Logical Approach to Pragmatics 1

Jacek Malinowski

1 Introduction.

In 1938 Charles Morris has published the book \Foundation of the Theoryof Signs". He has distinguished there three areas of logical investigations:syntax, semantics and pragmatics. This book is commonly recognized as astarting point of investigations in the area of pragmatics. As the matter offact the book of Morris don't give any contribution to pragmatics but ratherindicated some problems of language understanding which cannot be handledwith the semantic methods and stressed then the need to solve them otherway. The concrete pragmatic investigations have been started in the 50-ties.From that time on the main results in the area has been achieved mainly by:linguistically oriented logicians and logically oriented linguists. This stressthe fact that pragmatics lies on the borderline between logic and linguistics.

This is not our aim to present the history of pragmatics. Let me onlymention that the logicians who gave essential contribution to pragmaticswere: Yehoshua Bar-Hillel, Richard Montague, David Kaplan, Dana Scott,David Lewis, Max, J. Cresswell, Robert Stalnaker. The presentation of theirtheories of language use would need a long series of lecture. The main aimof this lecture is:| to give clear (although not formal) de�nition of pragmatic, to explain howit is related to logic and proof that it is related very close to it;| to present the essence of the most current theory of interpretation ofsentences (also in commonsense language);| to give an outline of the theory of speech acts;| to present Grice's theory of conversational implicature;

1This is a �rst draft. Any comments are welcomed, the more critical, the better. But

please don't make any citation, it is much to early for it.

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| the proof Leach's thesis that the rules of kindness govern (are more fun-damental than) the Grice theory.

2 What is pragmatics?

The most general de�nition of semantics is that it is \the study of linguisticmeaning", or \the study of the meaning of words and sentences. Thoughwe may �nd it easier to think of words as relating to "things" in the world,semanticists point out that many words do not in fact refer to the externalworld at all. So the focus of the modern subject of semantics is on the waypeople relate words to each other within the framework of their language.

In discussing semantics, linguists normally use the term lexeme (as op-posed to word), so that word can be retained for the in ected variants. Thusone can say that the words walk, walks, walked, and walking are di�erentforms of the same lexeme.

There are several kinds of sense relations among lexemes. First is theopposition between syntagmatic relations (the way lexemes are related insentences) and paradigmatic relations (the way words can substitute for eachother in the same sentence context). Important paradigmatic relations in-clude:synonymy - a relation of "sameness", e.g pavement and sidewalk;hyponymy - a relation of "inclusion", e.g a cat is a type of animal;antonymy - a relation of "oppositeness", e.g big vs. small or buy vs. sell;

Pragmatics is often de�ned as the theory of the way we use language.Theories of pragmatics links so the language and language user while, se-mantics links the syntactical entities of language with their meanings. Onemay think that semantics su�ce to use language. Thus having an appro-priate semantics an competent user know meanings of words and sentenceswhich is enough to use the language proper way. The reality appears to bemuch more complicated. Thus, very often, especially when commonsenselanguage is concern, we utter sentences in the way which seems to have norelation to its meanings. Lets consider the following example: On the streetsomebody said to us the following sentence:

(1) Would you be so kind to tell me what time is it?

Logically (to) educated person will recognize that it is an yes-no question.

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S/he has at hand an appropriate theory of questions of this kind and knowwell that speaker expected from him one of the answers: \yes" or \know".An analysis of what is the matter of this question, even if proper, gives nochances to answer the question the proper and commonly known way. We allknow that the speaker don't expect any answer of the form \yes" or \no".

The following example seems to belong to the common experience ofall teachers lecturing logic. The rules of introduction of AND and OR areobviously logically valid. Nevertheless students, especially whose not veryinteresting in mathematics, use without problems the former and hardlyaccept the later. An psychological experiment performed by Rips in MITgave the results that the former rule is commonly accepted while the later isaccepted only by 17% of respondents.

