Abstract In this paper, I argue for two principles to determine the temporalinterpretation of modal sentences in English, given a theory in which modals areinterpreted against double conversational backgrounds and an ontology in whichpossible worlds branch towards the future. The Disparity Principle requires that amodal sentence makes distinctions between worlds in the modal base. The Non-Disparity Principle requires that a modal sentence does not make distinctions on thebasis of facts settled at speech time. Selection of the modal base will set these principlesagainst 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 anon-root modal base, the principles cooperate. Non-disparity determines a non-futureinterpretation and disparity requires the sentence to go beyond what is known by thespeaker.

Keywords Future interpretation of modals Æ Branching worlds

1 Introduction

In this paper, I attempt to derive the apparent temporal ambiguity of a class ofmodals 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, USAe-mail: twerner@andrew.cmu.edu

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Nat Lang Semantics (2006) 14:235–255DOI 10.1007/s11050-006-9001-8

ORI GI N A L P A PE R

Future and non-future modal sentences

Tom Werner

Published online: 5 December 2006� Springer Science+Business Media B.V. 2006

(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 ofaffairs or about some future happening. (l) could be said about Jim’s not beingcurrently visible among an assembly of guests, or it could be said about his being lateto a future event. (2) could be said with reference to a phone that is now ringing, or itcould be said in projecting who some winner will be. (3) could be said about acurrent possibility of where Jill is, but it could also be a form of permission with afuture 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 onthe part of the speaker about our current representative, or it could be talking abouta future impossibility for John.

The same sentences are also apparently ambiguous with respect to their modalreadings, and in particular with respect to root versus non-root interpretations. Iassume that the epistemic reading, for all cases, except possibly (1), is a non-rootinterpretation. (1) and (2) are both either epistemic or stereotypica1. The stereo-typical reading is a root modal interpretation and is based on what a normal state ofaffairs is. (3) and (4) are both either epistemic or deontic. A deontic reading is a rootmodal interpretation and is based on some set of normative standards. Finally, (5) iseither epistemic or circumstantial. A circumstantial reading is a root modal inter-pretation and I assume that it is based on laws of physics or biology or some otherinviolable laws.

My claim is that the temporal readings are associated with particular modalreadings; and I adopt the position strongly implied in Kratzer (1977) by whichdifferent modal readings are due to contextual dependence and not to lexicalambiguity. It is consistent with this assumption that the differing temporal inter-pretations are also not due to lexical or syntactic ambiguity, but derive from thecontextually sensitive nature of modals. For the purposes of this paper, I take thestrong position that there are no syntactic differences within this class of modals intheir root and non-root readings. This position differs from a number of proposals inthe 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 arelike intransitive verbs and lack any such subject. Lightfoot (1979) gives a theory bywhich non-root modals are in effect raising verbs, while root modals are controlverbs.1 Cinque (1999) posits that epistemic modals appear in a higher position thanroot 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 thatepistemic may is a raising verb, or intransitive in Ross’s sense. However, the examplesin (1)–(5) suggest that there is little or no syntactic difference associated with thedifferent modal readings, At the very least, the idea of syntactic differences betweenmodal 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 interpreta-tion. For now, I have no evidence that the differences in temporal interpretation aredue to any syntactic differences for the English modals I am considering.

My claim is that the contextually dependent temporal interpretations correlatewith the root/non-root interpretations of the modals, and further, that thatdistinction involves an ontology of branching worlds. The branching worlds ontologyincorporates the idea of indeterminism, entailing a basic asymmetry between thefuture and the past. Worlds in a branching structure are the same up to the time ofbranching, in the strongest sense of being identical and not merely similar. I willadvance the idea that a root modal has a base consisting of a single branchingstructure that divides up at the time of speech. The modal base for a non-rootepistemic modal will in effect consist of a set of such branching structures.

One consequence of the asymmetry between the past and present versus thefuture 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 currentstates of affairs. Either way, this is uncertainty about existent facts, or previouslyexistent facts. On the other hand, we can be uncertain about the future in twodifferent ways. We can either be uncertain about virtual certainties, or we can beuncertain 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 takeit. Perhaps John is taking the train to get here. Since trains are a reliable form oftransportation, his being on a train virtually guarantees that he will arrive at a fixedtime. However, if we don’t know which train he has taken, we can still be uncertainabout 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 muchless fixed. Any number of chance happenings may now befall him, and when con-sidering his arrival time, we experience a different kind of uncertainty.

