The predictions of the text

by Giampaolo Lai ([1]) and Pierrette Lavanchy ([1])

Draft for the Accademia’s meeting The logic of prediction in Milano on Sunday November 9^th; and for the Conference The analysis of conversation to be held at the University of Bologna on Saturday November 22^nd .

                0. Introduction. The aim of our presentation is to display the calculus for the text’s predictions. The text’s predictions are actual descriptions, in a initial world u, of possible configurations of future texts, in a final world w, inferred from the formal textual indicators of the world u. The operations of our calculus will be restricted to the logico-modal figures.

1. The text. A fragment of the conversation “The hold up of the Bank”, recorded with  Agatha il 2.1.2002.

╔1 Agatha: Well, it is some time since I am alone, without my old family, I have been away with Michele and Duccio, then I went back here for some days, then went back to the mountains, and so I had no bother. When I went back here I took care not to turn up with my father and my mother, and so now, when I was coming here, all the problems were a little softened by this kind of nice pad.

1 Conversante: Yes.

2 Agatha: Which however makes me think, and it was in some way that which, upon which I have also thought over in these ten days, it makes me think that I must succeed in detaching myself more.

2 Conversante: Yes.

3 Agatha: But, in another way, I also feel, and here I think it is true, but it is not clear, that I must break with them in order to go ahead in my, in my own way. Because, in my opinion, they are really a dead weight to me. When I hear myself reason in a certain way, or I find myself again, like last Christmas, in front of a reality, which is exactly the one I want to leave, because it is the one that has prevented me from making my few, many, small, big steps, there is also this need to, really to put an end to a certain way of being.

3 Conversante: Yes.

4 Agatha: For example, my sister was telling me of my father: “One does not understand, he says, and I agree with him, why you don’t put up a publisher’s business”. And I come across these things once more, I say; “Well, because I would like too write books, not to sell them”.

 4 Conversante: Here you are, here you are, let me also add what I think I have understood. That is, on the one hand you want to keep distant from them, end it with them, break off, anyway it is them you are dealing with. On the other hand, there is something more strictly yours, “I want to write a book”, which is of course a way to, to, to get off from a dimension of theirs, where they change you into a publisher, but above all it is a way to go along a direction which is yours, writing.

5 Agatha: Which is what I do.

5 Conversante: To me it seems that I have understood two directions that you...

6 Agatha (breaking off): Yes, just so. As to two directions, I am not quite able. I already get tired walking along one street, if I also have to walk along two I am not going anywhere. I feel I won’t manage in writing the book if I keep them on my back. What I succeeded in doing has been, for instance, and there it seemed to me it was all right, but who knows, if also the experience, yet, after all, I dare say, yes, every time one may always choose, each time, yet then one should keep a bit of a direction in order to build oneself, when Costanza has gone away, which Clelia and I had wished for so much (she laughs), and instead one should indeed, okay, never mind, I have survived to my imaginary or to my father’s actual expectations by writing a book. And this has been the salvation for me. And now I am doing the same thing.

6 Conversante: Sure. You used two formulas which allow you to see things from two different points of view, on the one hand you said that you must free yourself from all your relatives in order to be able to write the book, or, that in writing the book you free yourself from all your relatives.

7 Agatha: Sure. Apart from the fact that, yes, eh, eeeh, that I too had thought of it a little, therefore probably what you are grasping is (interrupted).

7 Conversante (cutting in): What you see is something outside, which regards just you, it is your passion, your desire to write. Well, that thing, you really see it.

8 Agatha: Yes, by now I do.

8 Conversante: Which is one side of the same medal as getting rid of them and going away towards something that belongs to you, not from the point of view of getting detached from them, but of going off towards something that belongs to you.

You see that.

9 Agatha: Yes, indeed, this thing of going towards something mine, I do see it. And this is what I am trying to do, with some obstinacy too. (silence 20”). But the way you put it seems to be simple: “The more you go towards something that belongs to you, the more you actually get rid of your relatives”.

