CEPA eprint 2725

On the supposed closure of normative systems

Dupuy J.-P. (1988) On the supposed closure of normative systems. In: Teubner G. (ed.) Autopoietic law: A new approach to law and society. Walter de Gruyter, Berlin: 51–69. Available at http://cepa.info/2725
Table of Contents
I. Ideas and their Destiny
1. The Relation to Cybernetics
2. The Closure/Openness Dialectic
II. Nozick’s Entitlement Theory
III. Law and Legislation: Comparing Hayek and Luhmann
“Validity is circularity” Niklas Luhmann
I. Ideas and their Destiny
My approach to the subject matter of this paper is one that could be subsumed under a genre that we might call the ecology of ideas. What is at issue is less the validity of ideas than the way in which they are born, circulate, take root in areas different from their place of origin and finally take on new, and sometimes unexpected, forms.
The theory of autopoiesis is the work of two Chilean biologists trained in cybernetics: Humberto Maturana and Francisco Varela. It was exported into the milieu of German sociology where it appears that the graft enjoyed great success. Thanks to the combined efforts of researchers like Hejl, Luhmann, Teubner and others, a new sociological and legal paradigm was born which continues to develop in an impressive manner.
The situation in France is quite different. It is clear that in France, the theory of autopoiesis is far from unknown. It has already given rise to numerous debates within the biological and philosophical communities and among specialists in cognitive science, artificial intelligence and in the social sciences (Dumouchel and Dupuy, 1983). The terrain is, in fact, so favorable that Varela, having decided to leave his own country, decided to settle in ours (and more precisely, in my center of research, the CREA). There has not, however, been, as in Germany, the construction of a complete sociolog­ical theory which, though certainly inspired by the ideas of the Chilean school of neuroscience, is largely autonomous of them. Legal autopoieticists refer to the autopoietic systems of Luhmann. There is no Niklas Luhmann in France and when we mention the theory of autopoiesis, it is to the original model of Maturana and Varela that we are referring. At least three reasons seem to me to explain the differences between our two countries concerning the reception of these ideas:
a) In France, there is a strong and long-standing distrust of any use of biological models in the social sciences (see for example Nerhot, infra).
b) No doubt for contingent reasons, the theory of autopoiesis has pen­etrated Germany through the ideas of Maturana and France through the ideas of Varela. Now, there are important differences between the respective approaches of these two founding fathers. Maturana’s could be seen as being more radical and essentialist. For Varela, autopoiesis is more a point of view on an object than an intrinsic quality of it. Varela insists on the complementarity between autonomy as a point of view and the more traditional approach of control. I note in passing that Varela would never speak of an autopoietic social system. One condition necessary for auto­poiesis (accepted long ago by Maturana) is the existence of a material, spatial-temporal boundary produced by the system itself. This does not mean that Varela refuses to extend the fundamental idea of operational closure to society. But, concerning these extensions of the biological notion, he prefers to speak of autonomous systems. This is the terminology that I will most often use.
c) It seems to me that in France we are more sensitive than in Germany to the fact that the theory of autopoiesis is not something invented ex nihilo but that it is rooted in a history and, above all, that it is not isolated. The common trunk of cybernetics has given rise to at least another conception of the autonomy of the living being: the model of “self- organization”, founded on the principle of “order from noise”. The basic idea goes back to von Foerster (von Foerster, 1960); it has since been taken up, transformed and developed in great depth by our colleague and friend, the Franco-Israeli biologist, Atlan (Atlan, 1979). In addition, there is another paradigm of auto-organization, born in the field of physical chemis­try around the work of Prigogine and the Brussels school (Nicolis and Prigogine, 1977). The ensemble of these concepts, models and paradigms constitutes a complex and conflicting picture: we are aware of its diversity and its nuances which prevent our establishing too radical a vision of its identity. In particular, we have recently undertaken the project of retracing the history of these various schools of thought and of their intertwined trails. It became evident as we worked on this history that it is, in general, very little known (Cahier du CREA, 1985).
Concerning the social sciences, I would like to say a word about what has been my attitude up to this point. Rather than seek to apply these ideas stemming from biology and the science of complex machines to human affairs, I asked myself if there weren’t already implicit within theories on society (from political philosophy to the positive sciences of man and society such as economics, sociology and anthropology) models proper to each of these disciplines which embody the idea that in these domains it is necessary to think in terms of operational closure. These models exist; we have shown that. Hence it is interesting and fruitful to look at the way in which they have situated themselves in relation to competing models in the social sciences and to compare it with the debates that the concept of autopoiesis and the different models of self-organization have incurred in the “hard” sciences. These two types of debates could, in fact, be of mutual benefit and it is this vein that I would now like to pursue. To this point I have concentrated on two highly contrasting visions of society: theories on the crowd (Dupuy, 1983) and the idea of society as a “global market”: here I refer to the tradition of the “invisible hand”, to the “liberal” vision of society. In the course of this paper I will refer to two current representatives of this tradition: the “neo-liberals”, Nozick and Hayek. I think that in a discussion such as ours it is impossible not to speak of Hayek, not only because he conceived of society and law in terms of a closed system but also because he has long been a fellow enthusiast of theories of self-organization. He was invited by von Foerster to one of the three famous 1960’s conferences on “self-organizing systems” and he participated, along with Bartalanffy, Weiss and Waddington, in the Alpbach Symposium of 1969, organized by Koestler, on the theme: “Beyond Reduc­tionism”. Rosenblatt, in conceiving his famous “Perceptron”, one of the first attempts to construct an “autonomous machine”, recognized the influence of Hayek (Rosenblatt, 1962). His “spontaneous social orders” have become, in today’s interdisciplinary conferences, the companion of the autopoietic systems of Maturana and Varela and of the “dissipative structures” of Prigogine.
