On Defining Modality

Home , Affect (linguistics), Alethic modality, Deontic modality, Epistemic modality, Modal operator, Propositional attitude

ON DEFINING MODALITY

FERENC KIEFER

1. INTRODUCTION The term 'modality' has been used to refer to a relatively great number of apparently disparate things in linguistic and logical literature. Sometimes modality has been restricted to expressions of possibility and necessity, in other cases it has been used äs a cover term for expressions of Speakers' attitudes. Modality may be identified with what expressions of propositional attitudes do in sentences,butit may also betaken to cover the meanings of a linguistically definable class of elements (modal auxiliaries, modal adver- bials, modal particles, parenthetical verbs, etc.). The logical tradition concentrates on the description of propositions. Consequently, the inquiry into modality is restricted to what may be considered to be 'propositional' in modality. The linguistic tradition, on the other hand, emphasizes the 'non-propositional' aspects of modality. It is pointed out that modal expressions in natural language are mainly used to express the speaker's attitudes toward states-of-affairs. In the present paper I wish to make explicit some of the notions of modality — I hope the most important ones — which underlie current inquiries into the problems of modality. The notions which I am going to discuss are the following:

(i) modality äs an expression of possibility or necessity, (ii) modality äs the meaning of propositional attitudes, (iii) modality äs expressions of speaker's attitudes.

I am going to show that the logical tradition and the linguistic tradition need not be in conflict, that there is a way to reconcile the two traditions.

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2. MODALITY AS AN EXPRESSION OF POSSIBILITY OR NECESSITY The notions of 'necessarily true proposition' and 'possibly true proposition' are well-known in traditional logic.1 A proposition is necessarüy true or necessarily false if its truth or falsity does not depend on the way the world actually is, that is, if its truth or falsity is already guaranteed by the very meaning of the proposition. On the other hand, a proposition is possibly (or contingently) true if it is not necessarily false and it is possibly false if it is not necessarily true. Though they represent distinct categories, necessity and possibility are not independent notions. Either one can be elimi- nated in favor of the other one. If we denote the necessity operator by and the possibility operator by 0 we may formulate the relationship between necessity and possibility äs follows.

(1) (a) D p = ~ 0 ~ p (b) 0 p = ~ D ~ p

In addition, the following two implications are valid.

(2) (a) D p => p (b) p =* 0 p

That is, from the fact that p is necessarily true it follows that p is true, and from the fact that p is true it follows that p is possibly true. The type of modality which is exclusively concerned with the necessary or contingent truth of propositions is often referred to äs logical or alethic modality. Examples for alethic modality with must and can are given in (3) (a) —(b).

(3) (a) Cats must be animals. (b) Cats can be dangerous.

By making use of the equivalencies in (1) (a)—(b) the sentences in (3) (a)—(b) can be paraphrased äs (4) (a) —(b), respectively.

(4) (a) It cannot be the case that cats are not animals. (b) It is not necessarily the case that cats are not dangerous. 69

Notice that the proposition Cats are animals is analytic, hence necessarily true. On the other band, the proposition Cats are dangerous is not analytic (it is contingent), hence possibly true. Alethic modality is a central notion in classical logic, in ordinary language, however, it is rather peripheric.2 Clear cases of alethically modal sentences do not occur frequently in everyday discourse. From a linguistic point of view the notions of epistemic and deontic modality are nrnch more important. Epistemic necessity and epistemic possibility are expressed by contingent propositions, i.e. not only 0 p but also depends on what the world is like. The proposition p is epistemically necessary iff p is entailed by what the Speaker knows about the world and the proposition p is epistemically possible iff p is compatible with what the Speaker knows about the world. The speaker's knowledge is representable äs a set of propositions.3 Epistemic necessity and epistemic possibility are interdefinable in the same way äs alethic necessity and alethic possibility are, i.e. the equivalence relations in (1) (a) —(b) hold with equal force in the case of epistemic modalities äs well. In addition, the implications (2) (a) —(b) remain valid. The following sentences may be illustrations of epistemic possibility and epistemic necessity, respectively.

(5) (a) It can be raining in Budapest, (b) It must be raining in Budapest.

The meaning of (5) (a) can be circumscribed in the following fashion: "In view of what I know it is not excluded that it is raining in Budapest". The sentence (5) (b), on the other hand, may be given the following Interpretation: "From what I know it follows that it is raining in Budapest". The deontic modalities have to do with Obligations and permissions* Instead of the modal operators D and 0» deontic logic exploits two deontic operators usually denoted by O (for 'obligatory') and P (for 'permitted'). Something is considered to be obligatory or permitted with respect to some moral or legal System (with respect to a System of laws). Ä proposition^? is obligatory iff it is not permitted that ~ p and it is permitted iff it is not obligatory that ~ p. These are the deontic counterparts of the equivalence-relations (1) (a) —(b) In deontic logic, however, the implications (2) (a) —(b) are not valid. 70

Consider

(6) (a) Op ^> p (b) p^Pp

That is, from the fact that p is obligatory it does not follow that p is the case, and from the fact that p is the case it does not follow that p is permitted. The sentence (7) (a) may be considered äs expressing deontic possibility and the sentence (7) (b) äs expressing deontic necessity.

(7) (a) Bill can go to Stockholm, (b) Bill must go to Stockholm.

The close relations between deontic and modal concepts are also reflected in natural language. In most languages, the expressions of certainty, necessity and possibility are also used for obligations and permissions. The modalities discussed so far do not exhaust all possibilities. Thus, for example, possibility and necessity in the following sentences may have to do with the speaker's desires (boulomaic modal- tty).

. (8) (a) Bill can be our leader. (b) Bill must be our leader.

Dlspositional modality refers to certain dispositions äs illustrated in (9) (a)-(b).

(9) (a) Bill can sneeze. (b) Bill must sneeze.

