Who-Questions: Some Pragmatical Principles

WHO-QUESTIONS:

SOME PRAGMATICAL PRINCIPLES

LIBERO VENZI

To Aqvist is due the first attempt at a systematic analysis of questions and not of answers (therefore he does not take an erotetic point of view) in the following two phases: i) questions are considered to be requests of information ii) the informational status desired by the questioner is analyzed in terms of an epistemic logic. This is what Hintikka(1975^)says in relation to Aqvist(1965) but, from a logical point of view, it seems more exact to say that the two phases are instead the following: i') same as i), ii') the informational status of the speaker-questioner is de-scribed as a logically complex entity formed by two ρ arts: a) an im-perative part in which an operator of command is interpreted as "Let it be the case that" to which is linked b) an epistemic part which can formally enter into the field of Hintikka's propositional and quantif icational epistemic logic (Aqvist(19723)). With the aim of formally keeping track of the imperative part however, Aqvist(1972)proposes an extension of Hintikka(1962^).

It is of methodological interest for us to pay attention to the fact that it is the descriptive adequacy of the formal instruments that in Aqvist(1972)permits the classification of questions: 1) those that are adequately formalizable within the imperative-epistemic propositional· logic PIE, and 2) those that are adequately formalizable within the wider imperative-epistemic quantif icational· logic QIE.

However, the imperative part is not considered in Hintikka(1975); his is instead an analysis of both questions and answers.

In his approach, the epistemic part of the question is called the desideratum. This concept will be amply used further on, but we shall see how it can take, on interpretations which are different

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in relation to a pragmatic approach instead of a logico-semantic ©

one, as is it in both Hintikka and Aqvist. From now on we will be concerned with the analysis of certain types of wh-questions (abo-ve all who-questions) and that is, wh-questions with affirmative answer, wh-questions with negative answer, rhetorical wh-questions, with particular interest in what Belnap(1969^)calls "'pragmatic' implications" (p.25). For example, asking a question implies usual-ly that the questioner does not know an answer and it also implies that the questioner either believes or knows that the answerer knows the answer. Further on other pragmatic implications will be taken into consideration, and these are interesting above all for the re-lationship that they have to the subsisting relation between wh-ques-tions and the presupposition of a wh-question (in a sense of the term which will be clarified). We might say that such "'pragmatic' implications" can be considered relations between the question (or better, the logical analysis of the questions) and the preconditions to the question on the part of the questioner, to be understood in a way that is similar to Bellert's(1970^)· Generally speaking, that which will be considered of the notion of precondition, as we under-stand it to be, is the knowledge status of the questioner analyzed in both epistemic and imperative-epistemic logical terms, and in relationship to the empirical context in which the question is asked; we shall also concern ourselves with the relationship between the knowledge status of the questioner and of the answerer (the lat-ter analyzed in both epistemic and imperative-epistemic logical terms) and of the "transition of the knowledge status" in the questioner, given the answer. We will frequently refer to the wh-question: Who lives here?

A principle, which seems to be intuitively true and which puts into relation a de re knowledge status, on the part of the questioner, with a de dioto knowledge status, on the part of the questioner, -but containing a de re knowledge status on the part of the answerer can feceive the following linguistic formulation:

[lj If I know someone who lives here, then I know that you know someone who lives here,

that is,

[2] if f3x; Κ F (x), then Kr ( 3 χ) Κ F(x) I I you

We should note how in the consequent K̂ . appears; we could in-stead use Β , so that we would then have:


W H 0 - Q U E S T I O N S 83

[3] If I know someone who lives here, then I believe that you know someone who lives here;

but the choice of one example over the other seems to be dictated above all by reasons of a contextual nature, in the sense that at the moment in which the question is asked it is certainly possible that "I know that you know...." instead of "I believe that you know...". [2] it does not seem to be false since in a question-answer interaction it does not seem possible that I know someone who lives here and I do not know that you, the listener, know someone who lives here. In fact, if I know someone who lives here, then that means that you have answered, for example with "b" (where "b" stands for a name)^, and from the knowledge acquired by means of such an answer, and from that fact that I know who "b" is, I can deduct "I know someone who lives here". But for this last example we should consult Hintikka(1975)· We can see how [ 2] might be more clearly interpreted in the following way: to put "(1χ) Κ F(x)" as true and as an antecedent signifies having achieved this knowledge and this only if the above conditions are satisfied. So I not only have acquired this knowledge, but I have also acquired the knowledge that you know what I know, that is the knowledge of which you have

just informed me. In order to underline the necessity of such a condition we could begin the discussion relative to the following principle:

[4] Only if I know that you know someone who lives here, then I know someone who lives here,

that is to say, there can be no other way for me to know someone who lives here other than that of knowing that you know someone who lives here; we might add then that such a principle seems to motivate mainly my asking you who lives here.

