The Role of Symbolic Language in the Transformation of Mathematics 10.1.1.88.8408

8/12/2019 The Role of Symbolic Language in the Transformation of Mathematics 10.1.1.88.8408

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DOI 10.1007/s10699-006-5909-1Foundations of Science (2006) 11: 249274 Springer 2006

WIM CHRISTIAENS

BASIC ONTOLOGY AND THE ONTOLOGY OF THE

PHENOMENOLOGICAL LIFE WORLD: A PROPOSAL

ABSTRACT. The condition of explicit theoretically discursive cognitive per-formance, as it culminates in scientific activity, is, I claim, the life world. I

contrast life world and scientific world and argue that the latter arises from

the first and that contrary to the prevailing views the scientific world (actually,

worlds, since the classical world is substantially different from the quantum

world) finds its completion in the life world and not the other way around.

In other words: the closure we used to search in a complete and comprehen-

sive scientific description of all aspects of experience by referring it back to

underlying atoms, genes and other scientific objects and the covering laws rul-

ing them, should be sought in a reintegrating and occasionally dissolving of

the abstract scientific model in the self-organizational fluidity and superpo-

sition-like indeterminateness and non-locality of the life world: We have to

acknowledge the indeterminate as a positive phenomenon (Merleau-Pontyin hisThe Phenomenology of Perception).

KEY WORDS:

1. INTRODUCTION

Some wild ideas are going around when it comes to interpret-ing quantum mechanics (QM). One physicist for example (DirkAerts) communicated to me that he is convinced that the worldhas something like the structure (or the nature if you will) of a

Hilbert space. A Hilbert space is the state space used for describ-ing the behavior of quantum mechanical physical systems. In thepresent paper I develop a view of the scientific world and of thebackground from which the scientific world arises, that accommo-dates this claim. Following a number of continental philosophers,Maurice Merleau-Ponty in particular, I reason from the premise

The author is post-doctoral researcher with the Flanders Fund for Scientific Research

(F.W.O).


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that besides the scientific world and the world of everyday appear-ances (the manifest image) there is also a life world. If we confineourselves to physical theories that are in a more or less invarianttheoretical format of laws and principles intersubjectively widelyused and accepted, then we can safely say the quantum world isthe final stage of the development of the scientific world. I claimthat the quantum world is in some respects the respects thatcaused and cause such a stir closer to what is called the lifeworld than it is to either the manifest image or the pre-quantum

scientific world (which I will refer to as the classical world). I willonly be able to present a general idea of my argument. I hope to fillin the gaps and elaborate on certain points in subsequent papers.

There are two more important premises. The first has to dowith the fact that there is no such thing asthescientific method. Iam here more or less on the grounds of analytical philosophy ofscience. Values and volitions are not different perspectives fromthe theoretical perspective, but they are part and parcel of the the-oretical perspective: unconscious psychological and sociologicalfactors play their part in the decisions the scientist takes. (In myopinion a good scientist is also guided by his love for the subject

and by aesthetic considerations.) Instead of lingering on this toolong or saying things that have been said many times before,1 letme take a positive view of this situation. Maybe there is somethinglikea scientific attitude: an inextricably interlocked set of desires,goals, values, norms and beliefs where the desires, goals, etc. arenot just founded or dependent on the beliefs, but whereeverythingis dependent on everything else characterizing the scientific wayof acting and reacting in the experiential flow. We can now safelyignore this issue and concentrate on the aim I stated above.

The second presupposition is derived from continental phe-

nomenological philosophy: I am working from the point of viewof aphenomenological reduction. I will not spend any time in trac-ing this concept through the work of Husserl. I construe and useit to fit my own purposes. How do I use reduction? I can definethe naturalistic attitude negatively as everything better: everylived act of consciousness that hides with respect to the man-ifest world or the scientific world the relevance and constitutiveactivity of consciousness. The point is that as long as we are in thenaturalistic attitude, the world of science (which has the character


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between the constitution of the classical object and materialisticprinciples: for example I witness that the materialistic principlesdetermine the constitution of the object and have therefore suchan implicit but inescapable hold when we are in the naturalisticor scientific attitude.

Finally a word about terminology. I use the wordentity in avery wide sense. The words object and subject derive their mean-ing from their mutual correlation. An entity is characterized neg-atively by the fact that it does not need the correlational structure

of subject and object. An entity can become an object, but notall entities are objects. The difference between entity and objectwill become clear as we proceed.

The remainder of this paper is divided in five sections. In sec-tion two I look at how the predicative-attitude/natural-worldcoordination incorporates the scientific-attitude/scientific-worldcorrelational structure. In section three I look at the double natureof the scientific world: its classical component and its quantumcomponent. Section four is devoted to the life-world/pre-predica-tive-attitude.Idiscussarecentproposalinanalyticalontologythatincorporatescentralaspectsofquantumtheoriesandseemstobethe

underlying ontologyof both thelife worldand thequantum world.

2. THE NATURAL WORLD AND ITS SCIENTIFIC COMPLETION

2.1. The Predicative Attitude and its Worlds

Showing the rightful place of the scientific attitude in conscious-ness will enlighten us immediately as to its nature. Conscious-ness the flow of mental acts: perception, thought, emotion,volition, remembrance, . . . has two modes: (1) it can be non-

positional, non-thetical, pre-predicative and pre-reflexive, (2) itcan be positional, reflexive, thetical and predicative. The latter ishow we usually think about consciousness. These are quite differ-ent attitudes. Following the Kantian incentive, more alive thanever in continental philosophy of science (cfr. the work of Bitbol,Petitot), we look for a subjectobject correlational structure. Letus look at the predicative attitude first.

