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Comparative Semantics for Nordic Languages
NORDSEM
Report 13
MODALS and MODALITY
Some Issues and Some Proposals
by
Finn Sørensen
Copenhagen Business School
August 2000
1. Introduction
How can we account for the characteristic semantic features of the class of verbs called
modals in a language like Danish? This is the main issue to be discussed in the following
pages.
This goal does not imply that all subissues known from the literature will find a place in the
discussion, nor that all issues mentioned in the paper will be solved. Maybe the most
significant proposal to be made is to organise the semantic field of modalities around what
will be called speaker information.
2. Preparatory Remarks
In this section I want to introduce some basic notions and distinctions in order to be able to
be as precise as needed in the following discussion.
2.1 Danish Modals
Danish grammarians normally classify the following verbs as modals (Mikkelsen 1911:349,
Rehling 1965:80, Diderichsen 1946:62):
(1) ville (want)
skulle (shall/must)
kunne (can/may)
burde (ought)
turde (dare)
måtte (must, may)
gide (feel inclined)
In my opinion only the verbs given in (2) are modals:
(2) skulle (shall/must)
kunne (can/may)
burde (ought)
måtte (must/may)
In modern Danish the verbs ville (want), turde (dare), gide (feel inclined), I think, are more
appropriately described or classified as attitude verbs, that is verbs used to ascribe a certain
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mental state or process to an individual. Heltoft 1999:73 also opts for the list in (2) rather
than the list in (1), while Davidsen-Nielsen 1990 and Brandt 1999 seem to stick to the list
given in (1). With one exception and one precision I will use the label modal of the verbs
given in (2). The exception concerns the verb behøve (need). Following Hansen 1972,
Heltoft 1999 and Davidsen-Nielsen 1990 I include this verb in the class of modals. As for the
precision I want to say that the verb måtte (must/may) correspond to two lexical items,
måtten (must) and måttep (may). The subscripts n and p should suggest necessity and
possibility, respectively, cf. also the English translations.
In the rest of this paper a modal is one of the six lexical items just mentioned. At this stage of
the discussion I take the characterisation as a list definition. It is nothing more than a first
approximation based on the grammatical tradition and in part established on hidden
presuppositions which will surface in the issues to be discussed.
2.2. Modal Constructions in Danish
As in other European languages modals are used according to the scheme in (3):
(3) NP Vm Vinf
where NP is the subject of the sentences, Vm is a modal, and Vinf is an infinitive phrase. An
example is given in (4):
(4) Det kan regne i Göteborg.
’It may rain in Gothenburg’
In order to have a name for the phrase Vinf following the modal I will call it the complement of
the modal.So in (4) regne i Göteborg (rain in Gothenburg) is the complement of kan (may).
Whether a verb is a modal or not will be decided (implicitly or explicitly) by the following
criteria: (i) the verb occupying the slot Vm in (3), and thus will be tensed, has a modal
meaning; (ii) the same verb, the supposed modal, does not impose any kind of selection
restrictions/appropriateness conditions on the subject; and (iii) the NP and the Vinf can be
combined in a sentence by selecting a tensed form of the lexical item underlying the
infinitive form used as head in Vinf. In (4) kan is the tensed form which is supposed to be a
modal. It is a modal because the verb has a possibility reading which is one of the modal
meanings (to be discussed presently); it is not the tensed verb, kan (may), which selects the
subject det (it), but the infinitive regne (rain); and det regner (it rains) is a sentence.
These criteria do not say anything about the infinitive marker at (to), which normally is
absent, but which may be used after behøve (need), cf. (5):
(5) Sandheden behøver ikke at komme frem nu.
’The truth need not be revealed now’
Note also that a verb like have, which normally is used to express possession, cf. Herslund
and Baron (to appear), can be used to express modality as in (6):
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(6) Du har at komme!
’You have to be there’
where the infinitive marker at is obligatory. There thus is an issue whether the criteria are
related to ’modals’ or ’modal uses of verbs’.
I also did not say anything about ’auxiliarity’, cf. the discussion in Davidsen-Nielsen 1990.
This problem concerns the categorial status of the unit occupying the place Vm in the
scheme (3). Some grammarians take the positions that the modal verb is an ordinary lexical
unit taking the Vinf as an grammatical object (Mikkelsen 1911) while others take modals to be
auxiliaries, or at least some og their uses (Davidsen-Nielsen 1990, Heltoft 1999). I return to
this issue. In characterising modal constructions by the scheme (3) I followed standard
practice. But when we talk about Danish, and not just English, it is important to note that
modals, as lexical items, have at least some of the forms normally associated with a verb.
