Michel Bitbol

The roles ascribed to consciousness in quantum physics : a revelator of dualist (or quasi-dualist) prejudice 1

Introduction

Let's ponder two simple questions : "how can consciousness interact with physical systems, thus imposing a reduction of their quantum state ?" ; or, conversely, "how can consciousness be produced by a process involving physical systems described by quantum theory ?".

The purpose of this paper is not to offer an answer to these questions that were raised by some of the best physicists of the twentieth century, from Eugen Wigner to Roger Penrose, but rather to ask more questions. Why did so many serious thinkers considered that they were legitimate questions at all ? What are the implicit ontological and epistemological presuppositions that underpin this sense of legitimacy ? Can we move upstream such presuppositions and adopt a standpoint from which these questions would no longer be taken at face value, but rather as symptoms of a conceptual and cultural bias ?

Sense, non-sense, and philosophy

This strategy that consists of asking questions about questions, instead of addressing them straightaway, can be perceived as a dodge. But it is in line with one of the most specific tasks of philosophy. Indeed, "what truth and falsity is to science, sense and non-sense is to philosophy" [START_REF] Bennett | Philosophical Foundations of Neuroscience[END_REF]. Even before trying to solve a problem by scientific methods, one should try to inquire philosophically into whether this problem makes sense at all, or at least under which intellectual (or existential) conditions one is prone to believe that it makes sense. If pushed far enough, and with sufficient boldness, this inquiry may lead up to overturning the system of presuppositions that made the problem acceptable in the first place. In the present case, as we will soon realize, such overturn is tantamount to adopting the standpoint of phenomenology, a philosophical discipline that deliberately favors a first-person approach of any issue dealing with what there is and what can be known.

Tacit presuppositions

So, what presuppositions are hidden under the former questions about the relation between consciousness and quantum mechanics ? In fact, these questions encapsulate virtually all of the presuppositions that guided the research effort of the West from the seventeenth century until now. They do so with such compactness that they turn out to be precious revelators of our common cultural background, provided we do not fall immediately under their spell.

To start with, our two initial questions involve a pair of terms: consciousness and physical systems (or processes). These terms having the grammatical status of substantives, they irresistibly call for the vague intuition that there are two "substances" that relate to each other, or interact with each other. Isn't it natural "to try to find a substance for a substantive", as Wittgenstein suggested in the very first page of his Blue Book [START_REF] Wittgenstein | The Blue and Brown Books[END_REF] ? One may refrain from falling immediately in this elementary trap, but the structure of the question makes the mental attractor of dualism almost irresistible in the long run. Even the archetypal opponent of dualism in the contemporary debate, namely physicalist monism, is not immune from this. Indeed, physicalist monists deny that consciousness exists independently of the neural processes. By saying so, physicalist monists implicitly accept that consciousness is something that may exist or not exist in the same sense as physical objects, and they thereby render themselves guilty of virtual dualism.

To sum up, the two major protagonists of the present debate in the philosophy of consciousness, namely (property or substance) dualists, and physicalist monists, share two presuppositions.

The first presupposition is that consciousness is either something or a property of something. Dualists consider that such something has an independent form of existence, and that it can act somehow on physical systems and processes; whereas physicalists try to understand how the property "consciousness" can emerge somehow from physical systems and processes.

The second presupposition (that is the reciprocal of the first one) is that there exist physical systems and processes apart from consciousness.

Phenomenology beyond presuppositions

But are these two presuppositions unavoidable ? The phenomenological tradition has disposed of them long ago.

According to phenomenology, consciousness is no thing or property that may exist or not exist. "Consciousness" is the misleading name we give to the precondition for any ascription of existence or inexistence. What makes this remark obvious for phenomenologists and almost incomprehensible for physicalists, is that phenomenologists are settled in the first-person standpoint, whereas physicalist researchers explore everything from a thirdperson standpoint. From a first-person standpoint, anything that exists (thing or property) is given as a phenomenal content of consciousness. Therefore, consciousness de facto comes before any ascription of existence.

Instead, from a third-person standpoint, nothing else than objects of perception and handling is to be taken seriously. Now, the behavioral or neurobiological correlates of consciousness are possible objects of perception and handling. They can be said to exist (if a subject is alive and awake) or not to exist (in other cases). Then, from this standpoint, saying that the neural correlate of consciousness (often taken as its "neural basis") may exist or not exist, amounts to saying that consciousness itself may exist or not exist in the same sense.

Let's now turn our philosophical attention on the second presupposition, that is the keystone of physicalist monism, but that is shared by dualism. What is the status of the tacit assumption that there exist physical systems and processes apart from consciousness? From the third-person standpoint, this is just a fact, that is so glaring that it hardly needs arguments apart from an evocation of common sense. But from the first-person standpoint of phenomenology, this is a bold metaphysical assumption that stems from the "natural attitude" of common sense and extrapolates far beyond it. We have already mentioned that, according to the phenomenological approach, it is prima facie obvious that physical objects are given as nothing else than correlates of conscious experience. They arise as poles of stability and identity within a flowing consciousness ; they are meanings constituted through consciousness, or intentional correlates of acts of consciousness [START_REF] Kockelmans | Ideas for a Hermeneutic Phenomenology of the Physical Sciences[END_REF].

Physical objects can still be said to "transcend" consciousness according to phenomenology, but in a sense that is itself rooted in certain features of consciousness. This is what Husserl called "the immanent transcendence" of the objects of our experience in §48 of his Cartesian Meditations.

The first feature that evokes transcendence is the fact that physical objects are presented incompletely to consciousness at each moment : one just perceives one facet of an object at a time and expects other facets, or one just measures one variable pertaining to a physical system and predicts (deterministically or probabilistically) the values of other variables. This gives rise to the impression that there is still more to come, that a physical system has always something additional in store beyond what appears of it at this very moment. But one must not forget that this feeling of incompleteness is itself generated by an even more primitive act of consciousness : the act of identifying past, present, and expected appearances as moments of one and the same object [START_REF] Husserl | Experience and Judgment[END_REF]. Once this act of identification has been performed, our everdeveloping expectations are understood as a sign of the incompleteness of our knowledge about this enduring object.

The second "transcendent-like" feature is that expectations may be disappointed ; that a surprise may occur. This is usually expressed by saying that physical systems are given to us, since we do not "control" how they manifest to us. But translating this "givenness" into standard ontological terms, asserting that physical systems are "external" entities of a "reality out there" which is completely foreign to their appearances in conscious experience, is a dubious inference. From a phenomenological standpoint, this ontologization of the "givenness" and transcendent-like behavior of certain patterns of experience is just a verbal trick used to favor the intersubjective stabilization of the poles of identity and intentional directedness that structure the field of consciousness.

A phenomenological critique of the concept of "physical system"

Let's notice at this point that the lack of ontological import of the concept of physical system in phenomenology makes the redefinition of the putative objects of physical theories much easier. It invites us to see the existence of physical objects as an open problem rather than an uncontrovertible fact. And it then prepares us for the most radical scientific revolution of all : a revolution in which not even the former ontological furniture of the world can subsist. To understand this, we must come back to the (mostly tacit) criteria we use in order to convince ourselves that a certain phenomenon is underpinned by a permanent entity of which it is the appearance. These criteria were described in exquisite details by Husserl [4] from a phenomenological standpoint, and also by Piaget [START_REF] Piaget | Introduction à l'épistémologie génétique, 2-La pensée physique[END_REF] from the standpoint of developmental psychology. Piaget summarized his criteria thus : "(A child) does not believe in the permanence of an individual object as long as she cannot find it again and again by coordinated actions". The key criterion for believing in an entity is active reidentification. But in microphysics, reidentifying a localized object with certainty is usually impossible (as can be inferred from considerations about Heisenberg's "uncertainty" relations, or about quantum statistics). It then turns out that the class of objects "localized particles", and more generally "spatio-temporal continuants", is highly problematic in microphysics [START_REF] French | Identity in Physics : a Historical, Philosophical and Formal analysis[END_REF].

Yet, physicists still speak in terms of independent "physical systems" having "states", on which various (mostly incompatible) measurements are performed. Can the general concept of "physical system" truly survive its most common variety ; can it survive the disappearance of the (more or less) localized individual particles ? Probably not. Some good reasons to think that not even the general concept of "physical system" can be left untouched by the quantum revolution, were given recently [START_REF] Grinbaum | How device-independent approaches change the meaning of physical theory[END_REF]. These reasons pertain to the structure of sets of experimental phenomena : certain sets of measurement outputs are not such that they can be ascribed to single physical systems. The provocative conclusion is that "physical theory may contain no physical systems" [START_REF] Grinbaum | How device-independent approaches change the meaning of physical theory[END_REF]. It thus turns out that a physical theory such as quantum mechanics might well be averse to the second common presupposition of dualists and physicalist monists. Physics no longer supports physicalism (at least not without contrived attempts to save it).

