Theories of Knowledge and Quantum Mechanics

Michel Bitbol
CREA/CNRS, 1, rue Descartes, 75005 Paris FRANCE

Published in: SATS (Nordic journal of philosophy), 2, 37-61, 2001

Full text in Word/RTF format on Pittsburgh Archive in the Philosophy of science


Quantum Mechanics has imposed strain on traditional (dualist and representationalist) epistemological conceptions. An alternative was offered by Bohr and Heisenberg, according to whom natural science does not describe nature, but rather the interplay between nature and ourselves. But this was only a suggestion. In this paper, a systematic development of the Bohr-Heisenberg conception is outlined, by way of a comparison with the modern self-organizational theories of cognition. It is shown that a consistent non-representationalist (and/or relational) reading of quantum mechanics can be reached thus.



Naturalizing epistemology means considering the acquisition of knowledge as a fraction of the natural processes which are supposedly described by our best scientific theories. If this is granted, there appears to be a hierarchical and one-way dependence between the scientific theories (which are taken to be our highest and most basic descriptive achievement), and the analysis of cognitive processes construed as a mere local application of these theories. However, things are not so simple. The conception of knowledge one has reached by this process may well have a feed-back effect on the meaning that is ascribed to the prevalent scientific theories. And conversely, new scientific theories may undermine those very epistemological presuppositions which had to be used for their formulation, and which were arrived at on the basis of previous scientific theories.
The purpose of this paper is to display this complex, non-hierarchical, and two-way set of relations between theories of knowledge and scientific theories, especially physical theories. A central theme is the deep-lying tension Quantum Mechanics has imposed onto traditional (dualist and representationalist) epistemological conceptions.

1-Multi-leveled epistemological circles

An "Epistemological circle" is a two-way relation between (i) a scientific theory and (ii) the way this theory pictures the processes by which it was itself formulated and corroborated. This concept of epistemological circle has undoubtedly some kinship with the concept of hermeneutic circle. However, there are also some differences. The most important element of a hermeneutical circle in its original acceptation is the set of preconceptions of the interpreter of a text; the possible discrepancies between this interpretation and parts of the text may then jeopardize these preconceptions, and lead to modify them. This process is performed again and again until a satisfactory reading is reached. In Heidegger's wider acceptation, the starting point of a hermeneutic circle is the set of spontaneous anticipations which underly everyday life. These anticipations are modified whenever a discrepancy between them and the resulting events of life occurs. But epistemological circles involve a systematic network of theoretical predictions instead. The mutual constraints between preconceptions and interpreted "facts" are thus much more stringent in the epistemological circles than in the two former varieties of hermeneutic circles.
In our culture, the epistemological circles of classical physics and classical science are still dominant. So, let me describe them from the outset. One may distinguish two epistemological circles in the paradigm of classical physics. The first circle relates: (i) a description of the two main entities of classical physics, namely material bodies and fields, and (ii) the description of the experimental apparatuses under the presupposition that these apparatuses are made of material bodies and fields obeying the laws of classical mechanics and electrodynamics. This means that testing the theories of classical physics depends on a pre-interpretation of the measured values by using these (and/or other) theories for the description of the measuring process. Conversely, the validity of this description of the measuring process depends on the validity of the theories which are used in it. I call this first epistemological circle the "measurement circle".
The second epistemological circle, which classical physics shares with classical science as a whole, is also made of two elements. It relates (i) the picture that the theories of classical science provides of its objects, and (ii) a meta-picture of the relationship which exists between these objects and the subjects of cognizance. The self-consistency of this circle is achieved if the validity of the picture is compatible with the meta-picture of the cognitive process that ended up in this description, and conversely if the meta-picture is isomorphic to the picture. For instance, the idea that a theory describes faithfully the motion of a set of interacting objects is made plausible by the meta-picture of a set of objects seen by passive subjects of cognizance. Indeed, if the subjects are purely passive, or if their activity has no bearing on the constitution of objects, their contribution to the epistemic contents can easily be substracted, and the intrinsic properties of objects can easily be reached. In other terms, the conception of subjects as passive receptors makes almost trivial the sought de-convolution of phenomena into a subjective and an objective side. Conversely, the classical meta-picture of the interaction between subject and object is isomorphic to the interaction between two material bodies whose boundaries define internal and external domains. I call this second epistemological circle the "subject-object circle".
The most common paradigm of cognitive science describes cognition as a succession of "inputs" from an "external" pre-structured world, of "internal" information processing (usually computational), and of performative or symbolic "outputs". This input-output paradigm is immediately compatible with classical science as a whole. To begin with, the input-output paradigm of cognitive science perfectly fits with the conception of the universe as a set of interacting pre-existing material bodies, since in it the cognizant system is only supposed to pick faithfully the information made available by these bodies, and to process it in such a way that it reaches a high degree of (symbolic or pragmatic) efficiency. Moreover, the input-output paradigm of cognitive science is also remarkably isomorphic to this conception of the universe, insofar as the separation between the objects and the cognizant system appears as a special case of the spatial separation between the material objects of classical science. This clearly promotes the project of a complete naturalization of epistemology in the same descriptive terms as classical science, namely in such a way that the cognizant system be construed as a material object of this science among many others.
Those two epistemological circles are not bound to be "vicious" or "tautological". Indeed they are not completely immune against criticism. But the conditions which may yield their revision are quite peculiar, and this is enough to explain their lasting prevalence after one century of growing strain.
On the one hand, no epistemological circle can be challenged by extrinsic circumstances. Nothing except an emergent lack of self-consistency may prompt one to question it. But, of course, this type of deficiency may trigger many other strategies than radical change. Other available strategies include:
(1) Compensation of the inconsistencies by ad hoc hypothesis,
(2) Explicit hope that future research will show that there are no real inconsistencies,
(3) Renunciation of the unity of knowledge, i.e. definition of cognitive sub-domains wherein consistency is locally recovered.
On the other hand, one must realize that the standard subject-object circle has its roots in the ontological pre-conceptions classical science has inherited from ordinary language and everyday life. Imposing thorough revisions onto the standard subject-object circle would thus generate a conflict between those theoretical contents which are embedded within the new circle, and most ways of speaking and behaving in the Umwelt of mankind. If a new epistemological circle were to prevail, this would only be possible provided the old one still underlies it as: (i) its basic presupposition in ordinary speech and behaviour, and (ii) its qualitative or quantitative limiting case within the most familiar areas of knowledge. This remark obviously generalizes Bohr's conception of the relationship between the measurement circles of classical and quantum mechanics. According to him, the predictive formalism of quantum theory could not even work if classical theories were not presupposed for the description of the measurement apparatuses which allow to test it, and also if one did not recover classical laws at the scale where the value of the Planck constant becomes negligible.
An important consequence of these constraints is that whenever a new epistemological circle is proposed, its very formulation is de facto dependent on the traditional subject-object circle. Let us consider, for instance, the way new paradigms of cognition, involving emergence and self-organization, have been formulated in the past. In these paradigms, the traditional relation between an autonomous object and a passive subject facing each other is thoroughtly criticized. But when the elements of the self-organizing cycle themselves are described, they are dealt with exactly as if they were pre-existing things (or states) in front of a passive subject. In this case, the meta-theory of knowledge is not consistent with the alternative first-order theory of knowledge which is advocated. F. Varela, a prominent supporter of non-standard theories of cognition, is perfectly aware of this problem . His answer to the criticism essentially amounts to downplaying the descriptive status of his own theory of cognition. One should realize, according to him, that concepts such as emergence, self-organization, or enaction, are not pieces of a description aiming at some absolute truth, but rather stages of a dialectical process purporting to free us from dualist or foundationalist schemes. This self-referential feature of non-standard theory of cognition could be analyzed for its own sake. But here, I wish to concentrate on the special form it takes in quantum physics. To begin with, what kind of relations are there between the classical and the quantum measurement circles?