In the first place, the predicative attitude has a subjectobject structure. The subjectobject structure is typical for the


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ONTOLOGY OF THE PHENOMENOLOGICAL LIFE WORLD 253

knowledge relation and knowledge and belief is taken to be basicfor all other acts: we can only emote, value, desire,. . . somethingif we know (or think we know) at least something about what itis, where it is, etc. Secondly, in the predicative attitude the nat-uralistic world appears as the proper world for all objects andeven for consciousness itself. We have to evaluate this from thepoint of view of the naturalistic reduction. The naturalistic reduc-tion allows us to see that within the bounds set by the subjectobject-correlation natural-attitude/natural-world, conscious acts

are objectifying the giveness of certain perceptions into objectsand systematically fit this into the natural world. The correla-tion scientific-attitude/scientific-world is a development withinthe predicative attitude where: (a) consciousness starts as the non-reflexive, non-positional, pre-predicative activity without subjector object, and (b) predicative consciousness constantly drawson the life world and is carried by it. This is not however howpredicative consciousness sees itself. The correlate of the natu-ral attitude, the natural world, is put forth as the condition ofthe positional acts of predicative consciousness, it frames them.Instead of seeing itself as constituting the objects of the natural

world, it sees itself as discovering them. Furthermore this uncon-sciousness towards constitution goes even deeper with respect tothe natural world as a whole. The natural world is not consideredas constituted and not even considered as being discovered, itis the unspoken shared assumption of all acts: ontological real-ism. So in a sense, the scientific world presupposes what it tries toobtain: the natural attitude and its objective correlate, the naturalworld. In recent times this has been calledthe closing of the circle

(Abner Shimony), but the idea has been present since Newtonand is usually referred to as naturalism.

Note the following facts. There is an intrinsic interrelationbetween materialism, ontological realism, scientific realism andreductionism, and they are all related to naturalism. I will referto this conceptual field asnaturalism-etc.Up until now when werefer to the scientific world, we generally read this as the world ofclassical physics: the world where there is no superposition typicalof QM. Only in the next section the dual nature of the scientificworld will be introduced. The predicative attitude can have thenatural world, the classical world or the quantum world as object.


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Following (1) above one could think pre-predicative-atti-tude/life-world is a subjectobject correlation, but that is incor-rect. In fact there is no subject and no object and no correlation.Process and product flow together, are indistinguishable. I willreturn to this in the next section. In this section I will take acloser look at the relation between natural world and scientificworld.

2.2. The central feature of naturalism-etc.

Let me give a short overview of the closing of the circle. I dis-tinguish three stages. In the first stage of the predicative modeconsciousness is a ray of light, thrown on an entity that in theprocess is lifted out of its place and put in the foreground as anobject. In a certain context, with respect to a specific problem, wedistinguish foreground and background, we direct our attentionand in so doing create an object. Entities are posited for me (thesubject) as substances bearing properties and standing in definiterelations.

How do physicists see this? Some approaches in physics

only concentrate on producing models, building theories. Otherapproaches, most of them in the foundations of fundamental the-ories like QM or quantum field theory, are more self-reflective,more attentive to their own presuppositions and open towards theexplicit theoretical incorporation of their principled presupposi-tions into physical theory. In other words, they are attentive to thesystematic role of consciousness in the production of the modeland incorporate this aspect into the physical theory. One suchapproach is operational quantum logic in the Genevan traditionof Jauch, Piron, Aerts and Coecke (see Coecke et al., 2000). In his

1982 and 1983 Aerts describes a rudimentary operational way ofbuilding physical models. He says that the world is the collectionofphenomena: rain, tree, electron. . . He does not define this cru-cial concept. Just like anybody else the physicist is caught up in thehustle and bustle of the world. Aerts says that the scientific modeis initiated by picking out certain facts that draw our attention,facts that strike us in a certain way. Because of this i.e. becausewe can experience some facts relatively separated from ambientfacts we are entitled to attribute properties to the phenomenon.


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The description of a phenomenon is not exhaustive, it is a per-spective. Aerts calls the locus of the properties an entity: Weshall study the set of properties that we want to attribute in thisway to a certain phenomenon. The thing described by this set ofproperties, and which is an idealization of the phenomenon in thesense explained above, we shall call an entity (Aerts, 1982, p.1134). There are some differences in the use of words between meand Aerts. What he calls a phenomenon is more along the linesof what I call an entity. What he calls an entity, I call an object.

From my reduced perspective everything is a phenomenon! Fromnow on I will use my terminology. Separability is the conditionfor being an object. A specific physical system is

some part of the ostensively external phenomenal world, supposed separated

from its surroundings in the sense that its interactions with the environment

can either be ignored or effectively modelled in a simple way (Moore, 1999,

p. 64).

Space-time relations play a central role in separating an entityfrom its surrounding, making it into an object. When the phys-icist decides to study a phenomenon he does not study all the

properties of the phenomenon in one model. He selects a par-ticular subset and constructs an object from this subset. Whichproperties are selected depends on the problem he is trying tosolve. If you want to study the kinematics of the collision of twobilliard balls, then you are usually not concerned with the coloror the temperature of the billiard balls (Aerts, 1983). FollowingVan Fraassen 1991 I believe that objectifying an entity, bringingit on a predicative level, means for the physicist constructing astate space. Typical for the scientific stance is the introduction ofmathematical structures. Arithmetic, classical logic, . . . are the

simplest examples of such structures. Hilbert space, relativisticspace-time, . . . are examples of very complex, highly developedmathematical structures. They are the typical end product of thecleansing of the messiness of the life world initiated in the predi-cative attitude (see the final paragraph of Section 4).

