Jusletter IT

«Iustum, Licitum est qvicqvid possibile est fieri à viro bono. Aeqvum, Debitum est qvicqvid necessarium est fieri à viro bono. Unde sapienter ICti Romani Legibus indefinita revocanda ajunt ad viri boni arbitrium.» Leibniz has given the modal logic a normative interpretation with these words above¹ . However, this thought remained unrepeated and unconsidered for a long time² . Only after the Second World War the Finn George Henrik von Wright, the German Oskar Becker and the Polish Georges Kalinowski, developed the first systems of the «deontic logic» again from the modal logic³ . Since then the modal logic had been much further developed, particularly thanks to the American Clarence J. Lewis, who has established a whole scale of modal logical systems, which are arranged according to the logical strength S4. With some of these systems now a strange phenomenon appears: an iteration of modalities: – «it is necessarily possible that something is necessary» – in this form.

Oskar Becker has immediately tried a juristic interpretation of the iterated modalities, by means of arrangements and permissions in a stage of appeal. An example of it⁴ : NMNa in abstract-normative interpretation: «The higher court instructs the mid-level one to permit that the lower court is enabled to sentence the misfeasance A (according to its own judgment).» In a concrete interpretation: «The president of the government directs that the district administrators permit the mayors to arrange the evacuation of houses with flood hazard according to their own judgment.»

The clever thought of interpreting the iterated modalities using stages of appeals is still popular until today – as long as people did not simply consider a normative interpretation of iteration as «sheer nonsense», just as D. Paul Snyder does⁵ .

The picture of the stage of appeal, or more generally that of the hierarchy of rules, is not only illustrative, but also particularly fascinating. Also even who is not involved in a official relationship and has not served as a soldier, is however – in a mediate way – always being affected by scientific or metaphysical hierarchy conceptions, according to Hans Kelsen or Dionysios Areopagita. But this picture is misdirecting. In my opinion, that results from the newer study on the modal logic. According to this, the iteration of the modalities is not to be understood with the conception of the things above and those below, but of things in front and those at back, where the people standing at the back possibly definitely has the better overview – however it may be possible that he stands as the last one in a queue. Beyond the frameworks of this article I would like to say that, two iterated modalities are not to be understood, just like a command on a command, in a public-legal way, but in a civil-legal way, just like a requirement on a requirement (see the «Conduction of the conduction» which has been described a lot in German civil-legal dogmatic)⁶ .

At the time Oskar Becker made people busy essentially making research on the modal logic on syntactic basis. Axiom systems were established, were then researched for their formal characteristics, like consistency and completeness. In terms of content, this research was only controlled by intuitive conceptions, which, also in normative aspect, would tend to mean possibility and necessity.

That has been changed fundamentally twenty years ago. At that time the logician Saul Kripke succeeded in precisely interpreting the different systems of the modal logic and logic of quantification models⁷ . Starting point was again a thought of Leibniz. He had characterized the one, which applies in all possible worlds, as necessary, and the one, which applies in some possible worlds, as possible. In the modern time of the science fiction this thought is capable to be refined substantially. One can easily imagine a world, from which he can look into other worlds. In that world one achieves a concept of «all worlds»: it is the other worlds and he himself. But this concept can be perceptively limited: perhaps he himself is observed by another world without being able to notice this.

With this viewpoint the relation of the accessibility is crucial – from a world is another one accessible. The relation of the accessibility can now be assumed – like relations in principle – with different characteristics: It can be e.g. symmetrical or transitive.

If it has both characteristics, then here concerns a relation of equivalence: one can now travel from any world and reach every other world. Surely, the characteristic of reflexivity still serves as the precondition (despite this, everything else is taken for granted, as we will see later): which means, each world is accessible against itself.

If one connects the Leibniz’ thoughts, which is, what applies in all the worlds is necessary, with the thought, that the concept «all worlds» is dependent on the relation of accessibility, then different modal logic systems appear according to the characteristics of this relation, and the systems differ themselves particularly in the points, whether and in which extent the modalities can be iterated. More about it will be elaborated later.