Before beginning an examination of the models of Nozick and Hayek and attempting a comparison with Luhmann’s approach (i. e., the closure of normative systems), I would like to make several points about certain concepts that are fundamental to the theory of autonomous systems.
1. The Relation to Cybernetics
It is important here to alleviate a misunderstanding. The different theories of self-organization are surely the descendants of cybernetics but this kinship does not preclude an antagonistic relationship. Not only do cy­bernetic notions of control, information, program and even feedback not belong to the theory of autonomous systems, they actually run counter to notions instituted by this latter theory. This is why many of the criticisms that Arnaud and other French researchers leveled at the theory of society and law as autopoietic systems seem to me to be unfounded. If there is one temptation to avoid like a trap, it is not the “biocybernetic temptation”.
Cybernetics was born in 1943 with the independent publication of two founding articles: “Behavior, Purpose and Teleology” by Rosenblueth, Wiener and Bigelow and “A Logical Calculus of the Ideas Immanent in Nervous Activity” by McCulloch and Pitts. Between the two of them, these articles purported to succeed in reducing the principal functions of the mind: i. e., will, perception, thought, memory and even consciousness, to the operation of a mechanism, – supposedly in the form of a brain. This mechanism takes the form of a computational input-output machine, of which the archetype is the Universal Turing machine. All totalities will be treated by cyberneticians according to this same model, be they ecosystems, human societies, ant colonies, living organisms, neural networks or the famous cybernetic “animals”, – rats, turtles, etc. Artificial totalities, then, in which the elements are anterior to the whole; nominal totalities which can only be completed by the organizing consciousness of a third party, in this case the cybernetician, as he perceives and conceives of them.
Very early on, however, this cybernetic conception of totalities is attacked using arguments which presage current theories on autonomous systems. From the point of view of the history of ideas, it is deliciously ironic to see cybernetics being indicted in this way by a school of thought which will then be nourished by the contributions of its descendants. These criticisms stem from Gestalt psychologists, neurophysiologists of the “holis­tic” school and especially by the embryologist, Paul Weiss, whose role in this story is fundamental. (The most heated moment in this controversy will be the Hixon Symposium in 1948.) Weiss demanded that one distin­guish between “machines” and “systems”, the latter being, of course, non- artificial, non-nominal totalities. (They exist in nature and are not only intellectual constructions.) For all that, they are not substances. We thereby already have two of the characteristics that Deggau assigns to “the unity of the autopoietic system: ”…it can be conceived neither as ontological in the sense of something ’given’, nor as simply a scientific construction. It is neither an objective nor a subjective unity”. The approach that Weiss advocated is not to be seen as reductionist nor as holistic. To the notion of processing information by an input-output machine, he opposes the autonomy of the system, already conceived of as informational closure. In place of reductionism, which provides itself with already constituted ele­ments and deduces from them the properties of the whole and of holism, which does the inverse, he would have us substitute the idea that the whole and its elements mutually determine each other. This circular causality between hierarchic levels which characterizes autonomy in Varela’s model is, therefore, already present, and it is against cybernetics that it expresses itself. It is the exact same property that Luhmann puts so much emphasis on in the portrait of what he calls “autopoiesis”. (“Even elements, that is, last components [individuals] which are, at least for the system itself, undecomposable, are produced by the system itself”) (Luhmann, 1985a: 4).
Another criticism, no less radical, directed at cybernetics will come from von Neumann (expressed for the first time also at the Hixon Symposium of 1948). To have shown that psychic functions are computable by a cybernetic automaton is a decisive result, he concedes, but it has no value unless one knows how to characterize the behavior in question, independently of the structure which is capable of producing it. However, von Neumann surmised that in the case of complex structures there is no simpler means of defining the behavior than to give oneself the structure. The complex automaton has no model simpler than itself. Therefore we see that this notion of complexity for which von Neumann correctly predicted a great future is intimately linked to that of self-reference. Today, the theory of algorithms (Martin-LOff, Chaitin, etc.) has taken up von Neumann’s definition: any being is complex whose information is incom­pressible: there is no program simpler than itself that would be capable of generating it. It is also through complexity that one defines the randomness of an object (but that should not surprise us if we remember that for Aristotle automaton signified chance). I note in passing that Luhmann and his colleagues assign to autopoietic systems the capacity for self- simplification and self-description. This seems problematic to me. If one admits that an autonomous system is ipso facto complex, then there is no sub-system able to constitute a model of it or a satisfactory description of it. We will see the importance of this point in the theory of Hayek.