This also seems to be true for the reason that in an analysis of questions (as requests of information) and of answers, we must assume that there can be no other way for me to know someone who lives here other than that of asking you, this being justified by the fact that I know that you know someone who lives here; but this argument undoubtedly has another general validity if we think of "you" (and "I") as of a free variable which "from time to time" can take as values names of "systems" wich are capable of answering (asking).

The definitive logical form of the principle being discussed could


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be:

[5] (1 χ) KT F ( χ ) - Κτ C3 χ) Κ F(x) I I you

only if [ 5 ] can be demonstrated in some formal system. We will at-

tempt a demonstration using Hintikka's(1962)formal instruments to

see either if the principle in this formalism is insufficient or if

the formalism itself is so, or both.

( 1 ) r 3 x) KI F(x) e u Ass.

(2) PT (1 χ) Ρ - F(x)e υ I you C.Ass.

(3) Kj. F(b) 6 μ ( 1 ) X (C. 3ep)

( 4 ) (3 χ) KT (b = χ) e u 1 ( 5 ) ( ν χ) Ρ - F(x) e u* you I (2) X (C.P* )

(6) F(b) e v* (3) X (C.K* )

(7) ( 3 x) KT (b=x) e v* ( 4 ) X (C. 3 Κ =

The demonstration succeeds only if we get - F(b) ε to something

(this will be clarified further on). But first we must eliminate

" V " in line (5). This is possible with an application of (C. * e p ) ,

but to do this we need line (7') such as:

(7') Π x) Κ (b=x)eut you I

instead of (7). To obtain this we must have the new assumption:

(0) KT ( 3 χ) Κ (b=x) e μ ι you

from which:

(7') (3 χ) Κ (b-x)ev* you I

because of the application of ( C . K * ) to t'ne considered assumption.

We may now obtain line:


W H O - Q U E S T I O N S 85

(8) Ρ - F(b) e U* (5) (7·) χ (C. Hep) you I

Now, an application to (8) of (C.P*) is possible only if Ρ - F(b) belongs to μ, that is (C.P*> is the following:

(C.P*) If "P p" e W and if μ belongs to a model system Ω, then there is in Ω at least one epistemic alternative μ * to μ (with respect to a ) such that ρ e μ*·

But in our case - F(b) belongs to μ * which is(already) an epis-temic alternative to μ with respect to I. It seems therefore necessary to generalize (C.P*) so that it allows for the "passage" from an epistemic alternative to μ * with respect to I to an episte-mic alternative to the epistemic alternative with respect to You. We indicate with μ* an alternative to μ with respect to I; so we

indicate with μ * * an epistemic alternative to μί with respect _ v you ι to You.

This situation is very similar to that predicted by Castafleda Q # ( _ (1970 ) for the derivation of a principle such as:

[ 7 ] Κ Κ, Κ Κ, ρ •*• Κ Κ, Κ ρ a b e d . a b α

which may be demonstrated as follows:

[8] (1) Κ IC Κ Κ^ ρ e μ Ass. a b e d

(2) Ρ P. Ρ - ρ 6 μ C.Ass. a b a

(3) Κ, Κ Κ, ρ 6 μ* b a d α

(4) Κ Κ. ρ e vT* , a d b I , *

)(C.K gen.) (5) * ρ e ν * * *

a a

(6) P e v * * * *

(7) Ρ Ρ - ρ e μ* b e a

(8) P a ~ Ρ € μ * * \ (C.P* gen.)

(9) - ρ e μ • ••


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Line (9) of our demonstration will be:

(9) - F (b)ev** (8) χ (C.P * gen.) you

Such generalized rules will, however, have to specify the relation-ship between alternatives with respect to different variables, and moreover they will have to contain an interpretation of such a re-lation; in Castafieda(1970)this relation is that of subsumption (p. 199) .