It is needless to say, that people have tried since a long time ago to include that idea of interpretation, which is profound as well as simple, into the deontic interpretation of the modal logic⁸ . The gain of the numerous efforts is however – according to my estimate – disappointingly low. In my opinion, only some insider problems, which concern for example «deontic paradoxes», were solved. People may therefore understand the logic better, but do not want to apply it.

By the way, until recently I tended to come to an argument, which is against the thought of a deontic interpretation of the modal logic, from this fact, in this sense: a conception like this was only justifiable so long, when the certain intuitive nature and inaccuracy of the interpretation of the logical forms still leave the deontic scholars some room, so that they can think about something that makes sense; but since Kripke that is not the case anymore.

If I have a different opinion meanwhile, that is because I believe that one merely understands a correct statement wrongly. One only takes relations and their characteristics from the warehouse of the pure logic and creates systems of deontic logic with their assistance, with the purpose of using the new system in the ought-to-sentences, which are assigned to be the regulation in different areas of the living environment⁹ . That is however totally the wrong way round; the right way should be proceeded in reverse. The living environment is a priori full of relations of – people may probably say – «existential» character. The relations are more or less unformed and inarticulate, but there are also already some parts – particularly in the modern law system – highly formalized and formulated. Now these relations are regarded to be understandable and can be modalized in the sense of a deontic logic – from the inside –, in order to gain an appropriate entrance to normative structures and also to the possibilities of their modification.

If one proceeds in such a way, he will immediately recognize that the well-known characteristics of relation have very deep normative roots. One has already often noticed: that the symmetry of a relation between persons corresponds to an old normative postulate. That is the principle of «reciprocity ». «DO ut!» «Tit for tat» «Tu quoque!»

The fact that there is also an old normative principle, which is the transitivity, is also widely well-known: «The friends of my friends are also my friends!» Who has read Karl May’s works, knows that. Certainly this principle has not been proceeded so far – different from the principle of reciprocity – by the philosophy of law and legal theory (if I do not get myself wrong), possibly because it actually carrieseinen Hauch von Balkan (experience a touch of Balcan).

While people tend to easily ignore transitive relations and their associated principles, they have again connected the relation of two-sidedness with the postulate of reciprocity and have confronted them with the normative relation of all-sidedness, which – as it still has to be shown – is determined by the equivalence, in the most diverse ways. In the philosophy of law this has been done firstly by Werner Maihof¹⁰ .

In my opinion, from a historical view we can say, the archaic, but also still being developed legal forms are more strongly determined by principle of reciprocity; while modern or having been developed legal forms are more likely determined by principle of the all-sidedness. The tu-quoque-argument of reciprocity plays e.g. in the international law a significant role, which still – for lacking in a central power – has some archaic features¹¹ . The argument was also of substantial importance in the German competition law in former times, as long as this contrasted only slightly from «the natural state» from the classical liberalism; and in the last decade, it has been continually restrained from the jurisdiction¹² .

Certainly, in the last years, some lawyers (Claus-Wilhelm Canaris for example) have specially stressed the alleged duality of bilateral («synallagmatic») relations on the one hand and that of all-sided legal relations (e.g. property) on the other¹³ – in my view, that happens, because they want the characteristic of the third relations, that is the transitivity, which have been forgotten before, obviously tries to catch the attention in the last years – to be reserved. The category of the transitivity is – from a practical-legal aspect – the category of the direct access. The demand for direct access is to be clearly perceived in the last decades in different areas, and it concerns the access of ultimate consumer to the manufacturer (manufacturer’s liability) or it concerns accessibility of usage with purchase with installments (the second-hand car is bought on credit; the credit institution cooperates closely with the second-hand car dealer; the car turns out to have a lot of faults: but nevertheless, the buyer still has to pay the advanced purchase price to the credit institution). Because of the conflict between systems, such possibilities of the access are still not acknowledged in the German jurisprudence until today. Now on the right there is an encompassing theory¹⁴ .