AND Introduction 1.00 Or Introduction 0.17P PQ

P AND Q P OR Q

What's the reasons of this di�erence? It seems to be clear that the re-spondents don't understand the second rule proper way. More precisely theits logical interpretation is mixed up with the following pragmatic interpre-tation: I told P , would I told then P OR Q. The AND rule is commonlyaccepted because both its logical and pragmatic interpretation are valid. Thepragmatic interpretation of OR rule is obviously not valid. If one tell \I willcome to you tomorrow" s/he will rather not tell \I will come to you tomorrowor in next month". Paradoxes like this one �nd an illuminating solution inGrice's theory of conversational implicature which is presented later in thislecture.

3 Theory of sentence interpretation.

The great part of achievements of contemporary logic comes from investi-gations of the language of mathematics and has been performed by mathe-maticians or more precisely mathematically educated logicians. As a conse-quence the �rst order predicate language is often considered as a good �rst

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approximation of natural language. Moreover, the properties of predicatelanguage are, in a sense, projected on natural language causing then illusionthat some typical language phenomena are paradoxical. We will recall belowtwo in uential apparent paradoxes (in fact typical language phenomenon):intentionality and occasionally. Their recognizing and explanation were amilestones in the hard way from classical logic to natural language.

According to Fregean paradigm of logic the meaning of a sentence is itstruth value. Thus to get the meaning of a sentence it is enough interpretationof its variables. The way is then clear and direct:

r r

sentence meaning

No doubts that when the �rst order predicate language is concern no prob-lems occur. Until late 60-ties most of logicians seemed to be unaware ofhow narrow part of natural language could be covered by the language ofpredicate logic.

Classical logic satis�es the principle of extensionality. Thus, the truthvalue of composed sentences depends only on truth values of components. Inthe natural language the principle of extensionality is satis�ed very seldom.The sentence:

(2) Kepler has known that more than 6 planets goes around the sun.

is false, while

(3) Kepler has known that more than 6 > 9.

is true. As a consequence sentences build up with the operator:

(4) Kepler has known that ... .

doesn't satisfy the extensionality principle. Thus, components of (2), and(3) { sentences \6 > 9" and \More than 6 planet goes around the sun." are

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both true, so according to the principle of extensionality both (2) and (3)should have the same truth value.

(4) is a typical example of an intentional operator. To �nd the meaningof a sentence like (2) or (3) it is not enough to compose meanings of itscomponents. We have to proceed more complicated way than the pictureabove shows. The meaning of (2) depends not only on how things are butalso on how they could be so, how the things are in other possible worlds.Possible world semantics invented by Saul Kripke form a powerful theoretictool for both logical and pragmatic investigations.

The great success of Kripke semantics for modal logic has been a big stepforward in direction of logical pragmatics. Kripke semantics has solved theproblem of meaning for intentional expressions.

r r

r

sentence meaning

possible world

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@@@@@

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Other aspect of the structure of interpreting sentences has came from thestudy of the phenomenon of occasionally. The sentence:

(5) Now I am here

cannot be uttered without being true. On the other hand we wouldn't tellthat it is a tautology. For such a sentences logicians has invented the notionof eternal sentences, sentences which meaning don't depend on who, when,where, (and so on,) utter them. The default assumption was that any sen-tence is fully equivalent to an eternal sentence. As a consequence, they wouldtell that there is no need to investigate sentences like (5). Many logicians,including so in uential as Quine, has arguing against this assumption. Nev-ertheless till now this assumption is still considered to be valid, especiallywhen we teach logic to students, considering examples coming from com-monsense language. From point of pragmatics it is a secondary question if

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and in what extend, this assumption is true. The point is that occasionalsentences like (5) are typical in the language use. We cannot then pretendthat that don't exist considering them as special, informal or improper. Itseems to be necessary for a logic of natural language to cope them directlyright way.