In the second stage the subjectobject correlation is extendedconsiderably. The scientific object can, in principle, be fitted intoa world: a stable, well-structured intricate but transparent con-tainer-like all encompassing structure called space-time; each


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thing or event in this structure is separated from each and everyother thing or event, and is as such the subject of properties andthe relata of relations, all of them built on the spatio-tempo-ral relation; covering laws complete this picture: all behavior, allchange or movement is determined by invariant laws ruling thethings and events. This is what I already referred to earlier as thescientific world.

The final stage of the closing of the circle is fitting the sub-ject into the world of the object (see Hooker, 1995 for example).

Human knowledge self-reflexively sees itself as a natural phenom-enon to be studied as any other natural phenomenon. The scien-tific image shows us as one species among many, recently evolvedetc. In this view cognition involves the active construction of somekind of model in our heads. This construction involves elemen-tary sensory-motor coordinations and elaborations on these. Thebasic referents of these constructions are situations in our exter-nal world that are causally mediated to us. Science is an aspector dimensions of a highly complex, highly interactive dynamicsystem of nested subsystems ranging all the way from internalneural organization to social institutions. (Here the mind-body

problem enters.)It would seem that we start in the natural world, go through

the three stages and end up with a more refined version of thenatural world: the classical world. In the definition of physicalsystem the concept of natural world is presupposed. After goingthrough the three stages the world comes out a lot more consis-tent and mathematical, but essentially the same in nature: it is aspatio-temporal structure with ud-localization as condition forexistence and individuality.

Is this entirely true? Theoretical physics is the highlight of

the Western tendency towards abstraction and idealization. Onecould think that the difference between classical world and natu-ral world is just a matter of degree, i.e., the degree of abstractionand mathematization. Yet I believe the difference between thepredicative attitude and the scientific stance is not just a mat-ter of degree. Most phenomena have a process-product duality. Iwant to draw attention to the philosophers fixation on the finishedproduct: the scientific theory. Actually the fixation on one spe-cific scientific theory: classical physics. This was true of Descartes,


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Hume, Kant, . . . It is still true for most philosophers today: eitheryou explicitly or implicitly adhere to this ideal or you resent thisideal and react against it. In both cases you accept the relevanceof the ideal. It finds expression in fights over naturalism-etc. Ourcurrent age suffers from too great a fixation on theoreticalphysics,on theoretical knowledge idealized after the image of theoreticalphysics. Strangely enough many theoretical physicists believe in

fallibilism. They are not afraid to abandon cherished theories.Fallibilism is something widely divergent views in analytical phi-

losophy of science will agree upon (as Van Fraassen notices in his2002). In Butterfield 1998 examples are given of situations wherescientists were prepared to give up one of the most fundamentallaw of physics, the laws of conservation of energy, if it would solvea problem satisfactorily. Apparently the physicists themselves (atleast some of them that determine the course physics takes) are

fundamentally fallibilist: they are prepared to give up anythinggiven enough reason to do so. Scientific practice in general isactually quite explicit and very careful in always contextualizingits own claims: experiments, statistical research and theoreticalmodels have most of the conditions that constitute their perspec-

tive and their constructive aspects spelled out. When you opena handbook of physics, models are presented in such a way thatit is quite clear that they are a very specific way of dealing withphenomena. But all of this intellectual hygiene is duringthe scien-tific activity, during the process. Outside of the practice of science,what was the specific constitution of one object (and possiblyalso the extrapolation of this object into a world) is dogmaticallyposited as the condition for any subjectobject relation and forconsciousness itself.

Can fallibilism go hand in hand with conservatism in and

about science? I do not see how. The question then becomes: isthe scientific attitude characterized by its striving for a deduc-tively closed system of the world, or is it rather more pronetowards fallibilism? I propose a solution inspired by Van Fra-assen (2002). We have to distinguish the scientific stance fromthe stance towards science. Fallibilism is part of the scientificattitude. The dogmatic closing of the circle is part of the atti-tude towards science and based on science. It is not because thescientific attitude uses the natural attitude that it also believes


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to be part of the natural world, i.e., that it endorses natural-ism-etc. The closing of the circle is a perspective on science,it is not per se part of science. I am not arguing against theattempts at naturalism-etc. ; I am arguing that naturalism-etc.is an attitude to be distinguished from the scientific stance. Actu-ally the fact that naturalism-etc. would work (which was and isthe prejudice of Western intellectual culture) would be close toa miracle. Imagine: a perspective with a particular way of con-stituting objects, which is then further developed into a com-

plete world, is finally posited as the background for every possibleobject of consciousness, and in the end for consciousness itself.Nowhere underway the fact that we are dealing with a perspec-tive is overcome, it is only forgotten or we were not conscious ofit in the first place (which as we know is typical for the naturalattitude).

Themanifest imageis a concept introduced by Wilfried Sellarsand is used sometimes by analytical philosophers of science (likeVan Fraassen) instead of life world or pre-predicative conscious-ness (which is more the parlance of continental philosophy). It isbest illustrated by using an example along the lines of Eddingtons

(Eddington, 1928, pp. ixx): the coffee cup of the manifest imageis a materially continuous substance within its physical bound-aries with certain properties like being white, the coffee cup of thescientific image however is mostly empty space and atoms. Onewould expect the manifest image to be closer to the life worldthan to the natural world, because it is used as a contrast with thescientific world. Actually it is closer to the natural world, than itis to the life world: the subject-predicate structuring has already astrong hold and every object is ud-localized (uniquely and deter-minately localized) in space and time. The manifest image is part

of the object-correlate of the predicative attitude. The naturalworld is initially a pre-scientific world. The manifest image isthat part of the natural world that is substituted by the scientificworld. Eventually the whole natural world can be substituted bythe physicists space-time manifold. So we should not confuse theconcept of manifest image (which is mostly used in analytical phi-losophy) with the concept of life world from continental philoso-phy. The latter concept is as far as I know completely absent fromanalytical philosophy. The idea of manifest image as a contrast


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to scientific image illustrates to what degree the natural world isdifferent from the scientific world. It is reminiscent of Lockesdistinction between primary and secondary properties.