Besides the branching worlds ontology, which shows up as a difference betweennon-root and root modal bases, we also need certain interpretive principles. Theinterpretive principles make sure that we make distinctions between worlds in themodal base, and that we make the right kinds of distinctions. There are two maininterpretive principles. One of these requires that distinctions of some kind be made.The other requires that future differences are ignored if past and present differencesare in play in the modal base. The non-conditional nature of the first principleguarantees that it will always be followed, and it results in a future interpretation forroot modals. The conditional nature of the second principle means it is only followedwhen 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 thatpast and future temporal interpretations are asymmetrical. Because modals are nottense markers, a future interpretation will be unlike a past interpretation. Whereas apast tense interpretation requires an event to be wholly contained in the past, afuture interpretation requires only part of an event be contained in the future.

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Another prediction concerns future epistemics. Since future epistemic uncertaintyinvolves the ordering of worlds rather than type of modal base, we expect existentialmay or might, but not their dual, will, to have future epistemic readings. This con-trasts with non-future epistemics, where universal must, along with existential mayand might, gets an epistemic reading. The reasons for this difference will be ex-plained below.

These predictions are a noteworthy difference between my theory and previoustheories concerning the future interpretation of modals like will, may, or might. Atheory in the literature similar to mine in certain respects is Condoravdi (2001).Although Condoravdi (2001) anticipates several ideas in this paper, the theoriesdiffer 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. Condoravdiproposes that one kind of modal base (‘ metaphysical’, in her terms) is a set ofbranching worlds and another kind (‘epistemic’) is a collection of worlds that canbe divided into such branching structures. In her theory, two interpretive principleswork together to derive the right kinds of modal interpretations, given suitabletemporal ones. Her Settledness holds for non-future facts; her Diversity Conditionrequires— for an existential modal—that the core proposition under the modal hasdifferent truth values in different worlds in the modal base.2 Together, theseprinciples require that if an existential modal sentence is non-future, it has anepistemic 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 apresent–future interval, and thus receive either a future or a present interpretationwhen there is suitable disambiguation. In Condoravdi’s theory, therefore, modals aretense markers and quantifiers over possible worlds. There is no prediction thatevents mentioned in a future modal sentence need be only partially future.

Condoravdi also treats future epistemics and proposes that the modal base forthese is epistemic. Her approach does not predict that may or might but not will canbe interpreted as future epistemics.

The class of modals I am interested in is made up of may, might, will, can, andmust, and to the extent that it is still in use in modern English, shall. These aremodals in English which have neither a past tense interpretation or a counterfactualreading, with the exception of might. I exclude would, could, and should from anygeneralizations I make here, and I only include might under its non-past, non-counterfactual readings.

My generalizations are also only meant to apply to modals in English, because oftheir peculiar morphosyntactic properties. Modals in English appear to the left ofsentential negation, they cannot take aspectual inflection, and in standard dialectsthey cannot appear with other modals in the same clause. My assumption is thatmay, will, shall, can, and must all have a feature TENSE which is PRESENT, as doesmight under the readings I consider here. Due to the feature TENSE, these modals musthead any sentence which contains them. That assumption yields the result that modalsappear 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 prag-matics or felicity conditions, such as Groenendijk and Stokhof (1975), pointing out that theseproposals 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 giveto 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 interpretativeprinciple, the Disparity Principle, by which an epistemic modal sentence must gobeyond what is known by the speaker. In this section, I also argue that the DisparityPrinciple is not pragmatic and I discuss why modals are used as hedges, In Sect. 3, Ishow how the Disparity Principle, combined with a root modal base, yields futurereadings. In Sect. 4, I take up the issue of the temporal interpretation of epistemicmodals. In 4.1 I show how ordinary epistemics get their temporal interpretation. In4.2, I show how future epistemics get their temporal interpretation. In Sect. 5, Idiscuss a prediction made by my theory that is not made by theories in which will is afuture marker.

2 The Disparity Principle

In Sect. 2.1, I show how the Disparity Principle can be made part of a theory ofmodal interpretation. In Sect. 2.2, I consider whether the effects I have attributed tothe Disparity Principle are not simply due to scalar implicatures. This discussion willlead, in Sect. 2.3, to issues raised by a reviewer. My response there will lead me tobriefly consider the semantic difference between epistemics and evidentials. InSect. 2.4, I will take up the related issue of how the Disparity Principle accounts forwhy 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 thespeaker 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, andthey 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 misleadingthe hearer as to the speaker’s epistemic state, while a speaker of (8) who knew Johnwas awake would be lying.