From early 70-ties on many logical solutions of the problem of occasionallyhas been given. David Kaplan, Robert Stalnaker, Max J. Cresswell haveconstructed logical systems which step by step has came closer and closerto common language use. Let me omit their details here. Roughly speakingthe result was that we have to distinguish between the sentence and what isexactly said - (between utterance and proposition) . The way from formerto later goes through the context. All the occasional utterances are contextsensitive. Nevertheless, as far as I know nobody has given yet and satisfactoryde�nition of the context. Bar Hillel has argued has a satisfactory de�nition ofthe context is unlikely to be given. Anyway, we can agree that the context ofan utterance is determined by the circumstances of utterance. Knowing themwe know the context. All this leads us to the way of proceeding depicted inthe following diagram:

r r

r

r

r

utterance proposition

context

meaning

possible world

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@@@

@@

@@@

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@@

@@@@@@

We have heard the utterance. To get know what is exactly said (a propo-sition) we need a context and then looking eventually at the appropriatepossible worlds we get to be able to establish the meaning of a given sen-tence.

One important step is missing here. A competent language user utter asentence. We necessarily have to distinguish between a sentence as a abstractlanguage entity and an utterance { a concrete case of using a given sentence.All this leads us to the diagram above.

To recall brie y the process of interpreting an utterance: An utterance is

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said. Using context we can get to know what is exactly said. We recognizethen a proposition. Then we interpret it using (eventually) the possibleworlds go get then its meaning { true of false.

Lets look at the (5) in the situation we have got. Hearing it in theparticular situation we get:

(6) Bill Clinton is in White House on the on April 30, 2000, 14:00.

It is true if Clinton had told it (or false if he hadn't) anyway it is not atautology.

According to the presented approach the problems in the subject arecentered upon the properties of context. The central problem here is todescribe the mechanism of how we use the context to �nd out the propositionindented by speaker.

4 Speech acts.

Logic investigates sentences \in the logical sense" thus sentences to which onecan correspond the truth values in a natural way. During a very long periodlogicians seemed to be unaware of the fact that the scope of the sentences inthe logical sense form just a small part of the set of all sentences. Two books:the �rst by John L. Austin's \How to do things with words" and \Speechacts" by J. Searle were a milestones on the way from classical logic to thelogic of the broadly understood language. We will present there some versionof their theories which is competitive to the results achieved by the foundingfathers. However, this versions seems to keep their main ideas unchanged.

Let us start however with some backgrounds of the subject. People uselanguage to accomplish many kinds of acts, broadly known as speech acts,as distinct from physical acts like drinking water or mental acts like think-ing about drinking water. Speech acts include asking for a glass of water,in addition to making promises, issuing warnings or threats, giving orders,making requests for information, and many others. In all European and mostworld's languages three type of speech acts can be realized in the syntacticway.

The speech act of assertion is realized by the declarative sentences (al-though not all the declarative sentences expresses an assertion), such a sen-

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tences conveys information, and are true or false, so they are the sentencesin the logical sense. Example:

(7) Jenny got an A on the test,

Interrogative sentences expresses the questions. They form acts of requir-ing information, like the sentences below:

(8) Did Jenny get an A on the test?

Orders and requests are expressed by means of imperative sentences.They cause others to behave in certain ways:

(9) Get an A on the test

Although assertions, questions and orders are fairly universal, and most ofthe world's languages have separate syntactic constructions that distinguishthem, other speech acts do not have a syntactic construction that is speci�cto them. Consider the English sentence,

(10) If you cross that line, I'll wipe that smile right o� your face!

Most English speakers would have no trouble identifying such an utteranceas a threat, but it is clear that if-constructions are not speci�c to the speechact of threatening. Such a construction might also express a promise, as in:

(11) If you work hard all week, I'll give you a bonus!

A consideration of the syntactic means available for expressing the variousspeech acts leads us to see that even for the three basic speech acts laidout above, speakers may choose means of expression other than the basicsyntactic type associated with the speech act in question.

