happening. (l) could be said about Jim’s not being
currently visible among an assembly of guests, or it could be said about his being late
to a future event. (2) could be said with reference to a phone that is now ringing, or it
could be said in projecting who some winner will be. (3) could be said about a
current possibility of where Jill is, but it could also be a form of permission with a
future interpretation. (4) could be a conclusion about Janet’s current living situation,
or it could state a future requirement affecting Janet. (5) could express incredulity on
the part of the speaker about our current representative, or it could be talking about
a future impossibility for John.
The same sentences are also apparently ambiguous with respect to their modal
readings, and in particular with respect to root versus non-root interpretations. I
assume that the epistemic reading, for all cases, except possibly (1), is a non-root
interpretation. (1) and (2) are both either epistemic or stereotypica1. The stereotypical reading is a root modal interpretation and is based on what a normal state of
affairs is. (3) and (4) are both either epistemic or deontic. A deontic reading is a root
modal interpretation and is based on some set of normative standards. Finally, (5) is
either epistemic or circumstantial. A circumstantial reading is a root modal interpretation and I assume that it is based on laws of physics or biology or some other
inviolable laws.
My claim is that the temporal readings are associated with particular modal
readings; and I adopt the position strongly implied in Kratzer (1977) by which
different modal readings are due to contextual dependence and not to lexical
ambiguity. It is consistent with this assumption that the differing temporal interpretations are also not due to lexical or syntactic ambiguity, but derive from the
contextually sensitive nature of modals. For the purposes of this paper, I take the
strong position that there are no syntactic differences within this class of modals in
their root and non-root readings. This position differs from a number of proposals in
the literature. Ross (1969) defends the idea that root modals are like transitive verbs,
having a null subject and taking a sentential complement, but non-root modals are
like intransitive verbs and lack any such subject. Lightfoot (1979) gives a theory by
which non-root modals are in effect raising verbs, while root modals are control
verbs.1 Cinque (1999) posits that epistemic modals appear in a higher position than
root modals within a highly articulated IP structure.
Evidence can be found both for the syntactic view and for the non-syntactic view.
For example, the modal in (6) can only have an epistemic reading.
(6)
It may be that Joan is unhappy.
Because the subject here is pleonastic, (6) would seem to support the notion that
epistemic may is a raising verb, or intransitive in Ross’s sense. However, the examples
in (1)–(5) suggest that there is little or no syntactic difference associated with the
different modal readings, At the very least, the idea of syntactic differences between
modal readings complicates the idea of contextual dependence. The issue is a difficult
1
Lightfoot (1979) also mentions the possibility that there is no syntactic difference.
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one and needs to be addressed separately from the question of temporal interpretation. For now, I have no evidence that the differences in temporal interpretation are
due to any syntactic differences for the English modals I am considering.
My claim is that the contextually dependent temporal interpretations correlate
with the root/non-root interpretations of the modals, and further, that that
distinction involves an ontology of branching worlds. The branching worlds ontology
incorporates the idea of indeterminism, entailing a basic asymmetry between the
future and the past. Worlds in a branching structure are the same up to the time of
branching, in the strongest sense of being identical and not merely similar. I will
advance the idea that a root modal has a base consisting of a single branching
structure that divides up at the time of speech. The modal base for a non-root
epistemic modal will in effect consist of a set of such branching structures.
One consequence of the asymmetry between the past and present versus the
future is a difference in the kind of epistemic uncertainty we can have about each.
On the one hand, we can be uncertain about what has happened, or about current
states of affairs. Either way, this is uncertainty about existent facts, or previously
existent facts. On the other hand, we can be uncertain about the future in two
different ways. We can either be uncertain about virtual certainties, or we can be
uncertain about happenings that are not yet fixed.
The two kinds of future uncertainty can in fact be found in an earlier example, (1),
which we temporally disambiguate as in (7) by giving it a non-stative predicate.
(1)
John might be late.
(7)
John might arrive late.
Even with the sentence disambiguated not to be present, there are two ways to take
it. Perhaps John is taking the train to get here. Since trains are a reliable form of
transportation, his being on a train virtually guarantees that he will arrive at a fixed
time. However, if we don’t know which train he has taken, we can still be uncertain
about the time of his arrival. We are therefore uncertain about a virtual certainty.
But perhaps John is driving to the party in a hail storm. The situation is now much
less fixed. Any number of chance happenings may now befall him, and when considering his arrival time, we experience a different kind of uncertainty.
Besides the branching worlds ontology, which shows up as a difference between
non-root and root modal bases, we also need certain interpretive principles. The
interpretive principles make sure that we make distinctions between worlds in the
modal base, and that we make the right kinds of distinctions. There are two main
interpretive principles. One of these requires that distinctions of some kind be made.
The other requires that future differences are ignored if past and present differences
are in play in the modal base. The non-conditional nature of the first principle
guarantees that it will always be followed, and it results in a future interpretation for
root modals. The conditional nature of the second principle means it is only followed
when the modal is non-root, and it results in a non-future interpretation.
My theory makes two key predictions that 1 will discuss. One prediction is that
past and future temporal interpretations are asymmetrical. Because modals are not
tense markers, a future interpretation will be unlike a past interpretation. Whereas a
past tense interpretation requires an event to be wholly contained in the past, a
future interpretation requires only part of an event be contained in the future.
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Another prediction concerns future epistemics. Since future epistemic uncertainty
involves the ordering of worlds rather than type of modal base, we expect existential
may or might, but not their dual, will, to have future epistemic readings. This contrasts with non-future epistemics, where universal must, along with existential may
and might, gets an epistemic reading. The reasons for this difference will be explained below.
These predictions are a noteworthy difference between my theory and previous
theories concerning the future interpretation of modals like will, may, or might. A
theory in the literature similar to mine in certain respects is Condoravdi (2001).
Although Condoravdi (2001) anticipates several ideas in this paper, the theories
differ with respect to these predictions.