This constraint on epistemic modal sentences does not follow directly fromstandard modal theory, such as Kratzer (1981a, 1991). According to that theory, withcertain 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¢ti(w) = 1 iff John is asleepin every j-best world in

Tf(s,w).

The modal base f here is epistemic, and the ordering source j is stereotypical. I makethe speaker an argument for the modal base, given that the epistemic modal basedepends in part on what the speaker knows. Here and throughout the paper, Iassume 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 betteraccording to the propositions in j(s,w), the ordering source, than any other worlds inthe modal base. If the modal is existential, ‘every’ in the truth conditions is replacedby ‘some’.

The truth conditions in (9) make no mention of time or tense. I will thereforerecast these truth conditions using a multi-sorted translation language which ex-tensionalizes worlds and time, using t0 as a designated variable which, when un-bound, 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 argu-ment 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 ofthe lower VP. (In this paper, I follow Ross (1969) in treating a modal as a verb withspecial 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 thesentence embedded under the modal has a present tense interpretation, withoutgiving 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(w) = 1 iff John is asleep at t in every j-best world in

Tf(s,w).

We find two occurrences of the designated temporal variable t0, one in the com-plement of the modal and one associated with the modal itself. As mentioned, Iassume that this modal contains the feature PRESENT as part of its lexical semantics.The designated temporal variable in the complement assures a present interpreta-tion 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 notknow whether or not John is asleep into the truth conditions. The constraint thatthe speaker does not know that John is asleep means that proposition does notcontain the epistemic modal base. The constraint that the speaker does not knowthat John is not asleep means that proposition forms a non-empty intersectionwith the epistemic modal base. We can capture this constraint by adding thefollowing clauses.

(14)Tf(s,w) ˙ skw0[asleep¢w0t0

(j)]ti „Tf(s,w).

(15)Tf(s,w) ˙ skw0[asleep¢w0t0

(j)]ti „ B.

According to (14), John can’t be asleep in every world in the modal base. Accordingto (15), John has to be asleep in some world in the modal base.

In this paper, I assume that the requirement that the embedded propositionis 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 DisparityPrinciple. For an epistemic modal reading, it means that the speaker does not knowthe truth value of the core proposition within the modal statement. For a root modalreading, 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 weakerof two related sentences, it can be inferred that the stronger version is not known bythe speaker to be true. Let us see if scalar implicature alone yields the constraint thata speaker of an epistemic modal sentence cannot know the truth value of theproposition 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) thestronger assertion.

This assessment of relative strength is justified by the version of Kratzer’s theoryadopted here, since by that version of the theory, for a true utterance of (8) only thebest worlds in the modal base are required to be worlds in which John is asleep. Thisleaves 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 allworlds from the common ground in which John is not asleep. If we equate thecommon ground with the epistemic modal base, then (16) is a stronger statementthan (8). (16) eliminates all epistemic alternatives in which John is not asleepwhereas (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 asleepshould 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 sen-tences 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 tenhours 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 thatshe worked for eight hours, since it entails it. But as (17) and (18) show, those twostatements can appear together. The implicature that the stronger statement is notknown 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 implicatureaccount. Scalar implicatures cancel, but whatever effect we are dealing with here isnot cancelled. This doesn’t mean that there is not also a scalar implicature involvedin the utterance of a modal sentence, but something else must also be involved. Itake 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 theeffects that I am seeking to explain with the Disparity Principle. The first part of thisobjection 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 implicaturemight be cancelled, what is known by the speaker is not what is relevant with respectto the first sentence in (19). What would be relevant is the maximal satisfaction ofcertain stereotypes. Or, in a second formulation, what would be relevant is whatfollows from a given piece of evidence and our stereotypes.

The view of scalar implicature cancellation assumed by the reviewer is apparentlyas follows. Implicatures can be cancelled just in case the meaning of the sentencewhich carries the implicatures is relevant in itself, apart from the implicatures. Forexample, the first sentence in (17) might be relevant if we are giving a bonus toanyone who worked on the project for 8 hours. The second sentence in (17) is notrelevant, but can be added to cancel the scalar implicature that Mary worked morethan 8 hours.