Quantum physics without physical systems

But then, what status can we ascribe to quantum mechanics, if we cannot even say that it provides us with a non-standard description of physical systems ? Some suggestions to that effect were made long ago by Bohr, when he wrote that "physics is to be regarded … as the development of methods of ordering and surveying human experience" [START_REF] Bohr | The unity of human knowledge[END_REF], and that quantum mechanics is "… a purely symbolic scheme permitting only predictions … as to results obtainable under conditions specified by means of classical concepts" [START_REF] Bohr | Essays 1933-1957 on Atomic Physics and Human Knowledge[END_REF]. The two key words here are "human experience" and "predictions": a physical theory like quantum mechanics provides us with probabilistic predictions bearing on a fraction of human experience that measurement devices help to shape into elements of experimental information. Similar ideas were further developed in neo-Bohrian circles. Some authors explicitly suggested that quantum mechanics bears on nothing else than pure information [START_REF] Brukner | Information Invariance and Quantum Probabilities[END_REF]. Other authors considered that quantum mechanics is just a probabilistic "user's guide" for agents confronted with the outcomes of their own experimental and technological activities [START_REF] Fuchs | An introduction to QBism with an application to the locality of quantum mechanics[END_REF].

In other terms, according to the latter authors, experience comes first, and a physical theory is a coherent bundle of expectations about its later developments. This puts physics in line with elementary animal and human cognition, thereby weakening the common belief that physical theories have something exceptional, that they represent a historical leap due to their innovative use of a combination of rationality and technology. Indeed, according to phenomenology, the essence of human condition is to live in the perspective of one's own possibilities of being/becoming, and never to remain trapped into flat factual actualities. The essence of human condition thus implies a permanent anticipation of what will come next, a projection of oneself onto an expected future [START_REF] Kockelmans | Ideas for a Hermeneutic Phenomenology of the Physical Sciences[END_REF]. Similarly, according to some significant naturalistic views, the function of cognition is to anticipate by certain bodily capacities and behaviors those features of the environment that are relevant for the survival of cognizing organisms. In particular, the function of the nervous system is to minimize the disruption of expectations, i.e. to attenuate the "surprises" of an organism confronted with accidental variations of its environment [START_REF] Friston | The free-energy principle : a unified brain theory ?[END_REF][START_REF] Bitbol | Neurophenomenology of surprise[END_REF]. This being granted, the previously mentioned neo-Bohrian approaches turn out to be an epistemological golden standard for quantum mechanics. Indeed, according to them, quantum mechanics no longer appears as a maverick theory, but, on the contrary, as one of the purest expressions of a central principle of knowledge, and one of the most straightforward formal extensions of a basic function of elementary cognition.

What must be assumed for the measurement problem to make sense ?

Now, how does this relate to the measurement problem, which was the main motivation for the disconcerting introduction of consciousness into physics ? As a preliminary to answering this question, we must make an inventory of the conditions under which the outcome of Von Neumann's quantum theory of measurement is seen as an enigma or a paradox. Let's remind that, according to Von Neumann's theory of measurement, the global "state vector" of the large system made of an object and a measurement apparatus becomes an entangled superposition after the measuring interaction has taken place. The enigma or paradox then derives from the apparent contradiction between this superposed "state" and the sharp observational state of the measurement chain.

However, for this apparent contradiction to arise, three assumptions must be made, tacitly or overtly [START_REF] Bitbol | Physique et philosophie de l'esprit[END_REF] : 1. Quantum mechanics describes the state of physical systems 2. The state of every physical system is ruled by quantum mechanics 3. There is nothing but physical systems

The first assumption is tantamount to adopting a scientific realist reading of quantum mechanics ; the second assumption asserts the universality of quantum mechanics in the domain of physics ; and the third assumption asserts the universality of physics in the domain of what there is (this is "physicalism").

Solving or dissolving the measurement problem ?

Three main strategies to solve or dissolve the measurement problem can be elaborated by renouncing each one of the three assumptions in turn. These strategies almost exhaust the propositions that have been made during the history of quantum physics. 1'. If one renounces the realist interpretation according to which certain vectors in Hilbert spaces describe the "(quantum) state" of something, the measurement problem is automatically dissolved. Indeed, there is no immediate contradiction between a sharp observational state and a (superposed) symbol that does not represent the state of anything. There can be no conflict of this kind if the latter symbol is just taken at face value, namely as a mathematical tool used to calculate the probabilites of sets of measurement outcomes arising in various experimental contexts. This is the reason why Bohr was unable to see a problem in the socalled "measurement problem". And this is also how several contemporary physicists dissolve the measurement problem : by considering "state" vectors as relational rather than monadic symbols, or as a mathematical expressions of the best strategy for gambling about interrelated sets of measurement outcomes. Thus, according to Carlo Rovelli [START_REF] Rovelli | Relational quantum mechanics[END_REF], it makes no sense to ask what the state of a system is in absolute terms, since each quantum state reflects the relationship between a physical system and another system playing the role of an observer. There is no state of a system, but only relative states. Relative to someone who has made no observation yet, the state of the large system made of an object and a measurement apparatus is a superposition ; and relative to someone who has observed the screen of the apparatus, the state is sharp. But there is no fact of the matter as to which of these two "states" (superposed or sharp) is the intrinsic state of the large system. The same dissolution occurs when vectors in Hilbert space are supposed to have nothing to do with states, not even relational states, and are rather taken as "user's guides" for making coherent bets [START_REF] Fuchs | An introduction to QBism with an application to the locality of quantum mechanics[END_REF]. 2'. The measurement problem can be solved if one considers that standard quantum mechanics somehow lacks universality in the physical domain. Indeed, in this case, some physical systems may escape the general process of entanglement and dissemination of state superpositions, that is typical of the quantum theory of (measuring) interactions. And they can accordingly impose the sharp definition of their own properties to quantum physical systems. In history, Bohr's insistance that measuring apparatuses should (to a certain extent) be described by classical concepts, was the first variety of this claim of non-universality of quantum mechanics. Later on, the same kind of claim has been systematized as a clause of distinction between theoretical and meta-theoretical entities [START_REF] Mittelstaedt | The Interpretation of Quantum Mechanics and the Measurement Process[END_REF]. But the claim of non-universality has also taken more conservative forms, in approaches that extend the domain of physical entities, properties, or processes beyond standard quantum mechanics. This is the case of Bohm's hidden variable theory, and Ghirardi-Rimini-Weber spontaneous collapse theory. 3'. Another strategy to solve the measurement problem is to accept that there exists something non-physical that automatically eludes the laws of quantum physics, and might therefore be able to break the unended chain of entanglement and superposition of "states". It is at this point that consciousness may irrupt, and we will then concentrate on the meaning and scope of this third line of thought.

An interlude : decoherence

Before we proceed on the theme of consciousness as a nonphysical "deus ex machina" for solving the measurement problem, however, a brief mention of decoherence must be made. For decoherence seems to fall outside the previous classification of strategies used to address the measurement problem. But is it so ?

The decoherence solution to the problem raised by the gap between the quantum domain of superpositions and the classical domain of sharp properties is called "environment-induced superselection" [START_REF] Zurek | Decoherence, einselection, and the quantum origins of the classical[END_REF]. The principle of this solution consists in showing that the phase coherences of the state vector (or density operator) of an apparatus correlated to a micro-system are rapidly diluted in its environment. Indeed, the virtually complete disappearance of the interference terms is equivalent to a superselection rule which only retains the eigenstates of a given observable.

This looks like a completely new kind of solution. But there are aspects of decoherence that resonate with each one of the three former strategies. We could even say that the reason why decoherence does not fit squarely with any one of these strategies is that it borrows something from all of them. Let's examine this threefold resonance in a different order with respect to the listed strategies.

Firstly, to derive a decoherence process from the evolution of a global state vector, one must split the latter into three sub-states ascribed respectively to a micro-system, an apparatus, and an environment. But this neat separation into sub-systems does not arise a priori from quantum mechanics ; it may become approximately acceptable only a posteriori, at the end of the decoherence process. Trying to derive decoherence from quantum mechanics by postulating such separation from the outset thus looks like a petitio principii. But it's no longer a petitio principii if the postulate of separation is ascribed a meta-theoretical, rather than theoretical, status. Decoherence thus borrows something from the second strategy : it implicitly denies the exhaustivity of quantum theory by making use of meta-theoretical assumptions in the physical domain.

Secondly, unlike the standard "reduction of the state", the decoherence process does not yield a single eigenstate of some observable (corresponding to a single measurement outcome) but an (improper) statistical mixture of eigenstates [START_REF] Espagnat | Conceptual Foundations of Quantum Mechanics[END_REF]. Selecting a particular eigenstate is arguably an additional extra-physical act, since its only justification is one's awareness of the actual measurement outcome. Therefore, the decoherence approach is not completely immune from the third strategy that consists in denying the exhaustivity of physics.

Thirdly, if one wants to avoid the latter consequence, an option is to suspend any reference to the actual measurement outcome. But this can be done only by considering that the status of quantum symbols is exclusively probabilistic; that they always bear on possibilities and never on actuality. In this case, the decoherence process must be interpreted as nothing more than a transformation of the predictive probabilistic structure, from a quantum interferential structure to a classical Kolmogorovian structure. This is tantamount to renouncing a realist reading of the state vector as the description of something, and accordingly a realist reading of decoherence qua "emergence of a classical world from the quantum world". Something of the first strategy is here creeping in : dissolving the measurement problem by a non-realist interpretation of quantum symbols. Indeed, decoherence deals with a purely probabilistic aspect of the measurement problem, and discards the rest of the problem which is the issue of how a unique measurement outcome is actualized. It concerns the predictive structure of quantum mechanics, and has no relevance for its alleged descriptive status.