2. The Closure/Openness Dialectic
From the theory of autopoiesis Luhmann and his colleagues extract the profound and difficult idea that the legal system is both open and closed. I think that to put some order in the discussion of this question it is necessary to distinguish very carefully between three different interpreta­tions of the dialectic between closure and openness:
a) The simplest way to present the matter is to attribute closure and openness to different domains. As Luhmann reminds us, the Chilean school of autopoiesis, following Ashby, insists on the fact that living autopoietic systems are ”…open to energy but closed to information and control.” In the same way it may be said that ”…the legal system is a normatively closed system and at the same time a cognitively open system”; or yet again that ”…the economic system … operates openly with respect to needs, products, services, etc. and it is closed with respect to payments.” (Luhmann, 1985b: 113-14).
b) Let us concern ourselves only with what Varela calls operational closure of the autonomous system. That evidently does not imply that the system is cut-off or isolated from its environment. The “closure” is a form of opening to the environment by means of which the environment acts on the system not by directing information to it (as in the case of cybernetic input-output machines) but by means of the perturbations that it inflicts on the system’s means of closure. This is done in such a way that the autonomous system knows its environment in knowing itself. It is this idea that Teubner applies to the legal system: “The legal system is forced by the uproar outside, by the ’noise’ of the economic actors, to vary its internal ’order’ until relative quiet returns. … Self-referentially closed systems can attain effects of regulating others only through self-regulation” (Teubner, 1987).
c) The most subtle form of dialectic between closure and openness and the most important in relation to the problem which has brought us together is that which I will call self-transcendence,[Note 1] or, resorting to an analogy with quantum mechanics favored by the Chilean theorists on autopoiesis, the bootstrap: that is to say, the exteriorizing of oneself in relation to oneself, the distancing of the self in relation to itself.
I know that this idea seems to have been rejected by Luhmann (1985a: 12) and this is precisely what should be one of the central points of our discussion. Luhmann refers to an argument by Hofstadter, who asserts that it is impossible for a program to be capable of ”…jumping out of itself”: “No matter how a program twists and turns to get out of itself, it is still following the rules inherent in itself”; and he further states: “A computer program can modify itself but it cannot violate its own instructions – it can at best change some parts of itself by obeying its own instructions” (Hofstadter, 1979: 477-78).
Now it is this argument that has played a crucial role in the history of cybernetics and in the birth of theories of self-organization. It is Ashby, in fact, who developed it in his famous 1962 article, “Principles of the Self- Organizing System” and who concluded that: ”…no system can correctly be said to be self-organizing” (Ashby, 1962). It is, therefore, against this argument that the two paradigms of self-organization (the Chilean school of autopoiesis and von Foerster and Atlan’s principle of order from noise) have had to establish themselves. It is therefore odd to see it being evoked by researchers who believe in the autonomy of systems.
Ashby’s argument, taken up by Hofstadter, can also be stated like this: let us try to make sense of the expression: “A self-programming program.” We can imagine a game of chess in which the rules depend on the configuration of the pieces. But there will always be fixed meta-rules which evade the program’s capacity for self-reference and which will order the variation of the rules depending on the configurations of the pieces. We can try to overcome this obstacle by then making the meta-rules also depend on the configuration of the pieces but this will be a wasted effort as there will be meta-meta-rules which will resist the mastery of program over itself. “Pure autonomy” would then be a logical impossibility. We can find a trace of this argument in Lempert’s otherwise fascinating paper: “Complete legal autonomy is, even in theory, unattainable. Law is a normative system and its norms must, at least in the first instance, come from somewhere” (Lempert, infra).[Note 2]
Now, all of this is concerned specifically with the logic of programs, that is to say of artifacts, be they machines, games or formal logical systems. In all of these cases, even if there is a system, or, in other words, a circularity, the system is programmed, which means that its meaning does not belong to itself but is rather the effect of a will which is exterior and transcendant to it: the will of he who conceived of the program and who put it into effect.
In the case of a natural (or social) system that has not been fabricated by anyone, Ashby’s argument becomes invalid. This is what both Atlan and Varela, each in his own way, have shown. I will mention here only the recent work done by Varela on the existence of “reflexive” domains; or, to put it in the terms used earlier, domains for which the level and the meta-level are isomorphic to one another. (It is understood that if such domains exist, Ashby’s argument immediately crumbles.)
An autonomous system does not get its meaning from an exterior and transcendent “meta-level” and yet, given that, we cannot say that it has complete mastery of its own meaning. It is because this meaning can partially evade it that there can be “self-transcendence”. There is no better way to clarify this than to return to von Neumann’s argument of complex­ity. In the case of a complex automaton, the complexity of the behavior of which it is capable is infinitely superior to that of the automaton itself. Although there is nothing in the functioning of the automaton which does not originate within itself, everything occurs as if the functioning were autonomous in relation to that which generated it.[Note 3]
This provides me with a transition into the work of Nozick and Hayek. Both are thinkers of the complexity of society before being thinkers of the autonomy of society. Belonging to the liberal tradition, the theoretical problem which they must face is that of the connection between two forms of autonomy, first of all, the autonomy of the individual released from all traditional forms of subordination to the sacred or to the State. Then there is the autonomy of the social level, which means not that men have mastery over society but exactly the opposite: that society evades them, seems to be endowed with its own life, foreign to the very men who composed it. The latter autonomy is, therefore, in relation to individuals, a heteronomy. The paradox is only too evident.