That is, (9) (a) may be taken to mean that in view of Bill's dispositions it is not excluded that he sneezes and (9) (b) may mean that in view of BilFs dispositions it is necessary that he sneezes.5 In view of the various modalities it is important to look for a general framework which can be made use of in the definitions of all these modalities. Such a general framework is provided by possible world semantics? Possible worlds meeting a certain condition are called accessible possible worlds. The following def initions hold: 71

p is necessarily true iff p is true in all accessible possible worlds and p is possible iff there is at least one accessible possible world in which p is true. In the case of alethic modality all possible worlds are accessible from any possible world. As for epistemic modality, given a possible world w, those possible worlds wl are accessible from w that are identical with respect to certain facts (what somebody knows to be the case). In the case of deontic modality the set of accessible possible worlds is the set of all worlds in which everybody acts according to some moral or legal System. Finally, in the case of boulomaic modality the accessible possible worlds are defined by the Speaker's desires: the accessible worlds are those that are compatible with the speaker's desires.7 In this way any number of modal concepts can be defined. Gen- erally, each modality will.correspond to a certain accessibility or alternativeness relation.8 It has also been argued that this relation can be replaced by the notionof background.9rfhus, what the Speaker knows defines an epistemic background, a moral or legal System defines a deontic background, the speaker's desires define a boulomaic background, etc. The concepts of possibility and necessity can then be reconstructed in terms of logical entailment and logical compatibility. The following definitions hold: p is necessarily true iff it is logically entailed by the background and p is possibly true iff it is logically compatible with the background. To summarize, the concept of modality can be explicated in the following fashion. The modality of p means that p is necessarily true or false, or possibly true or false with respect to a certain background. Or, alternatively, the modality of p means that p is necessarily true or false, or possibly true or false in a certain set of possible worlds. This set is defined by the accessibility relation considered. For further reference we shall call this definition of modality the logical definition of modality. The logical definition of modality can easily be extended to cover graded possibilities äs well.10 We have todo with graded possibilities in the following sentences.

(10) (a) There is a slight possibility that Bill will arrive to-morrow. (b) It is highly probable that Bill will not be able to attend the meeting. 72

Likelihood-modalitiee, too, can be traced back to the notions of oecessity and possibility.11 Itgoes without saying that the logical notion of modality covers a lot of linguistic phenomena. Most uses of the modal auxiliaries are expressible in terms of the categories of neeessity and possibility. Impersonal constructions such äs it is possible that . . . , it is likely (hat. . . , it is probable that. . ;,etc., too, come under this heading. Since the deriyational suffix -able (and its variants), too, expresses possibility, it is accounted for by the logical definition of modality. For the latter consider

(11) (a) Your handwriting is quite reädable. (b) This solution is conceivable.

What falls outside of the scope of modality, then ? For a linguistic expression to be,an expression of modality according to the logical definition of modality two conditions niust be fulfilled. First, the meaning of the expression must be^elatable to the notions of neeessity or possibility. Second, it must be propositional. Thus, verbs of propositional attitude are propositional but they do not exprese neeessity or possibility, henee they are excluded from the domain of modality.12 Modal adverbiale, on the other hand, very often carry a meaning which is traceable back to neeessity or possibility but they are not propositional, äs we shall see presently.13 Consequently, they> too, must be excluded from the set of modal expressions. The sentences under (12) (a) —(b) illustrate the case of propositional attitudes, those under (13) (a) —(b) the case of modal adverbiale.

(12) (a) Bill believes that John is sick. (b) Bill regrets that John is sick. (13) (a) John is probably sick. (b) John is very likely sick.

Modal adverbiale, äs we shall see, can best be interpreted äs expressions of speaker's attitudes. In addition to modal adverbiale, expressions of speaker's attitudes include parenthetical verbs, modal particles, Intonation, word order, etc. Most expressions of speaker's attitudes are not traceable back to neeessity or possibility. All expressione of epeaker'e attitudee will turn out to be non- 73

propositional. Since linguistic tradition seems to consider the expressions of Speakers' attitudes äs the main means to express modality in natural language, we have to conclude that the logical definition of modality has but little to say about modality in linguistics.

3. MODALITY AS EXPRESSION OF THE SPEAKER'S ATTITÜDE In traditional linguistic accounts of modality the essence of modality is often characterized by locutions such äs 'modality is the speaker's relation to reality', 'modality expresses the speaker's evalüation of states-of-affairs', 'modality is the speaker's cognitive, emotive or volitional qualification of a state-of-affairs', etc.14 We will use the term 'speaker's attitude' to refer to the speaker's cognitive, emotive or volitional qualification of a state-of-affairs. The term will become clearer, I hope, äs we proceed. Before embarking on the discussion of the notion of speaker's attitude a few remarks must be made 011 the distinction between descriptive and non-descriptive sentences. A descriptive sentence provides a description of reality, it refers to a state-of-affairs, hence it represents a proposition. Everything representable in terms of propositions can be known. Furthermore, propositions can be used in Statements (they can be stated, asserted about reality) and, of course, they can be denied (negated). Lin- guistically speaking, a sentence representiiig a proposition (a descriptive sentence) can be embedded under know and assert and it can be negated by using 'it is not true that. . .'. The sentence John is sick is descriptive, it represents the proposition 'John is sick', hence (14) (a) —(c) are grammatical sentences.

(14) (a) Bill knows that John is sick. (b) Bill asserts/states that John is sick. (c) It is not true that John is sick.

A non-descriptive sentence, on the other hand, does not provide a description of the world, or, at least, the description of the world is only part of its function. As a whole it cannot represent a proposition. Its content cannot be known in the same way äs propositions can be known. Such a sentence cannot be used äs a statement about reality (it cannot be asserted about reality) and, therefore, 74 it cannot be denied (negated). Lingustically speaking, a non- descriptive sentence cannot be embedded under know, assertjstate and cannot be negated. The sentence John is probably sick is non- descriptive, 'John is probably sick' is not a proposition. This makes sentences (15) (a) —(c) ungrammatical.

(15) (a) *Bill knows that John is probably sick. (b) *Bill asserts/states that John is probably sick. (c) *It is not true that John is probably sick.

Now, we will assume that the presence of an expression of speaker's attitude makes a sentence necessarily non-descriptive.15 Expres- sions of speaker's attitudes are thus non-propositional. The non- propositional character of such expressions also explains some further properties of non-descriptive sentences.16 Non-descriptive sentences cannot occur in if-clauses (they cannot be premises) which is testified by the ungrammaticality of (16) (a)-(b).