For the modal case, the meaning of the sentence would involve the maximalsatisfaction of certain stereotypes. The implicatures have to do with what thespeaker knows. If a case is designed by which only the meaning of the modal sen-tence 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 musthave touched the knife. In fact, we all know he did, since he confessedto 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 thefirst sentences in these examples is only what follows from the evidence, not theepistemic state of the speaker. Neither (21) nor (22) is strange, so there is no reasonnot to take the effect in question as due to a scalar implicature after all, according tothe reviewer.

The reviewer formulates what would have to be relevant about the modalsentence—for cancellation of scalar implicatures to be possible—in two ways, but byeither formulation, an issue is raised that goes to the very heart of the DisparityPrinciple. According to the first formulation, the context must be such that it is onlyrelevant 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, whatwould have to be relevant is not what is known, but what follows given some piece ofevidence 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 propositiontrue in stereotypically best worlds from a proposition true in all worlds in the modalbase? What is true in all worlds in the modal base is also true in all worlds in thestereotypically best worlds in the modal base. A proposition can only be true in theset of stereotypically best worlds in virtue of their being stereotypically best if it isnot true in all the worlds in the modal base. But that is the very thing the DisparityPrinciple guarantees. Thinking in terms of the second formulation, what matters iswhat follows from the evidence and the stereotypes. But a proposition can only besaid to follow from the evidence and the stereotypes if it is not true in all the worldsin the modal base. Again, it is the Disparity Principle that guarantees this.

Whichever formulation of cancellation we choose, in order for the meaning of themodal sentence to be relevant, the Disparity Principle must be in place. As long aswhat matters is what is true in the stereotypically best worlds, or what follows from aset of propositions, given certain stereotypes, this principle cannot be eliminated. Wecannot construct a case where all that is relevant is what holds in the stereotypicallybest worlds in an epistemic modal base, and not what holds overall in the modalbase.

How do we explain the examples in (21) and (22)? The reviewer’s claim is that allthat should be relevant is what holds in the stereotypically best worlds. What holds inthe 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, butthe modal sentence within (21) is not ruled out. (22) states directly that the speakerknows that there was carbon monoxide in the room, but the modal sentence in (22) isnot ruled out. It would appear, then, that we are seeing cancellation of a scalarimplicature in both sentences.

However, for these examples to be reliable counterexamples, we have to makecertain 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 interpretednot epistemically but evidentially. The set of propositions in an evidential modalbase 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 aproper subset—of the intersection of the epistemic propositions. That means thedisparity principle can hold in the evidential modal base for the embedded propo-sition, even if it doesn ’t hold in the epistemic modal base.

It makes sense that natural language provides a device for cordoning off somepart of a speaker’s knowledge and assigning it a special status. In (21), the modal isinterpreted with respect to the subset of the speaker’ s knowledge constituted bycertain physical evidence. The same is true for (22), where the subset of knowledge isconstituted by certain physical occurrences. Clearly it is convenient to be able pointout that something follows from certain types of very tangible knowledge—such asphysical evidence—even if access to general knowledge makes such statementsinformationally redundant. This is what the evidential modal base enables.

My conclusion is that scalar implicature does not fully explain the effects that Ihave explained by appealing to the Disparity Principle. In fact, it seems that theDisparity Principle is a necessary component in establishing the relevance of a modalstatement even in situations in which we are only interested in what is the case in thestereotypically best worlds.

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2.4 Modals as hedges

The operation of the Disparity Principle helps explain a certain feature in the actualusage of epistemic modals. Sentences in an epistemic mood appear in discourse inplaces where we might expect to find indicative mood, and the modal is a form ofhedge. The modal apparently lets a person say something without the same degree ofcommitment, and this effect follows in a straightforward fashion from the DisparityPrinciple.

The first point to make is that what counts as a deduction in actually occurringdiscourse is not necessarily what a logician would count as a deduction. Consider thefollowing real-life example.

(23) This clue enabled Holmes to deduce that the murderer must have beensomeone familiar to the victim’s dog because the dog did not barkwhen the murderer appeared. (Kardes & Sanbonmatsu, 2003)

Here we find the word deduce but this doesn’t mean that Holmes reached his con-clusion through the application of the kind of logical rules formalized in a naturaldeduction system. Such a deduction would involve paring down the set of epistemicalternatives, following a kind of update procedure. The end result would be that allthe worlds in the updated set would be worlds in which the murderer was familiarwith the victim’s dog. But instead, Holmes bases his reasoning on the backgroundknowledge that dogs tends to bark at strangers. This reasoning is based on what isnormal or stereotypical. The proposition that dogs tend to bark at strangers will becontained in the ordering source. Holmes reaches his conclusion by finding bestworlds 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 havenot pared down the set of epistemic alternatives to just the set of worlds in which themurderer is familiar with the victim’s dog. There is something provisional in thisreasoning because it is not strictly speaking a logical conclusion that Holmes hasreached.