Men create their own society, – that is the first autonomy; but they know neither what they are doing nor how they are doing it, and that is the second autonomy. Here, then, is the paradox, but we instantly note that this is the same paradox as that incurred in making an automaton, i. e., a being which depends only on itself as the instigator of its movement; or, the paradox of being the cause of a being which is the only cause of itself. We understand why Hayek was able to find an unexpected source of inspiration in theories of self-organization. In both cases it is the principle of complexity which resolves the paradox concerning the connection be­tween the two autonomies.
That said, the meaning of this insistence on the autonomy of the social level remains to be explained. The problem at hand that needs to be resolved is without a doubt the key problem of liberal democratic societies: how to arrange it so that sovereignty evades the control of men in order to preserve liberty. Even Rousseau, one of the kings of constructivism and therefore one of the principal enemies of Hayek, was aware of the gravity of the question. The ultimate political problem according to him is how to put law above men when it is men themselves who have made the law and they are aware of this. We recall that he compared this problem to the squaring of a circle.
II. Nozick’s Entitlement Theory
For liberals, it is not only a political problem that the complexity of society is supposed to resolve, but also a problem of justice: how to ascribe rights with equity (and especially property rights) in the Great Society (Smith) or in the Open Society (Popper).
What is the rapport between the idea of complexity, implying opacity and lack of visibility, and the idea of justice, which, on the contrary, one ordinarily associates with the transparency of rational debate? The following quotation from Hayek answers this question:
It was the discovery that an order definable only by certain abstract characteristic would assist in the pursuit of a great multiplicity of different ends which persuaded people pursuing wholly different ends to agree on certain multi-purpose instruments which were likely to assist everybody. Such agreement became possible not only in spite of but also because of the fact that the particular results it would produce could not be foreseen. It is only because we cannot predict the actual result of the adoption of a particular rule, that we can assume it to increase everyone’s chances equally. That it is thus ignorance of the future outcome which makes possible agreement on rules which serve as common means for a variety of purposes is recognized by the practice in many instances of deliberately making the outcome unpredictable in order to make agreement on the procedure possible: whenever we agree on drawing lots we deliberately substitute equal chances for the different parties for the certainty as to which of them will benefit from the outcome (Hayek, 1976: 4).
This is exactly the same idea that Nozick expresses when he writes: “If all the people deciding knew the particular distribution that would be yielded by [a given principle of justice], they wouldn’t agree to it” (Nozick, 1974: 200).
To continue, we must insist on one distinction that Rawls (1971: 85) takes from Barry (1965: ch. VI): that between pure procedural justice on the one hand and perfect and imperfect procedural justice on the other. In the latter case, we have at our disposal an independent criterion for what is a just state of affairs, “a criterion defined separately from and prior to the procedure which is to be followed.” Perfect procedural justice obtains when it is possible to devise a procedure that is sure to give the just outcome. Example: the sharing of a cake. Let us suppose that we consider it fair that all get equal portions. Under certain rather evident hypotheses, there exists a perfect procedure: he who cuts the cake is he who serves himself last. Imperfect procedural justice obtains when there is no such procedure which leads infallibly to the sought-after result. Example: a criminal trial. We consider it fair that the guilty party be condemned and that the innocent be set free, and yet we know that it is impossible to avoid judicial errors.
By way of contrast, in pure procedural justice there is no independent criterion which defines the justice of a state of affairs. Instead we define the fairness of the procedure and we agree that a state of affairs is just, whatever it may be, if:
i. it is the result of a fair procedure
ii. this procedure has actually been carried out.
The importance of clause ii becomes clear if we consider gambling as an example. Say that we have agreed on the rules considered fair by all. The result, one can see, may turn out in any number of possible ways since it is the result of chance, and yet everyone will consider this result just. Nevertheless, we can see that it would be fraud to claim that a particular result which happens to work to our advantage is the correct one because it could have been reached by following a fair procedure. It is an indispensable condition that the procedure actually be carried out.
Both Rawls and Nozick admit that in a complex society, the justice of institutions must be defined in terms of pure procedural justice. Nozick reproaches Rawls precisely with not respecting this principle which he nevertheless claims to take seriously and this because he remains a prisoner of the contractualist, and thereby constructivist, framework of his theory of justice.
I will not go any further into the interesting debate between Rawls and Nozick. I will concern myself simply with the theory of rights of the latter, which he calls Entitlement Theory. This theory illustrates perfectly the links between the question of complexity (and of self-transcendence) and that other question which presently concerns us: the operational closure of normative systems.
The merit of Nozick’s theory is that it makes obvious the self-referential character of pure procedural justice: “Whatever arises from a just situation by just steps is itself just” (Nozick, 1974: 151). That is what in logic is called a recursive definition: justice defined by justice. It is still necessary to provide a criterion for defining these “just steps”, what Nozick calls the “principle of justice in transfer”. This criterion is the liberal criterion par excellence: any transformation (or procedure) is just to which is accorded the agreement of all the concerned parties: voluntary exchange, voluntary gifts, etc. Here justice is identified with liberty.