(16) (a) *If John is probably sick, then we have to stay at home. (b) *If Bill lives perhaps in Budapest, then we should visit him.

Normally, expressions of speaker's attitudes cannot carry contrastive stress (logical emphasis). Consider the ungrammaticality of(17)(a)-(b).

(17) (a) *John is probably sick. (b) *Bill lives perhaps in Budapest. where ' means contrastive stress. In general, expressions of speaker's attitudes cannot be coordi- nated (though some of them can occur combined in a sentence). Consider

(18) (a) *John is regrettably and probably sick. (b) *Bill lives perhaps and fortunately in Budapest.

Expressions of speaker's attitudes cannot be quantified äs shownby (19) (a)-(b). 75

(19) (a) *John is often probably sick. (b) *Bill always fortunately lives in nice places.

In sum, then, logical operations which normally can easily be performed with propositions or propositional elements are blocked by expressions of speaker's attitudes. Notice, incidentally, that an interesting observation can be made with respect to scope relations in connection with the examples (19) (a)—(b). In these sentences we have to do with two operators: one is a quantifier, the other an attitudinal operator. The sentences are ungrammatical if it is made clear that the latter operator falls into the scope of the former. If, however, the attitudinal operator takes scope over the logical operator (the quantifier), the sentences become grammatical. Consider

(20) (a) Probably, John is often sick. (b) Fortunately, Bill always lives in nice places.

This seems to indicate that no attitudinal operator (no expression of speaker's attitude) can fall into the scope of a logical operator, though logical operators can occur within the scope of an attitudinal operator. This conjecture is also borne out by the be- havior of negation. As pointed out above, sentences containing an expression of speaker's attitude cannot be negated. Negation is a logical operator and the negation with the construction 'It is not true that. . .' makes it clear that negation must have the widest scope among the operators in the sentence. If, then, the attitudinal operator falls into the scope of a logical operator, we get an ungrammatical sentence. If, however, the attitudinal operator takes scope over negation, the sentence becomes grammatical. Con- sider

(21) (a) John is probably not sick. (b) Perhaps, Bill does not live in Budapest.

We may thus conclude that the semanticstructureof non-descriptive sentences consists of two parts: (a complex of) attitudinal operator (s), which is the non-propositional part of the sentence and the propositional content of the sentence.17 Let us denote the complex of attitudinal operators (which may consist of a single 76 operator) by Att and the propositional content of the sentence by p'. The schematic semantic structnre of a non-descriptive sentence can then be rendered by (22).

(22) (Att, p')

What kind of linguistic objects do we find among the attitudinal operators? (i) Modal adverbiale such äs perhaps, probably, certainly, eurely, evidently. etc. (ii) Modal particles such äs really, actually, eventuatty, well, indeed, namely, just, say, etc.18 (iii) Parenthetical verbs such äs believe, know, imagine, think, guess, etc. in cases such äs

(23) (a) He will be here by to-morrow, I believe. (b) Bill, I know, is not the best person for this Job. (c) I think, this must be the best solution.19

As can easily be gathered from the above examples, parenthetical verbs are the verbs of propositional attitudes used parenthetically. In the sentences (23) (a) —(c) / believe, I know and / think are clearly non-propositional, äs can easily be demonstrated. On the other hand, the same verbs are definitely propositional in the following sentences:

(24) (a) John believes that he will be here by to-morrow. (b) He knows that Bill is not the best person for that Job. (c) He thinks that this is the best solution.

(iv) Certain uses of modal auxiliaries. Consider, for example, the 'subjective epistemic' readings of may and must in the following sentences.20

(25) (a) Bill may be a liar. (b) Bill must be a liar.

In Hungarian the 'subjective epistemic' reading is much clearer because of minimal pairs such äs 77

(26) (a) Pisti beteg lebet. 'Steve may be sick' (b) Pisti lebet beteg. 'It is possible that Steve is sick' where ' denotes the focussed constituent. In (26) (a) we get the 'subjective epistemic' reading which may be paraphrased by, say, Perhaps, Steve is sick. The focussed constituent is beteg 'sick', tbe modal lehet 'may be' is unstressed and follows immediately after the focussed constituent. (26) (b), on the other band, can only be interpreted äs Objective epistemic possibility': 'it is not excluded that Steve is sick'. (26) (a) is a non-descriptive sentence, whereas (26) (b) is descriptive. In (26) (b) the focus-position is occupied by the modal lehet 'may be' and the adjective beteg 'sick' is moved after the focussed constituent. Thus, in Hungarian focus and word order are used to distinguish the two modal readings from each other.21 The list is far from being complete, but this will do for the moment.22 The examples cited thus far will suffice to demonstrate the central role of attitudinal operators in linguistic structure. Let us now return to the semantic structure (22). Evidently, the meaning of sentences with such a structure cannot be accounted for in terms of truth conditions. One may, however, formulate fulfillment or satisfaction conditions instead, of which truth conditions constitute a special case.23 It should be made clear that Att in the formula (22) may stand for a complex of attitudinal operators. We have no reason to assume that sentences may contain only one attitudinal operator.24 We are now prepared to formulate what we will call the linguistic definition of modality: The modality of a sentence is determined by its attitudinal operators. Before trying to assess the domain covered by this definition we have to look at yet another class of linguistic phenomena which is often considered äs the main domain of modality in linguistic tradition.

4. MODALITY AS THE DETERMINING FACTOR OF SENTENCE-TYPES Traditional grammars distinguish five main sentence-types: (i) declarative sentences, (ii) interrogative sentences, (iii) optative sentences, (iv) imperative sentences and (v) exclamative sentences. 78

Though it is not always clear what criteria have been used to estab- lish these sentence-types, it has often been pointed out that they express radically different modalities.25 Let us disregard declaratives for the moment since they pose special problems, äs we shall see immediately. The remaining four sentence-types are illustrated in (27) (a)-(d).

(27) (a) Who has seen Bill? (b) Oh, were I grown-up. (c) Come with me. (d) What a foolish fellow he is.