Condoravdi (2001) combines the theory of will as a future marker in Abusch
(1998) with the idea of will as a quantifier over possible worlds. Condoravdi
proposes that one kind of modal base (‘ metaphysical’, in her terms) is a set of
branching worlds and another kind (‘epistemic’) is a collection of worlds that can
be divided into such branching structures. In her theory, two interpretive principles
work together to derive the right kinds of modal interpretations, given suitable
temporal ones. Her Settledness holds for non-future facts; her Diversity Condition
requires— for an existential modal—that the core proposition under the modal has
different truth values in different worlds in the modal base.2 Together, these
principles require that if an existential modal sentence is non-future, it has an
epistemic modal base.
As this implies, Condoravdi derives the modal interpretation from the temporal.
By her truth conditions, will, may, and might pick out a future interval, or a
present–future interval, and thus receive either a future or a present interpretation
when there is suitable disambiguation. In Condoravdi’s theory, therefore, modals are
tense markers and quantifiers over possible worlds. There is no prediction that
events mentioned in a future modal sentence need be only partially future.
Condoravdi also treats future epistemics and proposes that the modal base for
these is epistemic. Her approach does not predict that may or might but not will can
be interpreted as future epistemics.
The class of modals I am interested in is made up of may, might, will, can, and
must, and to the extent that it is still in use in modern English, shall. These are
modals in English which have neither a past tense interpretation or a counterfactual
reading, with the exception of might. I exclude would, could, and should from any
generalizations I make here, and I only include might under its non-past, noncounterfactual readings.
My generalizations are also only meant to apply to modals in English, because of
their peculiar morphosyntactic properties. Modals in English appear to the left of
sentential negation, they cannot take aspectual inflection, and in standard dialects
they cannot appear with other modals in the same clause. My assumption is that
may, will, shall, can, and must all have a feature TENSE which is PRESENT, as does
might under the readings I consider here. Due to the feature TENSE, these modals must
head any sentence which contains them. That assumption yields the result that modals
appear to the left of negation, that they cannot take aspectual inflection, and that they
2
Condoravdi (2001) relates the Diversity Condition to proposals in the literature based on pragmatics or felicity conditions, such as Groenendijk and Stokhof (1975), pointing out that these
proposals do not extend to metaphysical indeterminism. Her proposal does.
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cannot double up. Because of the feature PRESENT, any temporal interpretation we give
to these modals must start from the perspective of the speech time.
This paper is structured as follows. In Sect. 2, I argue for my main interpretative
principle, the Disparity Principle, by which an epistemic modal sentence must go
beyond what is known by the speaker. In this section, I also argue that the Disparity
Principle is not pragmatic and I discuss why modals are used as hedges, In Sect. 3, I
show how the Disparity Principle, combined with a root modal base, yields future
readings. In Sect. 4, I take up the issue of the temporal interpretation of epistemic
modals. In 4.1 I show how ordinary epistemics get their temporal interpretation. In
4.2, I show how future epistemics get their temporal interpretation. In Sect. 5, I
discuss a prediction made by my theory that is not made by theories in which will is a
future marker.
2 The Disparity Principle
In Sect. 2.1, I show how the Disparity Principle can be made part of a theory of
modal interpretation. In Sect. 2.2, I consider whether the effects I have attributed to
the Disparity Principle are not simply due to scalar implicatures. This discussion will
lead, in Sect. 2.3, to issues raised by a reviewer. My response there will lead me to
briefly consider the semantic difference between epistemics and evidentials. In
Sect. 2.4, I will take up the related issue of how the Disparity Principle accounts for
why modal statements are used as hedges.
2.1 The Disparity Principle
As noted, there is an observation, apparently made at various times in the literature,
that an epistemic modal assertion cannot be about a proposition known by the
speaker to be true, or known by the speaker to be false. By that observation,
someone who asserts (8), for example, cannot know that John is actually asleep, and
they cannot know that John is actually not asleep.
(8)
John must be asleep.
At the very least, a speaker of (8) who knew John was asleep would be misleading
the hearer as to the speaker’s epistemic state, while a speaker of (8) who knew John
was awake would be lying.
This constraint on epistemic modal sentences does not follow directly from
standard modal theory, such as Kratzer (1981a, 1991). According to that theory, with
certain simplifications, truth conditions for (8) are as follows.
(9)
For any w W, given speaker s, assignment function g, modal base f,
and ordering source j,
with i = <s,g,f,j>, sJohn-must-be-asleep¢t
i(w) = 1 iff John is asleep
T
in every j-best world in f(s,w).
The modal base f here is epistemic, and the ordering source j is stereotypical. I make
the speaker an argument for the modal base, given that the epistemic modal base
depends in part on what the speaker knows. Here and throughout the paper, I
assume that the ordering source takes the same arguments as the modal base. For
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simplicity, I assume that there are j-best worlds. These are worlds that fare better
according to the propositions in j(s,w), the ordering source, than any other worlds in
the modal base. If the modal is existential, ‘every’ in the truth conditions is replaced
by ‘some’.
The truth conditions in (9) make no mention of time or tense. I will therefore
recast these truth conditions using a multi-sorted translation language which extensionalizes worlds and time, using t0 as a designated variable which, when unbound, gets as its value the time of speech. The modal itself gets the translation in
(10), showing that must is an expression that denotes a function whose first argument is a proposition.
(10)
must kQkw0[must¢w0,t0(Q)]
<
<w,t>,<w,t>
>
The LF for (8) is partially represented by (11), where I put the subject in the Spec of
the lower VP. (In this paper, I follow Ross (1969) in treating a modal as a verb with
special modal features.)
(11)
[VP must [VP John [V¢ be asleep]]]
Now the translation for (8), or (11), will be as in (12). For now I just assume that the
sentence embedded under the modal has a present tense interpretation, without
giving any explanation for how that might come about.
(12)
kw0[must¢w0,t0(kw0[asleep¢w0,t0(j)])]
The truth conditions now look as follows.
(13)
For any w W, given speaker s, assignment function g, modal base f,
and ordering source j,
with i = <s,g,f,j>, and g(t0)=t, skw0[must¢w0,t0(kw0[asleep¢
w0,t0(j)])]ti
T
(w) = 1 iff John is asleep at t in every j-best world in f(s,w).
We find two occurrences of the designated temporal variable t0, one in the complement of the modal and one associated with the modal itself. As mentioned, I
assume that this modal contains the feature PRESENT as part of its lexical semantics.