Other examples show conclusions framed in modal statements where we seementitled to expect Indicative statements. In these cases, the modal apparentlyfunctions as a hedge. Consider first a made-up example.

(24)A: We know that either the butler did it or the maid did it, and weknow that the maid didn’t do it.

B: Then the butler must have done it.

From the premise that the butler did it or the maid did it, and the further premisethat the maid didn’t do it, the conclusion that the butler did it follows as a case ofDisjunctive Syllogism. The set of epistemic alternatives resulting from this updatewould only contain worlds in which the butler did it. But B does not say that thebutler did it, only that he must have done it, making it appear that the DisparityPrinciple is not in play in the interpretation of this modal. If it were, the interpre-tation of B’s response would require that the set of epistemic alternatives wouldcontain 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 anotherparty as 100% certain. In (24), it is evident that B has not fully accepted A’sassertion. Given the Disparity Principle, B’s statement indicates a reluctance toeliminate the possibility that the butler didn’t do it.

Other cases where one might balk at a definitive conclusion involve the com-plexity of the calculation. Consider a second real-life example. In this example, whatis being discussed is a puzzle in which one player is to arrange six red cards and oneblack card so that a second player turning the cards over one by one can at no pointdeduce that the next card is black.

(25) You cannot put it in the bottom, 7th position, for I can certainly deducethat it is black if I get down to the last card and I haven’t seen a blackone . . . What about the 6th position? Well when I get down to the 6thcard, I can deduce that it must be black since we have already eliminatedthe 7th position. (Felkins, 2000)

The question here is, why does the speaker say that for the 7th card one can deducethat it is black, but for the 6th card, one can deduce that it must be black? If you’veturned over six red cards, there is one short step to deducing that the seventh isblack. But if you’ve only turned over five red cards, the reasoning is more compli-cated. It has to include considerations of how far the first player has thought thingsthrough. When one reaches a fifth red card, therefore, it is somewhat premature toeliminate 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 ismeant to illustrate a mathematical deduction.

(26) We have a rule which states that the product of two negative numbersis a positive number.Thus, if we have the specific case of ()3) · ()4) we can deduce that theanswer must be a positive number. (A General Rule which helps us todeduce a specific case.) (E-Z geometry.com)

A rule is applied to get the answer, but the use of the modal suggests a certaintentativeness.

Here is one final example.

(27) In view of what the Weather Channel said it must be raining in Bostonright now.3

There is an interesting contrast to be made with respect to this example. Letus 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 inBoston? But there is an issue here involving the vagueness of language. Rain hasspread, but does that mean it is raining in every single location in that half of thestate 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. Con-junction Elimination gives us that it is raining in Boston. We hardly need a hedgehere, so (27) with its epistemic modal would be odd.

In actual cases in which a conclusion is supposed to follow logically from a set ofpremises, 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 asa modal assertion. Because of the Disparity Principle, this implies a reluctance toeliminate all worlds from the set of epistemic alternatives where the conclusion doesnot hold.

3 The future interpretation of root modals

In this section, I explain how the Disparity Principle, combined with the right sort ofmodal base, yields future interpretations.

In this paper, I adopt the idea of indeterminism, and this is reflected in the modelby having possible worlds that branch. Branching worlds are worlds that, up to agiven time, are identical in the strongest sense, and subsequently diverge. The firsttask, 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, aplurality 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 whenapplied to a world gives back the singleton set containing that world. In other words,for a totally realistic modal base fTR, for all w 2 W,

TfTR(W) ¼ {W}. The intuition is

that the totally realistic modal base is an exhaustive or unique description of thatworld. 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 weneed is totally realistic, up to a time. This function takes a world and a time asarguments, and gives back the set of worlds that branch from that world at that time.In other words, for a totally realistic modal base function up to a time fTR,

TfTR(w,t)

is the set of worlds that branch from w at t. In the rest of this paper, I will refer to thisfunction 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 tothe time of speech. Together with the Disparity Principle, we now have the toolsto 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-internalsubject hypothesis. Semantically, an ordinary VP will be type <i,<w,t>>, wherei 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 comple-ment, and in turn to combine with a higher auxiliary. If the auxiliary is tensed, then itis 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 thesame type as a tensed auxiliary: <<i,<w,t>>,<w,t>>. When such a modal combineswith 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 mustappear leftmost within a string of auxiliary verbs. My semantic theory does notdepend on this syntax, but it will make the presentation simpler.