(27) (a) is an interrogative, (b) an Optative, (c) an imperative and (d) an exclamative sentence. For the purpose of the present paper I will assume that there are sufficiently clear structural criteria to war- rant the postulation of five main sentence-types in English.26 The question I wish to address in the first place is what the modality expressed by these sentence-types is. It is quite evident that the sentences (27) (a) —(d) are non- descriptive, they do not express propositions. Notice the ungrammaticality of (28) (a) —(c).

(28) (a) *Bill knows that come with me. (b) *Bill asserts/states that come with me. (c) *It is not true that come with me.

The same holds true for interrogative, Optative and exclamative sentences äs well.27 This seems to indicate that what is generally referred to äs the modality of sentence-types has to do with Speakers* attitudes. Let us thus assume that the modality of (27) (a) —(d) consists of the pertinent Speakers' attitudes. But what are these attitudes ? The propositional content of (27) (a) is the set of individuals for which it is true that each of them has seen Bill. This propositional content is qualified by the speaker's attitude which can be circumscribed in the following fashion: "I want to know who these individuals are". As to (27) (b) the propositional content is am grown-up' and the speaker's attitude can be paraphrased äs something like wish to b egrown up' ( wish that the propositional content in question be true'). The propositional content of (27) (c) is 79

'You are coming with me' (i.e. 'The addressee is coming with the Speaker') and the relevant speaker's attitude is something ke º want the future action described by the propositional content to become true'. Finally, the propositional content of (27) (d) is ¹β is a foolish fellow' and the Speaker expresses bis surprise over this state-of-affairs. That is, the speaker's attitude can be rendered by something like º am surprised to see that. . Ë A caveat is in order here, however. The explicit renderings of the speaker's attitudes can only be considered to be very rough approximations since no explicit paraphrase will do f ll justice to the kind of attitudes involved here. Let Qu, Opt, Imp and Excl stand for the respective speaker's attitudes. Then, the schematic semantic structures of (27) (a)—(d) can be formulated s follows. (29) (a) (Qu, p') (b) (Opt, p') (c) (Imp, p') (d) (Excl, p') with the approximative interpretations for the speaker's attitudes (30) (a)-(d). (30) (a) Qu: º want to know . . .' (b) Opt: º wish it to be the case that...' (c) Imp: º want the addressee to perform . . .' (d) Excl: º am surprised that ... .'

It would, however, be wrong to replace the respective speaker's attitudes by these explicit paraphrases for various reasons. One of the problems is that it would, quite mistakenly, propositionalize something which is not propositional. But there are others which we don't have to bother about in the present context.28 (29) (a) is the semantic structure of questions. A question can be asked but this is not a necessity. Therefore, (31) cannot be considered to be a paraphrase of (29) (a).

(31) I ask you who has seen Bill.

Similarly, a sentence with the semantic structure (29) (c) can be used to issue an order. Consider 80

(32) I order you to come with me.

But, again, this is not a paraphrase of the semantic structure at band. The way in which a sentence is used depends heavily on the context and is therefore a matter of pragmaties. (31) and (32) spell out only one of the possible uses of the respective sentences. What about declaratives ? It has often been stipulated that declarative sentences, too, express a modality but this modality is characterized by the absence of linguistic markers. The modality of a declarative is then referred to äs 0- or unmarked modality.29 One can argue that Frege's distinctions between 'thought', 'judgement' and 'assertion' can profitably be used in the description of declaratives. 'Thought' is what corresponds to 'propositional content', 'judgement' may be considered äs an attitudinal operator with the approximative sense 'to consider to be true* or 'to take for granted' and 'assertion' is what belongs to pragmaties (a declarative can be used to make assertions). The judgement-operator, which will be denoted by Decl, turns a propositional content into a proposition. That is, (33) (a) can be represented äs (33) (b).

(33) (a) Bill is sick. (b) (Decl, p') where p' Stands for the propositional content 'Bill is sick'. If we adopt this analysis of declaratives, then we have to modify the characterization of descriptive sentences put forward above. We can no longer claim that non-descriptive sentences are non- descriptive because they contain an attitudinal operator whereas descriptive sentences lack such an operator. Rather, we have to say that all sentences have the semantic structure (22), which squares well with the traditional observation that there are no sentences without modality, each sentence consists of a 'modus' and a 'dictum'.30 It still makes sense to talk about descriptive sentences, however. Descriptive sentences are sentences which contain the judgement-operator in their semantic structure. All other sentences are non descriptive. By using certain structural criteria one may thus postulate a number of sentence-types, each of them being determined by an attitudinal operator. Good candidates for such attitudinal operators are, äs we saw above, Decl, Qu, Opt, Imp and Excl. Let us call 81 them sentence-type modalities. It is easy to see that the linguistic definition of modality given in the previous section need not be altered in order to cover sentence-type modalities äs well. Sentence-type modalities are not expressed by modal adverbiale, * parentheticals, modal particles, modal auxiliaries and the like. The linguistic expressions of sentence-type modalities include things like (i) question words, (ii) Intonation, (üi) word order, (iv) mood. In languages with an elaborate System of moods, mood is often considered to be the most basic linguistic means to express sentence-type modalities.31 We have already pointed out that it may happen that the semantic structure of a sentence contains more than one attitudinal operator. The following examples seem to suggest that certain com- binations of attitudinal operators are quite possible.

(34) (a) Fortunately, Bill is no longer sick. (b) Unfortunately, Bill may still be sick. (c) Is Bill perhaps still sick ?

In (34) (a) the evaluative attitude expressed by fortunately is combined with the attitude Decl since Bill is no longer sick is taken for granted, it is a fact not to be disputed. The sentence (34) (b), on the other hand, contains the subjective epistemic may and the evaluative adverbial unfortunately. Finally, (34) (c) is characterized by the attitudinal operators Qu and PERHAPS (where PERHAPS Stands for the attitude expressed by the linguistic element perhaps) We have to assume, then, that Att in the semantic structure of sentences Stands for a complex of attitudinal operators. The com- binability of attitudinal operators and their scope relations are problems for themselves which we cannot enter into in this paper.32 In most cases we will confine ourselves to cases where only one attitudinal operator is involved. There is, however, one problem which crops up in connection with examples such äs (34) (a) and (35) (a)—(c) which has to be clarified.