2-The measurement circle of quantum mechanics

According to David Bohm, the problem which arises from the interpretation of quantum mechanics is twofold. The first aspect of the problem is that there is no natural ontology of quantum mechanics, in the sense of a set of objects and properties "(...) taken to be essentially independent of the human observer". And the second aspect of the problem is that, due to this lack of a natural ontology, standard quantum mechanics seems unable to give rise to a proper, self-consistent, epistemological circle. One should remember that in classical physics "The epistemology was almost self-evident because the observing apparatus was supposed to obey the same objective laws as the observed system, so that the measurement process could be understood as a special case of the general laws applying to the entire universe" . Bohm's attempt at providing an "ontological" interpretation of quantum mechanics is thus overtly aimed at recovering a satisfactory epistemological circle; a circle of measuring and measured as remarkably closed as that of classical physics.
But what are exactly the obstacles which prevent the constitution of an epistemological circle in quantum mechanics? Did Von Neumann not exhibit such a circle by way of a quantum description of the measurement set-up (his well-known "Quantum theory of measurement")? The difficulty is still there, however, and its name is the measurement problem. As we shall see, this well-known problem is really intractable in its usual (quasi-descriptive, not to say ontological) form, but it becomes much easier to tackle in a purely predictive version.
To begin with, we must remind the usual form of the measurement problem. Let us first ascribe a state vector to the experimental set-up, and let us suppose that this state vector is ruled by the same law as the state vector of the measured system. If this is granted, a quantum variety of the measurement circle is created. Let us suppose next that the state vector of the system is not identical with an eigenstate of the observable measured by this experimental set-up, but that it is a linear superposition of such eigenstates. During the measurement process, the state vector of the super-system (micro-system + apparatus) develops according to a Schrödinger equation whose Hamiltonian includes an interaction term between the two components of the super-system. When this process is over, it is usually impossible to factorize out the state vector of the apparatus from the global state vector of the super-system (micro-system + apparatus). It is usually said that the respective states of the micro-system and the apparatus are entangled. At this point, the global state vector of the super-system consists in a linear superposition having exactly the same structure as the initial superposition in the state of the micro-system.
If one takes seriously the popular idea that a state vector somehow captures the "state" of the object to which it is associated, it must be accepted that the quantum theory of measurement represents neither the micro-system nor the apparatus as being in a sharply defined final pure state. Rather, it represents the state of both components of the super-system as being "(...) mixed or smeared out" . The quantum theory of measurement thus seems to contradict the elementary experience of any physicist in his laboratory, according to whom the apparatus is in a well-defined state after the experiment has taken place (but of course here, as B. Van Fraassen cogently pointed out, the word "state" is playing two distinct roles). Even more strikingly, taken at face value, the quantum theory of measurement seems to contradict one of the most basic conditions for testing any physical theory, i.e. the comparison between what this theory says and a set of well-defined measurement outcomes. But if this is true, the circle of the quantum theory of measurement does not fulfill the requirements for a proper epistemological circle. Indeed, in order to formulate a proper epistemological circle of the measurement variety, it is not enough to connect a physical theory with a theoretical account of the experimental process derived from this physical theory. It is also necessary that this account be compatible with the minimal epistemic conditions which enable one to test physical theories in general. But the quantum theory of measurement does not fulfill this requirement, as long as it does not include any structural equivalent of the elementary requirements of uniqueness and strict determination of experimental outcomes.
The first reaction to this obvious difficulty consisted in enforcing the "projection postulate", according to which the state vector of the micro-system (and/or the state vector of the super-system) instantaneously collapses at some point of the measurement process. This collapse transforms the state vector of the micro-system into one of the eigenstates of the relevant observable. The problem is that this reaction is tantamount to renouncing any attempt to close the epistemological measurement circle of quantum mechanics. Indeed, imposing a sudden collapse to state vectors whenever a measurement occurs, means that the measurement process is somehow construed as an exception in the physical universe. All the processes of the physical universe are supposed to be ruled by the Schrödinger equation, but not the measurement process. This situation gave rise to a large variety of thoughts. N. Bohr merely noted that the very attempt at closing the quantum epistemological circle is likely to be flawed from the beginning, since the experimental set-up and the outcomes must be described in classical terms (in order to enable unambiguous communication). D. Bohm (see the beginning of this section) attempted to recover something like a classical epistemological circle, by means of his hidden variable theory. Another, more recent, reaction was Ghirardi's, Rimini's, and Weber's with their idea of inserting a "spontaneous collapse" term in the Schrödinger equation . This idea is interesting for the present discussion, insofar as it amounts to closing the epistemological circle of quantum mechanics by modifying the theory of objects in order to fit the partial theoretical description of the measurement process, rather than the other way round. But it is also fraught with difficulties . I shall thus insist on a radically different strategy of dealing with the measurement problem. This strategy consists in using a deflationist conception of quantum mechanics, which concentrates on the predictive contents of the state vector, rather than on its putative ability to describe the "state" of various objects.
Defining a purely predictive interpretation of the symbols of quantum mechanics is not very easy, because in the past this reading has been inextricably mixed up with descriptive elements. A litteral interpretation of quantum mechanics according to which this theory provides us with probabilities for experimental outcomes after a given preparation, has usually been mixed up with typically descriptive concepts such as those of "micro-systems" or "states". Few authors have seriously developed all the (philosophical) consequences of a purely predictive construal of quantum mechanics . Yet, holding consistently to such a predictive reading throughout could well result in an entirely recasted formulation of the measurement problem. This could also give some hints towards a solution of this problem (not to mention a serious adumbration of a true dissolution of it).