Consciousness as an extraphysical gimmick, and the phenomenological deflation

Let's now come back to the third strategy for addressing the issue of actualization : suspending physicalism. To begin with, what about the (loose) words we have used until now to state what physicalism is, and what it would be like to suspend it ? Physicalism has been roughly characterized as the claim that physics is universally valid in the domain of what there is. Suspending physicalism then means assuming that there is something that is not physical. Hence the dualist idea that, in addition to physical entities, there might be some vague nonphysical stuff called "mind" or "consciousness" ;

and the correlative claim that the irruption of this non-physical stuff might explain the disruption of the law of evolution of quantum physics by way of "state reduction". The trouble is that, in addition to its well-known metaphysical weakness, such dualistic option is a nonstarter from a phenomenological standpoint.

To understand this, remember that phenomenology goes upstream from established ontologies to identify the elementary criterion that allows us in practice to believe that something belongs to the domain of what there is. This phenomenological criterion of being is that the pattern of expectations which shapes our concept of something is fulfilled by a perceptual content of experience. In phenomenology, to be is to appear, or at least to have the possibility of appearing. According, e.g., to Heidegger [START_REF] Heidegger | Introduction à la métaphysique[END_REF], "being means appearing". From this criterion it may easily be inferred regressively that experience, the most specific component of consciousness, is not something ; experience does not belong to the domain of what there is. This sounds paradoxical, but becomes almost obvious after a little reflection. Experience is not presented in experience, for it coincides with presentation itself. Experience fulfills no expectation, for both fulfillments and expectations are experienced. Therefore, experience is not something, and does not belong to the domain of what there is. Does it follow that experience is nothing at all ? By no means, since experience is the universal precondition for anything to be considered as existent ! We could summarize what has just been said by diverting a remark of Wittgenstein [START_REF] Neumann | Mathematical Foundations of Quantum Mechanics[END_REF] : "(experience) is not a something, but not a nothing either !". However, this remark is weaker than the conclusion of phenomenology, which could be expressed thus : "(experience) is not a something, but it's more than anything else, since it is in it and by it that the existence of anything is ascertained".

Transcendental ego and introspection

This exterritorial status of conscious experience, which phenomenology insistantly brings out, played an important role in the reflection of some quantum physicists of the past. It is often said that a whole lineage of physicists, von Neumann, London & Bauer, Wigner, Stapp, etc. advocated the idea that the state vector reduction is triggered by consciousness. But in this list, only the two last authors were unambiguously dualists, dealing with consciousness as if it were something non-physical. Von Neumann and London & Bauer were much more nuanced, sometimes coming remarkably close to a phenomenological vocabulary and approach. Even Everett, as we will see later on, can be understood as a crypto-phenomenologist.

Let's start with von Neumann [START_REF] Neumann | Mathematical Foundations of Quantum Mechanics[END_REF]. His key sentence is : "But in any case, no matter how far we calculate -to the mercury vessel, to the scale of the thermometer, to the retina, or into the brain, at some time we must say: and this is perceived by the observer". According to von Neumann, the measurement problem would not be solved by just invoking some physical event that occurs in the brain of the observer at the end of a measuring interaction. For such event would remain "inside the (quantum) calculation" and would therefore do nothing to break the chain of entanglement and superposition. But von Neumann does not make use of some nonphysical entity either. What he mentions is only a change in the level of description, between the superposition and the sharp eigenstate. From a neutral mode of description, one switches to a situated mode of description. To a view from nowhere, one substitutes a view from somewhere (or rather for someone). A quantum entangled superposition (involving the system and anything correlated with it) holds for anyone who would like to anticipate probabilistically a measurement outcome, whereas a sharp state holds for someone who has observed this outcome and wants to take it into account for anticipating the outcomes of future measurements. No miracle occurs here, but only a change in one's self-ascribed epistemological status : from anonymous predictor to specific observer, from a neutral stance to a situated view. Both state vectors (superposed and sharp) can be used alternatively by one and the same person, according to her needs: either providing a weighted list of possible experiences available to anyone, or indicating the actual experience of someone who happens to be oneself.

This non-substantialist construal of observers and their consciousness is confirmed by von Neumann's use of the quasi-Husserlian expression "abstract ego" (Husserl would have written "transcendental ego"). According to von Neumann, the divide between the observer and the observed system can be moved back further and further until nothing (not even a brain) is left on the observer's side. It can be moved until the observer is represented only by her "abstract ego", whereas all the rest is treated as a global (quantum) system. This procedure clearly precludes any reification of the observer's residue. What is left on the observer's side is no thing, even though it is not nothing. In other terms, the expressions "Abstract ego" or "transcendental ego" do not refer to some nonphysical entity. They play the role of the indexical "I", that does not refer to anything or anyone [START_REF] Anscombe | The first person[END_REF], but indicates the source of every act of reference.

A similar conclusion can be drawn from London and Bauer's famous analysis of the measurement problem [START_REF] London | La théorie de l'observation en mécanique quantique[END_REF]. London and Bauer give priority to the act of becoming aware, not to some reified concept of consciousness. According to them, the transition from a superposition to a reduced state vector expresses a change of perspective. The entangled superposition holds from an external standpoint, whereas the reduced state holds from the internal standpoint of an observer who partakes of the measurement chain. The said observer does not need to make a measurement (which would be a sort of self-measurement) in order to know her own state. It suffices for her to resort to the privileged relationship she maintains with herself through her "faculty of introspection". By realizing immediately and non-observationally (through this faculty of introspection) that she is in a definite state, she can "(...) constitute by virtue of her (self-)observation a new objectivity by attributing a new state to the object: (an eigenstate of the observable)". To sum up, it is not necessary for an observer to approach herself indirectly from outside (qua brain or reified consciousness) to get knowledge of herself. Some kind of direct self-knowledge is available, and this radical change of approach and angle of view is sufficient to break the quantum superpositions that hold in the standard approach, namely from the usual (external) angle of view. This alternative approach is what London & Bauer try to convey with their use of the term "introspection". But this term is ambiguous insofar as it connotates the "inspection" of some inner realm, thus assuming a kind of dualism of the subject and object of inner knowledge. It would be better to use the expression "knowledge by acquaintance" as opposed to "knowledge by description". One knows the superposed entangled state vector of a measurement chain by description, but one finally knows the observed outcome of a measurement by selfacquaintance. Here again, both modalities of knowledge hold for the same concrete situated person, but with two different stances : the stance of an anonymous predictor, and the stance of an individual observer becoming aware of the outcome of a particular measurement.

The phenomenological flavor of Everett's interpretation

Surprisingly, the same ideas were suggested (though cryptically) by a physicist who declared that his interpretation of quantum mechanics is "realist", and who insisted that neither consciousness nor the "abstract ego" have any role to play in it. This physicist is Hugh Everett. Yet, his crucial move consists not so much in adding one more element to the measurement chain (an observer or, may be, a recording robot), but rather in appending a new symbol to it. The new symbol is a "memory bracket", that contains a list of measurement outcomes observed and recorded in the past. There are as many memory brackets as there are terms in the entangled superposition of the global state vector of the measurement chain. So, each memory bracket is supposed to hold relative to the corresponding term. In the many-world metainterpretation of Everett's interpretation, this relativity is made even more concrete by a daring reification. There, each memory bracket holds within the world that corresponds to this term.

However, the mere addition of a symbol to each term of the superposition is not sufficient by itself to solve the measurement problem, since no collapse is triggered by it. What really does the trick in this (or these) interpretation(s) is the situated meaning ascribed to the symbol "memory bracket". The measurement problem is arguably solved when one endorses one of the two following statements : a)

"In this universe (where I live), a sharp outcome appears to be obtained, even though in the multiverse there is a superposition" b)

"From my observer's point of view, it appears that a sharp outcome has been obtained, even though from the standpoint of distantiated predictors, the initial superposed state still holds". So, the solution of the measurement problem here arises from full awareness that one occupies an idiosyncratic situation, and that this situation self-manifests in one's conscious realization of some particular measurement outcome. Here again (as in von Neumann and London & Bauer) consciousness does nothing to the physical world. Instead, the physical world is reinterpreted as what is either predicted or observed from the standpoint of a conscious agent. And this dual reinterpretation of the physical domain, as (i) that about which predictions are made after having been triggered according to the prescriptions of conscious agents and (ii) what is observed by conscious agents, is entirely encoded in a superposed state vector with memory brackets.

Turning an alleged "realist" interpretation of quantum mechanics such as Everett's into a phenomenological interpretation may sound surprising to some. But even John Bell [START_REF] Bell | Speakable and Unspeakable in Quantum Mechanics[END_REF] found a phenomenological reading of Everett compelling in view of the latter's "replacement of the past by memories" (with a strong critical undertone, however, since Bell accordingly accused Everett of "radical solipsism" : solipsism of present experience).

QBism and phenomenology

However, the most consistent phenomenological approach of quantum mechanics is presumably QBism [START_REF] Fuchs | An Introduction to QBism with an Application to the Locality of Quantum Mechanics[END_REF]. QBism is an acronym for "Quantum Bayesianism" or "Quantum Bettabilitarianism". In QBism, "state" vectors are probabilistic valuations, in a Bayesian sense. They are not statements about what is the case, but statements about what each agent can reasonably expect to be the case. Ultimately, they are just expressions of subjective guesses; they express subjective agent's willingness to place bets about each outcome. Hence the expression "Quantum Bettabilitarianism".