(35) (a) Bill is perhaps sick. (b) Bill is probably sick. (c) Bill may be sick. 82

The attitudinal operator Decl is present in (34) (a) but it is absent from (35) (a) —(c). By uttering a sentence such äs (34) (a) two functions are fulfilled: it is asserted that Bill is no longer sick (due to the presence of Decl) and at the same time the Speaker expresses his evaluative attitude (fortunately) toward this state-of-affairs. Still the whole sentence is non-descriptive.33 (35) (a)—(c) are plain non-descriptive sentences: the attitudes expressed by perhaps, probably and may exclude Decl. Disregarding sentence-type modalities, there are two basic types of attitudinal operators. One type can be combined with Decl, the other cannot. The former can be said to have a factive use, the other is definitely non-factive. Sen- tence-type modalities are, of course, mutually exclusive by definition. As shown by (34) (a) Decl can only be decisive if no other attitudinal operator is present in sentence structure. The following principle may thus be stipulated: Assign the operator Decl to the semantic structure of a sentence iff no overt attitudinal expression is present in the sentence. This principle shows that Decl is in a sense the default case and it bringe out the unmarked character of Decl quite neatly. It must be clear from what has been said thus far that the content of Speakers' attitudes is only in a'few cases related to necessity and possibility. The Speaker may express his emotional reactions toward a certain state-of-affairs, his evalution of a certain state-of- affairs, his desires and wishes, etc. There would be hardly any point in trying to find a common semantic denominator for all these meanings. The presence of an expression of speaker's attitude, äs I have argued, may be responsible for the fact that a sentence is non- descriptive. In view of what was said about sentence-type modalities we have to slightly modify our assumption. It must first be made clear that the speaker's attitude Decl, too,is non-propositional. The sentence Bill is not sick, for example, cannot be taken to mean don't take it for granted that Bill is sick', rather, it means take it for granted that Bill is not sick'. According to the linguistic definition of modality, then, modality is essentially non-propositional. What is propositional in a sentence is the 'dictum', the propositional content. But Decl is the only attitude that turns the 'dictum' into a proposition, i.e. into a descriptive sentence, äs we saw above. It follows from this view of modality that everything which is 83 propositional is excluded from the domain of modality. In some cases this conclusion may seem particularly awkward. Consider the examples (36) (a)-(b) and (39) (a)-(b).

(36) (a) Bill is probably sick. (b) It is probable that Bill is sick.

(37) (a) Bill is presumably sick. (b) It is presumable that Bill is sick.

(38) (a) Bill is sick, I believe. (b) I believe that Bill is sick.

(39) (a) I think, Bill is sick. (b) I think that Bill is sick.

There is a fairly clear connection between the (a)-sentences and the corresponding (b)-sentences. What is expressed non-propositionally in an (a)-sentence is formulated propositionally in the corresponding (b)-sentence. The correspondence is, of course, approximative rather than complete. Yet it would be rather odd to consider the non-propositional elements äs modal expressions but not the corresponding propositional expressions. According to the adopted framework a sentence such äs (36) (a) would be represented schematically äs (40) (a) and the corresponding 'propositional' sentence äs (40) (b).

(40) (a) (PROBABLY, 'Bill is sick) (b) (Decl, probable ('Bill is sick')) where PROBABLY Stands for the speaker's attitude expressed by probably. The Situation is similar in the other cases. In (40) (b) probable is propositional operator which is in the scope of the non- propositional operator Decl. The operator probable belongs to the modal operators according to the logical definition of modality. Consider now (41) (a) — (b) äs the schematic semantic structures of (38) (a)-(b).

(41) (a) (BELIEVE, 'Bill is sick') (b) (Decl, believe (Speaker, 'Bill is sick')) 84

Once again, BELIEVE is a non-propositional (attitudinal) operator which is expressed by the parenthetical / believe. In (41) (b), on the other hand, believe is a propositional operator and it is excluded from the domain of modality both by the linguistic definition of modality (since it is propositional) and by the logical definition of modality (since it does not express necessity or possibility). What one would like to say is that modality can be expressed either propositionally or non-propositionally but in order to be able to do this we need a definition of modality which covers both the non-propositional and the propositional means of expressing modality.34 The first step to this end is to develop a logical definition of modality which covers verbs (in general, predicates) of propositional attitudes s well.

5. PROPOSITIONAL ATTITUDES AND MODALITY Propositional attitudes are expressed by verbs which take a £Aa£-clause. Such verbs are, for example, know, believe, assume, think, doubt, suppose, etc. The logician is not interested in the linguistic characterization of these verbs. Consequently, we are never told exactly what kind of verbs belong to the class of verbs expressing propositional attitudes.35 From the various examples given in logical literature one may gather that verbs of propositional attitude must fulfill the following two conditions: (i) they must express a cognitive, emotional or volitional state (hence they must be stative) and (ii) they must take a ίΑαί-clause.36 This seems to be a fairly clear characterization of these verbs and I will have to say nothing more about this matter in the present paper. Propositional attitudes express attitudes toward propositions. Non-propositional attitudinal expressions always express the speaker's attitudes. Propositional attitudes, on the other hand, are attitudes of the person referred to by the subject of the main clause. How should these attitudes be characterized semantically ? It has been suggested that by using an expression of propositional attitude we are considering more than one possibility concerning the world, i.e. several possible courses of events. Each propositional attitude involves a division of all the possible worlds into two class- es: into the possible worlds which are compatible with the attitude in question and into those which are not. For example, 'John knows that p" can be characterized by the set of possible worlds which are 85 compatible with what John knows. That is, John's knowledge im- poses a certain restriction on the set of possible worlds. The possible worlds meeting a certain condition are called accessible possible worlds. Hence each propositional attitude attributed to a certain person can be characterized by a set of accessible possible worlds. To be a little bit more explicit, one may say that a given individual and a given possible world is associated with a set of possible worlds which are accessible from the given possible world. This relation between possible worlds is called accessibüity or alternativeness relation. This means, that each propositional attitude (of a given person) defines an accessibüity or alternativeness relation.37 But exactly this characterization has been proposed earlier for modalities.38 We have pointed out that in terms of possible world semantics each modality (epistemic, deontic, boulomaic, circumstantial, etc.) corresponds to an accessibüity or alternativeness relation. The various accessibüity relations can be used to account for the different meanings of the modal auxiliaries must and can, i.e. for the different interpretations of 'necessity' and 'possibility'. In general, the accessibüity relation in question is not made explicit in the sentence: it has to be recovered from the context. This is why the accessibüity relation can be replaced by the notion of (conversational) background. In the case of propositional attitudes, however, the accessibüity relation to be considered is expli- citly given by the verb of propositional attitude, it belongs to the structure of the sentence, no conversational background is re- quired. To say that 'a knows that p9 means that in all possible worlds which are compatible with what a knows it is the case that p. Or, to put it differently, the proposition (a knows that p9 is true in a possible world w iff it is true in all the possible worlds which are accessible from w. Similarly, to say that 'a believes that p9 means that in all possible worlds which are compatible with what a believes it is the case that p. That is, the proposition 'a believes that p9 is true in a possible world w iff it is true in all the possible worlds which are accessible from w. Recall now the definition of 'necessarüy true proposition' in possible world semantics: a proposition p is necessarüy true iff it is true in all accessible worlds. Consequently, 'a knows that p9 is true iff p is necessarüy true. 86