The designated temporal variable in the complement assures a present interpretation for that clause, but I postpone an explanation of that to Sect. 4.
Somehow, we need to build the requirement that the speaker of (8) does not
know whether or not John is asleep into the truth conditions. The constraint that
the speaker does not know that John is asleep means that proposition does not
contain the epistemic modal base. The constraint that the speaker does not know
that John is not asleep means that proposition forms a non-empty intersection
with the epistemic modal base. We can capture this constraint by adding the
following clauses.
T
T
(14)
f(s,w) ˙ skw0[asleep¢w0t0(j)]ti „ f(s,w).
T
(15)
f(s,w) ˙ skw0[asleep¢w0t0(j)]ti „ B.
According to (14), John can’t be asleep in every world in the modal base. According
to (15), John has to be asleep in some world in the modal base.
In this paper, I assume that the requirement that the embedded proposition
is open with respect to the modal base is part of the meaning of all modal
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statements—at least for the modals I consider. I call this principle the Disparity
Principle. For an epistemic modal reading, it means that the speaker does not know
the truth value of the core proposition within the modal statement. For a root modal
reading, the same principle will help determine the temporal reading of the sentence.
Before turning to that issue, several questions need to be addressed.
2.2 Why these are not scalar implicature effects
Scalar implicature is the pragmatic principle by which, if a person utters the weaker
of two related sentences, it can be inferred that the stronger version is not known by
the speaker to be true. Let us see if scalar implicature alone yields the constraint that
a speaker of an epistemic modal sentence cannot know the truth value of the
proposition under the modal. Consider the following pair of related sentences.
(8)
John must be asleep.
(16)
John is asleep.
Within this pair, it would appear at first glance that (8) is the weaker and (16) the
stronger assertion.
This assessment of relative strength is justified by the version of Kratzer’s theory
adopted here, since by that version of the theory, for a true utterance of (8) only the
best worlds in the modal base are required to be worlds in which John is asleep. This
leaves open that there might be worlds in the modal base in which Join is not asleep.
An utterance of (16), having been accepted by both speakers, would remove all
worlds from the common ground in which John is not asleep. If we equate the
common ground with the epistemic modal base, then (16) is a stronger statement
than (8). (16) eliminates all epistemic alternatives in which John is not asleep
whereas (8) allows that some such alternatives can still be in play.
But if (16) is stronger than (8), then the utterance that John might be asleep
should implicate that the speaker does not know that John is asleep.
Scalar implicatures can be cancelled, so the next step is to see if our two sentences can appear together within the same discourse. First, consider (17) and (18),
typical examples of scalar implicature cancellation.
(17)
Mary worked for eight hours on the project. In fact, she worked for ten
hours on it.
(18)
Mary worked for ten hours, so she worked for eight hours.
The statement that Mary worked for ten hours is stronger than the statement that
she worked for eight hours, since it entails it. But as (17) and (18) show, those two
statements can appear together. The implicature that the stronger statement is not
known is cancelled when the sentences appear together.
(19) and (20) are parallel examples to (17) and (18), respectively.
(19)
??John must be asleep. In fact, he is asleep.
(20)
??John is asleep, so he must be asleep.
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Sentences (19) and (20) are still odd, and this is evidence against a scalar implicature
account. Scalar implicatures cancel, but whatever effect we are dealing with here is
not cancelled. This doesn’t mean that there is not also a scalar implicature involved
in the utterance of a modal sentence, but something else must also be involved. I
take that to be the Disparity Principle.
2.3 Further arguments against a scalar implicature account
A reviewer has objected to this argument against a scalar implicature account for the
effects that I am seeking to explain with the Disparity Principle. The first part of this
objection is to say that (19) is not actually analogous to (17). The reason that (19)
wouldn’t be analogous to (17) is that in a context in which any scalar implicature
might be cancelled, what is known by the speaker is not what is relevant with respect
to the first sentence in (19). What would be relevant is the maximal satisfaction of
certain stereotypes. Or, in a second formulation, what would be relevant is what
follows from a given piece of evidence and our stereotypes.
The view of scalar implicature cancellation assumed by the reviewer is apparently
as follows. Implicatures can be cancelled just in case the meaning of the sentence
which carries the implicatures is relevant in itself, apart from the implicatures. For
example, the first sentence in (17) might be relevant if we are giving a bonus to
anyone who worked on the project for 8 hours. The second sentence in (17) is not
relevant, but can be added to cancel the scalar implicature that Mary worked more
than 8 hours.
For the modal case, the meaning of the sentence would involve the maximal
satisfaction of certain stereotypes. The implicatures have to do with what the
speaker knows. If a case is designed by which only the meaning of the modal sentence matters, and not the implicatures, cancellation should be possible. To this end,
the reviewer proposes the sentences in (21) and (22).
(21)
Since his fingerprints have been found the knife, the defendant must
have touched the knife. In fact, we all know he did, since he confessed
to doing so.
(22)
Since the dog died, there must have been carbon monoxide in the room.
In fact, we know there was carbon monoxide in the room, since . . .
Examples (21) and (22) are claimed to be truly analogous to (17). The issue in the
first sentences in these examples is only what follows from the evidence, not the
epistemic state of the speaker. Neither (21) nor (22) is strange, so there is no reason
not to take the effect in question as due to a scalar implicature after all, according to
the reviewer.
The reviewer formulates what would have to be relevant about the modal
sentence—for cancellation of scalar implicatures to be possible—in two ways, but by
either formulation, an issue is raised that goes to the very heart of the Disparity
Principle. According to the first formulation, the context must be such that it is only
relevant to find out what is true in the stereotypically best worlds in the modal base,
but not in all worlds in the modal base. According to the second formulation, what
would have to be relevant is not what is known, but what follows given some piece of
evidence and various stereotypes we hold. In either case, we need to determine what
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holds in the stereotypically best words, in virtue of their being stereotypically best,
but it is just here that the Disparity Principle comes into play.