One subtype of direct speech acts exists in English and in many other lan-guages, and allows us to expand the kinds of direct speech acts we can makebeyond the three basic types that have their own special syntax. These arethe direct speech acts that use performative verbs to accomplish their ends.Performative verbs can also be used with the three basic speech act types asexempli�ed in (12) - (14), associated with making statements, requests andcommands respectively:

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(12) I assert that Jenny got an A on the test.

(13) I ask you who took the photos.

(14) I order you to close the window.

To these can be added performative verbs that allow us to directly conveypromises, threats, warnings, etc.

(15) I advise you to keep up the payments on your car.

(16) I warn you not to step across this line.

(17) I promise you that I will pay the money back by the end of the month.

(18) I bet you a dollar that it'll rain on the parade.

In the last sentence, the utterance of the sentence actually accomplishes theact of betting (possibly along with setting aside the money for the bet), andas such, it belongs to the class of ceremonial utterances that accomplish otherkinds of changes in the world:

(19) I now pronounce you husband and wife.

(20) I name this ship Sojourner.

(21) I dub thee Sir Galahad.

It is clear that not all uses of verbs that can be performative are actu-ally performative in particular utterances. For example, if we change theperson or the tense in any of the last seven sentences, they are no longerperformative:

(22) He advises you to keep up the payments on your car.

(23) I named this ship Sojourner.

In both these cases, the utterance simply reports, and does not accomplishthe act of advising or of naming. A test of whether or not a particularsentence is a performative utterance is whether or not you can insert hereby

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before the verb. If the resulting sentence doesn't make sense, it is not aperformative:

(24) I hereby name this ship Sojourner; but

(25) *I hereby named this ship Sojourner.

In order to "do things with words", certain things must be true of thecontext in which speech acts are uttered. In other words, a sentence mustnot only be grammatical to be correctly performed, it must also be felicitous.

Lets consider three types of felicity conditions: Preparatory conditions,such as that the person performing the speech act has the authority to doso, that the participants are in the correct state to have that act performedon them, and so on { the marriage performed by an utterance like (19)cannot happen unless the participants are of age, and not already married,and unless the person who says the words has the authority to marry people.Conditions on the manner of execution of the speech act, such as touching thenew knight on both shoulders with the at blade of a sword while intoningthe words in (21); and Sincerity conditions, obviously necessary in the caseof verbs like apologize and promise.

Some of the felicity conditions on questions and requests as speech actsare as follows, where "S" = speaker; "H" = hearer; "P" = some state ofa�airs; and "A" = some action.

(26) S questions H about P.

a. S does not know the truth about P.b. S wants to know the truth about P.c. S believes that H may be able to supply the information about P that Swants.

(27) S requests H to do A.

a. S believes A has not yet been done.b. S believes that H is able to do A.c. S believes that H is willing to do A-type things for S.d. S wants A to be done.

We can see what happens when some of these conditions are absent.In classrooms, for example, one reason that children may resent teachers'

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questions is that they know that there is a violation of A.1: the teacheralready knows the answer. A violation of B.2 can turn a request into a joke:"Would you please tell it to stop raining?"

Elementary utterances are of the form F (P ), where F is an illocutionaryforce, and P is a proposition, which establish a content of the utterance.Thus 7, 8 and 9 have the same propositional content (supposing that 9 isaddressed to Jenny) and three di�erent illocutionary forces. Those contentis a proposition describing the fact hat Jenny has received an A on the test.

Any illocutionary force is consist of the following six components:illocutionary point: direction to �t between words and worlds, in the caseof (27) it relay on making hearer will take care to change a present state ofa�airs in appropriate manner.

mode of achievement: of illocutionary point { an illocutionary point mightbe achieved on many ways. A mode of achievement distinguish all of modescorresponding to given illocutionary force. Mode of achievement allow us todistinguish between \request" and \command" illocutionary forces with thesame illocutionary force.

content conditions { de�ne the domain of the operator F of illocutionaryforce. In our example a content should describe some future state of a�airs.

preparatory conditions { A preparatory condition in (27) say that speaker isconvinced that hearer's help will be up to himself.

sincerity conditions { describe mental states (propositional attitudes) of speakerappropriate for a given illocutionary force. In (27), it said that speaker reallywant hearer will do what speaker ask him to do.

degree of strengthening the mental states of sincerity occurs with di�erentstrengthenings in di�erent illocutionary forces. Degree of strengthenings tryto \measure" them.