The following ideas characterize the scientific world: ud-local-izability, locality, separability, countability, consistency, com-pleteness and maybe some others. I think these are the principalones. These principles already ruled the natural world. Howeverthey come in a new guise, generally a mathematization. For exam-ple, while consistency has been around as an intellectual principle

since Aristotle, the principle of non-contradiction is now part ofclassical formal logic, a mathematical system. Space and time arenow a differentiable manifold with vectors, tensors, wordlines etc.It is similar to the difference between materialism and physical-ism. Materialism involves mainly ud-localization, but not per sein some mathematical entity like space-time (we have to realizethat the scientists space and time is a differentiable manifold of aspecific kind). Physicalism has to do with the mathematical worldof theoretical physics: differentiable manifolds, state spaces, mol-ecules, atoms, genes, electricity, gravitation, etc.

We have a tendency to equate scientific world with classical

world. The classical world and the underlying principles act eitheras a priori conditions or (weaker) as a criterion for the ontologicalstatus of objects. If for example I am presented with an object thatis marked by intrinsic vagueness, non-locality, non-separability,non-countability, inconsistency, etc., then this object will not getthe label real. It will not do as proper facts. Every time I referredto the scientific world, I actually meant classical world and I amsure that most people understood it that way. However, we cannow no longer ignore the fact that the scientific world is ruled bysomething else besides the classical principles mentioned.

3. THE SCIENTIFIC WORLD FINDS ITS COMPLETION IN A

NON-CLASSICAL WORLD

The physical description of the world is not obvious. The intro-duction of scientific ideas needed a good deal of convincing, and along preparatory period preceded the physics of Galileo andNew-ton.2 Is the development in our past from life world to manifest


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image and from natural to scientific world necessary? I am con-vinced there were moments of bifurcation. Poppers example ofclouds and clocks shows how. Clocks can be built into identicalsystems from the same building blocks. When we set them run-ning they run the same time. Although clouds are all of themmade up of the same stuff, it is impossible to find two clouds thathave even approximately the same shape. The weather is a typi-cal domain where we have non-linearity. This was ignored for along time because we construed clouds like clocks or as special

cases of clocks. The whole idea of hidden variables is nothingelse: when we cannot objectify entities into particulars, we sup-pose that there are hidden variables present that would restore theclassicality. The billiard ball world is the paradigm, the preferredmodel. But, says Popper, we could also take clock-like entities asspecial cases of cloud-like entities. If you let clocks run a longenough time we will find that their behavior becomes erratic andunpredictable. Non-linearity and vagueness, usually shunned byscientists, would be paradigm. A science built on such princi-ples would in all probability be quite different from the classicalworld.

I now add a crucial element to my story: quantum theory. Iwill not get into this too much and just list the three things thatset QM apart. First, the indeterminateness of physical variables,especially the variables that carry all the metaphysical weight:position and velocity. Neither CM nor QM describe the mea-surement interaction and both for a classical and for a quan-tum system the measurement interaction can change the stateof the system (Aerts, 1983). The difference is that for a classi-cal property we know with certainty that if we would carry outthe measurement the system would have the property. In a clas-

sical context, if we can only predict with probability less thanone, then nobody doubts that this probability is just a lack ofknowledge about a completely determinate reality. What is spe-cial for a quantum system is that (i) the probabilities are not dueto a lack of knowledge about reality and (ii) while the measure-ment is being carried out a new part of reality is created, whichdid not exist before the measurement was carried out (Aerts ina number of papers: see his 1995, 1998, 1999a and b and otherreferences mentioned there).3 This implies that the variable was


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definitely indeterminate. In QM two kinds of state transitions aredescribed: state transitions according to a deterministic evolu-tion equation and state transitions according to the projectionof a state vector on the state space (a Hilbert space). It is thelatter kind, also called the jump of the state vector, that is thefocus of debate. It is interpreted as the state transition of a quan-tum entity during or due to a measurement.4 Secondly: quantumentanglement. Most of us have heard about EPR-experimentsshowing how a quantum physical system compounded from two

quantum systems can exhibit behavior that would indicate it is anon-separable whole, even if the two compounds are located inseparated regions of space. This continues to be one of the mosthotly debated issues in the foundations and philosophy of QM.Thirdly: non-countability. This can be illustrated with an exam-ple. Suppose you have a box with two physical entities in it thatare moving without colliding. At all times you know that the boxcan be in one of four possible states: two particles on the left sideof the box, two particles on the right side of the box, one particleon the left and one on the right or the state where the particleon the left and the particle on the right switch sides. If we do

the same experiment with electrons we get a different situation.There is a state where both electrons are on the right, there isa state where both electrons are on the left and there is a statewhere there is an electron on the right and an electron on the left.The peculiar thing is that the latter state cannot be further dis-tinguished into two states as we could do for classical particles.This is because of the possibility of superposition states in QMand the fact that electrons have no individual characteristics thatallow to distinguish them. I will not go into the matter here andrefer the reader to specialized literature: French (1998) and Seibt

(1999).While Poppers argument could be swept under the rug by thehidden variables argument, quantum phenomena resist such asolution. These are phenomena not just in our sense, but in thephysicists sense! Although we do not need QM to show how thenatural attitude is a false consciousness, QM kind of hardens theblow, it gives more punch to it, because it is the apotheosis ofscience and lies at the heart of science.