9 Conversante: Yes.

10 Agatha: Eh, you see it as simple, instead it is not. ╗

╔10 Conversante: Yes, of course. Try and imagine, try and imagine, this is a play I sometimes engage in when I drive downtown, I say: “If I were a robber who has to go and assault a bank, I won’t get angry with that other driver who cuts in on me. I have got quite another and more important thing to do, I can’t waste my time over such a trifle. I have got to hurry up to get to the bank, the rest doesn’t matter”. On the contrary, if I am in no special hurry, I dwell upon the obstacle.

11 Agatha: Quite so, I agree, this is a thing that I too would, yes absolutely, absolutely. I mean, I notice I behave differently whether I have a clear aim or whether I don’t.

11 Conversante: The passion, the urgency to get there prevents one from seeing small obstacles, small flies. ╗

╔12 Agatha: Yes, this thing you are saying sounds cute to me. The point is that they are not small obstacles. Sure enough, you would tell me: “It is your business to make them small. The more you listen to that passion, the more they become small obstacles” (silence 6”). Yes, I think what you are saying is true. Then clearly things are not perfect. Because, if you were a robber who meets up with one obstacle after another, you would say at the end that you will never arrive at the bank. And I often feel as if I were in this, I am a very weak driver who let herself (silence 10”). Yes, yes, you are perfectly right, this is true. But, my God, it is as if they succeeded  in multiplying the obstacles, with which it is easy (sentence suspended).

12 Conversante: Yes, where the center is set on you and not on them, not so much to say: “I   have got to detach myself from them”, as to say: “I have got to go and assault my Bank”.

13 Agatha:  Yes and afterwards, when I don’t know where to go because everything is in crisis, I have got to go on telling myself: “If I knew what I want, I would see them less”, and instead I say: “Really, is robbing banks a good thing? Perhaps it is better not to rob banks. After all, I could find a work as an employee in the bank”. And so my nerves break at the first traffic light.

13 Conversante: Some would say: “Faithless woman”, that is, you don’t have any faith in

14 Agatha (cutting in): No, none.

14 Conversante: in your aim.

15 Agatha: I lack strength, more than faith. I seem to lack it. But it is true, what you are telling me is, I think you are right. I keep to my aim to write the book.

15 Conversante: Yes.

16 Agatha: Then freeing myself from them becomes consequential. It is not an aim, but a consequence.

16 Conversante: That’s it.

17 Agatha: It ought not to be an aim. I ought never to think of freeing myself from them.

17 Conversante: That’s it.

18 Agatha: I ought never to think of them. I ought not to look at them. You are right. The Medusa. ╗

2. The subdivision of the text. The transcribed fragment of Agatha is treated as a whole, named world W. The world W is a set of worlds, that contains three sub-sets, indicated in the text by the signs  ╔ ... ╜, and named with the symbols u, for the initial world which contains Agatha’s verbal turns from 1 to 10; v for the middle world which contains the therapist’s verbal turns 10 and 11; and w for the final world with Agatha’s verbal turns from 12 to the end.

3. The  relations between the worlds u, v and w from the standpoint of results or of predictions. We shall study the relations of the three worlds, the initial world u, the middle world v and the final world w,

(1)  u  R  v;

(2)  v  R  w;

(3)  u  R  w;

and in particular the relation

(c) u  R  w.

Looking from w to u, retrospectively, the difference between u e w is the result of the conversation. Looking forward, from u toward w, when w is not yet present, we can guess what kind of logico-modal figure, in w, we are able to construct from the textual indicators of the world u. 

            4. The aim of the presentation of Agatha’s text. The aim of our presentation is therefore to display the calculus for the text’s predictions. The text’s predictions are actual descriptions, in a initial world u, of possible configurations of future texts, in a final world w, inferred from the formal textual indicators of the world u. The operations of our calculus will restrict themselves to the logico-modal figures.