An illocutionary point is, in a sense, most important here. It allows usto give an interesting logical classi�cation of speech acts. Any utteranceis giving a link between world and language. In a �rst approximation atype of utterance is determined by the direction to �t between them (i.e.between world and word). There are four possible illocutionary points. An

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assertive illocutionary point: Any utterances with this point (thus assertion,predictions, suppositions, doubts for example) are utter with the aim to �tthe content of utterance to the appropriate state of a�airs in the world. So,a speaker is going to �t the content of an utterance to the world. Thus anyassertive utterances have direction to �t \word to world".

An opposite direction: \world to word" possesses all commissive anddirective illocutionary forces (thus command, promises, threats requirements,questions, begs for example). A speaker who utter herself with this point isintended to cause an appropriate change of the world being intended to act inan appropriate way (commissive speech acts) or wanting to make somebodyto take care about an appropriate change of the world (directive speech acts).

An double sided direction to �t between world and word is an illocutionarypoint of most of the utterances constructed by means of performatives. Bap-tizing, nominating, naming, appointing are examples of illocutionary forceswith double sided illocutionary point. Their common feature is that thespeaker change the state of world by uttering with this illocutionary point.

The fourth \empty sided" illocutionary point occurs in all utteranceswhich are designed to express speaker's psychic states (like: \How that youcame" for example).

Illocutionary counterpart of the notion of true sentences is the notion ofperformed utterance. We will say that an utterance F (P ) is performed byspeaker in a given situation i i�:1. Speaker achieve an illocutionary point of an illocutionary force F withcontent P in mode which agree with mode of achievement of F , and P ful�llscontent conditions, of F in a given situation;2. Speaker presupposes all propositions determined by preparatory condi-tions for P .3. Speaker express with degree of strengthening of F all mental states deter-mined by sincerity conditions of F .

Lets look on the components of an illocutionary force from an uniformpoint of view using for it a bit of formalities.

Mode of achievement is a function h, which to any situation and propo-sition correspond value of success or insuccess.

h : I � U 3 (i; P ) 7�! fS; =Sg

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the function divide the set I of all situation into two subsets: A set of situa-tion in which given utterance is performed according to mode of achievement(value of success), a set of situations in which given utterance is not performedor performed with violation of mode of achievement (value of insuccess).

Similar structure have sincerity condition, mode of achievement, prepara-tory conditions and degree of strengthening. An illocutionary point, al-though, in principle, most important, is only a special case of the modeof achievement and could be easily reduced to it. All the functions de�ningthe properties above have the same structure. They design a set of situationsin which appropriate conditions are ful�lled.

In situation semantics it is quite common assumption that situation isidenti�ed with the set of propositions which are satisfy in it. Lets assumethat a satis�ability relation j= is given. We read it as follows: a propositionP is true in situation s i� s j= P . If we would identify a situation with theset of true sentences then a relation j= is identical to relation of belonging.s j= P i� P 2 s. Situation s is identical with s0 i�

fP 2 U : s j= Pg = fP 2 U : s0 j= Pg:

Assuming the condition above we can replace all the conditions given by:mode of achievement and preparatory conditions and sincerity conditions,illocutionary point and degrees of strengthening to the following one essentialcondition.

Given a set of possible situations I, set of propositions U , and relationj= of satis�ability. An essential condition of performing an utterance withillocutionary force F we will call a function ~F , which to any pair (s; P ) 2 I�Ucorrespond a set of propositions ~F (s; P ) � U . We will say that an utteranceful�lled in s its essential condition i� for any Q 2 ~F (s; P ), s j= Q.A domain of an illocutionary force F we will call any set of propositionsDF � U .