The recognised and attested forms are presented in fig. 7:
Form
Present
Past
Infinitive
Participle
skulle(must)
skal
skulle
skulle
skullet
kunne(can)
kan
kunne
kunne
kunnet
burde (ought)
måtten/p(may/
must)
bør
burde
burde
burdet
må
måtte
måtte
måttet
behøve(need)
behøver
behøvede
behøve
behøvet
Verb
Fig. 7.
This formvariation opens up for more constructions than found in English, cf. the remarks in
Langacker 1991:271. In Danish we thus find modals embedded under the future marker vil
(will):
(8) Vi vil skulle lave planen om.
’We will have to change the plan’
And we also find modals in the present and past perfect:
(9) Kommunerne har skullet aflevere opgørelse af tekniske grunde.
’The local authorities have had to......’
(10) Kommunerne havde burdet gøre det af sig selv.
The local authorities HAD HAD to
Beside this constructional richness due to the number of existing word forms, Danish, and
other German languages, has a construction of the form given in (11):
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(11) NP Vm PP
and exemplified in (12):
(12) a. Peter skal i skole.
’Peer MUST in school’
b. Peter bør i skole.
’Peter MUST in school
c. Peter må i skole.
’Peter MUST in school’
As should be evident from the examples and their glosses there is no infinitive following the
modals, but only a PP. The modals, which can be used in this construction, are of the type,
which expresses a kind of necessity. So you can use mitten (must), but not måttep (may).
And it is impossible to use kunne (can/may). Furthermore the PP has to denote a direction,
not just a location.For precision see Hansen 1972, Heltoft 1999 and Boje (to appear).
2.3 Modal Structures
The traditional way of looking at the semantic structures carried by modal constructions is
that the modal verb indicates or expresses an attitude (of the mind of the speaker) towards
the content of the sentence containing the modal,cf. Jespersen 1924:313. This view of
modal structures fits well with the logical approach to modality in this century (see Kneale
and Kneale 1962 and Hughes and Cresswell 1968) because logicians also distinguish
between two elements in a modal structure, i.e. a modal operator and a (descriptive) position
being an argument of this operator. So a modal structure seems to have the structure given
in (13):
(13)
modalising attitude
modal operator
Modal structure
descriptive content
proposition
which can be written as in (14):
(14) mod (p)
where mod is a modal element associated with a modal and where p is a unit containing the
descriptive content of a modalised sentence, i.e. proposition.
In order to have an well-adopted terminology I will call the element mod in (14), and thus the
corresponding element in (13), the modaliser. The intention is that the modaliser is a
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semantic element which has its origin in a modal and which, as a consequence of its
semantic properties, has a semantic effect on the rest of the modal structure, which I will call
the modalised part/proposition/etc of the modal structure. Note that the binary structure at
the semantic level, here something like (14), does not correspond to the syntactic structure
in (3) that has three constituents. So in order to relate (3) and (14) some mechanism must
impose the isolation of the modaliser and the combination of the object associated with the
subject and the complement of the modal utterance. This mechanism could be either a
raising rule (subject-to-subject raising), see Vikner 1988:13 for a discussion of Danish and
Postal 1974 for a general discussion. It could also be a less dynamic mechanism as the
typed feature account proposed in Sag and Wasow 1999. My point at this stage is that the
assumption of (3) and (14) produces a mismatch between syntactic and semantic structures
for which one has to compensate if syntax and semantics are seen as related domains.
2.4 Situation Semantic Assumptions
This paper is intended to be a continuation of the discussion presented in Sørensen 1999
and a step toward an informational based theory of modality expressed in terms of semantic
objects being elements of the type of semantic universe used in situation theory (Aczel and
Lunnon 1991) and situation semantics (Barwise and Cooper 1991). However, I do not intend
to go into more formal and technical details than needed for the discussion of modals and
modality. At this point I just need a few concepts which are ’innocent’ in the sense that they
are borrowed from the existing literature on situation semantics. Note that except Schulz
1993 and Barwise (in press) there seems to have been no attempt to construct a modal
theory in a situation semantic context.
In situation semantics the basic claim with respect to language is that an utterance u carries
(or gives/conveys etc.) the information that y under the circumstances c. For the present
purpose I will take the part ’that y’ to be a proposition. So a grammar of Danish must
calculate a set of propositions by means of a recursive process which combine the signs of
Danish in a way similar to the proposals made by Cooper in a number of works, the most
recent and encompassing being Cooper 1994. Note that the result obtained by these
assumptions is not a ’pure’ semantic universe, but a linguistic universe in which syntactic
and semantic objects are paired under certain circumstances.