As to the connection between the notion of 'possibly true proposition' and propositional attitudes notice first that *ai does not know that p9 means that* there is a possible world compatble with what a knows in which ~^ p is true. Recall now that possibility is defined in possible world semantics in the following fashion. A proposition p is possible iff there is at least one accessible world in which p is true. That is, the proposition 'a does not know that p9 is true iff ~ p is possible. Similarly, one could say that (a does not know that ~ p9 means that there is a possible world compatible with what a knows in which p is true. In other words, *a does not know that ~ p9 is true iff p is possible. This seems to indicate that necessity and possibility have to do with the truth of a (modal) proposition, modality itself is defined by the accessibility relations. Thus, instead of defining modality in terms of necessity and possibility it seems to be more appropriate to define it in terms of accessibility relations. The modality of p highlights the f act that several possible courses of events are considered. Each modality of p defines a different partitioning of possible worlds, i.e. different sets of accessible worlds. Modality may thus be identified with the ensemble of the various divisions of possible worlds. Logically, the number of the possible divisions of possible worlds is infinite. We may, however, propose the following plausible restriction on this division: the accessibility relation must manifest itself in linguistic struc^ure.39 An accessibility relation which meets this condition may be called a linguistically relevant accessibility relation. We are now prepared to formulate the following definition of modality: Modality is the set of linguistically relevant accessibility relations. This definition may be termed the modified logical definition of modality. It is quite obvious that whatever is covered by the logical definition of modality is also covered by the modified logical definition of modality. In fact, the modified logical definition of modality accounts for all propositional aspects of modality. In the foregoing discussion we have tacitly assumed that the expressions related to necessity and possibility and the verbs (predicates) of propositional attitudes exhaust the propositional 87 aspects of modality. This assumption needs some justification, however. There are some further candidates for the propositional aspects of modality which crop up now and then in the pertinent literature. Such candidates are (i) negation, (ii) illocutionary verbs, (iii) perlocutionary verbs and (iv) the alleged 'temporal modalities' and (v) 'evaluative modalities'.40 Let us have a closer look at these candidates. From the above discussion of the notion of modality it should be clear what the function of modality is: modality relativizes the validity of a proposition to a set of possible worlds. The truth or falsity of the proposition can only be assessed in this set of possible worlds. How does negation fit into this picture ? Consider

(42) It is not true that Bill is sick.

To paraphrase (42) in the adopted framework we would have to say that the proposition 'Bill is sick' has to be evaluated in those possible worlds in which this proposition is false. This sounds rather odd and does not seem to make much sense. We must therefore conclude that negation, though it may interact with modality in various ways, is not a modal category. As to illocutionary verbs, these verbs refer to an act and are not used to relativize the validity of a proposition. Consider

(43) (a) I assert that all men are mortal. (b) I conclude that Socrates is mortal.

What does it mean to say that something is compatible with what I assert ? I can only assert (if I am honest) things which I believe to be true but whether I assert something which I believe to be true or not, is often a matter of chance. Illocution is alien to the notion of modality. The same holds true for perlocution. The effects that an act may bring about in the addressee cannot affect the act itself, i.e. the proposition which describes the act is independent of the eventual consequences of this very act. This observation can be generalized to cases where the ίΑαί-clause describes the cause and the main clause the effect. For example,

(44) (a) I am glad that you have come.41 88

(b) He was angry that you didn't call him last night.

So-called temporal modalities' occur in sentences (45) (a) —(b).

(45) (a) Yesterday, John went home early. (b) Sometimes, John sät up late.

True enough, yesterday restricts the validity of the proposition 'John went home early' in a way. So does sometimes with the proposition 'John sät up late'. It is also possible to extend the validity of a proposition by means of a temporal adverbial.

(46) John always goes home early.

It would, however, be conipletely mistaken to treat temporal quantifiers äs modal expressions. They are not used to express the possibility of several courses of events, their meanings cannot be reconstructed äs a division of all the possible worlds in any straight- forward way. In general, evaluations refer to existing states-of-affairs, äs for example, in (47) (a) —(b).

(47) (a) It is good that Bill has arrived. (b) It is bad that Bill is late.

In (47) (a) it is taken for granted that 'Bill has arrived' which is thus a semantic presupposition of the sentence. Similarly, 'Bill is late' is a semantic presupposition of (47) (b). The validity of these presup- positions is independent of their evaluations, it is not relativized to a set of possible worlds. Consequently, evaluations of the type exemplified in (47) (a) —(b) should not be considered äs modalities.42 We may thus conclude that it is reasonable to assume that propositional modalities are expressed by stative predicates de- noting a person's cognitive, emotive or volitional states.43