According to the purely predictive interpretation, the quantum theory of measurement institutes a very peculiar kind of epistemological circle : a circle of probability assessments, rather than a circle of descriptions. The probability assessments themselves are about two types of measurements: the first-level measurement bearing on the micro-system, and a meta-measurement bearing on the experimental set-up with which the first-level measurement is performed. Within this framework, the measurement problem assumes a new form. In the same way as the descriptive circle of measuring and measured, the probabilistic circle has a problem of closure. Closing the descriptive circle required that the description of the measurement process be a special case of the general description of physical processes. Closing the probabilistic circle requires that the probability theory which applies to the meta-measurement outcomes be of the same type as the probability theory which applies to the first-level measurement outcomes. The latter condition is not trivial, however. At the macroscopic level of the meta-measurement process, the theory which has to be used is Kolmogorov's classical theory of probabilities, whose probability assessment can be satisfactorily interpreted as an expression of our ignorance of pre-existing phenomena. But predicting the results of the first-level measurement requires a quantum theory of probabilities which involves interference terms, isomorphic to those of a wave process. This presence of interference terms does not allow an ignorance interpretation of the probabilistic assessment. (To qualify this assertion, the ignorance interpretation is precluded only at the immediate level of the phenomena ; but it can still be carried on at the level of hypothetical "hidden" processes such as Bohm's).
If we put Bohm's theory aside, the question is then as follows. Can one close the circle whose elements are (i) the probabilities of the outcomes of a first-level measurement and (ii) the probabilities of the outcomes of a meta-measurement bearing on the very process of first-level measurement? In order to perform this kind of closure, one would have to demonstrate that the classical theory of probabilities, which operates at the macroscopic scale of the experimental set-up, is a limiting case of the quantum theory of probabilites which is supposed to operate at any scale. But decoherence theories are precisely aimed at providing such a demonstration. They are aimed at showing that when applied to complex processes involving a micro-system, an experimental device, and a vast environment, the quantum probabilities converge (to a good approximation) towards classical probabilities. Indeed, in this case, the interference terms tend to vanish, and the kolmogorovian additivity rule for disjunctions of events can accordingly be enforced. The only thing which usually hides this purely probabilistic status of the decoherence theories is the dominant descriptive interpretation of the state vector and the density matrix .
An important defect of this method for closing the epistemological circle of quantum physics is that, in order to derive the probabilistic structures which prevail at the meso-macroscopic scale of the human experimenters from the quantum probabilistic structures, the specialists of decoherence theories could not avoid making anthropocentric hypotheses. W. H. Zurek for instance assumed that the measurement chain consist of three elements : the micro-object, the apparatus, and the environment (I have also used this assumption verbally for the sake of easy writing). But, admittedly , this division only holds at the emergent level of the macroscopic manifestations ; it is by no means obvious a priori in the domain of validity of quantum mechanics. It is thus crypto-anthropocentric. Another instance of an anthropocentric assumption was used by M. Gell-Mann in his theory of decoherent histories. Gell-Mann assumes a coarse-graining of the consistent histories, and he justifies this coarse-graining by the macroscopic scale of a population of anthropomorphic "Information Gathering and Utilizing Systems" (IGUS).
This level of petitio principii becomes a real problem only if one hopes that decoherence theories are strong enough to prove that a (quasi-) classical probability assignment is the unique form a quantum probability assignment can assume at macroscopic scale. But if what one expects from decoherence theories is only a proof that classical probability is one among the many possible emergent forms of probability assignments at the macroscopic scale, then things are quite different. In particular, if one only needs a proof that the classical theory of probabilities can emerge from the quantum theory of probabilities under some restrictive conditions which encapsulate the basic constitutive presuppositions of human knowledge, then decoherence theories provide a perfectly satisfactory answer. True, the closure of the measurement circle is not the unique and unavoidable outcome of the mode of functioning of quantum mechanics, but decoherence theories prove that it is a possible byproduct of its formalism. Moreover, provided these basic presuppositions are assumed at the level of the meta-apparatus (the apparatus used to monitor the processes within the measurement device), a rapid suppression of the coherence terms has been observed experimentally .
The urge for univocity cannot, therefore, be satisfied within the field of quantum physics. But it can be satisfied by appealing to some additional non-quantum considerations. This ampliative strategy was adopted by Zurek and Gell-Mann, when they used Darwinian arguments in their reflection on decoherence theories. Thus, according to Gell-Mann, the aim of somebody who wants to solve the measurement problem should not be to prove that a classical world necessarily emerges from a quantum micro-level; it should only be to show, within the framework of quantum physics, that Knowing Systems (IGUSes) cannot be stable, i.e. survive, if their actions and epistemic structure do not develop at a quasi-classical level . Later on, S. Saunders showed that decoherence can be derived from those conditions which make possible the life of an autonomous metabolic system .
To summarize:
(1) Decoherence theories are not able to prove that the emergence of a classical world is a necessary and unique consequence of quantum physics at the macroscopic scale;
(2) Decoherence theories provide a tool for dealing quantum-mechanically with the process of co-emergence of a Knowing System and its macroscopical quasi-classical Umwelt.
If this is true, that means that in order to close the measurement circle of quantum physics, one must rely on a project of closure of the subject-object epistemological circle (the general circle of the knowing and the known). Let us then examine this larger epistemological circle.