For the purpose of this paper I assume that the grammar outputs simple kernel sentences
which each becomes associated with a proposition. By a simple kernel sentence is meant a
sentence with a tensed verb, past or present, which are combined with all the arguments
specified in its lexical representation. So there are no ’missing’ arguments and no modifiers
of the verb or the sentence. Verbs starts out in the lexicon as lambda expressions of the
form  [a, b] where the object a has the form Sub, that is a parameter X indexed with sub
from the index set I={sub, obj, adj}. The members of I should suggest the grammatical
relations subject, object and adject used in the valence theory proposed by the present
author in collaboration with Michael Herslund (Herslund and Sørensen 1993, 1994, and, as
far as adjects are concerned, Davidsen-Nielsen 1996). The object b has the form s |= <<rel,
xsub, …>> where rel is the relation carried by the verb, xsub the parameter touched by the
abstraction, and the dots are the rest of the arguments of the verb. To have a name of the
lambda expression introduced above I call it the (basic) v-object. In this context the v-object
is the representation of an infinitive phrase, i.e. a phrase containing an infinitive of some
verb and its complements.
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Semantically speaking a v-object becomes a proposition by being applied to an appropriate
object oi. So applying  [a, b] to oi gives s |= <<rel, osub, …>>, a standard proposition in
situation semantics. Note that, if I wanted to accept (14) I could say that the modal
construction in (3) produces (14) by applying the s-object (the object denoted by the subject)
to the c-object (the object denoted by the complement), which is a v-object, and by letting
the vm, the modal, be associated with a standard modal operator of the type mentioned in
(13) and (14). At this point I only make the claim that the vinf in the modal construction in (3)
is associated with a v-object. And, as I do not want to discuss all the objects that can be
associated with the subject, I just write: osub. Note that osub is not an object of the theory but
just a way of saying that here is the s-object.
3 . Possibilities
What is the subject matter of modal utterances (or modal discourse)? It is, I claim, the
possibilities which remain when you in a certain context take away what is assumed to be
actualities and what thus must be impossibilities.
This claim can be made precise in the following way where I follow Barwise (preprint) up to a
certain point. Let S be a set of situations. S is supposed to be non-empty and to contain all
situations about which a speaker has a certain amount of information. Furthermore let  be a
set of state of affairs (or soas). A soa  () has had many names in the literature on
situation theory/semantics. I have chosen soa because it fits well with Danish where we call
it ’sagforhold’. Other terms that have been used are type, fact and infon. A soa is intended to
be an object that represents information about a situation. Finally, we may define an
information context as the tuple <S, , |=> where |= is a subset of (S x ) and where ”s|= ” is
a proposition stating that ”s supports ” or ”  is about/holds of s”.
Given a particular information context C we define:
(15) a. The state of a situation s is the set of soas s ={|s|=}.
b. A state  (or a soa ) is realised in the situation s iff  =s (or   s)
c. A state  (or a soa ) is impossible if  (or ) makes C inconsistent
d. A state  (or a soa ) is possible if s (or   s) for all s in C
and if  (or ) is not impossible in C.
As said above an information context C is intended to be a model of the information
available to the speaker, that is a kind of deictic information centre which is used by the
speaker engaged in information exchange in a discourse and which may and often will
change over time.
The important and linguistically relevant features of an information context is:
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(16) a. Whenever the speaker gets more information fewer possibilities will
be available to him, and vice versa.
b. Whenever the speaker has the information that some soa 
holds of the situation s (s|=)  is not a possibility for him.
c. Speakers with different information contexts have
different sets of possibilities.
d. All modal utterances are about possibilities.
(16d) is the property of an information context I will focus on in this paper. It means that one
of the features of a modal utterance is that the embedded soa in the proposition associated
with it is claimed to be a possibility in relation to the information context C a of the speaker a.
(4), for example, claims that the described soa is a possibility and it can only be used by a
speaker who lacks the relevant information about the weather in Gothenburg. Note also that
a negated version of (4) also is about a possibility. But it claims that the described soa is
impossibility in relation to the information context of the speaker, maybe because he has the
information that it does not rain in Gothenburg.