We can on the other hand show how the formula:

[9] KT(lx)K F(x) ->- C 3 x)KTF(x) I you I

is not demonstrable.

[10] (1) KT ( 3iJ Κ F(x) <= u Ass. I you

(2) C»xJ Ρ - F(x) e μ C.Ass.

(3) f 3 χ) Κ F(x) e y ι (1) x (C.K) you

(Α) κ F(b) e ν you

(5) (3 χ) Κ (b-x) t μ you

(3) χ (C. 3 ep)

In order to be able to arrive at -F(b) we must be able to substi-tute b for χ in (2) but in order to do this, an additional premise such as ( 3 χ) Κ^ (b=x), which we do not have, is necessary. But let us ask ourselves: What meaning could we attribute, on the level of a pragmatic analysis of the relationship between questions and answers, to such a situation?

The above formula is readable in the following manner:

[ll] if I know that you know someone who lives here, then I know someone who lives here,

which can easily be false since I can know that you know someone who lives here and still not know someone who lives here. If we had the additional premise ( 3 χ) Κ(b=x) that is "I know who this some-one is" then we would have the cognitive situation on the basis of


WHO-QUESTIONS 87

which I could predicate about this someone the property "living here". Now let us consider the principle which is able to be formulated from a linguistic point of view in the following manner:

[12] Only if I know that someone lives here, then I know some-one who lives here.

We can consider the part upheld by "only if" as a precondition to the knowledge, on the part of "I", of someone who lives here,at least in the sense expressed in the following proposition:

[13] There can be no other way to know someone who lives here other than that of knowing that someone lives here,

which evidently, in the area of asking a question, can assure, in an intuitive manner, the truth of the principle [12 J. It is also clear that we can, as in the case of the principle discus-sed before, consider, on the level of the precondition, believing more than knowing,the difference between the two cases still being dictated by reasons of a contextual nature. But we can give another pragmatic interpretation to the principle given above which might serve to underline the relationship between belief and know-ledge. Before asking the question the questioner might believe or know that someone lives here. Let us suppose that he only believes. Having obtained the answer we would have instead that the question-er knows that someone lives here since he knows someone who lives here. We can therefore say that there has been a "transition" from a de dioto belief status to a de dicto knowledge status.

On the other hand, the converse is not true:

[14] If I know that someone lives here, then I know someone who lives here,

as is demonstrated intuitively in the following proposition:

[ 15 ] [14 ] can very easily be false since I can know that someone lives here and still not know someone who lives here.

Formally, then, [12] takes on the following aspect:

[16] Π χ) Κj F(x) + Κ (Ix) F(x)


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which can be demonstrated with Hintikka's(1962Knstruments. We will abandon the demonstration since [ 16 ] corresponds to (116) Hintik-ka's(1962), and we will also not show how the converse cannot be de-monstrated, since, in essence, the demonstration of this is in Hin-tikka(1962)on page(163). The antecedent is the desideratum in Hin-tikka' s opinion'; the antecedent without the operator of knowledge is the presupposition in Hintikka's o p i n i o n . W e call the conse-quent "K-precondition"; in the case of the operator of belief we will have a "B-precondition".^

The following demonstrable principle:

[17] Κ F(b) - F(b)

can receive the following pragmatic interpretation. Since F(b) is the answer to a wh-question, then it says that the answer is a ne-cessary condition for my knowledge. This also describes a prelimi-nary step which is necessary in order to obtain the desideratum.

The case of real wh-questions with negative answer leads to an interesting principle which we can formally represent in the follow-ing manner:

[18) ( 3*;· F(x) - - ( 3x) Κ F(x)

for which the demonstration is:

19] (1) Κ - (ix) F(x) e μ Ass.

(2) ( 3 x) Κ F(x) e μ C.Ass

(3) Κ F(b) e V ) i

|(2) χ (C. 3ep) (4) ( 3 x) KT (b=i) e μ J

(5) F(b) e μ* (3> x (C.K* )

(6) ( 3 χ) (x=b\ e |1Φ (4) χ (C. K « * )

(7) λ χ ( Ix) - F(x) G μ (1) x (C. - 3)

(8) (Ix) - F(x) e μ* (7) χ (C.K*)

(9) - F(b) e μ* (6), (8) χ (C. V„)


WHO-QUE STION S 89

for which the reading is:

[20] If I know that no one lives here, then I don't know anyone who lives here.