We are now able, to formulate a de�nition of performed utterance.

An utterance F (P ) is performed in s i� an utterance F (P ) ful�lls in s anessential condition of F and P belong to the domain DF of F .

An illocutionary force F1 we will call stronger than an illocutionary forceF2 i� DF2

� DF1, and for any proposition P and any situation s ~F2(s; P ) �

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~F1(s; P ). So, an illocutionary force F1 is stronger than an illocutionary forceF2 i� their domains included in themselves in proper manner, and essentialcondition of F2 is a logical consequence of essential conditions of F1.

5 Gricean Conversational Maxims.

The work of H.P. Grice takes pragmatics farther than the study of speechacts. Grice was a student of conversation, and he enunciated the basic prin-ciple that, outside of the theater of the absurd, most conversationalists seemto hold to: the Cooperative Principle. It has four sub-parts or maxims, thatconversationalists are enjoined to respect.

(A) The maxim of quality. Speakers' contributions ought to be true.

(B) The maxim of quantity. Speakers' contributions should be as informativeas required; not saying either too little or too much.

(C) The maxim of relevance. Contributions should relate to the purposes ofthe exchange.

(D) The maxim of manner. Contributions should be orderly and brief, avoid-ing obscurity and ambiguity.

The maxims works in two modes: the speaker mode and the hearer mode.The speaker mode has a normative sense: Do formulate an utterance so wayto keep all the maxims. The hearer mode is more sophisticated: Wheninterpreting an utterance remember that an speaker kept all the maxims. Sowhen you �nd out that an speaker has outed some maxims you have tointerpret an utterance anew. Lets consider two examples:

S: Where is Bill?H: There is a yellow Porsche outside Sue house.

S: Can you tell me the time?H: Well, the mail has just come

In both examples the simplest hearer interpretation of what H has told isthat he did break the communication. So, according to the hearer mode ofexploiting the maxims of relevance S should interpret the utterance anew

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appealing to their common knowledge that Bill is a fried of Sue and has ayellow Porsche or that postman comes always at 11 am.

Grice was using observations of the di�erence between "what is said"and "what is meant" to show that people actually do follow these maximsin conversation. We can see how this works in considering the maxim ofquantity at work in the following made-up exchange between parent andchild:

Parent: "Did you �nish your homework?" Child: "I �nished my algebra".Parent: "Well, get busy and �nish your English, too!"

Further proof is that when people "violate" or " out" these maxims,particular meanings are conveyed. It is certainly possible that the child couldcome back and (typically in a teasing tone) say that he had also �nished allhis other subjects. After all, he did not say he had not �nished the rest ofhis homework. If you were to hear someone described as having "one goodleg", you would be justi�ed in assuming the person's other leg was bad, eventhough nothing particular had been said about it. Conversationalists arejusti�ed in making the inferences they typically do, because they as well asGrice have understood the di�erence between "what is said" and "what ismeant".

The maxim of manner is crucial for understanding the di�erence betweenthe following two utterances:

Miss Singer produced a series of sounds corresponding closely to the score ofan aria from Rigoletto.

Miss Singer sang an aria from Rigoletto. manner

The content of both the sentences is more or less the same. The laterutterance expressed it direct way. While interpreting the former utterancehearer must ask herself why the speaker expresses so simple matter in socomplicated way. The hearer mode of maxim of manner cause that theremust be some reasons for such a way of utterance. Thus, the speaker like toavoid of using the word sing, stressing that it isn't sing what Miss Singer isdoing. This means miss Singer is bad singer.

This volume is well-bound, and free of typographical errors.

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This example outs the maxim of quantity saying less than is normal fora book review, and probably the maxim of relevance as well, since bindingand typographical errors are less signi�cant to potential readers than thebook's contents. What is implicated is: \This volume stinks!".

Using maxim of quantity utterance \John has three cows" entails thatJohn has exactly three cows.