Thinking in terms of the first formulation, how can we distinguish a proposition
true in stereotypically best worlds from a proposition true in all worlds in the modal
base? What is true in all worlds in the modal base is also true in all worlds in the
stereotypically best worlds in the modal base. A proposition can only be true in the
set of stereotypically best worlds in virtue of their being stereotypically best if it is
not true in all the worlds in the modal base. But that is the very thing the Disparity
Principle guarantees. Thinking in terms of the second formulation, what matters is
what follows from the evidence and the stereotypes. But a proposition can only be
said to follow from the evidence and the stereotypes if it is not true in all the worlds
in the modal base. Again, it is the Disparity Principle that guarantees this.
Whichever formulation of cancellation we choose, in order for the meaning of the
modal sentence to be relevant, the Disparity Principle must be in place. As long as
what matters is what is true in the stereotypically best worlds, or what follows from a
set of propositions, given certain stereotypes, this principle cannot be eliminated. We
cannot construct a case where all that is relevant is what holds in the stereotypically
best worlds in an epistemic modal base, and not what holds overall in the modal
base.
How do we explain the examples in (21) and (22)? The reviewer’s claim is that all
that should be relevant is what holds in the stereotypically best worlds. What holds in
the modal base generally should not affect the acceptability of the modal sentence.
(21) states directly that the speaker knows that the defendant touched the knife, but
the modal sentence within (21) is not ruled out. (22) states directly that the speaker
knows that there was carbon monoxide in the room, but the modal sentence in (22) is
not ruled out. It would appear, then, that we are seeing cancellation of a scalar
implicature in both sentences.
However, for these examples to be reliable counterexamples, we have to make
certain that the modal base really is epistemic, and that is far from clear. In fact, (21)
and (22) provide excellent examples of modals that probably should be interpreted
not epistemically but evidentially. The set of propositions in an evidential modal
base would be a proper subset of the set of propositions in the epistemic modal base.
The intersection of the evidential propositions would be a proper superset—not a
proper subset—of the intersection of the epistemic propositions. That means the
disparity principle can hold in the evidential modal base for the embedded proposition, even if it doesn ’t hold in the epistemic modal base.
It makes sense that natural language provides a device for cordoning off some
part of a speaker’s knowledge and assigning it a special status. In (21), the modal is
interpreted with respect to the subset of the speaker’ s knowledge constituted by
certain physical evidence. The same is true for (22), where the subset of knowledge is
constituted by certain physical occurrences. Clearly it is convenient to be able point
out that something follows from certain types of very tangible knowledge—such as
physical evidence—even if access to general knowledge makes such statements
informationally redundant. This is what the evidential modal base enables.
My conclusion is that scalar implicature does not fully explain the effects that I
have explained by appealing to the Disparity Principle. In fact, it seems that the
Disparity Principle is a necessary component in establishing the relevance of a modal
statement even in situations in which we are only interested in what is the case in the
stereotypically best worlds.
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2.4 Modals as hedges
The operation of the Disparity Principle helps explain a certain feature in the actual
usage of epistemic modals. Sentences in an epistemic mood appear in discourse in
places where we might expect to find indicative mood, and the modal is a form of
hedge. The modal apparently lets a person say something without the same degree of
commitment, and this effect follows in a straightforward fashion from the Disparity
Principle.
The first point to make is that what counts as a deduction in actually occurring
discourse is not necessarily what a logician would count as a deduction. Consider the
following real-life example.
(23)
This clue enabled Holmes to deduce that the murderer must have been
someone familiar to the victim’s dog because the dog did not bark
when the murderer appeared. (Kardes & Sanbonmatsu, 2003)
Here we find the word deduce but this doesn’t mean that Holmes reached his conclusion through the application of the kind of logical rules formalized in a natural
deduction system. Such a deduction would involve paring down the set of epistemic
alternatives, following a kind of update procedure. The end result would be that all
the worlds in the updated set would be worlds in which the murderer was familiar
with the victim’s dog. But instead, Holmes bases his reasoning on the background
knowledge that dogs tends to bark at strangers. This reasoning is based on what is
normal or stereotypical. The proposition that dogs tend to bark at strangers will be
contained in the ordering source. Holmes reaches his conclusion by finding best
worlds in the modal base and seeing what is true in them. By the Disparity Principle,
the salient alternative is kept alive. The end result of this reasoning is that we have
not pared down the set of epistemic alternatives to just the set of worlds in which the
murderer is familiar with the victim’s dog. There is something provisional in this
reasoning because it is not strictly speaking a logical conclusion that Holmes has
reached.
Other examples show conclusions framed in modal statements where we seem
entitled to expect Indicative statements. In these cases, the modal apparently
functions as a hedge. Consider first a made-up example.
(24)A:
B:
We know that either the butler did it or the maid did it, and we
know that the maid didn’t do it.
Then the butler must have done it.
From the premise that the butler did it or the maid did it, and the further premise
that the maid didn’t do it, the conclusion that the butler did it follows as a case of
Disjunctive Syllogism. The set of epistemic alternatives resulting from this update
would only contain worlds in which the butler did it. But B does not say that the
butler did it, only that he must have done it, making it appear that the Disparity
Principle is not in play in the interpretation of this modal. If it were, the interpretation of B’s response would require that the set of epistemic alternatives would
contain worlds in which the butler did it and worlds in which the butler did not do it,
and the required update disallows that.
However, it is too soon to close the case. B’s response reveals a certain hesitation.
Why not come out and just say that the butler did it? The fact is that in a conver-
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sation, a person is not always prepared to accept every assertion made by another
party as 100% certain. In (24), it is evident that B has not fully accepted A’s
assertion. Given the Disparity Principle, B’s statement indicates a reluctance to
eliminate the possibility that the butler didn’t do it.
Other cases where one might balk at a definitive conclusion involve the complexity of the calculation. Consider a second real-life example. In this example, what
is being discussed is a puzzle in which one player is to arrange six red cards and one
black card so that a second player turning the cards over one by one can at no point
deduce that the next card is black.