Now we need to consider the truth conditions for a modal sentence with a totallyrealistic modal base and a stereotypical ordering source, such as (30). The syntacticstructure 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 fromtimes 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 basefunction f, and ordering source function j, with i = <s,g,f,j> andt = g(t0), skw0[will¢w0t0

(kt0kw0[fall¢w0,t0 (the-Sycamore-branch¢)])]ti(w) = 1 iff for every j-best world z in

Tf(s,w,t), there is a time t¢ such

that skt0kw0[fall¢w0t0(the-Sycamore-branch¢)]ti(t¢)(z) = 1; andT

f(s,w,t) ˙ skt0kw0[fall¢w0t0(the-Sycamore-branch¢)]ti(t¢) „

Tf(s,w,t); andT

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 atotally realistic modal base, the speaker argument has no effect, since the modal basein this case is objective and not particular to a given speaker. The ordering sourcetakes the same three arguments, something not reflected in the notation. For astereotypical ordering, as this is, the addition of a time argument helps capture theidea that what is normal changes over time. The speaker argument for j here has noeffect, but with an epistemic ordering source, it will.

The truth conditions for (34) yield a future interpretation. Every best world in themodal base is a member of some proposition or other that results when the core isapplied to some time. Any such proposition, according to the disparity clauses, mustcontain some modal base worlds and exclude others. Since the modal base is a set ofspeech-time branching worlds, a proposition true in some worlds and not others mustbe at least partly future. A time that combines with the core to form a propositioncontaining some but not all accessible worlds must be at least partly future withrespect 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. Thefuture interpretation of will comes from an interaction between the DisparityPrinciple and the totally realistic modal base. The ordering source here was ste-reotypical, 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 givesus root modals that are stereotypical, deontic, or circumstantial,4 which all saydifferent 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 thetemporal interpretation of epistemics relates to the ontological asymmetry betweenthe 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 offirst-order uncertainty. Past or present facts already hold or don’t hold. The onlykind 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 certainregularities, are virtual certainties. We can have certainty about these facts, but wecan also have uncertainty, if we don’t know what the regularities are. However, thereare other facts that are not fixed, knowledge or lack of it notwithstanding. I assumethat 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. Ouruncertainty here about the future is of a different order.

These different kinds of uncertainty are conceivable, but are they expressible innatural language? I will argue that English does distinguish between non-future andfuture uncertainties, but that it doesn’t distinguish between different kinds of futureuncertainty. There is no way to distinguish future uncertainty about what is virtuallyguaranteed from future uncertainty based on the indeterminacy of events. Onlyadditional information lets us know the intended meaning.

4.1 Non-future epistemics

In our theory, temporal interpretations follow from modal interpretations. Rootmodals get their temporal interpretation by a requirement that modal sentencesmake distinctions that go beyond distinctions implied by the modal base. Becausethe modal base is totally. realistic, the resulting temporal interpretation is future.Modals with a non-root interpretation—those interpreted with an epistemic modalbase—need to get a non-future interpretation. However, as before, we want thetemporal 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 thatexhaustively describe the past and present of the world of utterance. The epistemicmodal base is made up of a subset of these. Some propositions are missing, and theseare the ones still in play, epistemically, even though they are settled. By theDisparity Principle, distinctions must be made, but they must be made on the basis ofsettled facts. We add the Non-Disparity Principle in (35).

(35) A proposition must make no distinction between speech-time branchingworlds.

4 In Kratzer (1981a, 1991) the modal base is circumstantial, and for circumstantial modals, theordering 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 realisticmodal base, distinctions can only be based on non-settled facts. We therefore stip-ulate that the Non-Disparity Principle in (35) is violable, but the Disparity Principleis 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. Theresulting sentence has a non-future interpretation but comes with the requirementthat 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 thepossibility that John was sleeping earlier. In other words, with the auxiliary have, thesentence is past; without it, the sentence is present. But since either sentence makes adistinction 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 be-tween past, present, and future. One way to capture a three-way distinction iswith two overlapping two-way distinctions. I have argued that in English there is atwo-way distinction between Disparity and Non-disparity. What might be the secondtwo-way distinction that would result in the needed three-way distinction?