3-The subject-object circle challenged: a parallel between quantum mechanics and the cognitive science

Challenging the subject-object circle of classical science, namely the dualist picture of an encounter between the knowing subject (the spectator) and the nature he purports to know (the spectacle), was considered indispensible by some of the most prominent creators of quantum mechanics. Bohr insisted that "(...) the new situation in physics has so forciby reminded us of the old truth that we are both onlookers and actors in the great drama of existence" . As for Heisenberg, he suggested repeatedly that quantum mechanics does not provide us with a description of the atomic processes themselves: it rather sketches jointly "(...) a tendency of events and our knowledge of events" . More generally, he thought that "Natural science does not simply describe and explain nature; it is part of the interplay between nature and ourselves; it describes nature as exposed to our method of questioning" . In other terms, according to Bohr and Heisenberg, quantum mechanics is the paradigm of a theory which does not describe intrinsic properties, but rather anticipates probabilistically the outcome of possible experimental relations. This is enough to dissolve the measurement problem, or at least to change radically its formulation, as I explained in the previous section by means of a purely predictive reading of decoherence theories. Indeed the state vector here does not represent anything like the state of something, but only a joint tendency manifesting itself in a potential future experiment. Superpositions are no longer surprising within this framework, provided it is shown that at the macroscopic scale these superpositions can be approximatively reduced to a list of classical probabilities.
This sort of epistemological interpretation of quantum mechanics was not really assimilated by the physics community. Even though they accepted it formally, physicists felt uneasy about it. For decades, they just mixed up some elements of "positivistic" conceptions of quantum mechanics with bits and pieces of descriptive language. Then, a strong tendency towards recovering a "realist" interpretation of quantum theories arose, and the Bohr-Heisenberg reading became marginalized. Quite apart from this realist prejudice, however, a reason for the progressive oblivion of the Bohr-Heisenberg views may be that they were not given enough systematic development by their authors.
But nowadays, such a systematic development is made much easier by the recent development of non-representationalist theories of cognition. The similarities between the type of non-dualist theory of knowledge Bohr and Heisenberg adumbrated and these non-representationalist theories of cognition are striking. To see this analogy, it is enough to compare the former quotations from Heisenberg with the following statement of a modern cognitive scientists: "The changed structure (of neural networks) does not represent the external world, but it represents - if one wants to stick to the term - the interactive process: input-organism's or environment-organism's interaction. (...) it means something to its owner although never in an absolute sense, but only in relation to the organism's actions in its environment" . This is clearly an incentive to draw a systematic parallel between the Bohr-Heisenberg theory of knowledge and the non-representationalist theory of cognition. The parallel will concern three distinct points.
A-The first similarity bears on the common motivation of both attempts at recasting epistemology. This common motivation is to free oneself from previous ontological patterns (borrowed from the "natural attitude", or from classical physics) when the status of knowledge is at stake.
Let us begin with cognitive science. The rise of the self-organisational paradigm after a long period of predominance of the representationalist, symbolic, and computational trend of cognitivism, can be explained by the partial failure of the initial program of Artifical Intelligence. For instance, the specialists of AI met many subtle obstacles in their project of implementing reidentification of material bodies by their shapes. This led some of them to think that : "(...) the world is an unruly place - much messier than reigning ontological and scientific myths would lead one to suspect" . It was thus necessary to avoid imposing in advance our too civilized formal concepts on the machines. For these formal concepts arose from the cognitive evolution of mankind, and nothing can assure us that they are appropriate to any type of machine as well. Designers of machine perception systems must therefore allow massively adaptative processes. If anything, they must implement "(...) notions of objects that are fluid, dynamic, negotiated, ambiguous, and context-dependent (...), rather than the black-and-white models inherited from logic and model theory" . They must not project onto their machines the ossified system of human ontological presuppositions, assuming wrongly that they correspond to something that was once discovered by men, and that has to be either implemented on or rediscovered by those machines. If a machine could orient itself in the world, it would be in its own world; not in the world of preconceived ideas of logicians and model theorists. To summarize, the mistake of classical cognitivism consists in its having judged in advance the relation between a machine and its environment, by imposing on it the byproduct of the former dynamical relation between men and their Umwelt.
One may explain similarly the renewed interest of the creators of quantum mechanics in the relation between the instruments of exploration and the explored microscopic domain. Their thoroughly relational approach was aimed at preventing quantum physics from getting stuck in the pre-existent ontological framework which classical physics shares with the "natural attitude". According to them, the formalism of quantum mechanics, and the set of predictive methods that are derived from it, express the emergent order of the new relations allowed by recent advances in experimental physics. It could by no means be adapted to a framework of formal concepts which express the emergent order of a much older type of cognitive relation: the relation between men and their mesoscopic environment.
B- As I have mentioned before, the central topic of the usual representationalist paradigm of cognitive science is a system of "information processing" construed as a locus of articulation of (i) inputs from a pre-structured external world, and (ii) processing of these inputs by way of a representation of the invariant features of this world, and (iii) performative or symbolic outputs. But this is obviously not the case in the non-representationalist, self-organisational paradigm. Here, the fundamental entities are operationally closed units. The only invariant of these units is their own dynamical organisation. And their "cognitive domain" is not a represented fraction of a pre-existing world, but a fraction of the environment which has co-evolved with them and in which their organisation may persist despite some disturbances. Using J. Piaget's vocabulary , the process by which an operationnally closed unit protects itself by incorporating the most common disturbances in its own dynamical organization is called assimilation. As for the process by which this unit transforms itself in order to be able to assimilate further disturbances, it is called accommodation. The appropriate behaviour of a self-organized unit then does not prove that it possesses a faithful picture of the world, but only that its internal working is viable in relation to environmental disturbances. Thus, the categories which underlie its behaviour are not the internalized copy of the intrinsic partition of a pre-ordered external world. They are the stabilized by-products of the history of a coupling between the unit and an environment which may well be chaotic . Each single predicate corresponds to an "eigenbehaviour", or to an attractor of the dynamics of the self-organized unit.