(25)
You cannot put it in the bottom, 7th position, for I can certainly deduce
that it is black if I get down to the last card and I haven’t seen a black
one . . . What about the 6th position? Well when I get down to the 6th
card, I can deduce that it must be black since we have already eliminated
the 7th position. (Felkins, 2000)
The question here is, why does the speaker say that for the 7th card one can deduce
that it is black, but for the 6th card, one can deduce that it must be black? If you’ve
turned over six red cards, there is one short step to deducing that the seventh is
black. But if you’ve only turned over five red cards, the reasoning is more complicated. It has to include considerations of how far the first player has thought things
through. When one reaches a fifth red card, therefore, it is somewhat premature to
eliminate all worlds from the context set except those in which the sixth card is black,
and so there is a hedge with the use of the modal.
These hedges are even found with mathematical examples. The following case is
meant to illustrate a mathematical deduction.
(26)
We have a rule which states that the product of two negative numbers
is a positive number.
Thus, if we have the specific case of ()3) · ()4) we can deduce that the
answer must be a positive number. (A General Rule which helps us to
deduce a specific case.) (E-Z geometry.com)
A rule is applied to get the answer, but the use of the modal suggests a certain
tentativeness.
Here is one final example.
(27)
In view of what the Weather Channel said it must be raining in Boston
right now.3
There is an interesting contrast to be made with respect to this example. Let
us consider what the weather forecaster might have said that would make (27)
a reasonable follow-up. Suppose it was the following.
(28)
Rain has spread across the entire eastern half of the state.
If Boston is in the eastern half of the state, how could it fail to be raining right now in
Boston? But there is an issue here involving the vagueness of language. Rain has
spread, but does that mean it is raining in every single location in that half of the
state at every single moment? We can’t say for sure, so there is a hedge.
3
Example from Angelika Kratzer (p.c.).
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Notice that (27) would not be a reasonable follow-up to (29).
(29)
It is raining right now in Boston and points east.
The weather forecaster has just said it is raining in Boston and points east. Conjunction Elimination gives us that it is raining in Boston. We hardly need a hedge
here, so (27) with its epistemic modal would be odd.
In actual cases in which a conclusion is supposed to follow logically from a set of
premises, extenuating factors often come into play. These can be a source of doubt,
giving the speaker a reason to hedge. One way to hedge is to state the conclusions as
a modal assertion. Because of the Disparity Principle, this implies a reluctance to
eliminate all worlds from the set of epistemic alternatives where the conclusion does
not hold.
3 The future interpretation of root modals
In this section, I explain how the Disparity Principle, combined with the right sort of
modal base, yields future interpretations.
In this paper, I adopt the idea of indeterminism, and this is reflected in the model
by having possible worlds that branch. Branching worlds are worlds that, up to a
given time, are identical in the strongest sense, and subsequently diverge. The first
task, then, is to capture the idea of branching worlds within a modal theory.
Central to the notion of branching worlds is the idea that, up to a point in time, a
plurality of worlds is really the same thing. Kratzer (1981b) discusses what she calls a
‘‘totally realistic modal base.’’ A totally realistic modal base is a function that when
applied to a world gives back the singleton set containing
T that world. In other words,
for a totally realistic modal base fTR, for all w 2 W, fTR(W) ¼ {W}. The intuition is
that the totally realistic modal base is an exhaustive or unique description of that
world. An exhaustive description of any branching world, up to a point in time,
would give us back the entire set of branching worlds. Therefore, the modal base we
need is totally realistic, up to a time. This function takes a world and a time as
arguments, and gives back the set of worlds that branch from that world at T
that time.
In other words, for a totally realistic modal base function up to a time fTR, fTR(w,t)
is the set of worlds that branch from w at t. In the rest of this paper, I will refer to this
function or the worlds it selects simply as the totally realistic modal base.
For evaluation of our root modals, we will use a totally realistic modal base up to
the time of speech. Together with the Disparity Principle, we now have the tools
to explain the temporal interpretation of the modals we are interested in.
For the syntax, I adopt Ross’s (1969) proposal that auxiliaries in English,
including modals, are simply verbs with special features. I also adopt the VP-internal
subject hypothesis. Semantically, an ordinary VP will be type <i,<w,t>>, where
i is the type for intervals. In the untensed case the V heads be or have will be type
<< i,<w,t>>,<i,<w,t>>>. This allows the auxiliary to select an ordinary VP complement, and in turn to combine with a higher auxiliary. If the auxiliary is tensed, then it
is type <<i,<w,t>>,<w,t>> and no further combinations are possible.
My assumption is that the modals we are interested in in this paper are of the
same type as a tensed auxiliary: <<i,<w,t>>,<w,t>>. When such a modal combines
with a lower VP, the resulting type is < w,t>. That means the tense feature is already
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embedded in the modal, and that explains why modals in standard English must
appear leftmost within a string of auxiliary verbs. My semantic theory does not
depend on this syntax, but it will make the presentation simpler.
Now we need to consider the truth conditions for a modal sentence with a totally
realistic modal base and a stereotypical ordering source, such as (30). The syntactic
structure is given in (31).
(30)
The Sycamore branch will fall.
(31)
[VP will [VP [NP the Sycamore branch] [V fall]]]
For the translation of the modal, we have this.
(32)
will kQkw0[will¢w0t0(Q)] <<i,<w,t>>,<w,t>>
The modal denotes a function whose first argument (the core) is a function from
times to propositions. The sentence in (30) translates as (33).
(33)
kw0[will¢w0t0(kt0kw0[fall¢w0t0(the-Sycamore-branch¢)])]
The truth conditions are given as follows.
(34)
For any w W, given speaker s, assignment function g, modal base
function f, and ordering source function j, with i = <s,g,f,j> and
(the-Sycamore-branch¢)])]ti
t = g(t0), skw0[will¢w0t0(kt0kw0[fall¢w0,t0 T
(w) = 1 iff for every j-best world z in f(s,w,t), there is a time t¢ such
that
T skt0kw0[fall¢w0t0(the-Sycamore-branch¢)]ti(t¢)(z) = 1; andT
Tf(s,w,t) ˙ skt0kw0[fall¢w0t0(the-Sycamore-branch¢)]ti(t¢) „ f(s,w,t); and
f(s,w,t) ˙ skt0kw0 [fall¢w0t0(the-Sycamore-branch¢)]ti(t¢) „ B.