Intuitively we can ask ourselves: can I know that no one lives he-re and still know someone who lives here? The answer is negative so that the principle given above can intuitively be held to be true. Let us note then how the knowledge acquired by "I" (i.e. Κ -( 3 χ) F(x) ) through the answer of "you" (considered as a necessa-ry condition in order to obtain such a knowledge; see the next principle [22]) is a sufficient condition for the negation of the desideratum of "I". Now let us show how there is a very strict relationship between K(B) - preconditions to real questions with either negative or af-firmative answers, knowledge acquired through answers to real ques-tions with negative answers, and rhetorical questions. Let us first of all note that if the questioner knows or believes that no one lives here, then he does not ask "you" who lives here; therefore, it seems that the principle:

f 21 ] KI - ( 3 x) F(s) - - ( 3 x> XT F(x)

is intuitively true, but in fact it is proved by the demonstration given above. We must however point out the pragmatic difference between this principle qnd the one demonstrated before. Here the antecedent is a K-preconditioq oi the speaker, there, it is a knowledge acquired through an answer; an indication which refers to s.uch a difference is due to the-eventual presence (since it is dictated by reasons of a contextual nature), in this case, of the operator B^, while in the other cannot be such a presence, if only for the fact that from an answer one obviously acquires some form of knowledge and not of belief. [21J can be considered a precon-dition of a general type. In the case of real questions with affirm-ative or negative answers we can say that they have the same pre-conditions, but the difference that we" might run into resides in the dif ference between the use of B^ and K^ in . he intecedent. If he who asks the question knows that someone lives here, then a ca-se of true negative answer does not seem possible; this type of ansvep would probably be considered a lie. If on the other hand the


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person who asks the question believes only that someone lives here then a case of a false negative answer is accepted and the speaker is given to considering his as a false belief. Even in the case of real questions with a negative answer we can consider a principle of form which is analogous to [ 17 1 and that is the following principle:

[22] Κ - (3x) F(x) - - Hx) F(x)

in which the consequent is the answer. Now we must examine the case of rhetorical questions, in particu-lar of wh- rhetorical questions. We would like to give a suitable definition to wh-rhetorical ques-tions which uses the concept outlined here, that is to say, we would like to see up until what point it is possible to give a defi-nition to wh-rhetorical questions which keeps in mind not only the hintikkian concepts of "desideratum", "answer", "presupposition", but also of the pragmatic concept of "precondition", as it has been outlined in the preceding pages. One of the most interesting characteristics which we can single out in wh-rhetorical questions,in keeping with the pragmatic point of vjk which we have taken in these pages, is that the questioner already knows the answer; the epistemic status of a rhetorical question is not that of a request of information, that is of knowledge, but in accordance with the traditional view, that of persuading (sugges-ting to) the listener to accept a knowledge which the questioner and the listener already own. This is definitely the central aspect of rhetorical questions, and it is so for the reasons which we shall now examine. We will try to outline the concepts of preaondi~ tion and of desideratum; moreover we will demonstrate an inter-esting resemblance between the behavior of such questions and that of real questions with a negative answer.The central point first outlined can be taken as partial. In this sense, if the speaker A asks the question x? to Β knowing the answer R, then x? can (but not necessarily) be rhetorical. The problem of knowing whether A has or does not have this knowledge is an interesting problem but one which we will not discuss here. It must be noted however that in many cases the answer is already explicitly contained, granmatically, in the question; the following

.19 . . . are examples taken from Carducci which are indicative of this:


WHO - Q U E S T I O N S 91

"And what is it worth to live without love if not to disturb people?" "And shouldn't instruction be, along with education, a development of intellectual and moral faculties, and a heading of these fac-ulties towards the true and the good?"

The problem is that of establishing which logical form of the questioner's knowledge is used for rhetorical wh-questions.

It is interesting to note at first how the context can play an important part in determining the rhetoricity of a question. For example, let us consider the following question:

[23] Who is it that has not read Dante?

This is obviously rhetorical in an ordinary context. But if we think of it asked by the teacher to the students of his class then it be-comes a test question: the desideratum of such a question is a knowledge relative to the knowledge of a composite listener: the question is not addressed to anyone in particular, but to a col-lectivity. We will see further on with an example that such cases can be given for rhetorical questions also.