What makes QBism so close to phenomenology is that it adopts a deliberately first-person standpoint (be it first-person singular or first-person plural). The project of both phenomenology and QBism is to reconstruct the so-called objective knowledge, starting everything anew from the first-person standpoint of knowers and an agents. Just as any good phenomenologist, a QBist thinker suspends judgment about a presumably external domain of objects. Her act of suspension resembles what Husserl called the epochè. Indeed, in QBism, the symbols of quantum theories do not refer to objects nor do they denote predicates of objects. And, since the attention of QBists is no longer absorbed by claims about object, it is reflectively redirected towards the epistemic function and the practical use of the symbols of quantum mechanics. QBists then point out that the symbols of quantum mechanics are primarily used by agents to assign probabilistic weights to the outcomes of experiments, so that such agents can make consistent bets. Pictures of objects can still play a role in QBism, but only as ancillary mental scaffoldings helping researchers to determine the best possible use of probabilistic valuations. This further reflective move is similar to what Husserl called the phenomenological reduction.

QBism without measurement problem

The measurement problem is addressed in this spirit. About Wigner's friend so-called "paradox", QBists do not invoke consciousness (neither Wigner's nor his friend's) to reduce the state vector of the measurement chain. However, the reason why they don't need to invoke consciousness as a deus ex machina is not that they believe the state vector reduction describes some completely autonomous "physical process out there", thus making consciousness irrelevant for it, but rather the opposite. According to them, the quantum "state" has no direct bearing on physical processes ; it is a symbolic tool within "a calculus for gambling on each agent's own experience" [START_REF] Fuchs | QBism, the perimeter of quantum bayesianism[END_REF]. This entails that (i) the reduction of the "state" represents no "physical" process, and (ii) conscious experience is the universal presupposition of the quantum "gambling", rather than some additional ingredient. Then, in QBism, there is no "objective reduction of the physical state", triggered by the allegedly non-physical consciousness. Even less is there the possibility of generating consciousness by this nonexistent "objective reduction". In QBism, there is only a change in expectations (the dispositions to bet) that takes into account previous experiences of measurement outcomes.

We can go as far as saying that in QBism, quantum symbols bear exclusively on experiences. They bear on their being expected or their being felt, on their being conceived as possible or their being sensed as real, and nothing else. Therefore, the fact that Wigner (who is outside the laboratory) does not use the same state vector as his friend (who is inside the laboratory), is not due to some spooky action of the friend's consciousness on the physical furniture of the laboratory. It is due to a difference in the informational basis on which those two researchers endowed with conscious experience rely for elaborating their optimal bets about future experiences. "One statement refers to the friend's potential experiences, and one refers to Wigner's own" [START_REF] Fuchs | QBism, the perimeter of quantum bayesianism[END_REF]. Since nothing else than conscious experience is involved in the symbols of quantum physics, no action of conscious experience on something else must be called for to account for sudden changes in these symbols.

QBism beyond idealism and instrumentalism

Does this necessarily imply some sort of solipsism, or subjective idealism ? By no means. No particular subject is able to create the experienced outcome of a measurement. And no subjective preferences are involved in the probabilistic anticipation of an outcome. Each outcome comes as a partial surprise ; it is given. And each anticipation, each bet, is framed by rational rules of coherence that ensure (in virtue of the Dutch book theorem) its effectiveness in the long run.

Claiming that "nothing else than conscious experience is involved in physics" would be shocking only for those who believe that conscious experience restrictively concerns some inner realm distinct from the outer realm of physical objects and events. In other terms, it is shocking only under the latent presupposition of dualism. But within the framework of phenomenology, the same claim is almost trivial, and does not have the (absurd) consequence that only the inner realm exists whereas the outer realm is inexistent. For in phenomenology, what there is, namely appearance or experience, is neither inner nor outer, but present. From the first-person standpoint of phenomenology, it is obvious that the so-called "outer" objects are always tinged of experience : they are either manifest or imagined, or dreamt, or conceived. In experience, in its anticipatory thrust and in its surprises, one finds all the resources to develop physics, with no need to take the metaphysical concept of a "real world behind the veil of appearances" too seriously. For even this metaphysical concept can be seen as one more aspect of experience : it affords representations that guide and motivate felt expectations, and it offers a background against which one can evaluate the meaning of unexpected experiences. The only particularity of physics, compared to ordinary knowledge, then lies in a tight feedback loop connecting its expectations to the technological activity that allows one to test them, through these heuristic representations.

To avoid the pitfall of pure instrumentalism or idealism, Christopher Fuchs has adopted a metaphysical position that fits quite well with the low level of ontological commitment of QBism. This metaphysical position has been called "participatory realism", thus immediately displaying that it is a (non-conventional) variety of realism. The idea behind it, is that the insuperable dependence of the symbols and propositions of quantum theories on our situation and experience indirectly reveals the nature of reality. Here, reality is so deeply entangled and holistic that our knowledge of it can only be participatory rather than representational, predictive rather than descriptive. Reality is so entangled that it cannot be described directly by a physical theory, but only suggested indirectly by the failure of descriptions and the use of pure predictions instead.

But how can such alternative metaphysical picture of reality "from nowhere" fit with the primacy of experience, and firstperson standpoint (from somewhere), that were advocated in the epistemological presentation of QBism ?

"Participatory realism" and Merleau-Ponty's embodiment

Quite surprisingly, the two standpoints can easily be put in agreement. This was shown long ago by a lineage of phenomenologists stemming from Maurice Merleau-Ponty. These Merleau-Pontian phenomenologists start from first-person experience, in line with the principle of their discipline. However, when they have performed the epochè (or suspension of judgment), they dig into their experience to reach a particular level of it that is especially relevant for the issue of participancy. This level is the sense of embodiment, the experience of being-in-a-body. It provides one with full awareness of a most remarkable item called my "own-body", whose "flesh" is simultaneously perceived and perceiving. A celebrated example, developed by Husserl and Merleau-Ponty is that of my hands : my right hand can be touched and thereby perceived (say by my left hand), but it is also capable of touching, and thereby perceiving, anything else. The latter experience of a bifacial flesh is both commonplace and stunning. It is commonplace because each one of us was born with it. And it is stunning because, through it, we witness what it is like to be coextensive with a fraction of the world. Since we are coextensive to a fraction of the world, we can but oscillate between detachment (when we perceive our own body) and radical commitment (when we realize that our own body is perceiving everything, including itself).

According to Merleau-Ponty, far from being a marginal epiphenomenon in a massively non-sentient universe, the experience of embodiment is paradigmatic. It is the only fact that fully illustrates the nature of this universe of which we partake : a highly integrated and entangled universe endowed with a potential for self-realization and self-objectification that is fully accomplished in us and through us, human beings. Merleau-Ponty then does not shy to endow this experience of participancy with a bold cosmological significance. Drawing the consequences of his deep epochè, Merleau-Ponty suspends even the process of positing boundaries between bodies, and accordingly describes one's own flesh in continuity with the rest of what appears. This particular bodily flesh is then considered as a locus of intense self-revelation of what Merleau-Ponty calls the "flesh of the world": "Where should we locate the boundary between the body and the world, since the world is flesh?" [START_REF] Merleau-Ponty | Le visible et l'invisible[END_REF]. It turns out that embodiment is precisely where the cosmological concept of participancy meets the phenomenological concept of consciousness. Feeling embodied is the most immediate experience of universal participancy we can have.

Illusory separations in a non-separate world

But then, how did we come to believe in a separate world ? And what happened in quantum physics to remind us so strongly of our participation in the universe ?

We came to believe in a separate world through a process that is coextensive to our life. I called it "self-objectification", but it is even more primitive than the act of objectification that is performed by language and science. Heidegger considered that self-separation defines our existence, and he called it the "ekstasis" : the fact for us to be always out of ourselves, trying to project into the future or to reflect upon the past. Sartre insisted that, for us, "existing (from the latin ex-sistere, to stand out of oneself)" means that we never content ourselves with being what we are, but constitutively tend towards what we have to be and what we hope to reach [START_REF] Sartre | L'être et le néant[END_REF]. As for Michel Henry, he bluntly asserts that "Consciousness is none other than the form of existence that arises in the tearing of Being", or that "Consciousness is nothing but the self-alienation of Being" [START_REF] Henry | L'essence de la manifestation[END_REF]. In other terms, consciousness is consciousness-of-something, not because the universe is made of things and consciousnesses (nor things producing consciousnesses), but because consciousness arises qua self-splitting of what there is. Now, how did quantum physics weakened this far-reaching process of separation and revive the idea of participancy ? Imagine, Bohr writes [START_REF] Bohr | Atomic Theory and the Description of Nature[END_REF], that we attempt to "orient oneself in a dark room by feeling things with a stick. When the stick is held loosely, it appears to the sense of touch to be an object. When, however, it is held firmly, we loose the sensation that it is a foreign body, and the impression of touch becomes immediately localized at the point where the stick is touching the body under investigation ". According to the latter option, the blind cane becomes part of our own body when it is held firmly. The locus of our separation from the rest of the world is then pushed far from our skin, at the tip of the stick. Something similar happened with experimental devices in the era of classical science. An experimental apparatus could easily be taken as a sort of prosthesis that extends our bodies (either as an extended hand or an extended eye) and helps us reach new types of objects. Indeed, the phenomena taking place at the tip of such apparatus obeyed the rules Kant assigned for constituting a (close or remote) domain of objective knowledge.