The similarities between this view of cognition and the Bohr-Heisenberg relational conception of quantum mechanics are made almost obvious by an overt mathematical analogy. F. Varela explicitly mentioned that the word "eigenbehaviour" is in perfect agreement with the use of terms like "eigenvalue" and "eigenfunction" to refer to the fixed points of linear operators (such as those of quantum mechanics) . But the converse is also true. Bohr and Heisenberg advocated a thoroughly interactional view of the quantum formalism of eigenvalues and eigenvectors of linear operators. Saying that eigenvalues and eigenvectors of quantum observable express the eigenbehaviour of the apparatus in its coupling with the micro-domain, rather than the intrinsic properties of micro-objects, would be very close to the spirit of their interpretation. At any rate this is essentially the idea Schrödinger was trying to convey in the 1950s. According to him, the quantum discontinuities and the corresponding probabilistic account do not reveal some intrinsic jump-like feature of atomic objects; rather, they express the functioning of "(...) contraptions that by their very nature cannot but give a discrete, discontinuous, response (...)" .
C-At this point we must investigate the content of the word "knowledge". Can it have the same meaning in a representational and in a non-representational theory of knowledge? A preliminary point to examine is the transition from a mere "eigenbehaviour" to something which can indeed be called knowledge. This transition will be compared to the corresponding transition from a relational conception of experiments in microphysics to the formalism of quantum mechanics.
According to J. Piaget , the decisive step from organized behaviour to knowledge consists in freeing oneself as much as possible from the irreversible aspects of any concrete operation. This freeing is achieved by means of gestural schemes tending towards perfect reciprocity of the caused transformations. A few elementary examples of these schemes of reciprocity are: moving an object and then putting it back at its original place; rotating an object until its initial profile is recovered; pouring a liquid in various containers, and then pouring it back in its original container (thus seing that the level has not changed); etc. These schemes have the structure of performative groups of transformations. They enable anticipation of what will occur, for they rely on methods for reproducing situations and for carving out domains of invariance; they extract elements of stability and iterativity from the Heraclitean flux. At the following stage of development in childhood, the gestural schemes of reciprocity are made systematic by being embedded within a logico-linguistic framework which is socially shared. The formerly extracted invariants are then organized as a set of objects referred to and of ascribed predicates. They are presupposed in speech, and used to suggest predictions. Finally, at the very end of the genetic process, new, non-linguistic, symbolic structures are elaborated. These structures convert the practical constraints into deductive constraints, and they also convert the performative groups into abstract groups of transformations. They are mathematical structures, more universal than the former logico-linguistic structures because they are not exclusively committed to the subject-predicate pattern, and therefore are more universally efficient as instruments of prediction. J. Piaget thus considers mathematics as a "general coordination of actions"; or, more precisely, as a general symbolic coordination of those actions which are embedded within schemes of reciprocity-reversibility .
This conception of mathematics suggests a plausible explanation of the special constitutive status of mathematics in physics. After all, the basic task of physics is to control sequences of phenomena by means of reversible and organized experimental actions. It is not surprising that mathematics, which coordinates systems of possible reversible actions by means of a deductive symbolism, is able to provide physics with very efficient instruments for anticipating the phenomena which result from actual (experimental) actions tending towards reversibility. According to J. Piaget, in physics, "(...) far from reducing to a language, mathematics is the structuring instrument which coordinates those actions and expands them into theories" . As a consequence of this view, the purpose of physics is not to elaborate a series of convergently faithful pictures of a nature given in advance. It is rather to accommodate and assimilate sequences of irreversible phenomena within the schemes of reversible actions which are formalized in mathematics.
This being granted, the usual dualist theory of knowledge, with its encounter between subjects and objects, appears to develop a very narrow variety of a much wider range of conceptions of knowledge. The basic tendency of the cognitive procedures of assimilation-accommodation is to reach invariance with respect to local or individual circumstances. This condition of invariance is fulfilled by embedding as much as possible of the primarily irreversible and non-reproducible phenomena within reciprocal schemes of activity. And its most useful byproduct is a set of predictive rules. Acting under the presupposition of the permanent identity of objects across time, and of the possession by these objects of intrinsic properties, is a possible method for reaching this aim of invariance and predictibility. However, one suspects that it is by no means the most general method, and that it involves stringent constraints which are not unavoidable.
We are then led to distinguish two varieties of knowledge. The first one is the general process of embedding phenomena within reversible schemes of activity, and to formulate a mathematical counterpart to these schemes in order to get an optimal set of predictive rules. Let us call it KnowledgeG (for General). The second one is that special variety of the process which is conditioned by the referential and predicative functions of language, insofar as it consists in ascribing properties to permanent objects. Let us call it KnowledgeS (for Special). Accordingly, we may distinguish two aspects of objectivity: a general one (which characterizes KnowledgeG), and a special one (which characterizes KnowledgeS). The general aspect of objectivity (let us call it ObjectivityG) is essentially negative, for it merely amounts to a lack of submission of performative schemes and anticipative rules to any indexical location (I, here, now, this). By contrast, the special aspect of objectivity (let us call it ObjectivityS) is positive. In agreement with the etymology of the word, it consists in projecting the disindexicalization of predictive formalisms onto a description of supposedly autonomous objects.
At this point, the reason for the lasting unease about quantum mechanics can easily be stated in two sentences. Quantum mechanics provides us with KnowledgeG, but it is irreducible to any form of KnowledgeS. Its statements are ObjectiveG, but they usually miss the positive contents which are typical of ObjectivityS. As long as KnowledgeS and ObjectivityS hold the position of a norm and value in epistemology, these two features of quantum mechanics are likely to be felt as major defects. But from the standpoint of non-standard theories of cognition, where KnowledgeS and ObjectivityS are only individual cases of KnowledgeG and ObjectivityG, the same features can be taken instead as major advances towards a universalized conception of knowledge in physics.