4. Motivated Possibilities
When a speaker a claims that something  is a possibility in C, he does not just claim that 
is possible. He also (implicitly) claims that he has some amount of information in C which
motivates his choice of the possibility  rather than any other possibility ’ available to him
given C. This picture of the context of modalised utterances, which I claim to reflect the
facts, can be illustrated in the following way.
Let (17) be the question my college asked me the other day because we both are going to a
meeting in Gothenburg and (18) be my answer:
(17) Hvordan er vejret i Gothenburg når vi kommer derop?
’ How is the weather in Gothenburg when we arrive?’
(18) Det kan regne (for normalt regner det når jeg kommer derop).
’It may rain (because normally it rains when I am there)’
Although the main clause in (18) is not a resolution of the issue raised by (17) it presents a
’possible resolution’. This resolution, which only is one of the possible resolutions given the
raised issue, is claimed to be a possibility by (18) but it also is motivated by (18), i.e. by the
for-clause (because-clause). So the information given by (19) is what I called the motivating
information:
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(19) Normally it rains in Gothenburg when I am there.
and the motivated possibility corresponds to the possibility introduced by the main clause in
(18). Note that from a linguistic point of view the motivating information is introduced by an
adjunct and that its function in the given context is both to select one of the possible
resolutions to the raised issue and to point it out as being the most likely possibility given
(19).
I now want to consider the proposed analysis of (18) to reflect the facts and to consider the
sketched picture of motivated possibilities as a plausible and still partial model of what is
going on in the utterance situations containing modals.
In a sense the proposed analysis, and thus the sketched model, is not surprising. Up to a
certain point it follows the pattern used in Mikkelsen 1911:349f to give a paraphrase of
modal utterances. In particular he uses the preposition ifølge (in accordance to/with) to say
that a modal claim is a claim which is in accordance with a law, some state of affairs, an
established norm, what is suitable in a certain situation, etc. I think that his use of ifølge is
significant because it means that something, here a claim about something being a
possibility, is said to fall within the class of instances which are consequences of the
information pointed out by the object of the preposition, e.g. the motivating information.
I also think that my approach is close to more recent proposals in the literature on modals
and modality. Kratzer (1981) uses a possible world approach in which a proposition p is a
possibility in world with respect to the conversational background f iff p is compatible with f
(w), the set of propositions which ’is known’ in w. It is clear that this approach contains
components having the same function as in the approach proposed here. However, I have
problems with her conception of the relation between a conversational background and a
proposition claimed to be possible. The reason is that the compatibility condition does not
restrict the choice of possibilities in a context as a function of its content, but only in terms of
truth-values. So if I said (20) in the context of (19) and if that context did not contradict the
possibility alluded to by (20) then this possibility is a possibility in the context (19):
(20) Peter may be snoring.
But such an approach is on the wrong track, I would claim, because modals are used to
point to possibilities which are motivated by the context, not just compatible with the world(s)
specified by the context.
That the context is a crucial element for the understanding of the meaning of modals is by
now, it seems, part of the general assumption made by different schools, see Klinge 1983,
Kratzer 1977, 1981, Papafragou 1998 and Sweetser 1990. But none of them, as far as I can
see, really catch what I have called motivated possibilities. So let me make this idea a bit
more precise as illustrated in (21):
(21) The information that Ba suggests the possibility that 
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In (21) Ba is supposed to be part of Ca, the information context C of the speaker a. And the
idea of making Ba a motivation of the possibility  is transferred to an unknown suggestrelation. The intended claim is that the information in Ba, and thus the content of the relevant
propositions, in some way to be made precise presently, allows the speaker to infer  rather
than any other possibilities.
Unfortunately (21) creates two not-so-easily-solved problems. The first concerns the
problem of how we integrate Ba as a component of the meaning of modals. The second
concerns the problem of how we can state more explicitly what it means for some
information to suggest some other piece of information. Before I propose a tentative solution
I want to look at some other semantic features which has to be integrated in the solution to
the two problems just mentioned. But as a first approximation to motivated possibilities I will
make use of (21).
5. Epistemic and Deontic Possibilities
5.1 Preparatory Remarks
So far I have talked about possibilities as a class of soas which was possibilities as a mere
consequence of what happened to be the actual information. But as is well-known from the
literature there are different kinds of possibilities, e.g. epistemic and deontic possibilities, a
categorisation which, as far as I know, goes back to von Wright 1951. This classification has
been adjusted and modified in many works on modality each time motivated in a different
approach to or a different perspective on modality. For Danish see Hansen 1972, DavidsenNielsen 1990, Brandt 1999, Heltoft 1999 and Boje (to appear). In my opinion there is a
primary classification of possibilities in two classes, roughly corresponding to the
classification alluded to above. This classification has, however, nothing to do with the
inherent properties of possibilities. It is imposed on possibilities from the outside, e.g. from
the motivating information. Contrary to the most recent descriptions of Danish (see the
references some lines above), I thus want to maintain a binary classification. So it cannot
surprise that I will define the traditional distinction in terms of the motivating information B a in
some information context Ca.