Even if we exit for a moment from the discussion it is worth paying attention to a very particular type of test-question. For example, let us consider the following;

(i) how many six legs do tree ducks have?

which apparently contains the answer, but which for its elliptical-

ness, which can be seen through the use of "times" between "how ma-ny" and "six", it seems to be an authentic test-question.

This becomes even more clear in the following example:

(ii) How many six legs do four ducks have?

in which the apparent answer given by "six" does not coincide with the eventual computation check "four times two" which can be done; in fact, this allows us to avoid the implicit tranello in the ques-tion itself.

But let us go back to [23], It is clear that the knowledge sta-tus of the speaker can be expressed in this way:

[24] A knows that there is no χ that has not read Dante,


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Formally, we may write this

[25] Κ - (3 χ) ("person (χ) S - has read (x, Dante) )

Again,

[26] What children do not like ice crcam?

for which A's knowledge status is:

[27 ] A knows that there is no χ that is a child and that does not like ice cream,

from which we can formally write,

[28] Κ - ( 3 χ) (child (x) & - likes (x,ice cream) )

that is:

[29] Κ ( 1 x) (child (x) + likes (x, ice cream) )

Even the question, "who lives here?", dependently on the fact that the questioner knows the answer and on the context, can be considered rhetorical.^

A common characteristic of these examples is the fact that, first of all, the questioner's knowledge, and of course that of the answerer,is relative to the negation of an existential quanti-fier. That gives place, in examples such as those relating to child-ren and ice creams, to the very interesting fact that the knowl-edge of the questioner takes on the form of a universal sentence of a conditional type. We can therefore propose the following af-firmation:

(a) The logical form of the precondition for a rhetorical wh-ques-tion is the following:

Κ - (ix) ( )

We must however specify further. As we have seen in the case of real questions (with either an affirmative or a negative answer) the logical form of the questioner's precondition, concerning the


WHO-QUESTIONS

epistemic operator, was dictated by reasons of a contextual nature the empirical context in which the question was asked determined the choice between Κ and B. In the case in point, instead, the choice of the epistemic operator seems to be contextually indepen-dent; the only possible choice is related to the K-operator. More-over, the answer and the precondition coincide.

We can also have rhetorical questions which because of their construction can be called epistemic; one example is given by

[ 30 ] Who is it that does not know the name of his own parents?

that is,

[31] Κ - ( 3 x) (person (x) S - knows (x, the name of his own par ents) ).

We will now try to analyze up until what point our pragmatic analysis is in agreement with the logico-semantical definition of a rhetorical question given by Harrah-Belnap.^

Belnap (1969) proposes the following definition:

A question q is rhetorical relative to a set of sentences S, if S logically implies some direct answer to q.

In agreement with the pragmatic vision of J. Schmidt-Radelfelt ( 1 9 7 7 ) ( a l so Belnap (1969) ) S is an extremely complex set which contains elements belonging to categories (which, for their role of being developed in the definition of a rhetorical question we can place together under the general heading "pragmatic") which are very different amongst themselves. For example, we can have the intentions of the speaker, a conmon knowledge shared by the speaker and the listener, acceptability of the presuppositions, etc. Of particular interest to the discussion which we are devel-oping is the second point, especially in its aspect of "the speak er's knowledge". Expressing such a knowledge, on the basis of (a), with K-(3x)P (x) let us consider the subset of S

Δ {Κβ - (Ix) P(x) } ; we can therefore notice how the prin ciple Κ - ( 3 χ) Pix) •* -Cix)P(x) is a logically valid principle of epistemic logic. It is therefore easy to prove how such reason-ing agrees with the definition given by Belnap.

We can at this point observe how such a principle can play dif-ferent roles and therefore receive different interpretations in


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the case of real questions with negative answers and in the case of rhetorical questions. On one hand the consequent is a direct answer (to use Belnap's terminology) which is not a part, at least not until it has been uttered, of the questioner's stored knowl-edge; the antecedent expresses the success of a piece of informa-tion-knowledge that has already been acquired. On the other hand, the consequent is the direct answer of the listener, while the antecedent expresses the knowledge of the speaker-questioner. This shows a first similarity of logical behavior between the two types of questions.