4-A survey of the tensions between quantum mechanics and the dualist theory of knowledge

Before I develop further the consequences of these remarks, however, I have to briefly justify the contention that Quantum mechanics is a typical piece of KnowledgeG but that it is irreducible to any form of KnowledgeS. For, after all, there is no consensus about this point. One must even say that, due to the normative role of KnowledgeS, finding a satisfactory "realist" interpretation of quantum mechanics (i.e. an interpretation according to which a description of properties of objects can be derived from quantum mechanics) is perceived by many philosophers as the major research priority. Their basic tenet (or hope) is that it is not impossible to show that quantum mechanics describes (either completely or incompletely) an intelligible realm of objects endowed with properties existing behind the superficial appearances.
The problem is that this attitude has not reached a stage where it may be considered unproblematic, even by its most eager proponents. Surveying the realist interpretations of quantum mechanics, one may easily display their major defects.
Firstly, the most efficient and popular hidden variable theory (Bohm's theory) is drifting further and further from the classical ideal, making it less and less attractive for some of its original supporters. True, Bohm's hidden variable theory manages to recover the predictions of standard quantum mechanics by committing itself to an ontology of interacting micro-objects endowed with properties (provided the interaction involves an all-pervading and instantaneous "quantum potential"). Taken at face value, it describes the trajectories in space-time of these objects, and even more general spatio-temporal processes. However, unlike the classical trajectories and processes, Bohm's trajectories are obtained at the cost of a radical dissociation with any possible experimental procedure. Here, experiments are what may modify a trajectory, rather than what only make it manifest. Accordingly, properties are posited as purely hypothetical invariants, for they are not the invariants of any effective operational scheme. The hidden variables thus satisfy an abstract urge for objectivity, but they remain very loosely and indirectly connected with concrete procedures of objectivation. To sum up, Bohm's original hidden variable theory is an empty variety of the scientific strategy of seeking invariants. This explains why it is hardly testable against standard quantum mechanics , and also against any alternative hidden variable theories able to recover the preductions of standard quantum mechanics.
Secondly, there is quantum logic. Quantum logic is not only a piece of pure formal architecture, aimed at disclosing the most basic structures of the quantum-theoretical scheme. From the very beginning, quantum logicians aimed at restoring realism in quantum physics against Bohr's mixture of instrumentalist and participatory views. Rather than sticking to "phenomena" as Bohr did, quantum logic apparently enabled one to recover the possibility of speaking in terms of "physical qualities" or of properties of systems, at the cost of changing the algebra of these properties. Instead of a Boolean algebra, one merely had to accept an "orthocomplemented non-distributive lattice." As soon as this result was obtained, however, the whole historical perspective was reversed by later quantum logicians. In history, non-boolean logic appears as the realist reply to Bohr's criticism of the ideal of a complete separation between an object and an observing agent. But some contemporary quantum logicians asserted that: "The rejection of the 'ideal of the detached observer' is the Copenhagen response to non-Booleanity." Thus, according to these views, the world is inherently non-Boolean, and Bohr's holism is a spurious epistemological interpretation of this ontological feature. But, actually, there is much to be said in favor of Bohr's original standpoint. Let me use, for instance, an argument of simplicity and intelligibility. From the elementary assumption that phenomena are irretrievably relative to their (sometimes incompatible) experimental contexts, it is easy to derive: (i) the full non-boolean structure of quantum logic , (ii) the quantization itself (through the commutation relations between conjugate variables), and (iii) the wave-like aspect of certain distributions of discrete phenomena . This derivation does not require any well-defined assumption about the structure of the world (with the exception of the non-zero value of the Planck constant). By contrast, starting from a detailed non-Boolean structure of the algebra of properties of the systems which constitute the world introduces a high amount of arbitrariness in the premises. The derivation of consequences from this kind of premise thus has little explanatory power.
Thirdly, let us consider some attempts at giving a straighforward descriptive status to the symbols of standard quantum mechanics. This was the main purpose of the many-worlds interpretation, of Dieks realist version of the modal interpretation, and of the spontaneous collapse interpretation. But none of these interpretations has proved as yet that it can cope in its own terms (namely without invoking meta-theoretical regulative principles) with some specific difficulties such as the preferred basis problem. True, decoherence theories claim to be able to provide a solution to the previous difficulties. But as we have seen in section 2, decoherence theories are pervaded by interest-relative postulates which do not make them liable to an ontological reading. Their being used in such circumstances is rather an incentive to challenge the standard "epistemological circle" of subject(s) and objects, and thus to drift away from the most basic presupposition of realism. More recently , a realist reading of state vectors and density matrices was derived from the analysis of so-called adiabatic or protective measurements. Indeed, a single protective measurement is enough to reach distributive parameters (such as expectation values) which are directly provided by state vectors but that would require a statistics over a large number of non-protective measurements. The realist conclusions drawn from the consideration of this class of measurements have nevertheless been challenged with sound arguments . It has been shown that only observables that commute with the system's Hamiltonian can be measured protectively. The protective measurement argument thus amounts to little more than showing that the structure of a set of commuting observables is quasi-classical.
Finally, one may discuss briefly the pragmatic attitude of physicists in their laboratories. Their priority is clearly instrumental: they relate day after day the outcome of a mathematico-symbolic activity to the outcomes of an experimental activity. But they also articulate, for heuristic purposes, fragmented models of objects. And they use terms such as "particles", "properties", "fields", etc. whose meaning drifted apart from their classical counterpart beyond recognition, but which still ignite the temptation of ontological projection. The all-pervasiveness of these models and of these crypto-ontological words could be taken as a proof that dispensing completely with the traditional dualist theory of knowledge in science is utopical. But the very way the models and terms are manipulated, shows that the dualist theory of knowledge is de facto dead in the practice of standard quantum theories. For the use of these models and terms is systematically made flexible and contextualized. They become successively predominant or marginal according to the theoretical and experimental context of discourse. They may have either to be taken at face (traditional) value in one context (say in chemistry), or to be thoroughly redefined in another context (say in high energy physics). They are nothing more than relative models and ontologies, loosely articulated with the remote hope of a unified (and hence presumably absolute) picture.