But these rules are no longer in effect in the domain of microphysical phenomena. Deterministic causation is suspended in the spatio-temporal domain, and the concept of "substance" (or spatio-temporal continuant) is no longer applicable. Then, experimental devices can no longer be taken as prostheses that open up a new realm of objects before us ; they have not managed to achieve the neat splitting operation that is necessary for complete objectification. With no complete separation between our devices and the environment they are meant to explore, the concept of participancy imposes itself. It is true that one could still maintain a separation between our bodies and the device (by due analogy with the stick when it is held loosely), or between a proximal and a distal part of the device. However, this alternative separation now sounds arbitrary. Bohr soon noticed this arbitrariness when he insisted that part of measurement apparatuses must be described classically, to allow partial objectification and sufficient grip for our language : but which part, at which level ? Participancy then becomes the norm, and the subject-object cut appears as a problem, a relic of the past, or an expedient tool.

Conclusion

To finish with a very short epilogue, I will ask two dualist questions and propose two non-dualist answers. Do we need consciousness to reduce the state of physical systems? No, since "reduction" is the name we give to a revision of conscious expectations, and "physical system" is the synthetic name we use for a coherent set of consciously expected phenomena.

Can consciousness arise from a physical process such as the alleged "objective reduction"? No, since physical processes are nothing else than objects of consciousness, and consciousness is the flux of the self-splitting of what there is into perceiving and what is perceived, expecting and what is expected, subjective existence and its objective targets.

 [START_REF] Bennett | Philosophical Foundations of Neuroscience[END_REF]This work was supported by the Agence Nationale pour la Recherche (ANR-16-CE91-0005-01).


Jan Tinbergen

Johan G Koopmans On Multiple

Michaël Assous

Equilibria and Coordination Failures

Keywords: coordination, duopoly, Jan Tinbergen, multiple equilibria, J. G. Koopmans B21, B23, B31, C62

In a 1932 policy paper, the Dutch economist Jan Tinbergen suggested that there could be two stable equilibria in a model with two firms acting in two sectors, with one of the equilibria having more production and employment. Arguing on the basis of a diagram that firms could not get out of the "bad" equilibrium on their own, he suggested that this justified government interventions to increase employment. While he referred to the general equilibrium systems of Walras and Cassel, he did not present a fully worked out model but referred to the unpublished study of one J. G. Koopmans. The latter was spurred by Tinbergen's reference to publish his ideas on the problem of multiple equilibria. In his three-part paper, he underlined that a Walrasian system could not show Tinbergen's coordination problem, because there could be no unemployment at an equilibrium point in a Walrasian model. The examples he presented, with three equilibria, showed that they could not be ordered. After this exchange, Tinbergen moved away from Walrasian multiple equilibria, and abandoned the general equilibrium approach to economic modeling in favor of the macrodynamic approach that was developed at the same time by Ragnar Frisch and Michal Kalecki.

In 1932, at the request of the Board of the Association for Economics and Statistics, Tinbergen was invited to give a talk "to explain the position of socialism with respect to the question of the regulation of production by private individuals."2 Tinbergen, a member of the board of the Dutch magazine The Socialist Guide (De Socialistische Gids), had already had several occasions to express his view, which he saw as one possible approach rather than "the" view of socialists. Tinbergen argued that "free competition" of individuals leads to a waste of resources, because he thought that in the absence of a planning device, economic activity was prone to recurrent crises and loss of "productive forces and thus to a lower level of prosperity than would be possible" (Tinbergen, 1932: 50). The problem presented itself even more pointedly when crises were manifesting as "unstable economic processes," making the return to equilibrium difficult or impossible, raising for him the question of instability in economic theory: "are there among the economic-dynamical processes, which theory teaches us, such that show an ever-increasing removal of the equilibrium state?" (Tinbergen, 1932: 58).

Although he recognized that the scope of the existing theoretical literature was still limited, he argued that on the basis of various extensions of existing models such as the cobweb model, one may eventually identify "theoretical (as well as experimental) cases of economic processes that do not automatically return to the equilibrium position" (Tinbergen, 1932: 58).

But there was more than a problem of instability, cyclical or not, for Tinbergen: there was a possibility that crises would leave the economy stuck in a position of "bad" equilibrium. From a theoretical point of view, Tinbergen wondered whether a way to represent this idea could lie in the Walrasian theory whose alleged merit was to leave ample room for multiple equilibria to appear. Along that line, he explored the possibility that the severity of the depression of the 1930s may be the result of a coordination failure which would be responsible for the fact that the economy may reach a stable, but "bad" equilibrium (with mass unemployment) from which no individual agent could unilaterally escape. In that context, Tinbergen referred to Walras and Cassel as well as to the unpublished works of J. G. Koopmans, but did not offer a system of equations. He only presented a diagram on the basis of which he described the behavior of two representative firms in an economy with two equilibria, one of which had much more unemployment.

Spurred by Tinbergen's reference to his work, in a three-part paper published in De Economist in 1932, J. G. Koopmans recognized that Tinbergen's system was determinate and could lead to non-trivial equilibria, but argued that Tinbergen misrepresented the meaning of the multiple equilibria arising from a Walrasian system.

He emphasized that Tinbergen's approach was different from his own. His point was that a Walrasian system was neither able to define a state of unemployment (in the absence of price rigidities), nor to show that an equilibrium may be better than another.

Finally, Koopmans touched upon the issue of stability by showing that as in Tinbergen's analysis, one can show that some equilibria may be stable and others unstable. But without specifying a specific dynamic adjustment process, his analysis, as Tinbergen's, remained incomplete.

In the following years, Tinbergen focused on the development of macrodynamic models and moved away from Walrasian systems. It took him several more years to develop a model that he used between 1934 and 1937 to illustrate unstable macroeconomic processes and express the view that a disturbance such as the 1929 stock crash could push the economy over the hill, into an abrupt and bottomless precipice (see Assous andCarret 2020, 2022). On that basis, he continued to emphasize the importance of multiple equilibria and of economic policies and normative choice in the model, using it to justify public interventions to reach a better equilibrium.

In the end, by embracing the development of macrodynamics, Tinbergen managed to provide an answer to the objections raised by Koopmans. This debate sheds new light on the reasons for which Tinbergen decided to move away from Walrasian economics.

A first reason, repeatedly claimed in the early 1930s by Tinbergen and Frisch, was that if Walrasian systems were determinate, they suffered from the fact they were static [START_REF] Frisch | Propagation Problems and Impulse Problems in Dynamic Economics[END_REF][START_REF] Tinbergen | Annual Survey: Suggestions on Quantitative Business Cycle Theory[END_REF]. A second reason, underlined here, is that Walrasian theory was an inappropriate framework to address issues related to unemployment and instability, which ultimately led Tinbergen to rethink the role of state interventions through his macrodynamic models.

I. Coordination and economic policy in Tinbergen's pre-advice

To the question "is popular prosperity so great under the system of free competition?" Tinbergen answered with mixed feelings. He underlined the recurrence of "breakdowns in economic life," which he thought should be avoided to obtain a smoother distribution over time of the "joys and burdens of life" (Tinbergen, 1932: 50 ff.). According to him, fluctuations in economic life, the source of so many ailments, prevented a full use of resources and led to a waste of technical and natural resources. Limiting the uncertainty brought on by the cyclical character of economic life would have the added benefit of eliminating strategic calculations between firms, a mechanism he tried to encapsulate in a diagrammatic representation of the economy. His remarks on the underutilization of productive capacities were illustrated by statistics on the available capacity of industrial enterprises in the United States and in Germany, which showed that even at the top of the boom, the economy was not using its full capacities.

More importantly, Tinbergen noted that in June 1932, the end of the disruption that had begun in 1929 was nowhere in sight; 3 this led him to discuss the possibility that the economic process was unstable and to reflect on the economic policy needed:

The question has been posed whether we are not dealing here with a movement process that no longer returns automatically to an equilibrium state, or whether we are not dealing here with unstable states. (Tinbergen, 1932: 56) This led to an entire section on "stable and unstable economic processes". 4Tinbergen argued that although previous crises were usually followed by a return to equilibrium, there were examples of unstable processes that did not lead to an automatic recovery, such as the inflation that plagued European countries in the early 1920s. This begged the question: "are there among the economic-dynamical processes, which theory teaches us, such that show an ever-increasing removal of the equilibrium state?" (Tinbergen, 1932: 58). Although such mechanisms were not discussed in the theoretical literature, Tinbergen was confident that he could find dynamic models accounting, for instance, for exponential movements away from the equilibrium.

The discussion was introduced with the hog cycle, in which case he noted that fluctuations usually led back to the equilibrium, but that if the elasticity of production became too great it could lead to fluctuations of increasing amplitude. 5 He also referred to his own model of the "shipbuilding" cycle, published in 1931, where he had observed that its solutions could yield fluctuations of increasing amplitude, depending on the values of certain parameters like the sensitivity of the supply of ships to the price of freight, and that "increasingly violent fluctuations" could arise. Although he was concerned with the shipbuilding cycle in this article, Tinbergen already viewed in 1931 the relevance of such mechanisms for the whole economy:

The basic problem of any theory on endogenous trade cycles may be expressed in the following question: how can an economic system show fluctuations which are not the effect of exogenous, oscillating forces, that is to say fluctuations due to some "inner" cause? (Tinbergen, 1931: 152).

He concluded his examination of the shipbuilding model by underlining the importance of finding a good dynamic mechanism to approach the problem of stability at the aggregate level:

It seems to me that this result is of vital importance to the theory of economic dynamics. … Moreover, it gives us a clue to a method of judging the stability of an economic system in general. (Tinbergen, 1931: 162).

