**Non-Representationalist
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

*Abstract:*

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.

Introduction

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 .