Let us now face the problem which is relative to the "deside-ratum" of rhetorical questions. We must answer this question be-fore: given that rhetorical questions cannot, for reasons which we have just discussed, be characterized as requests of information-knowledge, and given that the central aspect of logical analysis of these questions resides in its desideratum, is it possible to uphold the idea that even rhetorical questions have a desideratum? It would be useful in this case to begin with an example. Let us consider the case of a defence attorney who in his speech turns to the jury with the following rhetorical question:

[32] What could the accused have done (in those circumstances) but to behave (.... in such a way...)?

The jury may answer in a truly particular sense of the term; in the council chamber an answer which denies the behavior (proposal of counterexample) suggested by the defense lawyer in his speech can be given. But the goal of the defense lawyer is exactly that of avoiding that the jury gives such an answer, and therefore we can think that the defense lawyer desires not to know of any form of behavior which denies the knowledge suggested (by him). We can, on the other hand, consider examples taken from more common contexts, such as that which concerns children who like ice cream. If the listener gives an example of a child who does not like ice cream, it is often empirically verifiable how the questioner is irritated, by such an answer. In fact, the questioner cannot not have the desire not to know any child who does not like ice cream. The logical form of the desideratum of a rhetorical ques-tion can therefore be the following:

[33] - ( 3 x) KT F(x)


WHO-QUESTIONS

where the imperative or optative part is ignored. We can therefore formulate the principle:

[34] KT - (3x) F(x) (3x) Κ F(x)

which can be interpreted in this way: [35] If I know that there is no χ that has the property F, then

(I desire) not to know any χ that has the property F. If we compare this principle with principle [18] we can discern a second similarity of logical behavior between rhetorical ques-tions and real questions with negative answer. It is clear that there is also a difference, to be seen at the level of pragmatic interpretation that we want to give to such a principle in the two cases. In the case of real questions with a negative answer, the antecedent,as we have already said, is a knowledge of the ques tioner acquired from the answer, the consequent indicates the modi fication which has come about in the desire of the questioner. In the case of rhetorical questions, the antecedent is a knowl-edge which is a part of the stored knowledge of the questioner , the consequent indicates a questioner's status which can be seen through this sort of irritation test which consists in answering (with a counterexample) a rhetorical question therefore consider-ing it in the same way as one would consider a real question.

If, however, we return to the interpretation of the preceding principle we can note how the absence of the imperative part seems to "mutilate" the rhetoricity of a rhetorical question. In other words, we want to uphold the concept that if on one hand the desideratum of real questions with a negative or an affirm-ative answer allows for the possibility of ignoring the imperati-ve part, this does not seem to be possible with rhetorical ques-tions; it is exactly this absence which would unite them in so-me way to real questions with a negative answer, in this way al-tering the meaning (of rhetorical questions). From the point of view of logical formalism we already have available instruments which enable us to face this problem; it involves taking advan-® tage of Aqvist s imperative-epistemic logic. The sentence: f 36 ] Κχ - ( 3 χ) F(x) •*•!-( 1 χ) Κ F(x)

where "!" is tead " Let it be the case that", can be demonstra~ ted in the following way:


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[37] (1) Κ - (Ix) F(x)e ν Ass.

(2) i(1 xj Κ F(x) e ν C Ass.

(3) J 3 χ) Κ F(x) e V* (2) x (C.i*)

(4) Κχ F(b) 6 L χ (c> Jep) (5) (Ix) Κ (b=x) e u* j

(6) F(b) e v* («) x (C.K)

(7) (Ix) (x=b) e u* (5) X (c. 3 Κ =)

(8) Κ (1 χ) - F(x) e ν (1) χ (C.- 3)(C.K)

(9) (ix)-F(x) e V* (8) χ (C.K* )

(10) - F(b) € V* (7) (9) χ (C.»„ )

For the sentence:

[ 38 ] KI - ( 3 χ) F(x) - - ! ( 3 χ) Κ F(x)

we have the demonstration:

[39] (1) Κ - C3 x) F(x) e ν Ass.

(2) / (Ix) Κ F(x) e μ C.Ass.