5-Relational approaches to quantum mechanics

Let us recapitulate what has been found up to now:
1) Pushing the Heisenberg-Bohr views of quantum theory to its ultimate consequences, one obtains a remarkable structural agreement with self-organizational and non-representationlist theories of cognition.
2) Only within a non-representationalist theory of knowledge does the measurement problem of quantum mechanics find a quick and natural (dis)solution. This is due to the fact that the measurement problem is tantamount to a lack of closure of the epistemological circle that quantum theories have inherited from classical physics and "natural ontology". Changing the type of epistemological circle according to a non-representationalist line (and reinterpreting the decoherence theories accordingly) is enough to get a satisfactory way out.
3) The recurrent attempts at providing a "realist" interpretation of quantum mechanics (i.e. an interpretation appropriate to the classical dualist theory of knowledge) are clearly unsatisfactory. Even though nothing may preclude that a fully satisfactory "realist" formulation of quantum mechanics or its successors will be found in the future, this is only wishful thinking for the time being. In the present situation, "realist" interpretations all appear artificial, contrived, and/or incomplete.
From point 3), it appears that quantum mechanics undermines the most basic epistemological presuppositions of classical physics, even though these presuppositions were the unavoidable departure point of the investigation that led to its formulation. Quantum mechanics institutes a tension within the epistemological circle from which it arose, and it therefore paves the way towards a radical redefinition of this circle.
From points 1) and 2), one gets a clear idea of what might well be the appropriate new epistemological circle: it is the circle which corresponds to non-representationalist and self-organizational theories of knowledge. However, if this is true, the meaning of each single element of the physical theory, and of its meta-theoretical account of measurement as well, has to be completely changed. Since quantum mechanics does not describe anything like the properties of its putative objects, the quantum theory of measurement does not describe anything like the properties of the measuring apparatus either. But if this theory and its meta-theory do not describe anything, what do they do?
The easiest answer to this question is flat empiricism, according to which quantum mechanics is a mere formal device enabling one to account as economically as possible for the statistical regularities of phenomena defined relative to certain experimental devices described in classical terms. What I called the "predictive" reading of quantum mechanics in section 2 is especially liable to this interpretation (although it does by no means reduce to it). But of course, one may easily understand that realist philosophers, and many scientists as well, are reluctant to accept a purely empiricist view of theories. Indeed (with the possible exception of Van Fraassen's constructive empiricism ), most versions of empiricism have proved unable to account for what is so crucial in everyday research, namely a well-defined perspective, a clear direction, and a strong motivation. They also lack a fully satisfactory explanation of the remarkable predictive success of a theory like quantum mechanics. Epistemological evolutionism is the best candidate to afford such an explanation within an anti-realist framework of thought, but if it remains isolated, it is not sufficient, especially when it is confronted with quantum mechanics. For it accounts for a plurality of viable (or approximately adequate) slowly drifting theories, whereas one has to explain the unicity and extreme stability of the general framework of theories afforded by the standard Dirac-Von Neumann's formalism. This is the reason why, in the past few years, I developed a full-fledged transcendantalist interpretation of quantum mechanics, which rejects both the realist idea that a physical theory is a (more or less complete) description of a pre-structured external world, and the empiricist view that it is reducible to a unified summary of efficient predictive recipes . While sticking to the purely predictive reading of quantum mechanics, I showed that one may provide it with much stronger justifications than mere a posteriori empirical adequacy, without invoking the slightest degree of isomorphism between this theory and the elusive things out there. The alternative justification is as follows. The structure of quantum mechanics necessarily arises whenever one tries to embed contextual and mutually incompatible phenomena within a unified and time-connected meta-contextual system of probabilistic anticipation. It is a formal condition of possibility of those unusual probabilistic assessments.
This kind of justification of quantum mechanics is obviously in better agreement with self-organizational and non-representationalist theories of knowledge than with either the realist or the empiricist variety of the classical epistemological paradigm. For here the theory is by no means construed as a (more or less precise) picture of a pre-existing nature; nor is it construed as a mere economical formula to express pre-given facts. The theory is rather taken as the structural expression of an all-encompassing strategy of gaining context-invariant anticipative capacity, in a situation where the contextuality of each single phenomenon cannot be ignored. As for the forms the theory assumes in various specialized domains, they are construed as the byproduct of the co-emergence of a given type of experimental activity and of the 'factual' elements which constrain it . In this reading of quantum mechanics, as in self-organizational theories of knowledge, there is no one-way dependence of the theory on either "external reality" or "facts". Rather, there is a two-way mutual dependence between the project of investigation and the system of constraints which has to be taken into account by it .