            5. The calculus upon the text’s logico-modal figures. To perform the calculus upon the text’s logico-modal figures we proceed as when one try to discover in a starry sky - and the starry sky are the words and the sentences of the text - the conformity of the stars’ agglomeration to the geometrical feature, say, of the triangle or of the trapezium. In the Table n° 1 you can find the four or five logico-modal figures canonically employed in Conversationalism. By definition, all the possible stars’ agglomerations shall conform to one or another of the four logico-modal figures, and to nothing else; moreover, no star can be said not to belong to the one or to the other logico-modal figure. __________________________________________________________________________ The alethic logico-modal figures (from aletheia ‘the truth’)

                               the Possible,      Mp (≡~N~p)                           ‘it is possible that p’

                               the Impossible, ~Mp                          ‘it is impossible that p’

the Necessary, ~M~p (≡Np)             ‘it is not possible that not p’ ≡ ‘it is necessary that  p’

The deontic logico-modal figures (from déon ‘the obligation’)

                               the Permission, Pp,                             ‘it is permissible that p’

the Prohibited, ~Pp,                            ‘it is not permissible that not p’ ≡ it is   prohibited that p’

the Obligation, ~P~p(≡ Op)            ‘it is not permitted  that not p’ ≡ ‘it is

                                                         obligatory that p’

The axiological logico-modal figures (from axios ‘moral value’)

                               The Good, Gp,                                     ‘it is good that  p’

                               The Evil, ~Gp,                                     ‘it is not good that p’                                                        the Indifferent, ~G~p.                        ‘it is neither good nor bad that  p’

The epistemic logico-modal figures (from episteme ‘the knowledge’)

                               il Sapere, Kp,                                       ‘he knows that p’

                               il Non-Sapere, ~Kp,                            ‘he does not know that p’

                               the Belief ~K~p (≡ Bp)                       ‘he believes that p’

The temporal logico-modal figures:

                               *Pp         ‘it has been true that p’; ‘it happened that p’ (week past)

                               Hp          ‘‘it has been always true that p’; ‘always in the past p’  (strong past)

                               Fp           ‘it will be true that p’; ‘il will happene p’ (week future)

                               *Gp        ‘it will be always true that p’; ‘always in future p’ (strong future)

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table n° 1.  The 5 logico-modal figures, with the corresponding operators. The symbol ~ stands for negazione, ‘not’; the symbol p stands for the propositional content, or the argument. The alethic operator of the Necessary is pointed as N, Np, which is more handy than the equivalent ~M~p; the alethic operator of the Possible with the symbol, M, Mp, otherwise, is defined in terms of N in the equivalent form ~N~p ≡ Mp. Likewise, the deontic operator of the Obligation will be written as O, Op, or defined in terms of P, ~P~p ≡ Op (≡ is the equivalence’s symbol).

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6. The conformity of the initial world u to the logico-modal  figures. We shall start by asking: to what logico-modal figure does the initial world u conform? We can follow two procedural guides: the first is a lexical one; the second is mediated by the paraphrases. The first, lexical, criterion is provided by the modal verb ‘devo’, ‘must’, ‘I must’, of the verbal turn 2: “I must succeed in detaching myself more”, repeated in the verbal turn 3: “I must break with them in order to go ahead”. It is not easy to decide whether ‘devo’ stands for a moral conditional obligation, or for an unconditioned natural necessity. In the first case, the world u would conform to the deontic figure of the Obligation, and the logical translation of ‘devo’ would be ‘I ought’ (as in the sentence: ‘I ought be honest’). In the second case, the world u would rather conform to the alethic figure of the Necessary, and the logical translation of ‘devo’ would be ‘I must’ (as in the sentence: ‘we all must die’). The first case is best represented by the model of Antigone, the second by the model of Icarus. Looking at the starry sky of the world u, we have had the impression that, from the point of view of comparative possibility, the world u is nearer to Np than to Op. This impression is greatly encouraged by the sentence in the verbal turn 3: ‘Because, in my opinion, they are really a dead weight to me (mi fanno proprio da zavorra)’, where the word ‘zavorra’ (literally ‘ballast’), points to the weight of the natural body which anchors Icarus necessarily to the earth. Anyway, we have summarized the entire verbal turn 10 of the therapist in the paraphrase:

(5) it is necessary that I (give attention to)mind my parents, in order to get rid of them.

If things go as we have tried to describe, we may conclude that the starting world u conforms to the alethic logico-modal figure after the modal operator of the necessity, Np.