He also referred to his work on market level price dynamics that had been presented in 1931, during the first European meeting of the Econometric Society in Lausanne (published in the first issue of Econometrica in [START_REF] Tinbergen | L'utilisation des équations fonctionnelles et des nombres complexes dans les recherches économiques[END_REF]). There, he started again from a simple cobweb model of supply and demand, which he extended first by introducing "speculation," whereby demand depends on the rate of change of prices. This transformed his model into a mixed difference-differential equations, but Tinbergen did not stop there: he introduced a "hyperbolic demand", transforming his difference equation into a nonlinear equation, a relationship between demand and the activity of the industrial sector, a durable consumption good, and finally introduced a second market producing a capital good. Thus Tinbergen had already started to build up toward a more intricate model of the economy and its interdependencies. In all those cases, he was chiefly interested in the periodicity of the oscillations and always used hypotheses on the parameters that would make those oscillations self-sustained. 6 However, the shipbuilding cycle as well as the cobweb mechanism remained focused only on one market and not the whole economy. Tinbergen pointed out in 1932 that if those models helped to identify new economic processes, they remained of little help to provide an appropriate framework to make sense of the working of the whole economy 6 This was precisely the approach adopted by [START_REF] Kalecki | A Macrodynamic Theory of Business Cycles[END_REF] that was criticized by [START_REF] Frisch | The Characteristic Solutions of a Mixed Difference and Differential Equation Occurring in Economic Dynamics[END_REF]. Tinbergen had prepared the ground for Kalecki's model, both through this approach of endogenous fluctuations, and his 1931 shipbuilding model, which was used by Kalecki to solve his own model. Following [START_REF] Boumans | How Economists Model the World Into Numbers[END_REF] idea that Kalecki's model was like a recipe, this shows that the ingredient coming from Tinbergen was more than a mathematical mold. The type of solutions favored by Tinbergen had a direct impact on Kalecki. and the factors responsible for the ongoing crisis, in large part because they did not explain satisfactorily a mechanism of "removal from the equilibrium state" (Tinbergen, 1932: 58).

In 1932, he claimed that the solution to account for aggregate phenomena may also come from the "Walras-Cassel" model of the economy. 7 According to him, this approach left ample room for multiple equilibria and instability to appear, and he described a possible mechanism illustrated with a diagrammatic representation of the interactions between two representative firms.

In this model with two sectors and two firms, Tinbergen claimed that the economy could get stuck in a "bad" equilibrium with high unemployment. Plotting the "profit lines" of each firm as a function of their employment levels and , that is, all the 𝑎 1 𝑎 2 combinations of employment for which the profits of firms 1 and 2 are constant, Tinbergen provided the following diagram (Tinbergen, 1932: 62).

7 "Further investigation of the equilibrium equations (of, for example, Cassel or Walras) which determine the size of production, the level of prices, etc. in a stationary society, shows that there is not one equilibrium (in the sense of economic science), but that in general different equilibria are possible with the same technical and psychological data. It is quite possible, and even most likely, that with some form of utility functions and technical coefficients, two equilibria at least exist, both stable, one for instance with significant unemployment and the other without" (Tinbergen, 1932: 60). Rodenburg (2010: 10) mentions Tinbergen's argument in the context of his debate with the Dutch economist Goudriaan on dynamics and equilibrium but without contrasting it with the arguments raised by Koopmans. Tinbergen underlined that an increase of employment from only one firm will correspond to a displacement along a vertical or horizontal line. Because the curves meet at their minimum point, this means that a firm increasing its employment will always see its profits go down if the other firm does not increase employment as well.

Tinbergen argued that the configuration where both firms have their profit curves crossing at their minimum points will thus correspond to stable equilibria, because there will be no incentive to deviate alone from such a situation. 8 In Figure 1, there are two such equilibria: and . We can readily see that in the second of these equilibria, 𝑃 1 𝑃 2 there is more aggregate employment than in the first; this begs the question of how to move the economy from the "bad," low equilibrium, to the "better," high equilibrium (Tinbergen, 1932: 61).

If we denote by and the two other points where the profit lines intersect, we can 𝑅 𝑄 see that the profits of both firms will only increase together in the quadrilateral.

𝑃 1 𝑄 𝑃 2 𝑅
But in order for the economy to move in this direction, it is necessary that both firms increase employment at the same time, so that neither has the incentive to reduce employment to go back to a higher level of profits.9 The bottom line is that a new stable equilibrium can be obtained for a specific ratio between and , and that only an 𝑎 1 𝑎 2 organized action may help to reach it: "In other words, it has been shown that there are cases in which competition cannot get out of a certain (low) situation, while organized action will make it possible" (Tinbergen, 1932: 61).

Unfortunately, Tinbergen did not explicitly state the set of equations that he might have used to derive the two profit lines, making it difficult to identify the exact mechanisms at work in the move of the economy from one equilibrium to the other. He described some potential mechanisms explaining how such a situation could arise, mainly from the mismatch in the increase of demand and supply when firms act alone, while when they act together this mismatch is construed to have a positive effect on profits because of a potential reduction in costs.

As he pointed out, in the case of a firm acting alone from equilibrium , "the increase 𝑃 1 in demand which would arise as a result would by no means outweigh the increase in the supply of the commodity produced by that company" (Tinbergen, 1932: 61). But with no other information on the consumption of the workers of the two firms and on the way both firms decide to invest, the argument is a bit enigmatic. The possibility that demand may eventually adjust to supply and reach the "good" equilibrium would in fact be due to the evolution of cost: "Expansion of the number of workers [...] also lowers the unit cost of production" (Tinbergen, 1932: 62), which, for reasons also left unexplained, is assumed to have a positive effect on the demand for both goods.

Whatever the limits of Tinbergen's argument, it is clear that he was already thinking about stability issues. From that point of view, the response Koopmans published a few months later proves helpful to clarify some features of Tinbergen's thinking and show how far Tinbergen was departing from the Walrasian approach.

II. J. G. Koopmans's criticism of Tinbergen's multiple equilibria

As we have seen, Tinbergen associated the idea of multiple equilibria with a Walrasian system of equations. In a footnote, he admitted that he was puzzled to see that while the idea was mentioned in passing in the literature, it had "not been elaborated

anywhere" except in "some unpublished studies of Mr. J. G. Koopmans," suggesting that his analysis derived from it (Tinbergen, 1932: 60). A couple of months later, Koopmans published a series of three papers with the aim to clarify his position with respect to Tinbergen's analysis. While he acknowledged in the first paragraph of his paper "the much appreciated help" which "as a non-mathematician" he received from Tinbergen (Koopmans, 1932: 679), he felt the need to underline the differences between his and Tinbergen's analysis. In fact, Koopmans made clear how far Tinbergen's analysis departed from his own approach and this for two main reasons.

First and foremost, Koopmans emphasized that neither in Walras's nor in Cassel's works, one can show that there might be an equilibrium let alone a "stable equilibrium" as far as a "significant degree of unemployment is assumed" (Koopmans, 1932: 682). 10Accounting for unemployment means that one market equation expressing the equality between demand and supply will have to disappear, leaving the system undetermined with the result that many potential solutions become possible: "this means that the whole complex of economic phenomena, as expressed by the equilibrium equations, becomes undetermined, that is to say, there are not only two or a few, but even, at least in principle, infinitely many alternative solutions of the remaining system of equations" (Koopmans, 1932: 683). In particular, as soon as one assumes that wages are fixed and known, it becomes possible to define a set of equilibria, each parametrized by a specific level of money wage. It is therefore no surprise that with the same technical and psychological data, it is possible to define a single "equilibrium state" for any given level of money wage.

Koopmans pointed out that it was unlikely that Tinbergen had understood the issue in this way: "it should be appreciated that, according to the continuation of his argument, the author certainly could not have meant the above statement in such a simple and almost trivial sense. For in reality he also speaks of a system in which the number of equations indeed corresponds to that of unknown quantities" (Koopmans, 1932: 683).

The unknowns chosen by Tinbergen are simply not the same as those chosen by

Cassel and Walras. The problem however remains similar as long as one can show when a system comprising as many unknowns as equations has multiple solutions. In that case, "the problem can indeed be regarded as "determined" in a similar sense as in the thinking of Walras and Cassel [...] from the formal-theoretical point of view, [the possibility of multiple equilibria] is indeed just as remarkable and of the same fundamental significance and scope as the corresponding possibility in a system of equations built up entirely in accordance with the method of Walras and Cassel, and in which all prices, including wages, figure as unknowns" (Koopmans, 1932: 684).

In addition, Koopmans doubted that on the basis of his graphical illustration, Tinbergen had managed to prove the existence of multiple stable equilibria. If it was clear to him that the two "lines of constant profit" were derived under the assumption that wages are rigid, it remained unclear why both lines could "run according to the starting point adopted by the author in the manner indicated by him in his drawing: a possibility which I do not want to dispute, but of which the proof has not been fully provided here on the spot" (Koopmans, 1932: 684). Koopmans argued that the rigidity of wages acted on the stability of equilibria but in an obscure manner. While he agreed with Tinbergen's concern with the possibility of defining a stable equilibrium, he regretted that he did not clarify the mechanisms allowing to identify which equilibrium among all the equilibria defined by a given level of money wage was likely to be reached.

The second issue raised by Koopmans concerned the possibility of ranking equilibria.

His point was that the equilibria displayed by Walrasian systems could not be ordered.