Here the modal base function takes worlds, times, and speakers as arguments. For a
totally realistic modal base, the speaker argument has no effect, since the modal base
in this case is objective and not particular to a given speaker. The ordering source
takes the same three arguments, something not reflected in the notation. For a
stereotypical ordering, as this is, the addition of a time argument helps capture the
idea that what is normal changes over time. The speaker argument for j here has no
effect, but with an epistemic ordering source, it will.
The truth conditions for (34) yield a future interpretation. Every best world in the
modal base is a member of some proposition or other that results when the core is
applied to some time. Any such proposition, according to the disparity clauses, must
contain some modal base worlds and exclude others. Since the modal base is a set of
speech-time branching worlds, a proposition true in some worlds and not others must
be at least partly future. A time that combines with the core to form a proposition
containing some but not all accessible worlds must be at least partly future with
respect to the speech time. In this way, the future interpretation for (30) is explained.
This treatment for will generalizes to other modals with root interpretation. The
future interpretation of will comes from an interaction between the Disparity
Principle and the totally realistic modal base. The ordering source here was stereotypical, but others are possible. I assume that branching worlds can also be
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evaluated on the basis of normative laws, or physical and biological laws. This gives
us root modals that are stereotypical, deontic, or circumstantial,4 which all say
different kinds of things about the future.
4 The temporal interpretation of epistemics
Given the general approach we have been following, it shouldn’t be surprising if the
temporal interpretation of epistemics relates to the ontological asymmetry between
the past and the future, and to the corresponding kinds of knowledge, or ignorance,
we can have about each. Our uncertainty about the past or present is a kind of
first-order uncertainty. Past or present facts already hold or don’t hold. The only
kind of uncertainty we can have is due to a lack of knowledge.
Facts about the future don’t hold yet. Some future facts, corresponding to certain
regularities, are virtual certainties. We can have certainty about these facts, but we
can also have uncertainty, if we don’t know what the regularities are. However, there
are other facts that are not fixed, knowledge or lack of it notwithstanding. I assume
that the universe is not determined and there is a role for chance and happenstance.
Since some events are not determined, we cannot know that they will happen. Our
uncertainty here about the future is of a different order.
These different kinds of uncertainty are conceivable, but are they expressible in
natural language? I will argue that English does distinguish between non-future and
future uncertainties, but that it doesn’t distinguish between different kinds of future
uncertainty. There is no way to distinguish future uncertainty about what is virtually
guaranteed from future uncertainty based on the indeterminacy of events. Only
additional information lets us know the intended meaning.
4.1 Non-future epistemics
In our theory, temporal interpretations follow from modal interpretations. Root
modals get their temporal interpretation by a requirement that modal sentences
make distinctions that go beyond distinctions implied by the modal base. Because
the modal base is totally. realistic, the resulting temporal interpretation is future.
Modals with a non-root interpretation—those interpreted with an epistemic modal
base—need to get a non-future interpretation. However, as before, we want the
temporal interpretation to be a consequence of the meaning of the modal.
What is it about a non-root modal base that leads to a non-future interpretation?
By assumption, the totally realistic modal base is made up of propositions that
exhaustively describe the past and present of the world of utterance. The epistemic
modal base is made up of a subset of these. Some propositions are missing, and these
are the ones still in play, epistemically, even though they are settled. By the
Disparity Principle, distinctions must be made, but they must be made on the basis of
settled facts. We add the Non-Disparity Principle in (35).
(35)
A proposition must make no distinction between speech-time branching
worlds.
4
In Kratzer (1981a, 1991) the modal base is circumstantial, and for circumstantial modals, the
ordering source is empty.
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The idea behind (35) is that only distinctions involving settled facts. can be made,
since speech-time branching worlds differ only by non-settled facts.
If the modal base is totally realistic, (35) must be ignored. With a totally realistic
modal base, distinctions can only be based on non-settled facts. We therefore stipulate that the Non-Disparity Principle in (35) is violable, but the Disparity Principle
is not. When the modal base is totally realistic, (35) is violated in favor of disparity.
When the modal base is epistemic, (35) is obeyed and disparity is obeyed. The
resulting sentence has a non-future interpretation but comes with the requirement
that the speaker cannot know the truth value of the core proposition.
A final detail must be added, as seen in (36) and (37).
(36)
John might be sleeping.
(37)
John might have been sleeping.
Sentence (36) mentions the possibility that John is sleeping now. (37) mentions the
possibility that John was sleeping earlier. In other words, with the auxiliary have, the
sentence is past; without it, the sentence is present. But since either sentence makes a
distinction based on settled facts, (36) is only non-past because of the absence of have.
The traditional view is that tenses in English make a three-way distinction between past, present, and future. One way to capture a three-way distinction is
with two overlapping two-way distinctions. I have argued that in English there is a
two-way distinction between Disparity and Non-disparity. What might be the second
two-way distinction that would result in the needed three-way distinction?
Enç (1996) mentions the idea, also reported in Ogihara (1989), that there is only
one tense in English, past tense. She suggests (p. 356) that present is the absence of
past tense. I interpret this suggestion to mean that tense is a two-way distinction
between past and non-past. With past tense morphology, there is past meaning. With
no past tense morphology, there is non-past meaning. Therefore I implement Enç’s
suggestion with the principle in (38).
(38)
Past interpretation if and only if past tense morphology.
The principles in (35) and (38) will only be fulfilled for a time t equal to the speech
time when applied to the truth conditions for (37) found in (39).
(39)
For any w 2 W, given speaker s, assignment function g, modal base f,
and ordering source j, with i = <s,g,f,j>, and g(t0) = t,
t0 & asleep¢w0,t(j)])]ti (w) = 1
skw0[must¢w0,t0(kt0kw0$t[t < T
iff for some j-best world z in f(s,w,t), there is a time t¢ such that
skt
T 0kw0$t[t < t0 & asleep¢w0,t(j)]ti (t¢)(z) = 1, and
T
Tf(s,w,t) ˙ skt0kw0$t[t < t0 & asleep¢w0,t(j)]ti (t¢) „ f(s,w,t), and
f(s,w,t) ˙ skt0kw0$t[t < t0 & asleep¢w0,t(j)]ti (t¢) „ B.