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logico-modal figure of the starting world u

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alethic logico-modal figure

modal operator of the Necessary, N (N is equivalent to ~M ~, but more handy)

p = ‘to mind the obstacles’

Np = ‘it is necessary that I mind the obstacles, in order to get rid of them’. ___________________________________________________________________________

Table n° 2. Which puts the alethic logico-modal figure of the Necessary at the architectonical vertex of the configuration of the initial world u, expressed in the summarizing paraphrase (5): ‘it is necessary that I mind my parents, in order to get rid of them’, particular form of the more general form: ‘it is necessary that I mind the obstacles, in order to get rid of them’. ___________________________________________________________________________

7. The algebraic calculus for the conformity of the middle world v to the logico-modal figures in the table 1. And now, we shall try to do the same calculus upon the middle world v, where is the verbal turn 10 of the therapist. Here we find an example of a special technique, named administration of autobiography (‘somministrazione di autobiografia’). In a technical sense, we speak of  administration of autobiography when the therapist, instead of dealing with the patient’s history, puts forward a fragment of his own biography for consideration. In order to study the logico-modal figure, we must summarize the entire turn 10 of the therapist in a paraphrase: 

(6) Se io fossi un bandito che va a assaltare una Banca non mi occuperei dell’ostacolo dell’automobilista indisciplinato.

(6) If I were a robber who holds up banks, I would not mind the unruly motorists

The form of this sentence is indeed, from the logico-modal point of view, extremely interesting. It is in fact a conditional statement of the form: “if ... then”, where the two components, both the antecedent and the consequent, are counter to facts: in the sentence (6) counter to the fact that the analyst is not a robber who holds up banks, and who is not indifferent to unruly motorists. For these reasons, the sentence belongs to the class of the counterfactual  conditionals. The counterfactual conditionals, based on the conditional dyadic operator -->, have the formula

(7) α  --> ß

read as ‘If it were the case that α  (α =  ‘the therapist is a robber who holds up banks’) then it may be the case that ß (ß = ‘the robber/therapist does not mind  unruly motorists’). An analysis of the counterfactual conditional α  --> ß refers to the existence of possible worlds. We may understand the possible worlds as ‘ways things may have gone’. Following this analysis, the example (6) is true just in the case in which the robber therapist does not mind unruly motorists in the closest possible world where he holds up banks. Thanks to the possible worlds theory, we can grasp easily that the middle world v conforms to the alethic figure, with the operator of the Possible: ‘it is possible that p’, Mp. Where p is, in particular, the propositional content of the therapist verbal turn: ‘it is possible that the therapist does not mind unruly motorists’, and, in general, in order to compare the p of the therapist with the p of Agatha: ‘it is possible not to mind obstacles’.

________________________________________ __________________________

logico-modal figure of the middle world v

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alethic logico-modal figure

modal operator of the Possible, M

p = ‘to mind obstacles’

M~p = ‘it is possible not to mind obstacles’

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table n° 3. Wich summarizes the conformity of the middle world v, according to the paraphrase: ‘If I were a robber who holds up banks, I would not mind the unruly motorists’, to the alethic figure of the Possible: it is possible-that-not-p ≡ M~p.

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8. The accessibility relation u  R  v. If we take the model <W, R, V>, where W is the set of world of the entire conversation; R is the relation that holds between the worlds u and v, members of W, such as {u, v}≤ W; V is the values that we assign to u and v, respectively, of Np and of M~p, we have

(8) Np R  M~p,

which reads as: ‘in the passage of time from the world u to the world v, we observe the transformation of the alethic figure of the Necessity, Np: ‘it is necessary to mind obstacles’, into the alethic figure of the Possible, M~p: ‘it is possibile not to mind obstacles’. We may ask: is this relation an accessible relation?, in other words: can we see v from u; or, in other terms, can we predict v from u? Before trying to answer, we shall go over to the calculus upon the world w.

9. The algebraic calculus for the conformity of the final  world w  to the logico-modal figures. The final world w displays two important features, lexical the first, syntactical the second, each of which seem to comform to a particular, different for each, logico-modal figures. The syntactical feature is linked with at least four hypothetical periods, in the form of conterfactual conditionals such as we already came across in the middle world v.