Thinking a little further, one realizes that this conception of knowledge is thoroughly relational. It is even relational in an exceptionally strong sense. For here, the terms of the cognitive relation, namely the project of experimental investigation underpinned by a theory, and the set of phenomenal constraints which are to be accounted for, do not come before the research activity which institutes the relation itself. The relata of the cognitive relation are produced by it, precisely as much as the other way round. This type of cognitive relation with no pre-existing relata is all the more interesting since it closely mimics a rising set of purely relational interpretations of quantum mechanics; a set interpretations according to which entangled state vectors express pure relations with no self-sufficient relata . Such an isomorphism paves the way for a new type of epistemological circle, wherein both the theory and the cognitive meta-theory are extensively relational.
In this situation, the task of the philosopher is no longer to explain the purely relational character of the phenomena of micro-physics by invoking some (mutually "disturbing") interaction between an object and an apparatus endowed with properties. It is rather, conversely, to explain why and how the familiar formal concept of monadic property could work so efficiently and for so long in the macroscopic domain despite the fact we ultimately live in a universe of pure relations.
This latter kind of explanation can take advantage of the concept of supervenience borrowed by P. Teller from D. Davidson , for his relational interpretation of quantum mechanics. In short, the explanation runs thus: classical physics was so successful in its program of de-convolution of the non-supervenient relations which are constitutive of phenomena, that nothing prevented it from working as if they were supervenient relations between monadic properties. Of course, this explanation has to be developed in order to become convincing.
What is then supervenience and how does this concept apply to relations? According to Davidson a class of entities B supervenes on a class of entities A if: (i) every single modification of an entity B is underpinned by a modification of an entity A (to paraphrase Davidson, there cannot be two events alike in all their A aspects but differing in some B aspect); (ii) there are alterations of entities A which leave entities B unchanged. In classical mechanics, one thus considers that: (i) every single modification of the relation between two material bodies is underpinned by some change in their (spatial, kinematic, and/or dynamic) properties, and (ii) there are modifications of the properties of these bodies which leave their relation unchanged (provided these modifications are coordinated in such a way that they respect certain similarities usually expressed by dimensionless numbers). To summarize, saying that relations supervene on monadic properties of objects amounts to ascribing them a secondary and derived status with respect to properties. It also means that the information contents of each relation is poorer than that of the related properties (for several couples of properties may yield the same relation). The problem is that this classical way of pushing relations aside and giving properties the central role does not help to figure out the reason why properties appear to be richer in information than relations.
Indeed, the most plausible reason for this richness is that properties express a large number of possible relations beyond the actual relation in which an object is involved. Saying that something possesses a property is a shorthand description of a wide range of relations in which this thing may possibly be involved. Ascribing a property to something means recognizing this thing a disposition to produce effects whenever it is involved in many possible relations to other things . This idea was familiar to the first Wittgenstein, who had thoroughly assimilated Boltzmann's and Hertz' conceptions of classical mechanics. According to him, "() there is no object that we can imagine excluded from the possibility of combining with others" . Thus, in his eyes , the autonomy of things and properties is a sort of illusion due to the boundless number of possible relations (or combinations, or connexions) which define them : "Things are independent in so far as they can occur in all possible situations, but this form of independence is a form of connexion with states of affairs, a form of dependence" . In other terms, the mutual independence of things and properties is the name we give to the indefinite openness of the network of interdependence in which they may be involved.
Wittgenstein's reflections reveal that the stratum of properties (layer n°1) on which the relations of classical theories and meta-theories are supervenient (layer n°2), presupposes an underlying stratum (layer n°0) of non-supervenient relations (i.e. primitive relations with no properties holding the role of relata). The reason why this ground-level layer of non-supervenient relations was almost ignored (or bracketed) by classical science becomes clear at this point. This reason is that it was especially easy to extract from it a number of effects invariant under large ranges of (cognitive) connections. Whenever a basically relational phenomenon remains invariant irrespective of its position within a set of successive or simultaneous experimental relations, it can perfectly be detached from the cognitive conditions under which it appears. It becomes natural to consider it as a mere reflection of a property. This opportunity of detaching the phenomenon from its cognitive contexts of appearance persists even when it is sensitive to variations of the experimental set-up, provided its changes can be ascribed to disturbing properties. Only in one case would the basically relational character of the phenomenon become inescapable : if the phenomenon were highly dependent on its position within a set of successive or simultaneous experimental relations, and if moreover the attempts at explaining this dependence in terms of disturbances were inacceptable or exceedingly contrived. This situation would so to speak impose a radical reflective examination of the constitutive relations of knowledge. But this is precisely the situation of quantum physics.
To conclude, a purely relational kind of epistemological circle is at the same time self-consistent, in natural agreement with the quantum paradigm, and able to account in its own terms for the absolutist kind of epistemological circle conveyed by the classical dualist theory of knowledge. This opens a potentially very fruitful research program, of which we are presently witnessing the first outlines .