The circularity of this definition of entitlements can be represented in this way:
This circle must, however, be open at its origin: it is certainly necessary to define justice at the point of departure. This is what Nozick calls the “principle of justice in acquisition.” I will not spend too much time on this point (Nozick is here elaborating one of Locke’s arguments) because it is in the nature of complex processes to erase the weight of origins in the mists of time. Does the fairness of the division of land in America today depend on the original violence which marked the occupation of the territory, the expropriation and the extermination of the Indians? I shall come back to this point when I compare Hayek and Luhmann. (Nozick also has a principle of rectification which deals with cases of past injustices.)
Can we then characterize those social states which will finally be consid­ered just? In other words, can we characterize the class of end states which result from processes of this type? No, Nozick tells us and it is this no that allows him to reject all currently accepted principles of justice (begin­ning with those of Rawls!)
Let us first consider all those “end state principles” which look only at distribution at a given moment (e. g., those which define justice by equality or by the maximization of the share of those who are the worst off, etc.) The Entitlement Theory states that the fairness of a social state cannot be appreciated unless one knows how this social state came about; it therefore recognizes only “historical principles”. For example, “the fact that a thief’s victim voluntarily could have presented him with gifts does not entitle the thief to his ill-gotten gains. Justice in holdings is historical; it depends upon what actually has happened” (Nozick, 1974: 151-52).
Most principles of justice are certainly historical but they are also “patterned”, in that they bring together just distribution with certain characteristics of individuals. For example: “To each according to his [merit, labor, usefulness to society, etc.]” or: “From each according to his [means, etc.].” However, Entitlement Theory is not compatible with any pattern. (This is another way of explaining its relationship with complexity, i. e., with the impossibility of reducing it to a simple form.) This can be easily established. Let us suppose that one has an affinity for a particular pattern and let E be a state of affairs that satisfies this condition. Within E, people choose freely concerning the usage of their holdings. They accept, for example, in large majority to pay a high price to see the performance of a baseball star or a singer: the new distribution of resources will have to be considered just since it arises from a just situation by just steps. But it is clear that this new distribution will not continue to respect the pattern that one has set as a criterion of justice. It is inevitable that “liberty upsets patterns” (Nozick, 1974: 160 – 64).
It is, therefore, not possible to characterize the social states that would be considered as just. The history which leads to them is incompressible. (In mathematics and in physics one would say that the process is not integrable in a state function.) I mentioned earlier that in our day random­ness has been defined in just this way: by the incompressibility of the information. We must, therefore, recognize that gambling, which serves as a privileged example to illustrate the concept of pure procedural justice, is, in fact, the only model, as in this case justice is reduced to drawing lots. The political necessity of this result is understandable in a de-sacralized society. Lacking the exteriority of religion, there remains only one possibil­ity for exteriority: the arbitrariness of chance, and one form of exteriority is necessary if one hopes to keep sovereignty out of the reach of men.
To make the connection with theoretical developments on autonomy, I would now like to show that this exteriority of complexity (or of chance) takes the form not of transcendence but of self-transcendence. To this end, it suffices to take seriously the parallel which Nozick established between the justice-preserving transformations in his Entitlement Theory and the truth- preserving transformations in a formal system in logic (“Any conclusion deduced via repeated applications of truth-preserving rules of inference from only true premises is itself true”). Unfortunately, Nozick himself doesn’t believe strongly enough in the value of his analogy. In fact, he immediately adds: “That a conclusion could have been deduced by truth- preserving means from premises that are true suffices to show its truth. That from a just situation a situation could have arisen via justice-preserving means does not suffice to show its justice” (Nozick, 1974: 151) and this is because pure procedural justice requires that the transformation actually take place.
This is true, but the difference is not so great if one poses the question in slightly different terms. Nozick is wrong, as is Hayek, in underestimating the possibilities of deductive reason (Hayek: “The ’radical doubt’ which made [Descartes] refuse to accept anything as true which could not be logically derived from explicit premises that were ’clear and distinct’, and therefore beyond possible doubt, deprived of validity all those rules of conduct which could not be justified in this manner”) (Hayek, 1973: 10). A Descartes coming after Giidel and Turing would know this. Let there be a formal system, i. e., a set of premises considered to be true and of truth-preserving rules of inference. Let there be any given sentence. We then enquire whether it is possible to prove this sentence in the formal system under consideration.
Although everything here is given and functions as a mechanism, the answer to this question is not generally decidable. More precisely, it is only semi-decidable. If the proposition is, in fact, provable, one will find it out sooner or later by mechanically unfolding the ensemble of provable sen­tences (or theorems); if it is not, one may never find this out by mechanical means. In other words, it is necessary to have actually followed a path leading from the premises to the given sentence in order to be able to be sure that it is provable. We are then not far from the case of pure procedural justice.