From the policy point of view, this was an important difference between Tinbergen's and his approach of multiple equilibria, because he claimed that in the absence of nominal rigidities and unemployment there was no way to choose among the different equilibria:

such an appraisal judgment can no longer be justified with the same certainty when it comes to the comparison between two (or more) alternative equilibrium states … which, after all, is characterized precisely by the fact that in neither of them there is a surplus of unused production factors … The remarkable thing about a double or multiple economic equilibrium in this last sense … consists precisely in the fact that the various alternative equilibrium states are in every respect, thus also viewed from a normative point of view, completely "equivalent", or in others words, that none of these equilibria can be given a "preference" over one or more of the others on the basis of any objective criterion. (Koopmans, 1932: 685, original emphasis) Thus Koopmans underlined that the different equilibria did not imply that some factors of production were underemployed, and they did not justify a socialist planning policy in order to obtain a higher employment equilibrium. It was necessary to introduce another criterion from which to establish that an equilibrium was better or worse than the other.

Koopmans sought to illustrate this equivalence of different equilibria in a Walrasian system with a numerical example exhibiting three equilibria.

III. Koopmans' multiple equilibria in a Walrasian system

While Koopmans started with a criticism of Tinbergen, he also made it clear that he had a limited knowledge of mathematics and that he relied mainly on others for his mathematical exposition, in particular on Tinbergen himself. But he still felt that he had something important to say about the importance of multiple equilibria in even the simplest exchange economy, and he did not think that Tinbergen had captured his ideas on the subject in his model.

The end of the first part of his paper was dedicated to setting up his model. First, Koopmans pointed out that the issue at hand had nothing to do with "the existence of so-called "indifference zones" generated by the discontinuity of supply and demand curves. It also had nothing to do with firms operating, as a result of a relatively high percentage of "fixed" cost in the production process (Koopmans, 1932: 690), in the decreasing part of the U-shaped supply curve. He acknowledged that both these cases allowed for an exploration of the possibility to "represent a position of 'stable' and one of 'unstable' equilibrium" (Koopmans, 1932: 690).

Koopmans emphasized that his own approach was based on the idea that supply curves could have inverse U-shapes: they started as normal, upward sloping schedules, before bending towards the bottom right in a price-quantity diagram: "which means that, even apart from decreasing costs, etc., as the price per unit increases, the volume of the supply no longer continues to increase beyond a certain point, but on the contrary decreases further and further" (Koopmans, 1932: 690). These supply (and demand) functions arose from the utility functions used by Koopmans, and the problem he sets up is that of a simple exchange economy with two people and two goods.

There are three types of equations in his system: equilibrium equations relating the ratio of marginal utility of the two goods and their (relative) price, "budget" equations relating the aggregate value of goods given up in the exchange with the aggregate value of goods received, and balancing equations for the total stock of physical units of each goods. In the case with two agents and two goods, at the equilibrium points the relative utility of each good is equal to the same (relative) price, one budget constraint will be given from the other budget constraint and the physical constraints, so that there are five equations and five unknowns, determining an optimal economic equilibrium. Koopmans argued that a solution existed because there were as many unknowns as equations in his system. But he also added that this did not mean that there was necessarily a unique solution, and in fact "even with the minimum number of two persons exchanging only two goods, … as a rule not one single, but three different solutions of the equations concerned are possible" (Koopmans, 1932: 694). To prove this, he gave a numerical example and obtained the following equations (Table 2), whose solution exhibits three equilibria, with each equilibrium being established at a different price (Table 3 gives the equilibria solving this system).

Agent Alpha Beta

Marginal utility seems to be what Koopmans had in mind when he described in a footnote the application of Bowley's and Pareto's "graphical method," which "had to be scrapped due to lack of space" (Koopmans, 1932: 772-773). The following figure produces such a diagram, based on Koopmans' numerical example. the "zero point of the exchange" (Koopmans, 1932: 773). Economic equilibrium happens when both offer curves are compatible, that is, when both participants are ready to exchange compatible amounts of goods I and II, or in other terms, they have the same relative price for the two goods: the two indifference curves and the budget line are tangent at the same point, which lies on the contract curve.

Three economic equilibria are possible in this system, and they all lie on the contract curve, as is made formal by the first fundamental theorem of welfare economics. This theorem appears trivial in this case, as the economic equilibrium is defined by taking the four unknowns and three equations defining the Pareto curve, and adding one unknown (the price ) and two equations (the equality of price and relative marginal utility 𝑝

, and the budget equation ), so that the system 𝑝 = But the fact that the system is determinate does not mean that there is only one equilibrium, as was the point of Koopmans' numerical example; a nonlinear system whose reduced form is a polynomial of degree more than one will in general have more than one solution (Koopmans discussed the problem introduced by complex solutions in the third part of his paper). Koopmans himself gave a form of his system reduced to one equation with the price as an unknown, showing that it was a polynomial of degree three, with three equilibrium solutions. This was underlined by Koopmans to show that this example had nothing exceptional, or special, but could appear systematically; this led him to wonder why previous writers had not underlined this possibility. It is likely that Tinbergen influenced him in this direction, as Koopmans had underlined his debt towards him for the solution of his model; Tinbergen himself had adopted this approach of reducing his systems to one equation already in [START_REF] Tinbergen | Ein Schiffbauzyklus?[END_REF], and continued this approach in his later models, such as the 1939 League of Nations model.

Because the marginal utility conditions are fulfilled in each of the three equilibria, Koopmans argued that "there is indeed no reason here to consider one of the three possible equilibrium states with respect to the two others as the 'best' or the 'worst'" (Koopmans, 1932: 702). This was the brunt of his critique of Tinbergen, and he argued in a footnote that the utility of each person in each equilibrium was irrelevant because incomparable.

While Koopmans is convincing in showing the possibility of multiple equilibria for simple, nonpathological preferences, he stops short of analyzing the coordination problem underlying his setup, as a result of the methodology he adopted. The problem of his analysis is that it is fundamentally an equilibrium analysis, and Koopmans says nothing of the way in which the two agents got to one equilibrium in particular, focusing instead on other numerical examples with more goods or more agents. But while interpersonal comparisons are not possible, it is apparent, without even looking at their utility function, that agent alpha prefers the third equilibrium while agent beta will prefer the first equilibrium. This result is a simple consequence of the starting endowments, as alpha owns the whole stock of good I while beta owns the whole stock of good II: in an equilibrium with a lower price for good I, beta will be able to buy more of it while alpha

will not be able to obtain as much good II as in an equilibrium with a higher price for good I. But Koopmans did not say how one equilibrium was chosen instead of the other, even though this seems like a fundamental problem: whoever can influence prices can obtain a favorable equilibrium.

In his original example, Koopmans examined the three situations arising from three different price systems, taking the price as given each time. The only hint toward the dynamic problem underlying the approach of equilibrium is found in the second part of the paper, where Koopmans described a change in price from the starting point of the second, unstable equilibrium: "a slight rise in price beyond this point has the effect of decreasing supply more than demand, so that a shortage arises in the market, the consequence of which is that the price will rise even further" (Koopmans, 1932: 771).

Koopmans noted that Walras himself had underlined this possibility of having three equilibria, with the middle one unstable (Walras, 1954: 112).

To prove the instability of the middle equilibrium, Koopmans relied on Walras's argument which was based on tracing out offer curves in a price quantity diagram, and looking at their intersections with demand curves. It is interesting to note that the implied dynamic analysis is not spelled out in terms of differential or difference equations, something that became one of Tinbergen's main contributions to the macrodynamic program whose goal was precisely to specify these dynamic adjustment processes (Assous and Carret, 2022, in particular chapter 8).

The model that Koopmans ended up building thus exhibited multiple equilibria that were very different in character from those of Tinbergen: while Tinbergen imagined a situation where maximality conditions could be satisfied at different levels of production, Koopmans built numerical examples showing that for a given amount of goods in the economy, different equilibria could be possible. They all satisfied marginal utility conditions, but they were impossible to rank without a normative criterion to choose an equilibrium. This later problem was raised briefly, but left unexplored by Koopmans, who kept his attention on marginal utility functions.

IV. Tinbergen's turn away from Walrasian economics Tinbergen often claimed he had moved away from the Walrasian system because he regretted that it was static (Tinbergen 1935: 241). This move also coincided with the debate with Koopmans which made clear that Walrasian systems were difficult to reconcile with macroeconomic policy issues, and most importantly with an analysis of unemployment. Nevertheless, he did not abandon the idea that there could exist coordination issues through the existence of multiple equilibria in the economy, and the fact that some of these equilibria may be globally unstable was central to the models he developed during that period (Assous and Carret, 2021, 2022a, 2022b). This is clear in Tinbergen's 1934 macrodynamic model he built with the aim to account for various economic trajectories, some stable, others unstable and to show how policy could be used to change it. On the basis of an analysis of the determinants production and the value of consumer goods sold, as well as the movement of employment but introduced a speculative dimension through the effects of the evolution of current profits on expected profits. As in his 1932 pre-advice, he could examine the possibility that the economy may stabilize in two situations of stable equilibria, one with high employment and high output and one with low output and low employment. He also pointed out that an external impulse through a small rise in public expenditures could lead to a higher level of employment and profits, without necessarily maintaining the initial expenditure at the source of the shock.

The idea of multiple equilibria, and how macroeconomic policy may improve the level of production and employment, was also discussed by Tinbergen in works he published between 1938 and 1943. In his 1938 Econometrica article "On the Theory of Business Cycle Control", he built a small model in which economies could move from one equilibrium to another: "In the case of a nonlinear final equation there exist other equilibrium positions or developments than the one chosen as reference developments and much depends on the situation of these other equilibria, which may be stable or unstable" (Tinbergen 1938b, 33). The main message was that the final position reached by the economy was as important as the trajectory leading to it and that economic policies could play a pivotal role in leading the economy to various stationary states.