Why are the mentioned characteristics of relations typically connected with certain normative characteristics, the reason is to be explained with diagrams. The relation of equivalence contains a lot of logic in it; an arrangement in this form is exhaustive and normative. Normative relations can be clearly specified in an abstract way by such an arrangement, and that also means: downwards from «above».

«Everyone should respect the property of others!» The property of others and of institutions should be treated in this abstractly regulated way, for example.

If however, only the symmetry of the relations is regulated, then that would not be unambiguous; there might still remain a large amount of room, which would have to be regulated individually.

The symmetry relation is obviously particularly suitable for the «law from the bottom upwards»: for contracts and quasi-contract relations. If such a regulation is effective from the top downwards in an unambiguous way, then it might be burdened because of the demanding individualization of the ones that are concerned.

On the upper left corner there is a world, which sees all the others, but cannot be seen by any others. On the bottom right there is a world, which is to be seen by every other world, but cannot see any other one. Which of the worlds – here are four of them – that had noticed the reaction of others, would remain totally open to the general arrangement of transitivity.

Anyway, transitivity is a substantially stronger characteristic than symmetry, and its character in the legal area is also peculiar problematic. For a law from above it is always too weak: the necessary individualization would again give the character of a measure law to the arrangement. For a law from bottom it is too strong on the other hand: because how could for example a third party be charged by agreements between two other ones? Perhaps the category makes it possible that the better acquisition of normative phenomena has an immense social importance in the entrenched structure. In old times family associations might be punished for the misdeeds of one of their members; in the modern economic life the possibilities of access might be multipolar, not simply bilateral. The awareness of the category transitivity could be heuristic here.

Moreover, there can also be case that, the agreement, which has been made on the basis of bilateral reciprocity can have the same normative effect as those, which have been made through arrangement of a normative relation of equivalence.

But if now there is a new fifth world, the difference would become immediately clear: it would have to be linked with each of the four already existed worlds with bilateral agreements; the normative character of the equivalence should be preserved; while with an original equivalence arrangement, the fifth world would be included in the first place. Therefore it is important to differentiate the genetic aspect of a normative relation from its functional one, that is to differentiate, like here, whether it concerns original all-sidedness relations, or it concerns those effective ones. The word «original» has quite relative meaning: from a historical view, the property is a late legal and abstract term, much later than that of the contract. William Seagle, world history of the law¹⁵ : «Before the establishment of debt obligation, there was no need to for a legal institution of property to exist.»

Now I want to say more about the reflexivity of the relation of accessibility. In the first fundamental essay of Kripke – quite different from the other characteristics of the accessibility – the reflexivity was not questioned, just as little as it has been mentioned in the later standard works of George E. Hughes and Maxwell J. Cresswell. Nothing was been missed so long as this one, as far as people want to extent the modal logic to the more demanding subject area. The postulate of «Recognize yourself!», which is based on the fact that, one cannot know himself from the very beginning, is finally one roots of philosophy and certainly is not self-evident. It is acknowledged in today’s psychology that the self-knowledge or – as it’s said in a more reserved way – the «self-consciousness» – will be influenced by the reflection in the reactions of the others: «looking-glass self». That applies particularly in the ought-to requirements, which people set for themselves. As regards to the sentence  of «Recognize yourself!», here is one comment of the old author that has quoted from the ancient works word for word. Epiktet¹⁶ : «What does it mean? If a choir singer is being asked to recognize himself, wouldn’t he think about the regulation, which requires him to pay attention to his co-singers and to the harmony of the songs? … And how about a sailor? Or a soldier?»

Kripke has been since early times actively abandon the precondition of reflexivity from the deontic logic and other authors have followed him in this respect¹⁷ . This first concerns a technical problem: people would like to expel the deontic possibility of the consequence from «being ought to» and restore to «being», because it is obviously missing, while the corresponding conclusion of ontic «must do» is unproblematic with «being». Also it is noteworthy, which subtle, yet with deep meaning method is used here, in order to identify the difference between being and ought to. But right now, a lot of analytical philosophers are surprised to find that there seem to be some people, who cannot identify this difference well.