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4. WORLD NOT WORLD

4.1. Consciousness (of) Self and Perception

I want to explore the nature of the life world and of the pre-pred-icative attitude. Predicative thought exists against a backgroundthat supports it and from which it springs forth. Because we areworking within a naturalistic reduction the phenomenologi-cal mode of making a purely descriptive observation of the pureworkings of all consciousness (i.e., the act of observing the streamof acts that takes its course) we observe that explicit predicativemental acts exist, not against a spatio-temporal container-likeworldly background of the natural world or classical world, butagainst a pre-predicative Gestaltlike complexity of forces: the lifeworld. I use forces here in the sense of tendencies or liabilitiesrather than in the sense of vectors. I liken them to forces for areason: I want to draw attention to their autonomous produc-tive nature. I start with some negative statements: what the lifeworld is not. First, it has nothing to do with the unconscious in apsychological sense. Secondly, there is no correlational structure.

One could think that pre-predicative consciousness is the subjectand the life world is the object, but that would be a mistake. Iinfer these facts from a combination of Sartres phenomenologi-cal observation of consciousness and Merleau-Pontys phenom-enological observation of perception.

The transition from pre-predicative to predicative conscious-ness is described by Sartre:

Consciousness and the world are given in one blow: essentially external to

consciousness the world is essentially relative to it . . . Being is exploding into

the world, going from a nothingness of consciousness and the world, and then

suddenly bursting out as consciousness-in-the-world.5

The key phrase is here: un neant de monde et de conscience.Nothingness should be understood in contradistinction withthe thingness of the natural and classical world. After burst-ing out into the world, consciousness apprehends itself as per-manently bursting out: it the nature of consciousness, referredto as intentionality, to be this constant and continuous seriesof eclatements. Sartre thinks that the condition of inten-tionality (perceiving something, thinking something, . . . ) is a


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self-consciousness of a specific kind: a consciousness of self thatno longer has a subject-object structure because it is not a knowl-edge relation. To emphasize this he writes, consciousness (of) self(conscience (de) soi). For example, my pre-reflexive conscious-ness of perceiving and the perceiving are one and indivisible. It ispure activity pure existence supporting itself: There is beingindivisible and indissoluble not a substance supporting propertiesthat are somehow less real than it [the substance], but existencethrough and through.6 Normally one would expect an activity

like consciousness to be supported by a substance: the body, thebrain, the ego,. . . 7

As before (see Section 1 and the way I treated Husserl) Ijust pick out the elements that interest me to make my ownconstruction, so I will not pursue a correct critical discussionof Sartres philosophy. Although it has been noted that Sartresconsciousness (of) self is already a departure from the usual viewof consciousness (which is much more reflexive, clear, entertain-ing distinct ideas in a discursive, predicative manner), it doesnot go far enough. Sartre pursues the ideas touched on here inthe direction of a strongly dualistic ontology: consciousness is

pour-soi and the world is en-soi. The first is qualified by non-identity, pure movement, refus de substance,. . . , the second bycomplete identity, inertness, . . . What I retain from Sartre is (1)the initial nothingness of consciousness and world, (2) the exis-tence of a consciousness (of) self that has the characteristics ofa pure process. Now I would like to add elements from MauriceMerleau-Pontys phenomenology of perception.

We have to resist the urge of looking only for the pure clarityof thought as the paradigm of conscious activity. We have to goback to the beginning, and the beginning is perception: a process

free from the thinglike substantiality and nomological related-ness of the natural and especially the scientific world. FollowingMerleau-Ponty I note that we generally do not perceive isolatedobjects in our environment, but a structural and changing net ofrelations, a perceptual field as he calls it. Two examples. First, thecolor red is different when it is the red of the fluffy sweater of thatyoung girl crossing the street than when it is the red of my drearyplastic coffee cup. Secondly, it happens that even though the girlcrossing the street drew my attention, afterwards I cannot tell you


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what color her hair was. Examples like these show the followingfacts about perception in its pre-predicative mode:

It is nowthe adherence of what is perceived to the contextand something like

its viscosity, nowthe presence in it of a positive indeterminatenessthat prohib-

its the spatial, temporal and numerical ensembles to articulate themselves in

terms that can be handled, that are distinct and identifiable.8

Merleau-Ponty shows that we cannot analyze the perceptual field

into a nomologically linked collection of spatially, temporallyand numerically distinct completely determinate things (wherethings = substances supporting properties). Furthermore, theperceiver himself is also a structural net of relations dynamicallychanging in a dynamically changing environment. At this stage,we cannot distinguish in any unambiguous manner subject fromobject, not even in an ontological sense of pour-soi and en-soi.The perceiver is always already actively implicated in the struc-tural net of relations. Determinate objects with definite propertiesand a lucid structure called the subject are constructed from Ge-staltlike dynamic structures of perception.9 Subject and object,

space, time, numerical identity, etc. are potentially there withinthe life world. They are an implicate order, whereas the nat-ural/classical world is an explicate order (both concept wereintroduced by David Bohm in the context of his interpretationof QM). Merleau-Ponty writes: We have to acknowledge theindeterminate as a positive phenomenon.10 This means that thedeterminate obtained from the indeterminate the natural/classi-cal-world obtained from the life world is just that: obtainedfromthe indeterminate. The determinate does not destroy or replacethe indeterminate, it cannot be substituted for the indeterminate

after having been obtained from it, as if the determinate wereprimordial, and we have discovered it behind the veil, the mereappearance which would be the indeterminate.