If t¢ is equal to the speech time, (37) will get a past interpretation.
With a totally realistic modal base, (38) again cannot be fulfilled. This is shown in
(40), where the reading is future.
(40)
John will have left by breakfast.
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The conflict is again with Disparity. If (40) were past, no distinction would be made
within the modal base. We once more mention that Disparity is not violable, while
(38) is.
4.2 Future epistemics
Here we take up the issue of future sentences that are true or false in virtue of what
the speaker knows and doesn’t know, making them epistemic as well as future. (41)
is an example modified from Condoravdi (2001).
(41)
It has been decided that John will meet the dean tomorrow or that
John will meet the provost tomorrow, but I don’t know which.
He may meet the dean and he may meet the provost.
The second sentence in (41) is epistemic. This sentence can only properly be uttered
by someone who doesn’t know the results of the decision.
In the situation described in (41), whom John meets tomorrow is a virtual
certainty. It is different than a settled fact, however.5 John’s meeting involves only a
plan and is not part of the decided substance of any world. Therefore, we make this
virtual certainty a matter not of the modal base but of the ordering source, and we
record the epistemic deficit there also. Worlds which differ only as to whether John
meets the dean or the provost tomorrow are treated as ties by this ordering source.
Given such an ordering source, the existential conjuncts in the second sentence in
(41) each come out true. For neither conjunct would the corresponding universal
sentence be true.
No linguistic means is provided to distinguish between future sentences with may
or might which are epistemic and those that are not. The truth conditions simply say
that there are some stereotypically best worlds (in the totally realistic base) in which
a certain outcome takes place. This is either because of ignorance on the part of the
speaker, or because the facts are not determined.
The difference in intended meaning can only be gleaned on the basis of extra
information, as we saw in (41). Consider also the following.
(42)
It might rain tomorrow.
Sentence (42) can be true, even if the chance for rain tomorrow is 100%, as long as
the speaker does not know this. However, there is something distinctly wrong with
the following sentence.
(43)
??The chance of rain tomorrow is 100%, so it might rain tomorrow.
By my theory, the difference in future existential modal reading is in the ordering
source, which in either case is stereotypical. Since there is no way of indicating
whether an epistemic deficit is involved or not, auxiliary information is the only way
to obtain the intended meaning.
5
There is in this connection also a settled fact that we may be ignorant of—whom John is to meet.
But that is ignorance about the present and it licenses the following sentence with an epistemic
modal base.
(i)
John might be meeting the dean tomorrow and he might be meeting the
provost.
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It is telling that existential may and might have readings as future epistemics but
that their dual will does not.6 The interpretation of future epistemics with may and
might involves an epistemic deficit resulting in otherwise resolvable ties between
worlds in the ordering. These ties allow several existential sentences to be true, as we
saw in the discussion of (41). The corresponding will sentences are false when uttered by a person in the relevant epistemic state. There is no analogous case whereby
a will sentence, or several will sentences, could be true in virtue of such ties, since the
quantification is universal. This contrasts with non-future epistemics in which we find
may or might, which have existential force, as well as their dual, must, which has
universal force. This difference supports the idea that non-future epistemic uncertainty is recorded in the modal base but future epistemic uncertainty is recorded in
the ordering source.
5 A prediction about future sentences
In this final section, I show how my theory makes an additional prediction about
future sentences, a prediction that appears to be borne out by the data.
The theory developed here derives the temporal interpretation of modal sentences from a requirement to make distinctions between worlds in the modal base, a
requirement that ultimately may be tied to a prohibition against vacuous ordering. In
the case of future sentences, the modal base is a set of branching worlds. These
worlds differ only by future facts, and it follows that distinctions can only be drawn
between these worlds on the basis of future differences. This is why these sentences
have future interpretations.
This manner of deriving future readings leads to a prediction not made by
theories in which will is a future tense marker, or a combined future tense marker
and quantifier over possible worlds. Such theories treat will as the reverse of a
past tense marker. A past tense marker says that some state or event was prior to
the speech time. A future tense marker says that some state or event is after the
speech time. But a theory in which what matters are differences between possible
worlds isn’t like that. Differences with respect to the future can still extend into
the past.
At first glance, many will or might sentences do require eventualities to be wholly
future. Here the expected symmetry between Past and will appears at first glance
to hold.
(44)
John washed the car today.
(45)
John will wash the car today.
Sentence (44) is true only of a washing event completely in the past. Similarly, (45)
might at first appear to be true only of a washing event completely in the future.
But now consider the following situation. John got up early and got a good start
on washing the car, and then was called away on business. The car is sitting in the
driveway, half-washed. You believe his promise that he will come home later in the
afternoon and complete the job. In that case, (45) does seem to be true. (44),
6
I mean will unadorned by possibility adverbs, such as perhaps. How such adverbs interact with
modals is an important subject that I put aside in this paper.
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however, is definitely not true. For the future expression in (45), the car washing can
overlap with the present and extend into the past. For the past expression in (44), the
car washing definitely cannot extend into the future.
The contrast becomes clearer with the addition of certain expressions that
emphasize the totality of activities. Consider the following pair.
(46)
John washed the car today from top to bottom.
(47)
John will wash the car today from top to bottom.
The intuitions are very clear here. The car washing in (46) must be wholly past, but
the car washing in (47) needn’t be wholly future.
To give a semantics for these sentences, we need a way to deal with frame adverbs
such as today and yesterday. From von Stechow’s (1995) paper, I borrow the idea
that a past morpheme has two indices syntactically affixed. One of these denotes an
interval associated with evaluation of the predicate (the reference time, in von
Stechow’s terms) and the other denotes a frame time as given by a frame time
adverb. The semantic translation for past is given in (48), which is also inspired by
von Stechow’s analysis but somewhat different from it.
(48)
PAST(j)i
kP[ti < t0 & Pti,tj]
For the semantics, I assume the following rule.
(49)
[P1,2] = 1 iff P holds at some sub-interval of g(1).
This means the predicate has to hold at the reference time. I assume the frame time
is brought into play with the following condition.