In order to understand this technique and also in order to master the skill of further analysis, we should do some more formal discussions:

Let us assume that the four «worlds» are lined one behind the other, and the vision only reaches the next one, which is just located in front of it.

In the fourth world (D) the sentence p is true, while in the others it is not. If I ask the entire world the same question, whether p is true or not, no world will say yes to it, except D.

If I later ask the question, whether p is necessary, then again D, and only D will answer it affirmatively. «Necessary» means something can be applied in all the worlds; but D knows only for itself but does not know for the others.

However, if I ask the question whether p is possible, then except D also C will answer it in an affirmative manner; because C has seen that, D had answered yes to this question. The conclusion that p is possible – seen by C, comes from D. P is even necessarily possible, in the point of view from C; because each world, which C can imagine – besides D –, has given a positive answer to the question about the possibility of p. If I continue to ask whether p is possibly possible, then except D and C, also B will answer yes to this question; if I then ask whether it is possible that p is possibly possible, then finally A will give a positive answer to it. It is obvious that this process can be carried on for a long time, until there are no more worlds like A», A’» and so on. This shows with the simple relation of accessibility a modal logic can correspond with iterative modalities with the same number of times.

We assume now instead of the above mentioned situation, from any one of the four worlds, people can see each of the other three worlds.

Again, only D will response to the question about p. To the question, whether p is possible, every world will give an affirmative answer. And that also means: we would get the same answer to the question, whether p is necessarily possible. If all the relations of accessibility between worlds in this system are somewhere and somehow possible, then it’s necessarily possible too: Mp NMp. It’s just trivial, that the reverse relation applies: NMp Mp. Therefore, it makes it plausible, that only simple modality can exist in a system with all accessibilities (equivalence relationships) or repeated modality can be reduced to the simple ones.

Let’s observe a world system with symmetric accessibilities, with following arrangement:

It’s obvious, that D would not affirm the question, if p is necessary too, naively, after he has affirmed the question about p. It would observe not only its own world but also the world of C, which has no p in it. It would last just as long as in system of simple observing relations till the knowledge of p is passed down to A. The knowledge of p will be also very mediatized by a multiple possibility. Because it basically can also be transferred beyond A, then even in a modality system based on symmetric relations, many modalities can still exist.

Let`s observe a system with pure transitive observing relations:

The knowledge, that p applies in D, is passed to A just in a heartbeat. If there are some worlds before A, the same situation would happen too. Iteration based on the worlds far away will not come again: even the furthest world has seen it through.

But there is still a flaw that is you may not look back from any world; in our example, especially not from D. Let’s assume the following world system:

If the worlds, including D, could look back (equivalence), then the next mode would be homogenous. If you ask for M, you will get several loud ones; if you ask for N, you will get a series of zeroes. If the worlds, if with transitive perspective, may only look to its right side, then you will receive a series of values of 0001 for the question for N. You may get a homogenous series of values: 1111 only when you ask next for MNp. You can also extract a further iteration through ingenious furcation, but then it’s the final conclusion:

After this technique was introduced, one should be possibly able to analyze some simple normative phenomena. But it should be remembered that it is not about implementing deontic logic to sentences in order to regulate people’s behavior but totally reverse: it’s about extracting the deontic structure from people’s behavior and making it aware. Deliberation is all. Therefore, we shouldn’t adhere to pure imperative and permissions, but firstly to normative phenomena with strong deontic impact. In the daily conversation, we can recognize the phenomena, it’s less easy to say: «It’s forbidden!» or «it’s permitted!» than «it’s impossible!» or «you can absolutely do that again!». It should be exemplified by the following two examples:

The logician Hughes and Cresswell have recommended a lovely game, which clarifies the modal logic structure¹⁸ . A group of players sit on the chairs in a room – representing the «worlds». Everyone has a paper in hand with a serial sentences – to make it simple, we use here p, q, r etc. to represent the sentences. A game master asks for every sentence, for instance «p?» – the player, who has the p, raises his hand; p applies in this world. The game master can also ask for Mp: then the gamers, who have known (from the question for p) that at least one player would answer, raise their hands up. If the game master asks for Np, then the players, who have seen all the other players in his visual range raised their hands, should answer. The different modal logic systems are realized, if we restrain the observing relations between players in an ingenious way – through a Spanish wall or something.