To mark the difference between the classical world and the lifeworld, I will also refer to the latter as (the) world or (a) world.This is not just a syntactical gadget. The function of the wordsthe and a is to singularize the words they precede. They local-ize them into something you can point to, into countable units,particulars as I will call them. In any case the brackets are just


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meant to symbolize (and constantly remind the reader of) thedistinction I want to make.

As I mentioned before, on the side of the natural and clas-sical world we have principle of non-contradiction, principle ofexcluded third, ud-localization, separability, locality, countabil-ity. (The) world does not endorse the negation of principle ofnon-contradiction, etc. as a principle, the way the classical worldendorses principle of non-contradiction, etc. It just denies thatthey are principles. These principles impose rational order, in the

life world this order is implicit (or implicate). Remark that a prin-ciple is something that conditions, and is thus universal. The prin-ciples mentioned here are constitutive for the possibility of anyobject of the natural and classical world. The only a priori of pre-reflexive consciousness is the absence of any definite a priorisexcept the natural life driven openness towards (the) world. Theidea of self-organization comes close, but is still to much biasedby the distinction between inside and outside, subject and object.

The above does not mean that everything is free-floating in(the) world. It just means that the way entities are related to eachother is not a space-time structure, and although it is not chaos,

i.e., it has some invariance, (the) world cannot be calleda structurein the usual sense. It is almost impossible to describe pre-reflex-ive consciousness. But that does not mean it is not there, thatdoes not mean it should not determine our reflexive theoreticalviews on what there is. In particular it should put boundaries onthe strong metaphysical claims like materialism, physicalism andscientific realism.

4.2. Free Process Theory

I will now try and make the difference between classical worldand life world more precise in yet another way. It is based onwork done in analytical ontology by Johanna Seibt: free processtheory (FPT).

I can see from my reduced point of view that without the pres-sure of the natural attitude so many entities can become objects ofconsciousness. I can see how the pressure of the natural attitudemakes it so that the predicative attitude enforces certain habits ofthought. What is a typical object? What kind of examples do we


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give, when we engage the topic of possible objects of conscious-ness? Let us first look at examples that are typically not given:love, anger, music, Nine Inch Nails The Fragile, clouds, rain-bows, running, moving, the singlet state of a compound entity inan EPR-experiment, a free quantum field described by a super-position state in a Fock space, . . . What we like to use as examplesis coffee cups, pens, chairs and tables, or billiard balls, genes andH2O-molecules. There is nothing innocent in choosing the latterexamples. It goes easy enough. You take the cup that is in front

of you as the nearest and seemingly innocent example. The pointis that coffee cups are ud-localized and thus quickly and withoutdiscussion amenable to the countable, separable, local, determi-nate etc. schema that typifies the predicative attitude and evenmore the scientific attitude. I will call these objects particulars.Ud-localization and countability are the basic features of partic-ulars. The natural and the classical world alike are also very muchparticulars. This becomes clear when we look at possible worldssemantics and the metaphysics associated with it. Possible worldsare a popular formal tool in analytical philosophy of science, usedto analyze and define concepts like determinism, causality, phys-

icalism, etc. I can think of this world and then I will picturethe classical world of the scientific attitude or the natural worldsupplemented with elements from the scientific world and I canthink of worlds different from this one by changing characteristicsin the present world. For example I could think of a world wherekangeroos have no tails, worlds where Newtons force law is afirst order differential equation, a world where the IMF does notimpose deregulation on Third World countries, etc. These worldsthat we are considering: they are completely determinate worlds,total universes; ours is one of them, contingently or necessarily

(that does not matter very much here) the real one. They are notud-localized, but each of them is internally completely determi-nate (especially spatio-temporally), consistent, local, separable,etc. We can differentiate them from each other: this one and thatone, and another one, which allows to count them: the first, thesecond and third, etc. They fit perfectly in a subjectobject corre-lational structure. As objects of consciousness they are basicallythe same as coffee cups, billiard balls and molecules (althoughwith molecules we are on dangerous ground).11


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FPT is rapidly becoming a sophisticated and multi-dimen-sional philosophy under the supervision of its originator J. Sei-bt. It introduces the idea of a free process: which is the oppo-site of a particular. Let me give an example. One running, tworunning, . . . That does not work. Neither does: one water, twowater, . . . One chairs, two chairs, . . . That does work. Also,running added to running gives running. Chair added to chairgives two chairs. Of course one can take amounts of running,but then we have already localized running into something else

that allows us to measure it. The point is that coffee cups, bil-liard balls, chairs, etc. are always already countable units, whileactivities (like running) and stuffs (like water) are not. Cassirerquotes Natorp who says that deriving numbers from things iscircular, since the concept of a thing has the concept of numberas a necessary component (Cassirer, 1955, p. 226). That is theonly way they can exist or can be thought of. Classical ontol-ogy is based on the combination of a substance with propertiesand relations: the first is concrete (i.e., ud-localized), propertiesand relations are universals and are not ud-localized. Free pro-cesses have this in common with universals that they are not

ud-localized, they have in common with particulars that theydo not need something else to subsist, they are themselves thesubstances. In FPT all free processes are on the same ontolog-ical level: they have the same characteristic free process qualityof not being ud-localized, of being non-countables, while havingthe potentiality of becoming ud-localized/countables. Entities areindividuated by their descriptive properties: when we encounterthe same descriptive properties then we have the same individ-ual. For example, every amount of water has descriptive proper-ties in common with every other amount of water. Water is the

individual identified by the descriptive properties of water: trans-parency, fluidity, etc. Although amounts of water are countable,the individual water is not countable. Neither is it uniquely local-ized. So water is a multiply localized and non-countable entity.Free processes are therefore also referred to as non-countables.For a better understanding we can take our cue from the follow-ing fact. We constantly say definite things about entities withouthaving to specify what we say in terms of space-time localiza-tion. For example when we say: There is a lot of violence in the