9.1. The counterfactual conditionals α  --> ß. Let’s take up the instances of counterfactual conditionals that appear in the final world w:

(9) se lei fosse un bandito che deve andare a assaltare una Banca e gliene venissero di ostacoli uno dopo l’altro, alla fine uno dice: “oh, alla Banca non ci arrivo”.

(9) if you were a robber who meets up with one obstacle after another, you would say at the end that you will never arrive at the bank.

                (10) [è come] se loro riuscissero a frapporre degli ostacoli poi mi scoraggerei

(10) if they succeeded in multiplying the obstacles, then I would get discouraged

(11) se io sapessi quel che voglio, loro li vedrei meno

(11) if I knew what I want, I would see them less

(12) Forse è meglio non assaltare banche. Dopotutto potrei trovare un lavoro di impiegato in banca”

(12) if I did not rob the bank, I would find a work as an employee in the bank .

From the point of view of the logico-modal figure, thanks to the possible worlds theory, as we have seen in the § 7, we can grasp easily that the middle world w, qua conterfactual conditional, conforms to the alethic logico-modal figure, with the operator of the Possible: ‘it is possible that p’, Mp. We must assign its value to the propositional variable p, i.e. the content of the paraphrase that seems more sound to us, for instance: ‘Agatha gives up the final aim of writing a book, due to the excess of the obstacles that she meets’. And this paraphrase adequately conveys the meaning of the sentences 9, 10, 12 (not of the sentence 11).

________________________________________ __________________________

logico-modal figure of the final world w, qua counterfactual conditionals

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alethic logico-modal figure

modal operator of the Possible, M

p = ‘to give up the final aim of writing a book’

Mp = ‘it is possible to give up the final aim of writing a book’

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table n° 4. Which summarizes the conformity of the final world w, expressed in the summarizing paraphrase: ‘Agatha gives up the final aim of writing a book, due to the excess of the obstacles that she meets’, to the alethic figure of the Possible, M, Mp   __________________________________________________________________________

9.1.1. The accessibility relation v  R  w.  If we take up again the model <W, R, V>, where W is the set of the entire conversation; R is the relation that holds between the worlds v and w, members of W, such as {v, w}≤ W; V is the values that we assign to v and w, respectively, of M~p and Mp, we have

(13) M~p  R  Mp,

read as: ‘in the passage of time from the world v to the world w, we observe the transformation of the logico-modal alethic figure of the Possible, M~p: ‘it is possible not to mind the obstacles’, into the logico-modal alethic figure of the Possible, Mp: ‘it is possible to give up the final aim of writing a book’. But, in this passage, whereas the modal operator M remains unchanged, the propositional content has changed. In the left term of the relation, p refers to the obstacles, in the right term, to the aim. It is therefore convenient, in order to avoid confusion, to use the symbol q for the right term:

(14) M~p  R  Mq.

We can ask: is this relation an accessible relation?, in other words: can we see w or predict w from v? or, in other words, is w deducible from v? From a clinical point of view, we can read the relation as a conditional inference of this type: ‘if it is the case that it is possible that Agatha does not mind obstacles, than it is the case that Agatha gives up her aim’. It would not be a great clinical result. It is in fact as if Agatha had adopted the logico-modal operator of the possible from the therapist while applying it to a different propositional content and so cancelling the implicit proposal of the therapist: ‘if one wants to reach the aim, he must not mind to the obstacles’. And now we can tackle the subject of the lexical features of the world w, which we hinted at before (§ 9).

9.2. The modal verb ‘ought’. The lexical features of the final world w,  which we hinted at before, are four instances of the modal verb ‘devo’, (in the verbal turns 17 and 18 of Agatha) that we have translated with the modal verb ‘ought’ for reasons that will be explained in the discussion. 

(15) ‘Non deve essere un obiettivo’ (‘it ought not to be an aim’)

(16) ‘Non devo mai pensare di liberarmi di loro’ (‘I ought never to think of getting rid        of them’)

(17) ‘non devo mai pensare a loro’ (‘I ought never to think of them’)

(18) ‘non devo guardarli’ (‘I ought not to look at them’).