Enc (1996) mentions the idea, also reported in Ogihara (1989), that there is onlyone tense in English, past tense. She suggests (p. 356) that present is the absence ofpast tense. I interpret this suggestion to mean that tense is a two-way distinctionbetween past and non-past. With past tense morphology, there is past meaning. Withno past tense morphology, there is non-past meaning. Therefore I implement Enc’ssuggestion 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 speechtime 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,skw0[must¢w0,t0(kt0kw0$t[t < t0 & asleep¢w0,t(j)])]ti (w) = 1iff for some j-best world z in

Tf(s,w,t), there is a time t¢ such that

skt0kw0$t[t < t0 & asleep¢w0,t(j)]ti (t¢)(z) = 1, andTf(s,w,t) ˙ skt0kw0$t[t < t0 & asleep¢w0,t(j)]ti (t¢) „

Tf(s,w,t), andT

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 madewithin 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 whatthe 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 thatJohn 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 utteredby someone who doesn’t know the results of the decision.

In the situation described in (41), whom John meets tomorrow is a virtualcertainty. It is different than a settled fact, however.5 John’s meeting involves only aplan and is not part of the decided substance of any world. Therefore, we make thisvirtual certainty a matter not of the modal base but of the ordering source, and werecord the epistemic deficit there also. Worlds which differ only as to whether Johnmeets 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 universalsentence be true.

No linguistic means is provided to distinguish between future sentences with mayor might which are epistemic and those that are not. The truth conditions simply saythat there are some stereotypically best worlds (in the totally realistic base) in whicha certain outcome takes place. This is either because of ignorance on the part of thespeaker, or because the facts are not determined.

The difference in intended meaning can only be gleaned on the basis of extrainformation, 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 asthe speaker does not know this. However, there is something distinctly wrong withthe 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 orderingsource, which in either case is stereotypical. Since there is no way of indicatingwhether an epistemic deficit is involved or not, auxiliary information is the only wayto 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 epistemicmodal base.

(i) John might be meeting the dean tomorrow and he might be meeting theprovost.

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It is telling that existential may and might have readings as future epistemics butthat their dual will does not.6 The interpretation of future epistemics with may andmight involves an epistemic deficit resulting in otherwise resolvable ties betweenworlds in the ordering. These ties allow several existential sentences to be true, as wesaw in the discussion of (41). The corresponding will sentences are false when ut-tered by a person in the relevant epistemic state. There is no analogous case wherebya will sentence, or several will sentences, could be true in virtue of such ties, since thequantification is universal. This contrasts with non-future epistemics in which we findmay or might, which have existential force, as well as their dual, must, which hasuniversal force. This difference supports the idea that non-future epistemic uncer-tainty is recorded in the modal base but future epistemic uncertainty is recorded inthe ordering source.

5 A prediction about future sentences

In this final section, I show how my theory makes an additional prediction aboutfuture sentences, a prediction that appears to be borne out by the data.

The theory developed here derives the temporal interpretation of modal sen-tences from a requirement to make distinctions between worlds in the modal base, arequirement that ultimately may be tied to a prohibition against vacuous ordering. Inthe case of future sentences, the modal base is a set of branching worlds. Theseworlds differ only by future facts, and it follows that distinctions can only be drawnbetween these worlds on the basis of future differences. This is why these sentenceshave future interpretations.

This manner of deriving future readings leads to a prediction not made bytheories in which will is a future tense marker, or a combined future tense markerand quantifier over possible worlds. Such theories treat will as the reverse of apast tense marker. A past tense marker says that some state or event was prior tothe speech time. A future tense marker says that some state or event is after thespeech time. But a theory in which what matters are differences between possibleworlds isn’t like that. Differences with respect to the future can still extend intothe past.

At first glance, many will or might sentences do require eventualities to be whollyfuture. Here the expected symmetry between Past and will appears at first glanceto 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 starton washing the car, and then was called away on business. The car is sitting in thedriveway, half-washed. You believe his promise that he will come home later in theafternoon 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 withmodals 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 canoverlap with the present and extend into the past. For the past expression in (44), thecar washing definitely cannot extend into the future.

The contrast becomes clearer with the addition of certain expressions thatemphasize 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, butthe car washing in (47) needn’t be wholly future.