5.2 Epistemic Possibilities
In order to illustrate what I mean by a possibility that is epistemic because of the nature of
the motivating information I will propose an analysis of the utterance given in (22):
(22) Peru og Japan skal forhandle med guerillaen.
’Peru and Japan is going to negociate with the guerillas’
(22) is an authentic example from the texts collected by the members of the Nordsem
Group. And it is clear from the context that the speaker using (22), a journalist wants to
inform the reader about a possibility, namely the possibility that the two states negotiate with
the guerrillas. But he also says that this possibility is motivated by some piece of information.
Which piece of information is relevant is not part of (22), but in the text surrounding (22) it is
clearly stated that the political leaders of Peru and Japan have decided to negotiate with the
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guerrillas. So the information available to the speaker, here the journalist, is the fact that
Peru and Japan have decided to negotiate with the guerrillas at some point in the future.
The speaker presents this fact by saying that the negotiation situation is possible (and in fact
necessary) by using the present form skal (MUST) of the modal lexical item skulle.
In general skulle is used to indicate that someone intends to do something or plans to do
something. But used in the epistemic mode skulle does not necessarily mention the ’source’
of the intention or the plan. The role of skulle is only to say that the modalised information is
the content of someone’s intention or plan. Whether the speaker reports the content of his
own intentions or of other persons’ intentions seems unimportant. The importance of his
remark is that skulle selects possibilities which are marked or pointed out by the speaker’s
information as being the content of someone’s intention and that other modals which
express the idea of a necessity, namely the modals burde (ought) or måtte, cannot be used
to indicate that an information is the content of an intention.
The two exceptions to the intention claim made above is the fate or destiny meaning in (23):
(23) Vi skal alle dø engang.
’We all have to die some day’
and the hearsay meaning in (24):
(24) Præsidenten skal være syg.
The president MUST be ill
’The president is said to be ill’
I would say that these exceptions are extensions of the intentional uses of skulle. But I
refrain from doing it here and now.
5.3 Deontic Possibilities
The sentence in (22) could have been used in a another context to say that someone, here
the political leaders of Japan and Peru, are obliged to negotiate with the guerrillas. I refer to
this use of skal by (22’). In this case the appropriate English modal is must. A suitable
context for this meaning could be an UN convention regulating the actions of political
leaders in conflicts involving guerrillas.
In (22’) the speaker, maybe the chairman of the UN’s Security Council, has the information
that is written down in the convention concerning guerrillas. The information given by the
convention creates a certain amount of possibilities (and impossibilities) involving an agent,
here the political leaders in question. But it is not just an agent; it is an agent that has the
responsibility of participating in a soa so that the soa becomes realised in a certain situation.
So in my terms (22’) means (25) where I use the ifølge-paraphrase (in accordance with)
introduced earlier:
(25) Ifølge FN’s konventioner har Peru og Japan her og nu ansvaret
for at forhandle med guerillaen.
’In accordance with UN’s convention Peru and Japan has, here and now,
the responsibility for negotiating with the guerrillas’
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Before integrating the relevant parts of (25) in the model of a speaker’s information context I
will briefly comment on (25). Note first that what is directly pointed out by (25’) as being the
meaning of (22’) is a possibility , the possibility in which Peru and Japan negotiate with the
guerrillas, and a modaliser, here the kind of necessity which can be imposed on a possibility
by the verb skulle (MUST). The fact that the two states in the utterance situations are
responsible agents stems from the convention in the information context. Note also that I
have included a ’here and now’ in (25). This space-time location of the responsibility has the
effect of locating the realisation of the negociation in the future, a not so bad property given
the fact that any obligation (or permission) is about the possible realisation of something at
some point in time after the obligation (or permission). So let me now turn to the problem of
making this more explicit.