This result is prodigious. (In technical terms: The set of values taken by a recursive function is not, in general, recursive. Its complexity therefore transcends that of the function which engendered it. I might mention again that “recursive” can be understood as: that of which the definition is self- referentially closed.) It means that, in general, a (Turing) machine is not really up to the level of its own output; the complexity of the output goes beyond that of the machine. This is just the case of self-transcendence such as we defined it using von Neumann’s criticism of cybernetics.
One can easily imagine that Nozick’s theory will lead into a justification of laissez-faire. Law in this theory appears as an emergent effect produced by the mechanisms of the unfettered free market.
Many criticisms could be directed at Nozick’s system. I will concentrate on just one here because it illustrates not that Nozick overuses the theme of complexity but that, on the contrary, he doesn’t follow his logic to its end.
Simplicity can engender complexity; that is one of Nozick’s principle messages (“Though the resulting set of holdings will be unpatterned, it will not be incomprehensible, for it can be seen as arising from the operation of a small number of principles: the principle of acquisition of holdings and the principle of transfer of holdings. The process whereby the set of holdings is generated will be intelligible, though the set of holdings itself that results from this process will be unpatterned”) (Nozick, 1974: 157-58). Each step is decidable and yet the global result isn’t.
Nozick doesn’t for a moment think that this paradoxical reversal could just as easily occur when the question concerns liberty. Each step is a free and voluntary transfer between the few agents concerned. How and with what justification could the third parties oppose such an arrangement when it doesn’t even concern them? Nozick acknowledges implicitly, as if it were self-evident, that this common sense remark could be applied with no problem to the entire process. In doing so he also falls into simplism.
Let us take the following example:[Note 4] three agents, A, B and C each possess a certain amount of the same two goods. Their “satisfaction index” is the product of the quantities of the two goods they possess. The breakdown of goods in the initial stage is as follows:
Initial StageA: (0,2)B: (1,1)C: (1,1)Satisfaction11
We then go on to an intermediate stage:
Intermediate StageA: (1/4, 1/2)B: (3/4, 5/2)C: (1,1)Satisfaction1/815/81
The modification was accomplished through an exchange between A and B in which B gave up 1/4 of the first commodity in exchange for 3/2 of the second. This exchange was to the advantage of both parties and did not adversely affect the third party, C.
We now move on to the final stage:
Final StageA: (1/4, 1/2)B: (1,2)C: (3/4, 3/2)Satisfaction1/829/8
This second modification occurred through an exchange between B and C in which B gave up 1/2 of the second commodity in exchange for 1/4 of the first. This exchange was to the benefit of both parties and did not in any way affect the third party, A.
If the initial stage is just (according to the principle of justice in acquisition) then the final stage must be as well according to Nozick’s theory: the three agents are entitled to possess the corresponding quantities. One can show that the final state possesses the following property: starting from this point, there is no exchange which makes someone better off without making someone else worse off; all possibilities for mutually advantageous exchanges have been exhausted. We can call this a “stable allocation”. All paths which constitute possible histories according to Nozick end up in such stable allocations.
Now then, I believe there is one criterion which allows us to state that in the example just considered the end result is unjust. And this criterion is perfectly within the spirit of Nozick’s principle of justice in transfer, a principle which leads him to assimilate justice and liberty. In accepting B’s offer of exchange which leads from the initial stage to the intermediate stage, A carries out an operation in apparent freedom, which is to his own benefit. In fact, one can see that in so doing he gives up his freedom. In reality, this exchange denies him henceforth the possibility of carrying out an exchange with C, an exchange which would have been much more to his (and to C’s) advantage. If A and C had joined their resources in the initial stage they might, in fact, have been able to end up with the following allocation of goods:
A:(1/4, 1)C: (3/4, 2)Satisfaction1/43/2
The existence of this possibility establishes that, in theory, the “coalition” formed by A and C should veto the realization of the final stage. It is then said that the final state does not belong to the “core” of the economy. (The core is composed of all the possible states which are vetoed by no coalition.) One can legitimately consider, within the very spirit of Nozick’s philosophy, that any state that does not belong to the core is unjust, because it has globally reduced the liberty of certain agents while the opposite seems to be true. It is a fundamental result of game theory applied to economics that if there are many agents the core of the economy is much smaller than the set of all stable allocations.
To sum up: Although they are recursive, i. e., self-referentially closed, the processes imagined by Nozick to justify the emergence of rights are not productive of a sufficient complexity. They do not prevent the existence of at least one criterion, if not of justice at least of injustice, on the level of end states.
III. Law and Legislation: Comparing Hayek and Luhmann
In the biological theory of autopoiesis, it is very important not to mistake one level for another in treating a set of elements as an autonomous system, i. e., as operationally closed, when they are not and are, in fact, only a component of a true autonomous system. For the theoreticians of the Chilean School, this is exactly the trap that molecular biology has fallen into when it treats the genome as a program. This cybernetic metaphor is unacceptable because the first of the autopoietic systems in the make-up of the levels of a living system is the cell in its entirety. At first view, this is exactly the same criticism that any of Hayek’s disciples would direct at Luhmann’s theory. Treating the legal system as an autopoietic system would be the same error as believing in the operational closure of the genome (we know very well that if the genome is a “program” it needs its own output in order to be run!) but here we must look a bit closer.