6. SPEAKER'S ATTITUDES AND POSSIBLE WORLDS It has been made sufficiently clear in the preceding sections that expressions of speaker's attitudes are non-propositional. It has also been pointed out that the semantics of non-propositional expres- 89 sions involves fulfillment- or satisfaction-conditions rather than truth-conditions. For propositions the locutions 'the proposition p is true in the possible world w' and 'the proposition p is satisfied (fulfilled) in the possible world w9 are identical. However, the latter locution can be extended to cover non-propositions äs well. Let us assume that the non-propositional attitudinal operator Att applied to the propositional content p9 produces the non-propositional meaning m. Then, it makes sense to say 'm is satisfied (fulfilled) in the possible world w9 or 'm is not satisfied (fulfilled) in the possible world w9. Though the Situation is much less clear in the case of speaker's attitudes than in the case of propositional attitudes, it seems to be reasonable to assume that speaker's attitudes, too, bring about a division of possible worlds. Thus, for example, the modal adverbial presumably expresses a certain epistemic state of the Speaker. The accessible worlds are those worlds that are compatible with this epistemic state, i.e. with the type of evidence which prompte the use of presumably. The modal adverbial certainly may be used to express a somewhat stronger evidence than presumably does. Again, we may say that the accessible worlds are those that are compatible with the speaker's epistemic state characterized by this kind of stronger evidence. The parenthetical believe does not have the same meaning äs the corresponding verb of propositional attitude. And this difference in meaning is not accountable in terms of the distinction 'propositional' — 'non-propositional', though it is undoubt- edly related to this distinction. By using the parenthetical believe the Speaker wants to make clear that he does not make any claim to truth but, at the same time, he indicates that he has at his disposal a certain evidence that makes him believe that the state-of-affairs in question may in fact occur. The details are, of course, far from being clear. Expressions of speaker's attitudes, in general, don't have clear-cut and precise meanings. However, this does not affect the main line of the arguments. One may assume that the parenthetical believe and the corresponding verb of propositional attitude lead to two different partitionings of possible worlds. The same holds true in other cases where there is a syntactic and semantic relation between the propositional and the non-propositional expression of modality.44 In view of what has been said above we may stipulate that the function of the expressions of speaker's attitudes, too, consists in 90 relativizing the validity of the meaning of sentences. That is, the satisfaction conditions have to be assessed in a set of possible worlds. If the above characterization of speaker's attitudes is by and large correct, then the modified logical definition of modality is going to cover the non-propositional means of modality äs well. That is, modality can be considered to be the set of linguistically relevant accessibility relations. Each accessibility relation defines a set of possible worlds in which the satisfaction conditions are assessed. In general, satisfaction (fulfillment) conditions have to be formulated for the characterization of sentence meanings. However, if the sentence meaning is propositional, the satisfaction (fulfillment) conditions will turn out to be the familiär truth-conditions. In sum, then, the essence of modality consists in the relativiza- tion of the validity of sentence meanings to a set of possible worlds. This view of modality has emerged from the non-technical locutions characterizing modality äs 'envisaging several possible courses of events' or 'considering the possibility of things being otherwise'. Though I think that my account of modality is basically correct, it should be made clear that there are a large number of problems yet to be solved. But I don't believe that the answers to these problems will require essential revisions of the approach outlined above.

Address of the author: Ferenc Kiefer Institute of Linguistics Hungarian Academy of Sciences Szentharomsag u. 2 H-1250 Budapest l (Hungary)

NOTES 1 Cf. Carnap 1967 for a thorough discussion of logical modalities. See also Reichenbach 1947. 2 This does not mean that it can totally be neglected. Cf. Lyons 1977 for a discussion of the linguistic relevance of alethic modality (Lyons 1977: 787 — 793). That alethic modality raises some interesting problems has been shown above all by Van der Auwera 1985 and Burton-Roberts 1984. 3 For the outlines pf epistemic logic see Hintikka 1962, for a linguistic discussion of epistemic modality Lyons 1977. 4 As to deontic logic cf. von Wright 1968, Hilpinen 1971, Hilpinen 1981. A linguistic discussion of deontic modality can be found in Lyons 1977. 91