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268 WIM CHRISTIAENS

world, then we are referring to a multiply or indefinitely localizedindividual violence in the world. Other examples are easyto find. A language for example has no definite location inspace. Naturalism-etc. requirer that it is in principle possibleto translate every statement that is not about determinatelylocalized things/events into statements of determinately localizedthings/events, that such statements are actually covert ways oftalking about ud-entities (kind of like a generalized statisticalphysics of all utterances). From such a point of view water is

identical to the spatio-temporally scattered amounts of water:to the water in and on our bodies, the seas and rivers, the lakesand the rain . . . However intricate or difficult, this should be pos-sible. But suppose it is not. We know this cannot be done for thequantum world: the failure of the principles of ud-localizability,locality, separability and countability is intrinsic to the mathe-matical models for quantum objects and are strongly confirmedby experiments. That might inspire us to take a new look at someentities from the natural world. In FPT we suppose some state-ments that only vaguely or derivatively relate to space-time thingsand events, refer just as they are. Those entities are individuated

by their descriptive properties not by space-time localization.In a theoretical mode of consciousness we tend to objectify

the world into (a building of) things and events, a structure ofobjects. When we look closer and leave out any a priori restric-tion on what counts as a theoretical scan of thematter of the worldthat impresses us (matter here used in a philosophical sense), wesee that matter and what we make of it (i.e., knowledge, theo-ries, models and what we make is usually a pattern, structure,invariance, symmetry, objects) that the detail of the pattern ismovement. This change of perspective requires us not only to

start looking at quantum theories from the inside, but also tostop using the cup of coffee in front of us or the chair we are sittingon, as the paradigm entity for philosophizing. At the very leastit requires realizing that the cup and the chair are not necessarilythe best instruments in the philosophers laboratory.

Metaphors do a lot of the initial work in the introductoryphase of some new way of looking at something. (And we arenot planning to get beyond an introductory phase in this partof the paper). The world is made of stories, not atoms, the


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American poet Muriel Rukeyser writes. An individualis activity, aquantum of process. The word free indicates that there is noth-ing underlying processes, it is processes all over the place and allthe way down (Bickhard). All structure is part of the movement, istaken up in it, is a moment, a perspective on the individual process(itself part of a process). When you look long enough everythingis water, Seibt says. Every reality, every entity is a Fluss des Wer-den as it were:12 instead of the thing cup of coffee, we havea being-a-cup-of-coffee, etc. 13 Like music, running, time, free

processes do not have an interior, neither can you break theminto pieces. For free processes is true what Sartre writes aboutthe ontological nature of consciousness: see the quotations fromBeing and Nothingnessabove. Consciousness, says Sartre, is like awhirlwind: when you put something in it, it will be thrown out intothe world. The difference I make is that while for Sartre the worldis just the opposite of consciousness (it is inert, en-soi), I thinkthat many if not most entities in the world are also whirlwinds.The life world is composed of entities that are fuite absolue,refus de substance.14 Although helpful these characteristicallycontinental ways of theorizing can be supplemented with more

analytical means. For more details and formal developments Irefer the reader to Seibt.

The suggestion of such a non-ud-localizable, non-countable,non-separable, pre-predicative consciousness, a neant de mondeet de conscience is not as outlandish as it might seem. In thefirst volume of his The Philosophy of Symbolic Forms Cassirerdescribes the transition of something like the pre-predicative tothe predicative and eventually the scientific. In perceptual experi-ence, in close contact with the original perception preceding sci-entific and even predicative thought, we have the inception and

development of the categories of space and time. Subsequently,for the category of number and thing we have to go one step fur-ther, we have to posit pure relations, i.e., pure laws of thoughtaccording to intellectual principles. The development of geome-try, logic, arithmetic and in time more sophisticated mathemati-cal structures is part of this development. Cassirer remarks thatoriginally language had no universal system of numbers as we donow and which can be applied to all kinds of objects to countthem:


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270 WIM CHRISTIAENS

in so far as one can speak of number, it appears not in the form of a specific

measured magnitude, but as a kind of concretenumerical gestalt, an intuitive

quality adhering to a totally unarticulated general imprecision of quantity

(Cassirer 1955, p. 233).

Just as the red of the sweater of the girl is different fromthe red of my plastic coffee cup, five girls is something differ-ent from five coffee cups: language originally had no univer-sal numerals applicable to all enumerable objects, but useddifferent numerical designations for different classes of objects

(Cassirer, p. 233). Cassirer quotes numerous examples of lan-guages of primitive peoples from all over the world to provehis point.

5. FINALLY

We shouldnot confuse tradition (the substance-property thinkingof the predicative attitude) with basic ontology.Basicontology isthe ontology of the life world. Tradition is the edification of thestructure of reflexive consciousness and especially the world that

is correlative to the predicative subject. However from a reducedpoint of view (the) world is the background against which we haveobjects of consciousness, it is the indefinite flow from which sub-

ject and object emerge. The mistake we make in the naturalisticattitude is to think that the background against which the objectsof consciousness exist is of the same ontic nature as the object wehave obtained from it.