In Hayek we find the same ideas of complexity and of the “bootstrap” (self-transcendence) as in Nozick but expanded into an ambitious global theory of society and law. The social order is guided by reference points which issue from it but which are nonetheless “exterior” to the individuals composing this social order, in the sense that not only do individuals lack the means of controlling them, they are often totally unaware of their existence.
These reference points take the form of institutions and rules which result from habit, tradition and culture. They allow us to benefit from knowledge that we don’t possess. This knowledge is constituted by rules and it cannot be controlled by anyone. These rules which we don’t know allow us to adapt to facts that we know no better because they are too complex. The “knowledge” at question here is evidently at the opposite pole of that for which Descartes set the forms (“ideas that are clear and distinct,” etc.). It is unexplicit, unconscious, embodied in the mind and not produced by it: “The mind does not so much make rules as consist of rules of action” (Hayek, 1973: 18). “We can make use of so much experience, not because we possess that experience, but because without our knowing it, it has become incorporated in the schemata of thought which guide us” (1973: 30-31). Just think of the way in which children learn the syntax of their language. Rules, though unconscious, are known, to the degree that they can be recognized.
A few words on the principal categories of Hayek: the social order is “spontaneous”; according to Adam Ferguson it is the “result of human action but not of human design”. We must distinguish between two kinds of laws: abstract rules, or rules of just conduct, which favor the emergence of the spontaneous order and which constitute the nomos, and laws which have been made, or “set”, or “posited” by authority (statute), – what he calls thesis.
The important point in what concerns us is the link with the problem of normative closure and self-transcendence. For Hayek, it is the social order in its entirety. (kosmos) and in the fullness of time which makes up the most “elementary” (if we can use that word) autopoietic system. The accumulated knowledge which it incorporates and which is embodied in the rules of just conduct (nomos) is not transcendent in relation to individ­uals: Hayek rejects the traditional conception of natural law being a transcendent and eternal law, issuing from the Gods and yet his theoretical system is not a historicism which would lead him to identify “is” with “ought”. The hermeneutic work on tradition provides the means with which to criticize certain elements of it. At first this seems paradoxical but the paradox is precisely that of self-transcendence:
It may at first seem puzzling that something that is the product of tradition should be capable of both being the object and the standard of criticism…but the basis of criticism of any one product of tradition must always be other products of tradition which we either cannot or do not want to question… Thus we can always examine a part of the whole only in terms of that whole which we cannot entirely reconstruct and the greater part of which we must accept unexamined” (Hayek, 1973: 25, Vol. 2).
What is the place of thesis in this kosmos? Even as he rejects the idea of a transcendent natural law, Hayek equally and forcefully rejects legal positiv­ism which identifies justice with the law. Now, this double refusal, which marks Hayek’s theoretical system as being highly original, is something which he shares with Luhmann. It does seem to me, however, that the reasons for which one and the other reject Kelsen’s doctrine are very different. In Luhmann’s case it is because the will of a legislator cannot possibly be the foundation for law when law can locate its foundation only within itself. In Hayek’s case, it is because he feels that to believe that spontaneous social order is the result of someone’s will is to fall into a primitive anthropomorphism which assumes that all regularity must neces­sarily proceed from an intention.
It appears that Luhmann retains from legal positivism the idea that the justice of the law is not to be sought beyond the legal system. For Hayek, the justice of thesis is to be found in nomos because, historically and logically, nomos precedes thesis: “Law is older than legislation.” This means that the universe of thesis, i. e., the legal system, is in no way normatively closed. It is, from this point of view, totally subordinated to nomos, to the rule of opinion:
The authority of the legislator always rests…on something which must be clearly distinguished from an act of will on a particular matter in hand, and can therefore also be limited by the source from which it derives its authority. This source is a prevailing opinion that the legislator is authorized only to prescribe what is right, where this opinion refers not to the particular content of the rule but to the general attributes which any rule of just conduct must possess…all power rests on, and is limited by, opinion… (Hayek, 1973: 92, Vol. 1).
The law is only that which makes explicit the just order, spontaneously created: it is its creative fomulation. It is something discovered and not made. The fundamental error of legal positivism, according to Hayek, is to conclude from the fact that the norm becomes valid only through its enactment by political authority that the content of the norm is created by that authority. Obviously we note that Luhmann too could be implicated under this criticism.
The task of judges and legislators is, however, fundamental in the thought of Hayek and in this sense constitutes a system which is relatively closed on the functional level but not on the normative level. The problem for a judge is to formulate a rule which already exists: he makes explicit what is implicit and, if he has to innovate in regard to the letter of the law, he always does so in order to recapture the spirit of the spontaneous, just order. It may sometimes happen that he is obliged to contradict an earlier formulation in order to be better in tune with the general pattern. This on-going search for a coherent formulation of the justice embodied in the spontaneous order cannot, however, be carried out completely deductively within the formal universe of norms only.