5.4 Concluding Remarks
It is clear that the kind of information context I introduced in 3. does not contain sufficient
structures to account for the distinction between possibilities which are claimed to be either
epistemic or deontic. One way to proceed is as follows. Given a particular information
context C as defined in (15) we add to the definition a set A of agents. Agents are to be
thought of as constituents of one or more soas in C and the constituent in a soa that brings
about the soa. We next impose on C a partition (d, r) where d is the set of ’purely
descriptive’ propositions and where r contains those descriptions that regulate an agent’s
participation in certain soas. The kind of propositions I am thinking of in connection with the
described partition of an information context can be exemplified in (26):
(26)a. The plan of Peru and Japan is to negotiate with the guerrillas.
b. UN’s convention prescribes that Peru and Japan has the
responsibility to negotiate with the guerrillas.
Note that both (26a) and (26b) are fact statements that can be evaluated by an examination
of the world even if such a project may be difficult. Note also that both (26a) and (26b) are
about the same possibility, the possibility that the two states negotiate with the guerrillas.
And finally note that prescriptions, contrary to descriptions, involve some kind of transfer of
responsibility from the prescribing proposition to the agent involved in the realisation of the
prescribed soa. Such an agent is called an responsible agent, and any member of r, the set
of regulating propositions, is assumed to assign responsibility to some agent such that he
has the responsibility for the realising of some soa. Although a viscous circularity is close to
be involved in this formulation I will talk about descriptive and regulating propositions as
propositions which impose the not necessarily exhaustive classification of possibilities in
epistemic and deontic possibilities, respectively.
6. Possibilities and Necessities
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6.1 Opening Remarks
It is often claimed that modality has to do with possibilities and necessities or that modality
has to with epistemic and deontic claims, see e.g. Kratzer 1981 and Papafragou 1998,
respectively. It would not be wise to challenge such claims as they are often used in a
context where the authors want to point out the field of modality from a pretheoretic point of
view. But it is reasonable to point to what is missing in such characterisations.
What I am thinking of is that positive modal claims made by modalised utterances are
uncategoric with respect to the issue whether the soa associated with the modalised
utterance, e.g. the soa which is part of the proposition in a modal structure (see 2.3). So I
would say that modality has to do with uncategoric claims about the likelihood of the
realisation of a soa in some situation given a particular information context. I return to the
problem of categoricity presently.
There is another problem that rarely is discussed when the focus is on modality expressed
by modals. Many authors insist on the fact that modals are ambiguous with respect to the
difference between epistemic and deontic modality or other such differences. But they do
not insist on the fact that there rarely is a similar ambiguity in the use of modals with respect
to the possibility/necessity distinction. On the contrary, a modal, taken as a lexical item (or
lexeme), is born with either a possibility meaning or a necessity claim (see the remarks on
måtten and måttep in 2.1). This fact can not be neglected in a linguistic account of modality.
And given the fact that in my terms modals express ’realisation likelihood’ (and not
’realisation in some or all accessible situations/worlds’) there might be a likelihood marker
between possibility and necessity. Lars Heltoft claims that such a marker exists in Danish
(Heltoft 1999).
Before saying anything about my approach to possibilities and necessities I want to
introduce some useful terms and to present a methodological point of view concerning the
’distance’ between syntactic forms and semantic structures.
That part of the semantics of modals which concerns the distinction between epistemic and
deontic meanings will be called the modal type dimension. Theories may differ within this
dimension with respect to the number of distinctions judged to be empirically motivated and
with respect to the internal structure of the space of modal types. The part of the semantics
of modals which concerns the distinction between possibilities and necessities will be called
the force dimension. Theories may differs within this dimension with respect to how many
forces it is necessary to work with and how the forces are related. Finally, I will call the
motivating information Ba in a information context Ca the modal base, a term which has been
proposed in Kratzer 1981. Whatever Kratzer’s intention might be I use the term modal base
to designate that part of an information context C which is pertinent to the determination of
the modal type and which has consequences for the choice of a value within the forcedimension.
The methodological remark I wanted to make concerns the ’distance’ between syntax and
semantics, e.g. how much work do I have to do in order to get from a syntactic to a semantic
representation of an utterance containing modals. I think this kind of remarks is appropriate
in this modal context because the distance often is thought of as being rather long, cf. the
12
structural differences between a modal construction (see 2.2) and a modal structure (see
2.3). It should be clear that a position involving completely independence between syntax
and semantics would also allow a long distance and it could be fruitful for certain purposes
to look at the two domains as unrelated. But in what I call linguistic semantics the distance
between syntax and semantic is claimed to be short, the ideal being that it is a one-to-one
mapping.
6.2 Categoricity
Consider the sentences in (27) –(30)
(27) It rains in Gothenburg.