I want to show now that we have come close to my original aim:substantiating Aerts suggestion that the world has the structureof a Hilbert space. It will be apparent by now for the reader that

the transition from pre-predicative to predicative consciousness,has a likeness to what in QM is called the jump of the statevector.15

The natural attitudeleads to the scientific attitude, but this pro-cess cannot be carried out completely when the scientific worldis identified with the classical world. The end-point of the sci-entific process of idealization while having its beginning in thelife world ends in a mathematical structure that is very close tothe life world in many respects. (The) world is already non-local,


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non-separable, non-countable, negation-incomplete and incon-sistent. Not the naturalistic materialism is the background againstwhich I judge for example quantum mechanical state vectorreduction, because then we would end up with all the conundrumsof philosophy of QM. I take the life world and the phenomeno-logical view of consciousness as the proper background for boththe classical and quantum world. The only reason why QM posessuch a problem is because we judge it according to the principlesthat underly the classical world (and the natural world). If we

realize that the life world is the original source of any theory orthesis whatsoever, then there are no quantum paradoxes.

I have come close to my original aim: Aerts suggestion aboutQM and the structure of the world. Some physicists have referredto the strange quantum phenomena as the ghost in the atom(Davies and Brown, 1986). Philosophers have called the mind theghost in the machine. The ghost in the atom (object-side) andthe ghost in the machine (subject-side) are one and the same.They are remnants of the primordial source from which subjectand object are borne, they are the background noise of the orig-inary creative Big Bang: the bursting out as consciousness-in-

the-world.

ACKNOWLEDGEMENTS

I would like to thank Jean-Paul van Bendegem and Bart Vanden-abeele for their helpful comments.

NOTES

1. I refer thereader to contemporaryintroductory texts (likeLadyman, 2001)andanthologies of analytical philosophy of science (likeBoyd et al., 1991).

There are a number of books that take stock of what has happened in ana-

lytical philosophy of science in the second half of the twentieth century:

Giere (1999), Van Fraassen (2002), Hooker (1995) are examples.

2. Thismacro-history is repeated in our personal development in highschool,

when we substitute the theoretical world of physics for the manifest image.

3. Other experts in the philosophy andfoundations of QM present this differ-

ently: see Redhead (1987), Albert (1994), Van Fraassen (1991) and other

books.


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272 WIM CHRISTIAENS

4. In QM when you measure a quantum variable represented by a linear

operatorQ (the special case where we have discrete values and no degen-

eracy in the eigenvalues, and a set of eigenstates {|qi}) it is quite com-

mon that we measure variables when the entity is in a superposition state

|=

ici|qi of the eigenstates of the variable that is being measured

(where |ci |2 are the probabilities that we will discover the entity to be in

state|qi). When there is no measurement interaction the state evolution

of a classical and a quantum system is perfectly deterministic. The super-

position

ici|qiis a description of a real indeterminateness in the value

ofQ.

5. My translation of: La conscience et le monde sont donnes dun memecoup: exterieur par essence a la conscience, le monde est, par essence,

relatifa elle (Sartre, 1939, p. 110); and of: Etre, cest eclater dans le

monde, cest partir dun neant de monde et de conscience pour soudain,

seclater-conscience-dans-le-monde (Sartre, 1939, p. 112).

6. My translation of: Il y a un etre indivisible, indissoluble non-point

une substance soutenant ses qualites comme de moindresetres, mais un

etre qui est existence de part en part (Sartre, 1943, p. 21). Italics in the

translation were added by me.

7. And then there is the famous quote from Heidegger: The how ((essen-

tia)) of being must, to the extent we can talk about it in general, be con-

ceived from its being ((existentia)). My translation of: Le comment

(essentia) de cetetre doit, pour autant quil est possible en general denparler,etre concua partir de sonetre (existentia) (Sartre, 1943, p. 21).

8. My translation of: Cest tantot ladherence du percu au contexte et com-

me sa viscosite, tantot la presence en lui dun indetermine positif qui

empechent les ensembles spatiaux, temporels et numeriques de sarticul-

er en termes maniables, distincts et identifiables (Merleau-Ponty, 1945,

p. 19). Italics in the translation were added by me.

9. We could identify what Aerts calls phenomena with the pre-predicative

Gestalten or structures.

10. My translation of: Il nous faut reconnaitre lindetermine comme un

phenomene positif (Merleau-Ponty, 1945, p. 12).

11. Consciousness is not a thing or event. It is a process: the pure flow of

acts, like perceptions, thoughts, remembrances, etc. The acts of predica-tive consciousness are countable. I can distinguish or separate one act

from another act (in principe although not always in practice). This is no

longer true for pre-predicative consciousness.

12. The metaphor is from Cassirer. See Bayer (2001, p. 76).

13. Although in our view, the water metaphor, though useful, is detrimental

for any kind of individuality concept when we extend its metaphorical

impact to a fundamental level. The metaphorical use of water does not

convey the intrinsic aspect of activity.


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14. That way the strict distinction Sartre upholds between consciousness and

world becomes very hard to make.

15. I want to be absolutely clear that what I claim is that the the jump of the

state vector resembles the transition from life world to predicative con-

sciousness, the transition from entity to object, not the other way around.

(The phenomenological description of perception and consciousness does

not need any scientific theory, and therefore does not want to profit from

the prestige of science in general and physics in particular!).

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Vakgroep Wijsbegeerte en MoraalkwetenschapUniversiteit GentBlandijnberg 29000 GentBelgiumE-mail: [email protected]

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