The system must open itself to the facts:
A new norm that logically may seem to be wholly consistent with the already recognized ones may yet prove to be in conflict with them if in some set of circumstances it allows actions which will clash with others permitted by the existing norms. This is the reason why the Cartesian or ’geometric’ treatment of law as a pure ‘science of norms’, where all rules of law are deduced from explicit premises, is so misleading… Norms cannot be judged according to whether they fit with other norms in isolation from facts, because whether the actions which they permit are mutually compatible or not depends on facts (Hayek, 1973: 106, Vol. 1).
This is a new blow to the idea of the “closed and internally validated nature of legal norms.” (Luhmann)
Of course, from the previous discussion one cannot conclude that Hayek is right and Luhmann wrong. I repeat that I am not interested here in the validity of ideas but rather in the strange state of affairs whereby from a common formal and epistemological trunk, two theoretical systems as different as those of Hayek and Luhmann were able to develop.
In conclusion, I shall try to interpret the disturbing and insistent claim of Luhmann and his disciples that “only the legal system can grant its elements legal-normative quality. Normativity has no ’purpose’ which lies outside itself” (Ladeur, infra). One first interpretation is that proposed by Lempert (infra). He is the first to show that it is untenable. If the autonomy of the law means that “it must be independent of society’s other mechanisms of social control” (power, status, ethics, etc.) then it is evident that such an autonomy is unattainable. At any rate it is an ideal, according to Lempert, while autonomy, as Luhmann uses the term, is a necessary property.
“The importation of extralegal values into the legal system is not recognized in Luhmann’s theory as a potential threat to autonomy”, Lem- pert tells us. In fact, Luhmann’s view of the autonomization of law seems to have all the properties of the sacred. In a religious society the sacred has just this property of transubstantiation: everything that it touches is thereafter part of its domain. Its capacity for autonomy is infinite. But we, the external observers of the society, see that this autonomy is illusory: society believes itself a product of the sacred but it is the other way around. What is autonomous (autopoietic) is society in its entirety (there is a circular causality between the individual level and the collective level) not the collective level embodied in the sacred (Durkheim), as if it were cut off from individuals. But we also know that it is an attribute of the sacred that it be seen as autonomous by individuals. This is an illusion, of course, but it is part of its nature.
This interpretation makes Luhmann the advocate of a sacralizing concep­tion of society and of law and, by the same token, makes Hayek a modern demystifier who unveils the fact that the legal system and all normative systems, in general, are not autonomous. I do not believe that this interpre­tation is any more acceptable (even if Luhmann writes: “Law is then valid by virtue of decisions which make it valid. The legal system itself is obliged to believe in this ground of its validity” (Luhmann, 1985c: 8).)
I shall propose the following interpretation which reverses the preceding terms in that it makes of Hayek an “ancient” and puts Luhmann at the height of modernity.
In a totally desacralized society which knows that its order does not rest on any extra-social foundation such as God, Nature, or History, and which sees at the same time the arbitrary nature and the irreducible groundlessness of law and the necessity for law, the only solution to the “squaring of the circle” that the political problem represents is to posit that law is self- legitimizing and self-founding. We encounter the same paradoxical form as in the sacred but this time we face it straight on, in clear light. This is the apex of modernity. By comparison, Hayek is an ancient. In his evolutionary schema, the best abstract rules will sooner or later be selected. His neo­Darwinism (which is furthermore incompatible with the theory of auto­poiesis) provides him with a standard, a fixed point, which allows him to escape from the vertigo of Grundlosigkeit.
The question of origin is crucial here. In the beginning, there are facts and opinions. To be the law, law must wrench itself from facts because the mixture of fact and law cannot be tolerated (Rousseau). It must cut itself off from opinions because conflict of opinion makes for civil war (Hobbes). Hence, Luhmann: “As law moves away from its origin it must posit itself as origin” (Luhmann, 1985c: 13).
Let it be the example of the diabolica probatio which brings us back to the logical problem posed by Nozick.[Note 5] The rights of an owner over his real estate are valid only insofar as he acquired it by legally accepted means and the previous owner also had a valid right to it. This is a recursive schema, one that goes far back to the dawn of time: the proof of a right to property is then “diabolical”. This recursive principle is a rational foundation of property rights but if that were all there were the situation would be undecidable. One must, then, decide. (From the latin, decidere: to cut off your enemy’s head). One can only ever decide in a state of undecidability. Therefore, in an arbitrary manner, one decides that three generations are enough. The problem of the absolute beginning is thus done away with; at the origin of law, there is law. The autonomy of the legal system is, finally, undecidably decided.
Translated from the French by Iain Fraser.
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The phrase was used at the Alpbach Symposium “Beyond Reductionism” by Viktor Frankl and the idea was taken up by Hayek in reference to Gödel’s theorem.
In France, Debray built his Critique de la raison politique on the same logical argument: “The government of a collective entity by itself – ’of the people by the people’ – would be a logically contradictory argument” (Debray, 1981: 264).
The technical argument that von Neumann was thinking of to bolster his intuition was later made more precise by Gödel: from the fact of the undecidability of the halting problem for a Turing machine there is no simpler way to describe its behavior than to enumerate all its possible output (an infinity).
I am borrowing here from Malinvaud (1975: 162-63).
Here I am following Ellul’s excellent essay (1975: 191-205).
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