(3) r 3x; Κ F(X) e u# (2) χ (c.!*)

as before

For rhetorical questions which are more complex, such as those in the preceding examples, we have the following three princi-ples, respectively:


W H O - Q U E S T I O N S 97

Γ40 Κ - (1 χ ) (CCx) & - L ( x , a ) ) •* - ( 3 χ ) Κ χ ( C ( x ) & - L ( x , a ) )

[ 4 1 ] Κ - ( i x ) ( C ( x ) & - L ( x , a ) ) - /- (3 χ) K J . ( C ( x ) & - Ι ( χ , α ) )

[ 4 2 ] Κ - (1 χ) ( C ( x ) S - L ( x , a ) ) -.' ( 3 χ) KT ( C ( x ) S - U x , a ) ) I j.

We would like to conclude with a discussion which is relative to V the possibility of applying imperative operators to principle [16]. The legitimacy of such an application, at least from an interpreta-tive viewpoint, (in the sense that the "translation" of a question comprises an imperative part as well as an epistemic one) is relative to the antecedent of [16] since it is a desideratum; we would there-fore have the following principle:

[43] / ( 3 χ) Κ F ( χ ) * Κ ( i x ) F ( x )

for which the demonstration is:

[44] (1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

/ ( 3 χ) Κ F ( x ) e

PT( I x ) - F ( x ) e

α χ) Κ F ( x ) e

K I F ( b ) e μ1

Π χ ) K^h-x)

( I x ) - F ( x )

F ( b ) e V*

( 3 x) (x=b) 6

- F ( b ) e V*

u

Ass.

C.Ass.

(1) χ (C. !*)

(3) χ (C.3ep)

(2) χ (C.P*)

(4) χ (C.K )

(5) χ (C.3K=)

(6)(8) χ (C. »„)

The reading of such a principle is:

[45] Only if I know that someone lives here, then let it be the case that I know someone who lives here.

We can also easily demonstrate the principle:

[46] ( i x ) Κ F ( x ) •* ! K j O x ) F ( x )

In fact, since we have the rule:

(S) h p + q »I-•' ρ * q

all we need to do is consider as antecedent of the rule the prin-ciple already demonstrated ( 3 x) K^ F(x) •* K^. ( 3 x) F (x) .


LIBERO VENZI

Let us note how the principle being discussed is in agreement ο with Aqvist's thesis on the basis of which "!" functions as a genuine imperative operator only when it is applied to sentences which contain Κ or P, as happens in the case in question, sin-ce we have ( 3 χ) Κ F(x) and K^ ( 3 x) F(x). In the case of ordinary sentences, if we didn't annul its efficiency with ρ «—»/ρ, we would find ourselves in the paradoxical position expressed by: .' Κ ρ «—• !p

The pragmatic principle being considered does not, therefore, seem to be subject to this paradox. It is instead easy to prove how an interesting principle which connects the answer to the knowledge acquired after its utterance can be subject to the pa-radox mentioned above; we are referring to principle [17].

Let us consider the following question:

[47] What is the number of Jews killed by the Nazis?

The answer is: "6,000,000". The paradoxical situation is clear:

[48] If it ought to be the case that I know that 6,000,000 is the number of Jews killed by the Nazis, then it ought to be the case that 6,000,000 is the number of Jews killed by the Nazis,

where we think of "!" as a kind of deontic ought-operator. We must, then, in such a case consider the principle ρ » ! p

since the consequent of [ X7] does not contain operators like Κ or p. The notion of presupposition that Xqvist arrives at beginning with ρ «—» !p i.e.:

Q presupposes ρ (Q: question, p : ordinary sentence) iff t— Q •* ρ together with the pragmatic principle which we have already demonstrated (i.e. ! ( 1 χ) Κ F(x) •* Κ ( 3 x) F(x)l(>) allows an interesting explication of the notion of questioner's precondition (Qr -p recond i t i on ) in its form of K-precondition (abbreviated: Κ (^-precondition).

Therefore, we have the following:

Kp is a KQr-precondition relative to Q (where $ is a question and ρ is a presupposition of Q) iff I— Q •* Kp.


WHO-QUESTIONS

It is easy to verify that this last formula is the principle

.' ( 1 x) Kj. F(x) Kj( 3 x) F(x) in which the antecedent is the analysis of the question and the consequent is formed by the operator Κ linked to the presupposition ( 3 x) F(x) of the question; evidently in the case of the notion of^presupposition, since we have ( 3 xj F(x) , the principle p*-*!p will have to hold,while this will not be the case for the notion of KQr-precondition.