6 Conversational rules of kindness.

In 1983 G. Leech has proposed a theory of conversational implicature basedon some rules of kindness. Without being kind we would, in principle, tellall the true independently of what kind of feelings it cause in the hearer.Everyday commonsense discourses are organized other way. We don't tellall the truth. We usually divide the truth into pleasant to hearer and theunpleasant one. We utter it then in a non symmetric way. Roughly speakingwe tell what is pleasant and try to avoid telling what is unpleasant.

Leech succeed arguing that all Grice's conversational maxim are governedby the following maxims of kindness. No Grice's maxim tell us why we use(1) instead to use more direct:

(28) What time is it?

That is common that we don't like to be seen as an unkind person. Uttering(1) we wont to stress that we are kind, and know that s/he has his own mat-ters to do but if s/he would nevertheless tell us the time we would appreciateit. Leech maxims us just about such a kind of thinking. The main idea ofthe maxims is that the speaker act so way to mini-max point in the twodimensional plane of a scale appropriate to a given maxim. Three di�erentalthough similar scales occur in maxims. Perhaps it is better to considerinstead one common scale of expenses and pro�ts. Some mis�ts may occurthen, especially in agreement maxim. On the other hand we will get then anuniform point of view of the theory. All the maxims work the following way:Let your utterance to act so way to achieve maximum pro�ts for hearer evenit will make maximum expenses for speaker.

A. Tact Maxim works for directive or commissive utterance. It work in thescale: expenses - pro�ts: Minimum expenses for hearer with maximum pro�ts

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for him. So we will tell:

(30) Help yourself once more.and rather not(31) I will help yourself once more.

B. Generosity Maxim works also for directive or commissive utterance andalso work in the same scale of expenses and pro�ts: minimum pro�ts for meand maximum expenses for me, so we will tell:

(32) Have you something against a cup of tee?and rather not(33) I have nothing against a cup of tee.

C. Approbation Maxim works in expressive or assertive utterance. in thescale of objections - praises: Minimum criticizing of hearer and maximum ofpraises of hearer. So, we tell:(34) Oh, how terri�c dinner you have preparedand not(35) Oh, how untasty dinner you have prepared

D. Modesty Maxim works also in expressive or assertive utterance in thescale of objections and praises: minimum praises for speaker and maximumof criticizing of speaker. We tell"(36) It was silly of me.but not(36) It was silly of you.

E. Agreement Maxim applies for assertive utterances in the scale of nonagree-ment - agreement: minimum of nonagreement between speaker and hearerand maximum of agreement between them. So we tell:(37) It is an interesting exhibition.and not(38) This exhibition wasn't interesting.

F. Sympathy Maxim applies also for assertive utterance in the scale reluc-tance - kindness: minimum of reluctance between speaker and hearer andmaximum of kindness between them. We tell then:

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(39) I am so sorry that your cat has die.but not(40) I am so glad that your cat has die.

No doubts that logicians may have objections against Grice's theory andeven more objections against Leech's one. Both of them are not only non-formal, the more, they are not formalizable. To be honest one should evenadmit that they are unclear. It seems that the proper answer for the objectsis the following: All the logical systems are charmingly precise, neverthelessthey are completely unable not only properly explain but even to recognize alarge number of typical language phenomena. Isn't it good enough reason tostart considering that those problems are to hard to solve them at once in theformal way. Perhaps the best strategy is to approach them approximatively.The �rst step is then unformal and perhaps not quite clear. Nevertheless astudy of both Grice's and Leech's theories give an impression that there issomething very new and deep inside.

In some extend the similar remarks can be applied to all the pragmaticsubjects presented above. One should admit that no one of the problemspresented above is solved in the good enough way, on the other hand allthose problems seems to be urgent and some step in direction to get themsolved is made here. This is why all the results gathered above together maybe considered at the same extend as satisfactory results of research and asresearch project which present just a \recognition by a �ght" of an area quiteunknown for logicians.

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