Through these four sentences, constructed upon the modal verb ‘ought’, Agatha seems to have recovered the propositional content not only of the initial world u, where p = ‘I must mind the obstacles’ (obstacles ≡ my parents), but also of the middle world v: ‘it is possible not to mind the obstacles’. The sound paraphrase is therefore: ‘non devo guardarli’, ‘I ought not to mind them’ (obstacles or parents).

________________________________________ __________________________

logico-modal figure of the final world w

__________________________________________________________________________

deontic logico-modal figure

modal operator of the Obligation, O

p = ‘to mind obstacles’

O~p = ‘it ought to be that not p’, ‘it ought to be that not to mind obstacles’

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table n° 5. Which conveys the conformity of the final world w, through the paraphrase: ‘I ought not to mind them’ (obstacles or parents, obstacles ≡ parents) to the deontic figure, with the modal operator of the Obligation, O, coupled with p in the formula: O~p. _________________________________________________________________________

                9.2.1. The accessibility relation v  R  w.  We take up again the model <W, R, V>, where W is the set of  worlds of the entire conversation; R is the relation that holds between the worlds v and w, members of W, such as {v, w}≤ W; V is the values that we assign to v and w, respectively. But, this time, the final world w is considered qua expression of the modal verb ‘ought’. Therefore, the assignment of V to v is the same as before (§ 9.1.1) = M~p but the value for w would be O~p. Consequently, we have the new formula as:  

(19) M~p  R  O~p,

read as: ‘in the passage of time from the world v to the world w (qua modal verb ‘ought’), we observe the transformation of the alethic figure of the Possible, M~p: ‘it is possibile not to mind the obstacles’, into the deontic figure of the Obligation, O~p: “it is obligatory not to mind the obstacles (or parents)’. In other terms, while the propositional attitude of the logico-modal figure has changed, the propositional content, i.e. the argument upon which the propositional attitudes exert their power, remains unchanged. And this trend is exactly the contrary of the trend registered in the passage from v to w qua counterfactual conditional, where we observed that the logico-modal figure of the Possible remained unchanged, while the argument changed from p = ‘not to mind the obstacles’ to q = ‘to renounce the final aim of writing a book’.

            10. Summary and discussion. We can now summarize the passages of our long journey through the text and discuss them, both from a formal and from a clinical point of view, both from the perspective of results and from the perspective of the text’s prediction.

10.1. The results of the text. As to the results, (id est the differences that an observer can appreciate looking at u from w,) we have seen that the text has changed from Np in the initial world u to O~p in the final world w: 

(20) Np -----> O~p,

from the figure of the Necessity to the figure of the Obligation. Is this a clinically good thing? Beyond this question, we may also ask: what is the reason or the cause of the change from u to w? In the search for the cause, if we follow the canonical criterion of contiguity and succession, the first element to be suspected is the autobiographical administration, in the form of a counterfactual conditional, which inhabits the middle world v, is contiguous both to u and w, follows u and precedes w. This investigative hypothesis would receive some support from the fact that, after the verbal turn of the therapist, Agatha takes possession, anaforically, repeteadly, for four times (see § 9.1), of the logico-syntactical figure of the counterfactual conditional, but adapting it in her own way. Actually, at first, Agatha takes up the formal figure of the Possible of the counterfactual conditional, but only as a formal figure, M, which she sews on an argument, q (q = ‘to give up the final aim’), different in respect of the counterfactual, p (p = ‘to mind obstacles’). Subsequently, in the 17° and 18° verbal turns, shapened by the modal verb ‘dovere’, ‘ought’, Agatha recovers the starting argument, p, ( p = ‘to mind obstacles’), but this time stiking it up the logico-modal figure of the Obligation, O~p.

(21) Np ----> M~p ----> M~q ----> O~p.

How can we interprete the two sequences, (20) e (21), in the three worlds of the conversation? May we think that they are connected through causal or supervenience links? Or do they consist of casual, accidental or fortuitous events?