To give a semantics for these sentences, we need a way to deal with frame adverbssuch as today and yesterday. From von Stechow’s (1995) paper, I borrow the ideathat a past morpheme has two indices syntactically affixed. One of these denotes aninterval associated with evaluation of the predicate (the reference time, in vonStechow’s terms) and the other denotes a frame time as given by a frame timeadverb. The semantic translation for past is given in (48), which is also inspired byvon 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 timeis 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 theframe time or vice versa. For the cases I look at here, I assume that the referencetime is always a sub-interval of the frame time.

We can now give truth conditions for our sentences. Consider (44) with the truthconditions 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) andJohn 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 basefunction f, and ordering source function j, with i = <s,g,f,j> andt = g(t0), skw0[will¢w0,t0(kt0kw0[wash¢w0,t0,today¢(j, the-car¢)])]ti(w) = 1iff for every j-best world z in

Tf(s,w,t), there is a time t¢ such that

skt0kw0[wash¢w0,t0,today¢(j, the-car¢)]ti(t¢)(z) = 1, andTf(s,w,t) ˙ skt0kw0[wash¢w0,t0,today¢(j, the-car¢)])]ti (t¢) „ f(s,w,t)Tf(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 speechtime and also a sub-interval of today. The truth conditions for (45) require thereference time to be a sub-interval of today. But since the reference time is other-wise constrained by the Disparity Principle alone, the reference time can overlapwith the speech time and even extend into the past, as long as it remains asub-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 forthe contrast. In any such theory, (45) is predicted to only hold of an event completelyin the future. This is not to say that a pure future theory for will could not beamended somehow to account for the contrast between (44) and (45), but it is noteasy to say what such an amendment would be.

The suggestion could be made that the puzzle has to do with the aspectualstructure of the relevant predicates. For example, wash the car is an accom-plishment 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 thepredicate, but just the interval associated with the culmination phase? A pasttense sentence still must be entirely about the past, since the past morpheme saysthe culmination is prior to speech time, but the onset and the activity phase arealways prior to the culmination phase. The predicate will, on the other hand, onlysays that the culmination phase is later than the speech time. The onset andactivity phase are prior to the onset time, so these could overlap with the speechtime 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 thatthe reference time must be contained within the frame time. (44) can only be true ifthe washing event is contained within the speech day. The washing can’t have beenstarted on a previous day. Similarly, the interpretation of (45) requires the carwashing to have begun on the speech day.

A theory in which a tense marker only looks at the culmination phase of an eventshould not put any restrictions on the onset and activity phases. It should beacceptable in (44) for the car washing to have begun before today, and this does notaccord with intuitions. Similarly, in (45), the car washing could have begun beforetoday. 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 wasbegun, only that it is completed today. This is not true for (44) or (45), where itmatters 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 ofspeech. 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 tensetheory, 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 distinctionconcerns the modal base. A root modal base is the set of worlds that branch at thetime of speech. The non-root modal base is in effect a set of such branching struc-tures. Given these assumptions, the temporal readings follow from two main inter-pretive principles.

The first principle is that the core proposition under the modal has to be true insome but not all modal base worlds. For a root modal, this means the interpretationhas to be future. For a non-root modal, this means the speaker cannot know whetherthe core proposition is true or false. The point of this principle is that the modalconclusion should go beyond the information contained in the modal base.

The second principle is a conditional one. This principle requires that a modalsentence should ignore unsettled differences between worlds. If there are settled dif-ferences to choose between, as with a non-root modal base, the principle makes thetemporal interpretation non-future. If there are no settled differences, as with a rootmodal base, the principle is ignored. The point of this second principle is to enforce achoice in the kind of modal conclusion to allow, whenever a choice is available.

An issue that arises involves epistemic uncertainty about the future. I haveargued that one can be uncertain about future facts which are virtually certain orabout future, non-determined facts. Future modals with existential force and a ste-reotypical modal base can have either meaning, and the sense in which they areintended can only be determined on the basis of additional information.

Two predictions can be deduced from this theory. First, because modals like willunder a root interpretation are not temporal markers, future interpretations are nota mirror image of past interpretations. Second, because an epistemic deficit aboutfuture virtual certainties is recorded in the ordering source, may and might shouldhave future epistemic readings, but their dual will should not.

Acknowledgements I would like to thank members of my dissertation committee, Veneeta Dayaland Mark Baker, for much assistance and discussion on issues in this paper. An anonymous reviewerfor Natural Language Semantics has raised challenging points, and I thank Angelika Kratzer for veryuseful 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 seeingthis through. All shortcomings in the work are mine alone.

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