(28) It may rain in Gothenburg.
(29) It does not rain in Gothenburg.
(30) It may not rain in Gothenburg.
where the issue to be solved in the discourse situation is the question whether it rains in
Gothenburg or not. In this discourse situation it thus is clear which situation the discourse
participants focus on, namely the weather situation in Gothenburg within a certain space of
time. What is unclear to the speaker who raised the issue is which soa (or soas) is realised
in the situation in question out of a certain amount of possibilities. So the alternatives among
which a particular information context can select are different soas that may solve the issue
raised by the speaker, and not different situations.
With respect to the raised issue (27) presents a categoric resolution because the claim is
that the soa ,  = [it rains], is realised in s, the weather situation in Gothenburg. (29) also is
categoric because it claims that  is not realised in s. But it does not solve the raised issue,
it only excludes one of the possible resolutions. (28) does not solve the issue either, and it is
uncategoric with respect to the raised issue because  is neither claimed to be realised in s
nor claimed not to be realised in s. It only is claimed to be, in my terms, a motivated
possibility. So modal claims made by modalised utterances, I claim, are uncategoric claims
with respect to the resolution of a certain contextual known issue. At least when the modal
claim is positive. When the modal claim is negative, as in (30), the motivated possibility may
be the soa ,  = [it does not rain]. In this case the modal claim with respect to the raised
issue also is uncategoric because (30) does not entail that any specific soa is realised in s.
(30) could also be used to say that the possibility that it rains is an impossibility. In this case
(30) is, I think, categoric with respect to the weather issue because it denies that ,  = [it
rains], is a possibility, and thus by implication that  is realised in s. There are many aspects
of the catgoricity characterisation given above that is in need of being more clarified both
empirically and theoretically. For the moment I leave the characterisation as it is, and I
assume that it is clear what it means when I say that modal claims are uncategoric claims
with respect to a particular issue which orients the topic of the discourse towards the
information given by the soa embedded in a modal structure.
6.3 Possible possibilities
I now want to look at modal structures of the form (31):
13
(31) pos (p)
where pos is a particular modal operator and p is a proposition, cf. 2.3. (31) makes the
claim that p is possible. As propositions are declared to denote possibilities as a function of
a particular information context pos is nothing more than a marking of p as a possibility in
relation to the assumed C. In Danish possibilities can be introduced by the modal lexical
items kunne and måttep. The verb kunne is used to make modal claims in the epistemic
mode. And the modal måttep is used to make modal claims in the deontic mode, a
generalisation I will take to be true. So kunne means ’epistemically possible’ and måttep
means ’deontically possible’, the two modifying elements of ’possible’ being an effect of the
context in which the verbs are used.
I now want to propose that the modal structure (31) has to be changed to something like
(32):
(32) pos (s-object, v-object)
or in a more situation oriented notation something like (33):
(33) s |= <<pos, s-object, v-object>>
where s is some situation which is claimed to be about the s-object’s possibility of being of
type v-object. Note that I use s-object and v-object to denote the semantic objects denoted
by the subject and the complement of the modal, respectively. My preferred paraphrase of
pos as a modal relation is given in (34):
(34) a has_the_possibility_of_being_of_the_type b.
This paraphrase is motivated by the following considerations. The element has is there in
order to suggest that pos is an ordinary binary relation between two objects, e.g. a transitive
structure. The element has is also used in order to suggest that a possibility claim is a claim
which ’locates’ the type b in relation to the object a rather than the other way round, cf.
Baron and Herslund 1997 and the references given there. The element possibility is there to
indicate that pos makes a possibility claim, not about a proposition but about the possibility
that a is of type b. Finally, being_of_type is there to suggest that b, as an object, must be a
type. And it must even be an o-type of that kind which is represented by -expressions, cf.
the discussion in 2.4. So pos holds of two objects <a, b> if and only if a is an object, b is an
objecttype and a is of type b. And the possibility soa in (33) is realised in s iff in s pos holds
of <s-object, v-object>, that is if the soa obtained by applying v-object to s-object is a
possibility. The only difference between kunne and måttep is thus that kunne selects an
epistemic motivating context while måttep selects a deontic motivating context, a selection
pattern which, if seems to me, must be part of the semantic descriptions of the modals.
6.4 Necessities
In the tradition necessity was considered to be an operator like pos. I will call it nec. As with
pos I want to propose that nec is a relation, e.g. a binary relation between two objects, one
of them corresponding to a type.