5 From a linguistic point of view at least one more modal concept should be added to the above list: circumstantial modality. Circumstantial modality has to do with the circumstances of the outer world ('empirical circumstances'). For example, (i) Here a high dike must be built. (ii) In my country-house you may work in quiet. The Interpretation of (i) may be circumscribed äs follows: In the place referred to be here the circumstances are such that a high dike must be built (äs a protection against inundation). Similarly, (ii) can be paraphrased in the following fashion: The circumstances in my country house are such that it will be possible for you to work there undisturbed. Note that circumstantial modality is sometimes called causal modality (cf. Kescher 1968). 6 An introduction to possible world semantics can be found in Hughes- Cresswell 1968. Various types of modalities are discussed in terms of possible world semantics in Lewis 1973. 7 Dispositional and circumstantial modality can be defined in a similar fashion. The accessibility relation is determined by someone's dispositions (the accessible worlds are those that are compatible with a given person's dispositions) in the case of dispositional modality and by empirical circumstances (the accessible worlds are those that are compatible with empirical circumstances of a certain type) in the case of circumstantial modality. 8 The two terms are used synonymously in the literature. 9 More preeisely, by the notion of conversational background. Cf. Kratzer 1978. 10 Cf. Lewis 1973 (who discusses comparative possibility) and Kratzer 1981 (who develops a general theory in order to account for graded possibility). 11 Likelihood-modalities are sometimes considered to constitute a separate modal category. Likelihood-modalities are expressed, for example, by 'It is likely that. . .' and 'It is probable that. . Cf. Rescher 1968. Likeli- hood-modalities are covered by Kratzer's account of possibility and necessity however (Kratzer 1978 and 1981). 12 Propositional attitudes were first mentioned in Russell 1940. Cf. also Reichenbach 1947. 13 This is in contrast with most of the earlier tradition. Cf., for example, Bellert 1977. To my knowledge, the first person who has pointed out that modal adverbiale are non-propositional, was Ilona Molnär (Molnar 1968). The same view has been espoused by Lang (Lang 1979). 14 One example from the East and one from the West: cf. Vinogradov 1947 and Bally 1950. 15 Interjections, too, are non-propositional elements of the languaged Their presence in a sentence makes the sentence non-descriptive. For example, Ah! is it you?, Alas, we must part! Interjections cannot be considere- as operators for a lot of reasons: (i) they can occur in Isolation äs sponta neous reactions to pain, they can express joy and surprise etc., (ii) if they occur together with a sentence, they do not modify the meaning of the sentence, their presence is accidental, (iii) they don't seem to have a semantically describable meaning. 16 Some of the properties mentioned here have also been dWiissed in Lang 1979. 17 The locution 'a complex of attitudes' may mean two things. Either there are attitudinal operators in the sentence each of them being represented by a separate linguistic expression, or a single linguistic expression is used to indicate two (or more ) attitudes at the same time. See the discussion further below. 18 In English modal particles have not been studies äs extensively äs in German. Cf., for example, Weydt 1977, Doherty 1985. It is also worth noting 92 that Hungarian is extreraely rieh in particles, the language disposes of about 70 (cf . Molnär 1969). In general, however, not all particles carry modal meaning. 19 Cf. äs to parentheticals Urmson 1962. As expressions of modality they have been studied by Molndr in Molnär 1969. But, again, not all parentheticals lend themselves to modal Interpretation with equal ease. 20 As for the distinction between 'subjective epistemic' and Objective epistemic' cf. Lyons 1977. Lyons claims that "In principle, two kinds of epistemic modality can be distinguished: objective and subjective." For example, by uttering the sentence Alfred may be unmarried ". . .the Speaker may be understood äs subjectively qualifying his commitment to the possibility of Alfred's being unmarried in terms of his own uncertainty." And then he concludes that "Under this Interpretation, which is probably the most obvious, (14) (— Alfred may be unmarried) is more or less equivalent to (18) Perhaps Alfred is unmarried." (Lyons 1977: 797 — 798) 21 Cf. Kiefer 1986 for a detailed discussion of this problem. 22 In connection with sentence-type modalities we will see that the list of modal expressions will have to include Intonation, word order, questioii words, etc. äs well. 23 Cf. Lang 1979 and 1982, Kiefer 1986. 24Cf.fn. 17. 25 Sentence-types are related to sentence mood. No wonder that mood is often considered to be one of the most important modal categories. Cf., for example, Bally 1950 who points out that ". . . l'expression la plus usuelle de la modalite est le mode du verbe dictal" (Bally 1950: 216). 26 It should be made clear, however, that clear cases of sentence-types are the declarative, the interrogative and the imperative only. The criteria which are normally used to identify sentence-types are not always so trans- parent in the case of the optative and the exclamative. 27 The tests should be used with a certain precaution. For example, (27) (b) may be non-propositional due to the interjection, (27) (a) cannot even be a candidate for a proposition because of the presence of the question word. And the sentence Bill knows what a foolish fellow he is is quite acceptable, yet what Bill knows is not what is expressed by the exclamative (27) (d). 28 The impossibility of explicit paraphrases is also a corollary of the pre- reflexive character of the attitudes in question. Cf. Bierwisch 1980. The approach adopted in the present paper shares some essential features with the ideas presented in Bierwisch's paper. 29 Bally assumes that the modality of the indicative has the value 0. This corresponds to Bierwisch's claim that ". . .declarative sentences are basic or neutral äs opposed to other sentence types and. . .their assertive Interpreta- tion is the neutral or unmarked case" (Bierwisch 1980: 23). Bierwisch makes use of Frege's ideas in order to distinguish between 'thought', 'judgement' and 'assertion'. Cf. Frege 1973. 30 The following quotation from Bally 1950 will make clear this point: "La phrase explicite comprend donc deux parties: l'une est le correlatif du proces qui constitue la representation (p. ex. la pluie, une guerison)-, nous l'appellerons, a l'exemple des logiciens, le dictum. L'autre contient la piece maitraisse de la phrase, celle sans laquelle il n'y a pas de phrase, a savoir l'expression de la modalite, correlative a l'operation du sujet pensant. La modalite a pour expression logique et analytique un verbe modal (p. ex. croire, se rejouir, souhaiter), et son sujet, le sujet modal·, tous deux constituent le modus, complementaire du dictum." (Bally 1950: 36) 31 Cf. fn. 25. and also the discussion of mood in Lyons 1977. 32 Some examples are discussed in Lang 1979. 33 In contrast to Lang (Lang 1982) I do not consider 'Bill is no longer siek' in (34) (a) äs a semantic presupposition induced by the sentence adverbial fortunately, it is what is asserted in the sentence. On the other hand, in the sentence It is fortunate that Bill is no longer sick 'Bill is no longer sick' is a presupposition. 34 Considering the fact that linguistic tradition mentions both propositional and non-propositional elements among the expressions of modality 93

(without making this distinction, of course), this ahn should not come äs a surprise. 35 In epistemic logic mostly know and believe are discussed, though Hin- tikka devotes some attention to perceive äs well (Hintikka 1969). He also mentions äs examples of propositional attitudes know, believe, hope, remember, strive. If he is right in elaiming that perceptual ternis, too, express propositional attitudes (feel, hear, see, perceive), then wehave to addto the characterization of propositional attitudes that they also include perceptual states. 36 The second condition is necessary since there are verbs which express a cognitive, emotive or volitional state and don't take a that-clause. 37 In what follows we will capitalize on the proposals put forward in Hin- tikka 1969. It should, however, be made clear that I cannot enter here into the discussion of the special problems raised by verbs of propositional attitude though I am quite aware of the fact that a simple account of thes© verbs in terms of accessibility or alternativeness relationsis clearly inad- equate. 38 See Section 2. 39 To be sure, this restriction must be made more precise but its intuitive content should be clear enough for the present purpose. 40 Kescher 1968, for example, includes the temporal and evaluative expressions among the expressions of modality. Perkins 1983 excludes them, but wants to include the illocutionary verbs. 41 The intended Interpretation is the so-called 'inceptive reading' of the stative: that you have come has brought about the state described by am glad'. 42 It is not quite clear whether one should also exclude evaluative sentence adverbiale such äs fortunately,unfortunately, surprisingly etc. from the domain of modality. As was pointed out above, these sentence adverbiale seem to be complex attitudinal operators containing also Decl, which is, of course, a modal operator. 43 Perhaps also perceptual states should be included, cf. fn. 35. Possibility and necessity are, of course, modal notions but they are derivatives of the semantics of propositional attitudes. 44 Thus, for example, the relationship between It is probable that he is sick and He is probably sick is similar to the relationship between the propositionai and the parenthetical use of believe.

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