Now, let’s modify this game a little: the players are not sitting on common chairs but on judgment seat of superior court or with a juridical profession. The one, who’s looking for the answer to a sophisticated legal problem must ask the crowd and the decision of the «players». This explicitness correlates itself again and it’s not hard for the interested reader to find out the already known feature again. There are some authors, who extensively mutually cite. The other citation relations run only in one direction: «cito ut cites» might not be answered. There are also significant transitive relations, such as the academic teachers mentioned authors. Equivalence character has the citation relation, for example, between the significant and criminal comments. (For inspiration: you may examine the citation relation in edited volumes, and also the changing practices of citations between science on the one hand, and supreme jurisdiction of the Supreme Court on the other.) It is clear that these structural features cannot be explained by limitations of the factual-intellectual accessibility. Rather, there is an acknowledge relation besides accessibility relation, which can also have the same features. With wordplay: accessibility – acceptability! Where the boundaries can be blurred, as indicated by the wordplay: The note «I do not understand» by a reputable (!) authority has a well known normative character. The acknowledge relation implies by no means that the opinion of the « reputable» person was correct; the other is recognized only as «vir bonus», the «arbitrium» one, so that one cannot escape it easily. (Leibniz seemed to have seen the importance of acknowledge relation. Anyway, I would like to assume so because of his extraordinary frugality in words, avoiding every superfluous word.)

It would be explained with a simple criminal case¹⁹ . Someone tells a deliverer to send himself some goods in order to provoke him; he lied to the deliverer that the addressee has made the order himself. Fraud? I do not think so. But since the Bavarian State Supreme Court pronounced this kind of actions in such cases to be fraud (which were made by some experts), the student who is committed to this solution would probably get a «rationale» for his practice work. This «reasonable» does not mean a intermediate value between «clearly correct» and «clearly wrong», like Klaus Adomeit assumes – I regard the adoption of fraud remains as clearly wrong – but you can no longer afford the practical and normative consequences from «mandatory» wrong solution. The fact that a supreme court takes a certain opinion is not just a mere fact, but changed the normative relations system in which a lawyer must orient themselves.

It makes the area of ​​jurisprudential opinions for deontic analysis particularly interesting, that normative modalities are here in an unusual explicitness iterated. A certain school thought is «possibly reasonable». Another theory may be «possibly forced». A third view is «must take it as possibly reasonable ». The last sentence could take the following acknowledgement structures as elements: a number of authors form a citation circle with all-round acknowledgement (equivalence). They are of course not of the same opinion, but the opinion that represents this circle is « reasonable». Supposed that an outsider holds a particular thesis. No one thinks it’s true in the narrow circles, but one explains it carefully and interestingly. The outsiders will then be considered «possibly reasonable». The diagram below clarifies how this occurs:


Ill.

The example of the legal citation circle is therefore particularly suitable for our purposes, because the articulation degree ofdifferentiated assessments is unusually high. But once you have become familiar with the phenomenon, you will recognize it easily anywhere in the world of life. In particular, the transition from a «mere outsider» to «associated outsider» is just the phenomenon that occurs repeatedly in social or political fore field. Religious groups and other unions, but also countries become typically «indirectly acknowledged» at first; for the present, people would probably think about the status of the PLO.