100 L I B E R O V E N Z I

NOTES

(1) See Äq ν i s t (19 6 5).

(2) See Hintikka (1975) but also Hintikka (1974).

(3) See Aqvist (1972), but also Aqvist (l 975).

(4) See Aqvist (1972): 29-30.

(5) "Also, asking the question "How many bones in a lion?" ordi-

narily implies that the questioner doesn't know the (true)

answer and thinks it likely that the respondent either knows

or can find out the number of bones in a lion.

The last-mentioned relation describes the questioner, the

respondent, and the empirical context in which the question

is asked rather than the topic of the question. We :nay call such

implications "pragmatic", since they are so closely related

to the speaker involved in erotetic situations".

(6) Italian translation, in M L a linguistica testuale" edited

by M.E.Conte, Feltrinelli, Milano, (1977).

(7) We will not discuss at this point the difference between

attributive and referential·, for this see, e.g., Boer and

Lycan(l975).

(8) See Castaneda (l970):i99.

(9) See Hintikka (1975): 279.

(10) As in note (9): 285.

(11) If we accept a thesis such as I— Kp •* Bp, then by substituting

the formula ( 3 x)F(x) for ρ we would have:

( 3 x) Κ F(x) + Β ( Jij F(x) For a discussion on the above thesis see, e.g., Lehrer

(1970).

(12) See respectively " Delle rime di Dante" and " A proposito del-

le scuole elementari serali" both in" Prose di Giosue Carduc-

ci MDCCCLIX-MCMIII1) Zanichelli, Bologna, 1909.


WHO-QUESTIONS 101

(13) A and Β are found on the threshold of the door of a hovel where only an animal could live (- context) and A asks Β "Who lives here?" with a facial expression depending on his state of mind; it is clear that A and Β have the same knowledge.

(14) We have used 'Harrah-Belnap' since Belnap accepts the definition given by Harrah (1961); we have chosen to refer to Belnap (1969) since his analytical method is closer to ours.

(15) See Schmidt-Radefeldt(1977>:377.

(16) In fact we can demonstrate the principle: / ( Ix) Κ F(x) - ( 3 x) F(x).

ο (17) In Aqvist 1972 the only change in the definition of a QIE

model system is the addition of a condition: ( C . * ) If ρ does not contain imperative or epistemic

operators, and if ρ e and μ* is an imperative alternative to g in (I , then ρ e u*.


102 LIBERO VENZI

REFERENCES.

Aqvist,L.(1965) A New Approach to the Logical Theory of Interroga-tives, Filosofiska föreningen, Uppsala.

— (1971)Revised Foundations for Iraperative-Epistemic and Interro-gative Logic, Theoria, 37: 33-73.

— (l972)On the Analysis and Logic of Questions, in R.E.Olsore and A.M. Paul (eds.). Contemporary Philosophy in Scandinavia, J. Hopkins U.P., Baltimore and London: 27-39.

— (1975)4 New Approach to the Logical Theory of Interrogatives: Analysis and Formalisation, TBL, Narr, Tübingen.

Bellert.I.(1970)0n a Condition of Coerence of Texts, Semiotica, 2: 335-363.

Belnap, Jr. ,N. D.(l969) Questions, Their Presupposition, and How They Can Fail to Arise, in K.Lambert (ed.) The Logical Way of Doing Things, Yale U.P., New Haven: 23-37.

Boer.S.E. and Lycan.W.G.(l975)Knowing who, Philosophical Studies: 299-344.

Castaneda.H.N.(ΐ97θ)θη Knowing (or Believing) that one Knows (or Believes), Synthese,21: 187-203.

Harrah.D.(1961) A Logic of Questions and Answers, Philosophy of Science, 28: 40-46.

Hintikka,J.(l974)Questions about Questions, in M.K. Munitz and P. K. Unger (eds.), Semantics and Philosophy, New York U.P., New York: 103-158.

— (1975)Answers to Questions, in H.Hiz (ed.), Questions, Reidel Dordrecht: 279-300.

Lehrer,K.(1970)Believing that one knows, Synthese·. 133-140.

Schmidt-Radefeldt,J.(1977)On so called "Rhetorical" Questions, Journal of Pragmatics, 1: 375-392.

Istituto di Filosofia Universitä di Bologna


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Who-Questions: Some Pragmatical Principles