10.2. The predictions of the text. On the other way round, from the point of view of the prediction, we may finally ask ourself whether it would have been possible to foresee, from the textual indicators in the initial world u, what kind of a logical figure was to be expected in the final world w. At first sight it does not seem that anything qua power (potentia, dynamis) belongs to Np, which would realize itself qua act (actus, energheia) in O~p. But let us examine separately the intermediate passages, first from u to v, and then from v to w.

10.2.1. The predictions of the text 1. It was impossibile to predict  M~p from Np. As for the first passage, it is immediately clear and evident that it was absolutely impossible, looking  from Np, to foresee M~p, because M~p (as one can more easily grasp in the equivalence M~p ≡ ~Np) is the opposite of Np, or, better, its contradictory. And for this very reason the verbal turn of the therapist, qua counterfactual conditional M~p ≡ ~Np, which contradicts the verbal turn of his patient, qua alethic figure of the Necessary, Np, is impredictable. There is not the case that a therapist contradicts his patient. It is possible that it happens, but not as a rule, not necessarily; not even for the most  part, but rather as an accident. And since ‘there can be no cognitive science of the accident’, then there is no rational possibility to predict M~p.

10.2.2. The predictions of the text 2. But it was possibile to predict O~p from M~p . But, if it was not possible to predict the logico-modal figure of the middle world v, M~p, looking from the initial world u, on the contrary, it is possible to foresee the figure of the final world w, O~p, looking from the figure M~p of the middle world v:

(22) M~p  ---->  O~p.

Then, in the middle world v, the proposition M~p asserts that ‘it is possible not to mind obstacles when one intends to reach the aim’. In the final world w the proposition O~p asserts that ‘it is obligatory not to mind obstacles when one intends to reach the aim’. In both the propositions the matter is p = ‘not to mind obstacles when one intends to reach the aim’. Only the logical-grammatical mode changes: ‘possible’ in one case, ‘obligatory’ in the other. But what we are saying does not help us to detect any transition from the Possible to the Obligatory: in the same manner the Necessary of the initial world u and the Possible qua not Necessary (M~p = ~Np) of the middle world v had seemed incommensurable to us. Nevertheless, whereas no medium term could be seen between the two contraddictory terms, Np e M~p = ~Np, to point out at the possibility that they belong to each other in some way, some common points  can be sensed between the two terms of the Possible and of the Obligatory. Intuitively, in fact, while the proposition: ‘for a thing, if it is necessary that it be, it is also not necessary that it be (Np & ~Np)’ doesn’t make sense, on the contrary the proposition: ‘for a thing, if it is obligatory, it is also possibile’, doesn’t sound odd. In some way, the Obligatory seems to entail the Possible, even as if the conversion (i.e. that the Possible entails the Obligatory) is not sound. We shall try to demonstrate the intuition that the Possible belongs to the Obligatory in the following way. Instead of subordinating  the propositional content p: ‘to mind obstacles when one intends to reach the aim’ to modal operators, we shall subordinate it to quantifiers: the universal quantifier (Πx = ‘for all x ...’, ‘all’) and the existential quantifier (Σx = ‘there exists x ...’, ‘someone’). Hence we have: ‘There exists at least a x such as, if x wants to  reach the aim, x doesn’t mind obstacles’, which translates the alethic figure of the Possible; and: ‘For all x, if x wants to reach the aim, x doesn’t mind obstacles’, which translates the deontic figure of the Obligatory. The use of quantifiers has the advantage of making thinkable the existence of a continuum between quantities, bigger or smaller, between a set that contains ‘one’ and a set that contains ‘all’. In fact, if we introduce a second member in the first set, meaning that there exist two x’s, such as ‘if x wants to reach the aim, x doesn’t mind obstacles’, and then a third x, and so on, the set that contained ‘one’ at the beginning moves over more and more toward the set that contains ‘all’. It is as to say analogically that the Possible shifts over toward the Obligatory. Think of the fashion world: from a world v, where it is possible that ‘one’ girl doesn’t hide the navel, and then that two girls, ..., and three, and hundred, ... one reaches the world w where it becomes obligatory ‘for all girls’ not to hide the navel. In other words, the Obligatory contains the Possible, as ‘all’ contains ‘one’, as ‘all the girls that dont hide the navel’ contains the ‘one’ girl who doesn’t hide it. Then, as it is possible, looking from the world v where ‘one’ girl ...so and so, to predict that in the world w ‘all’ the girls... so and so, then by  analogy, looking from a world v where the proposition “for ‘one x’ who wanted to reach the aim it is possible to not mind obstacles” is true, it would be possible to foresee that in a subsequent world w the proposition “for all x’s who want to reach the aim it is obligatory to not mind the obstacles” will be true. Q.E.D.