Two things are in my opinion for deontic logic necessary, in order to distinguish them from normal modal logic. First, we must assume that there are special relations of acknowledgement in addition to the relations of accessibility, and second, one must put the reflexivity of relations of acknowledgement in question. Putting it in question is not simple denial – as with the more formally oriented logicians – but a cautious experiment: abandon, add, modify. As for the relations of acknowledgement, the example of the jurists of republic of the scholars is very good, because of the high degree of explicitness – about questioning of self-acknowledgement, this is less true. The following example is thus undoubtedly more realistic: Two women meet on the way to the same event. One wears a simple day dress, the other the famous elegant «Kleine Schwarze». Each looks with horror at the other, and it forms a peculiar spiral that could be represented as follows (p here implied the «Kleine Schwarze»):

Ill.

The diagram shows a disturbing feature of the psycho-normative situation²⁰ :

It is unstable. Although only two people are involved, the modality can be iterated indefinitely. A: «For heaven’s sake – so we have to be dressed elegantly!» (B: «For God’s sake – how much would I stand out!») If the woman A recognizes by her behavior that woman B has actually suitably dressed, then woman B could be reassured: in fact she will not feel reassured in the least, because she has the reciprocal fears about the need to be dressed not outstandingly. The fear increases with each turn of the spiral.

We do indeed hope that after some «back and forth of eye contacts», each of the two will recognize, that she herself is the one, who the other one tries to orient to. This may lead to the result that everyone would be accepted in the way that they are wearing – the relation of acknowledgement gets a reflexive character. Now the situation is simplified immediately and become stable.

It is certainly conceivable that relation of acknowledgement is reflexive at only one of the two women (without that the relation with the other one is thus given up).

Woman A will still keep the opinion and forms her final opinion that she is dressed wrongly, but woman B does not think her own dress as «impossible». Above all, the oscillation of the mutual orientation has stopped; also these situations become stable.

It is remarkable – surprising at the first glance, but totally understandable – that among three persons, one of which is different (dressed) than the other two. It is certainly a stable constellation. If the majority is not coalesced against the minority and the relation of acknowledgement is disconnected, the psycho-normative status of the minority is not that bad.

However: a stable solution will be not so easily found, if everyone involved think that one of the others – different to himself – has a special normative relation of accessibility, for example (to return once again to the example), they have been informed by the host about what «people» should dress for the occasion.

Finally, it must be emphasized again that the deontic structures that I have outlined here are still quite elementary. For example, the relativity of relation of acknowledgement – such as from A to B – substantiates by no means the relativity of the normative character – as well as that A is obliged to B and, conversely speaking, B is entitled to A. A developed legal logic must be able to express this. And the relativity of service relation must differ from the relativity of demand relation (although there are links between the two): For example, A may be obliged to B, to do something to C²¹ . For example, symmetrical obligations and symmetrical performance (value exchange) might be involved – such as the purchase contract -; but this is not necessary: see a company’s agreement.

From another point of view, it makes sense to continue to process the concept of deontic logic given here in ethical and legal ethical terms. Here, the reflexivity of relation of acknowledgement is the focus of interests and self-acknowledgement is proportional in relation to symmetric, transitive and «equivalent» expectations. It connects the elements of deontic logic with the psychological questioning techniques of sociogram (Jacob L. Moreno) and interpersonal perception (Ronald D. Laing).

The other obvious extension is in the analysis of those obligations, which involve more than 2 parties and have won more and more economic importance and jurisprudential interest in recent decades. Core of this analysis is probably the relational character of transitivity.

Such analysis will certainly be much more technical now. But the fear that the legal logic will reinforce the trend towards a purely technical legal understanding has no reason, in my opinion. On the contrary: it seems to me that in the modern law, which becomes more and more technical, those elementary structures are tend to be visible again, which can reconnect anthropological, historical, natural and philosophical foundations of the law with each other. It can harm nothing when – with the perception of basic structures – in the investigation of possibilities of accessibility, the old saying of the «friends of the friends», or the picture of the liability of the family bond is again up to date.

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Prof. Dr. Lothar Philipps
Universität München
loth@jura.uni-muenchen.de

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