(50)
A sub-interval relation exists between g(1) and g(2).
Condition (50) leaves it open whether the reference time is a sub-interval of the
frame time or vice versa. For the cases I look at here, I assume that the reference
time is always a sub-interval of the frame time.
We can now give truth conditions for our sentences. Consider (44) with the truth
conditions in (51).
(44)
John washed the car today.
(51)
For any w W and assignment function g, skw0[t1 < t0 & washw0,t1,today¢
(j, the-car¢)]tg(w) = 1 iff g(t1) is before g(t0) and
John washes the car in w at g(t1) and g(t1) ˝ stoday¢tg.
Now consider the will sentence, (45), with the truth conditions in (52).
(45)
John will wash the car today.
(52)
For any w W, for speaker s, assignment function g, modal base
function f, and ordering source function j, with i = <s,g,f,j> and
[wash¢w0,t0,today¢(j, the-car¢)])]ti(w) = 1
t = g(t0), skw0[will¢w0,t0(kt0kw0T
iff for every j-best world z in f(s,w,t), there is a time t¢ such that
skt
T 0kw0[wash¢w0,t0,today¢(j, the-car¢)]ti(t¢)(z) = 1, and
Tf(s,w,t) ˙ skt0kw0[wash¢w0,t0,today¢(j, the-car¢)])]ti (t¢) „ f(s,w,t)
f(s,w,t) ˙ skt0kw0[wash¢w0,t0,today¢(j, the-car¢)])]ti (t¢) „ B,
and t¢ ˝ stoday¢tg.
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The truth conditions for (44) require the reference time to be prior to the speech
time and also a sub-interval of today. The truth conditions for (45) require the
reference time to be a sub-interval of today. But since the reference time is otherwise constrained by the Disparity Principle alone, the reference time can overlap
with the speech time and even extend into the past, as long as it remains a
sub-interval of today.
The theory presented here accounts for the contrast between (44) and (45),
whereas any standard treatment of will as a pure future marker does not account for
the contrast. In any such theory, (45) is predicted to only hold of an event completely
in the future. This is not to say that a pure future theory for will could not be
amended somehow to account for the contrast between (44) and (45), but it is not
easy to say what such an amendment would be.
The suggestion could be made that the puzzle has to do with the aspectual
structure of the relevant predicates. For example, wash the car is an accomplishment predicate, with an onset, an activity phase, and, a culmination phase.
Why not say that tense markers are sensitive to, not the entire interval of the
predicate, but just the interval associated with the culmination phase? A past
tense sentence still must be entirely about the past, since the past morpheme says
the culmination is prior to speech time, but the onset and the activity phase are
always prior to the culmination phase. The predicate will, on the other hand, only
says that the culmination phase is later than the speech time. The onset and
activity phase are prior to the onset time, so these could overlap with the speech
time and extend into the past. That would explain the difference between (44)
and (45).7
This objection ignores the problem of the frame time, however. It turns out that
the reference time must be contained within the frame time. (44) can only be true if
the washing event is contained within the speech day. The washing can’t have been
started on a previous day. Similarly, the interpretation of (45) requires the car
washing to have begun on the speech day.
A theory in which a tense marker only looks at the culmination phase of an event
should not put any restrictions on the onset and activity phases. It should be
acceptable in (44) for the car washing to have begun before today, and this does not
accord with intuitions. Similarly, in (45), the car washing could have begun before
today. By culmination-only theories, (44) and (45) would be equivalent to (53) and
(54), respectively.
(53)
John finished washing the car today.
(54)
John will finish washing the car today.
But such is not the case. In neither (53) nor (54) does it matter when the action was
begun, only that it is completed today. This is not true for (44) or (45), where it
matters when the activity was begun, and neither is it true for (46) or (47).
In my theory, the interpretation of will is constrained by the Disparity Principle,
whereas the past tense marker indicates that something occurred prior to the time of
speech. This represents two very different ways of placing an eventuality within time,
and we don’t find a symmetry in their meanings.
7
Mark Baker alerted me to the possibility of explaining these facts through a revision of tense
theory, such as the one mentioned here.
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6 Conclusion
In this paper, I have linked the temporal readings of modals to their modal readings.
The generalization for the class of modals I consider is that root modals are future,
and non-future modals are non-root and epistemic. The root/non-root distinction
concerns the modal base. A root modal base is the set of worlds that branch at the
time of speech. The non-root modal base is in effect a set of such branching structures. Given these assumptions, the temporal readings follow from two main interpretive principles.
The first principle is that the core proposition under the modal has to be true in
some but not all modal base worlds. For a root modal, this means the interpretation
has to be future. For a non-root modal, this means the speaker cannot know whether
the core proposition is true or false. The point of this principle is that the modal
conclusion should go beyond the information contained in the modal base.
The second principle is a conditional one. This principle requires that a modal
sentence should ignore unsettled differences between worlds. If there are settled differences to choose between, as with a non-root modal base, the principle makes the
temporal interpretation non-future. If there are no settled differences, as with a root
modal base, the principle is ignored. The point of this second principle is to enforce a
choice in the kind of modal conclusion to allow, whenever a choice is available.
An issue that arises involves epistemic uncertainty about the future. I have
argued that one can be uncertain about future facts which are virtually certain or
about future, non-determined facts. Future modals with existential force and a stereotypical modal base can have either meaning, and the sense in which they are
intended can only be determined on the basis of additional information.
Two predictions can be deduced from this theory. First, because modals like will
under a root interpretation are not temporal markers, future interpretations are not
a mirror image of past interpretations. Second, because an epistemic deficit about
future virtual certainties is recorded in the ordering source, may and might should
have future epistemic readings, but their dual will should not.
Acknowledgements I would like to thank members of my dissertation committee, Veneeta Dayal
and Mark Baker, for much assistance and discussion on issues in this paper. An anonymous reviewer
for Natural Language Semantics has raised challenging points, and I thank Angelika Kratzer for very
useful comments and examples. Mandy Simons has provided continuous support and encouragement.
Most of all, my dissertation chair, Roger Schwarzschild, deserves thanks for all he has done in seeing
this through. All shortcomings in the work are mine alone.
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