This approach of nonlinearities and its consequences on fluctuations was later continued until the publication of an article published in Dutch in 1943. Although Tinbergen examined for the first time the implications of multiple equilibria in a Keynesian cross diagram, his approach consisted in outlining the conditions for which multiple equilibria could occur and remained conceptually the same. Again, the issue was to make clear, depending this time on the slope of the expenditure demand curve relative to the 45°line, when multiple equilibria may appear. In view of the possibility that the expenditure may be non linear and S-shaped, Tinbergen considered the case in which three equilibria may be defined: two stable for extreme values of activity for which the slope of the expenditure curve is lower than 1 and one unstable for which the expenditure line is higher than one. With reference to Goudriaan with whom Tinbergen had debated several times in the 1930s (see Rodenburg 2010), Tinbergen could argue that the importance of the multiplier effect would dramatically change depending on whether public expenditures are increased by the appropriate amount. In particular, Tinbergen could argue that, from a state of low equilibrium, it is only when changes in expenditures shift the expenditure line so that it becomes tangential with the 45°line that the economy will eventually stabilize in a state of high equilibrium and public expenditures have a full impact on employment.

Conclusion: multiple equilibria, coordination and policy

In Koopmans setup, the policy problem that arose was one of distribution because efficiency was always obtained (preferences were satisfied). Looking at Table 3, we see why it was necessary to have a normative criterion to rank the different equilibria: total production is always the same, but the distribution of this production changes according to the relative price. Such a criterion could for instance be based on notions of justice and equality in the physical distribution of goods: in this respect, the least unequal distribution if the one arising from the first equilibrium, which is actually the worst possible equilibrium for Alpha and the best possible for Beta. The problems raised by this type of analysis made a comeback in the postwar period, especially after Arrow The use of such models had its price in the sense that they made it impossible to ground policy recommendations on welfare statements derived from optimizing behaviors. Tinbergen was much much more concerned after 1932 in deriving his models from aggregate behavioral equations than in developing models based on optimization, as demonstrated by his strong interest in macrodynamics, an interest that was shared with Frisch and other early econometricians.

It took five more decades for macroeconomists to return to the connection between multiple equilibria, normative statements and optimization. This was made possible by the implications of imperfect competition, where the first fundamental theorem of welfare economics no longer applied. The market power wielded by some agents in these models questioned the idea that the public interest could be served without coordination or cooperation. Instrumental in these new developments were the tools of noncooperative game theory, developed after the Tinbergen -Koopmans debate. A major research effort in the early 1980s resulted in the development of a new class of models in which a universally better outcome could, in some cases, be achieved by coordinating the activity of otherwise non-cooperative agents.

Such a result was the outcome of the presence of several equilibria, some of which could be inefficient, and which could be ranked according to Paretian criteria [START_REF] Silvestre | The Market-Power Foundations of Macroeconomic Policy[END_REF]. If one can show that the economy can stabilize in an inefficient equilibrium, then one can conclude on the existence of a coordination failure. The reason is similar to the one outlined by Tinbergen who understood that if everybody simultaneously moved to the better equilibrium, once reached, there would be no incentives to deviate from it. If the only equilibrium is inefficient, then the socially better allocations won't be reached unless agents become cooperative, or if the game is changed as a result of an institutional change. Tinbergen was clearly more concerned with problems of coordination than with problems of cooperation, but instead of turning to imperfect

Figure 1 :

 1 Figure 1: Tinbergen's illustration of a coordination problem(1932: 62)

Figure 2 :

 2 Figure 2: Edgeworth Box derived from Koopmans' numerical example

  becomes determinate with five unknowns and five equations.

  of aggregate purchasing power, Tinbergen was led to a nonlinear equation describing the relation between prices, production and the value of consumer goods sold, as well as the movement of employment. As for Walrasian systems, it did not escape him that the possibility of multiple equilibria was here totally natural while any action on the structural parameter of that equation may change the trajectory of the economy. Using that model in a series of articles published in 1935 and 1936, Tinbergen wondered how a change in initial conditions resulting from temporary shocks may change the trajectory of the economy and started showing concern for policy intervention likely to throw the economy over its stability zone into a region of instability that could potentially trigger a complete collapse of the economy. At the same time, he drew attention to the importance of designing an economic policy likely to prevent such dangerous paths. It is however only in a 1937 article that he really returned to the idea of coordination failures in the framework of a reflection on Kahn's multiplier and the effect of a rise in public expenditures. His basis was a simplified version of a Dutch model he had presented at the Namur meeting of the Econometric society in 1935, and which he went on to expand while working for the League of Nations in 1936-38. Tinbergen kept the idea central in his 1934 model that there exists a non linear relation between prices,

(

  1951) monograph and the renewal of welfare theory. But in the move to macrodynamics made by Tinbergen, individuals disappeared as the analysis was always carried out at market clearing equilibrium. Coordination problems in macrodynamic models arose from technical issues such as the production length, lags in investment, and other accelerator and multiplier relationships, and led to different policy problems.

Table 1 :

 1 The known quantities are endowments (for good I and good II respectively, Equilibrium equations ofKoopmans' system

	agent alpha has and and agent beta has 𝑘 𝑙	𝑚	and ) and preferences (in the form of 𝑛
	linear marginal utility functions with parameters	𝐴, 𝑎, 𝐵, 𝑏	for alpha and	𝐶, 𝑐, 𝐷, 𝑑	for beta,
			𝑥	𝑦		𝑧	𝑢
	rate of exchange (price	𝑝)	between the goods. The equations determining the three
	equilibria are presented in Table 1.
	Agent		Alpha			Beta
	Marginal utility		𝐴-𝑎𝑥 𝐵-𝑏𝑦 = 𝑝			𝐶-𝑐𝑧 𝐷-𝑑𝑢 = 𝑝
	Budget		𝑝(𝑘 -𝑥) = 𝑦 -𝑙	(determined by the others)
	Quantity		𝑥 + 𝑧 = 𝑘 + 𝑚		𝑦 + 𝑢 = 𝑙 + 𝑛

respectively for good I and good II). The unknowns of the problem are the final quantity held by participants after the exchange ( and for alpha, and and for beta), and the

Table 2 :

 2 Equilibrium equations ofKoopmans' numerical example

		Relative	Alpha		Beta
		Price I / II
			Good I	Good II	Good I	Good II
	First	1	2	5	5	5
	Equilibrium
	Second	2	3	8	4	2
	Equilibrium
	Third	3	4	9	3	1
	Equilibrium

Table 3 :

 3 Equilibrium solutions of Koopmans' numerical example These three equilibria can be represented in an Edgeworth box diagram, which

Contact: michael.assous@univ-lyon2.fr, vincent.carret@univ-lyon2.fr. We are grateful to the participants of the workshop Coordination Issues in Historical Perspectives where this paper was presented.

See Knoester and Wellink (1993: 19-20) on this address and the rest of the paper as well as their book on the wider context of the talk, one of five given by Tinbergen in front of the Association, that became the Netherland Economic Association in 1950 and received the "Royal" title in 1987. This talk was published along with the one given by R. van Genechten on the same subject.

Tinbergen uses here and later the term "labiele" which also exists in French, German and English but English usage has consecrated the term "unstable" which we use in the rest of this paper.3 "The crisis which broke out in 1929 led to a disruption of production which did not occur in any previous crisis … And still nothing can be noticed of an end of this disruptive process"[START_REF] Tinbergen | Hoeverre Kan Het Regelen van Den Omvang Der Voortbrenging of van Het Aanbod van Bepaalde Goederen Door Producenten[END_REF]

56).

The hog cycle was first studied by Arthur Hanau of the Berlin Business Cycle Institute, and Tinbergen continued to emphasize the importance of his work almost sixty years later in his interview with Morgan and Magnus(Tinbergen et al., 1987).

"Presence of two stable equilibrium points means, as can be easily ascertained, that there are two points P1 and P2, in which the profit line of 1 has a horizontal tangent and that of 2 has a vertical tangent.

"Only an organized action -changing the number of workers in both firms at the same time -creates a movement along other lines. Now, from the point P1, one can only reach the point P2 without going through 'regions of lower gain', if one stays within the hatched curvilinear quadrilateral. And again, this is only possible if one does not go along horizontal or vertical lines."(Tinbergen, 1932: 62).This nevertheless means that any change in the number of workers in one's own enterprise results in a reduction in profit: the condition for a stable equilibrium. In the figure, the action of separate companies always means a movement along vertical lines (for firm 2) or horizontal lines (firm 1)"(Tinbergen, 1932: 62).

"After all, one of the essential conditions for the existence of a state of equilibrium in the sense of these two authors[Walras and Cassel] is precisely that, at the prices applicable to that situation, the supply of all end products and production factors, including human labor, is fully absorbed by demand. The equations in which this condition is expressed are therefore an indispensable constituent of the whole system of "equilibrium equations" through which, in the thinking of the aforementioned authors, the economic phenomena are examined"(Koopmans, 1932: 682).

competition which he surveyed at the same time [START_REF] Tinbergen | Annual Survey of Significant Developments in General Economic Theory[END_REF], he turned to the new tools of macrodynamics. In the end, it was in both cases by moving away from Walrasian economics that different research programs were opened.