14
In Danish strong possibility claims are made by the use of the verbs skulle, måtten, burde,
behøve. As there are special constraints on the use of behøve I will not say anything about it
here (see Hansen 1972, Heltoft 1999). As for the other three verbs I propose the structure
given in (35) and more situationlike in (36):
(35) nec (s-object, v-object)
(36) s |= <<nec, s-object, v-object>>
The relation nec is paraphrased as in (37):
(37) a is_by_necessity_of_type b.
The element is indicates that nec is a binary relation and that a is located in relation to b
(rather than the other way round). The element necessity modifies the location to be a state
towards which there is a strong tendency. And type makes it explicit that b must be a type.
So the nec relation holds of a pair <a, b> if a is of type b and if the soa obtained by applying
b to a is a necessity, that is a possibility in relation to the information context which is the
only alternative in that context. Note that a necessity does not imply that the possibility is
realised, but it does imply that the inverse possibility is not realised. So a sentence like (38):
(38) Peter må være i Paris nu.
’Peter must be in Paris now’
which is epistemic and expresses a necessity, does not imply that in fact Peter is in Paris.
But it does imply that ’Peter is not in Paris’ is not a possibility.
6.5 Conclusion
The distinction between possible possibilities and necessities is a distinction that is lexical
determined. So each modal lexical item is used to make either possibility claims or necessity
claims. As semantic properties they belong to a force dimension and expresses different
forces with which a possibility is pointed out or suggested by the motivating information in a
given context, that is a modifying element which is added to the suggest-relation mentioned
in (21). Let us now say that some amount of information I suggests the information that  is
realised in s if and only if:
(39)a. I is a part of C, the context information available
to the speaker.
b.  is possible in relation to I.
c.  is part of some situation s’ in I (but not realised in s’).
d. s is possible in relation to I, that is for some soa ’ which is possible
in relation to I ’ could be realised in s.
15
e. For some soa ’’ ’ is realised in s in relation to I.
Roughly speaking (39) makes the following claims in order for the suggest-relation to hold.
(a) is a reminder of the context dependency of the characterisation. (b) states that  must be
possible not just in C but in particular in relation to I. This condition follows from the general
use of information contexts. (c) is a tentative proposal that makes clear what it means to be
a motivating context. The condition says that , the soa referred to in a modalised utterance,
must be part of I without being realised. (d) should be evident, and (e) says that s, the s in
which  might be realised, must be known to the speaker because some soa supports s in I.
Given (39) it is easy to see how the destination between possible possibilities and necessary
possibilities can be obtained by way of standard quantifiers over possible states in the
following way. A possibility claim means that there is a possibility  such that  satisfies the
conditions in (39). And a necessity claim means that for no possibility  it is the case that 
does not comply with the conditions in (39). So (39) is an explicit way of saying what it
means for a piece of information I to suggest that something is the case, the crucial
conditions being (39c and e). And this then can be used to quantify over possible states to
obtain the distinction between a weakly suggested possibility (a possible possibility) and
strongly suggested possibility (a necessity).
7. General Conclusion
In the preceding sections I have claimed and to some extent demonstrated that:
(40) a. Modal claims are uncategoric claims.
b. Modal claims are possibility claims relative to some fixed
context information.
c. The classification of modal claims in epistemic and deontic
claims is imposed by the information context.
d. The deonticity of a deontic claim depends on an information
context in which an agent is declared to be a responsible agent.
e. Modal relations are binary relations.
f. Modal claims are about motivated possibilities (or suggested
possibilities).
g. Suggested possibilities and necessities involves quantification
over possibilities determined by the information context.
In a linguistic context (40a), (40b), (40e) and (40f) seem to be underestimated by the
literature I know of. In connection with Danish I think that the theory developed here must
pass at least three tests to be accepted as a tentatively accepted explanatory theory. It must
predict the possibility of having structures without infinitives and with PPs, see 2.2. This kind
of prediction is prepared by the two kinds of modal relations, have-modalisers and is16
modalisers. In this connection I cannot retain the information that Chomsky has stated
somewhere that for a person a to have the language L means that L is in (the mind of) a.
This is the kind of inversion I thought of when I proposed the paraphrases of the modality
relations. The second test concerns the embeddability of modals under other modals. I think
that a theory of Danish modals should have something to say about the embeddability of spassives and blive-passives under modals, an issue which has been known since Mikkelsen
1911 and which is discussed in Heltoft 1999. Finally there is the issue whether all kind of
modalities can be embedded under all modals. So there is still work to do.
17
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