            10.2.3. Summary. This paper, that we have prepared for the discussion at the meeting, is part of a research program of the Accademia delle tecniche conversazionali upon fragments of recorded and transcribed conversations. The conversations are carried out according to the practical algorithm of our Conversational techniques. The technique we take in consideration here is the administration of autobiography from the therapist to the patient, couched in the logico-syntactical form of counterfactual conditionals. The transcribed fragments of conversations are examined through theoretical filters: here we take in consideration only the algorithm of the logico-modal figures: alethic, deontic, axiological, epistemic. The starting point of this algorithm is the segmentation of each fragment of the whole text, designed as world W, in three segments or worlds: the initial world u, the middle world v and the final world w. If we look at the initial world u from the final world w, we may study the relation u  R  w which tells us the results of the text, i.e. the therapeutical, clinical, transformation from u to w. And, eventually, we look at the middle world v as the possible causal point of the transformation. If, instead, we look at the final world w from u (when w has not yet happenend, is still a future event), the relation u  R  w allows us to consider the problem of the text’s predictions, i.e. actual descriptions, from the initial world u, of possible configurations of the future text, in the final world w, inferred from the formal textual indicators of the world u. Keys words: textual results; text’s predictions; logico-modal figures; counterfactual conditionals.

            10.2.4. Bibliografy.

For the calculus of the logico-modal figures cfr:

                Carnielli W.A., Pizzi C. (2001), Modalità e Multimodalità, FrancoAngeli, Milano.

                Dolezel L. (1998), Heterocosmica. Fiction e mondi possibili, trad.it. Bompiani, Milano, 1999.

                Galvan S. (1991), Logiche Intensionali. Sistemi proposizionali di logica modale, deontica, epistemica, FrancoAngeli, Milano.

                Hintikka J. (1962), Knowledge and Belief. An Introduction to the Logic of the Two Notions, Cornell University Press, Ithaca, N.Y.

                Hughes G.E., Cresswell M.J. (1996), A New Introduction to Modal Logic, Routledge, London and New York.

Priest G. (2001), An Introduction to Non-Classical Logic, Cambridge University Press, Cambridge

                von Wright G. (1968), An Essay in Deontic Logic and the General

Theory of Action, North-Holland, Amsterdam.

For the counterfactuals conditionals cfr:

                Lewis D. (1973), Counterfactuals, Blackwell, Oxford.

                Pizzi C. (1974), La logica del tempo, Boringhieri, Torino.

                Pizzi C. (1983), Una teoria consequenzialista dei condizionali, Bibliopolis, Napoli.

                Stalnaker R. (1968), A Theory of Conditionals, in Studies in Logical Theory, ed. by Nicholas Rescher, Blackwell, Oxford.

For the calculus of supervenience and cause cfr:

                Kim J. (1982), Psychophysical Supervenience, Philosophical Studies, 41: 51-70.

                Kim J. (1993), Supervenience and Mind. Selected Philosophical Essays. Cambridge University Press, Cambridge.

                 Pizzi C. ( 1997), Eventi e cause, Giuffré, Milano.  

For the translation of the modal verb ‘dovere’ with ‘must’ in the initial world u and with ‘ought’ in the final world w, cfr:

Lewis D. (1973), Counterfactuals, Blackwell, Oxford (especially, chapter 5).

Mackie J.L. (1977), Ethics. Inventing Right and Wrong, Pelican Books,

Great Britain (especially chapter 3.2 The meaning of ‘Ought’).