Gödelian Aspects of Nature and Knowledge *

1. Quantum physics and levels of Reality

The major cultural impact of the quantum revolution has certainly raised questions for the contemporary philosophical dogma of the existence of a single level of Reality [1] .

Here the meaning we give to the word "Reality" is pragmatic and ontological at the same time.

By Reality I intend first of all to designate that which resists our experiences, representations, descriptions, images or mathematical formalizations. Quantum physics caused us to discover that abstraction is not simply an intermediary between us and Nature, a tool for describing reality, but rather, one of the constituent parts of Nature. In quantum physics, mathematical formalization is inseparable from experience. It resists in its own way by its simultaneous concern for internal consistency, and the need to integrate experimental data without destroying that self-consistency. Elsewhere as well, in so-called "virtual" reality or in computer generated images, there are mathematical equations which resist: a single mathematical equation gives birth to an infinite series of images. In potentia , those images are already present in the equations or in the series of numbers. Abstraction therefore forms an integral part of Reality.

In so far as Nature participates in the being of the world one must ascribe an ontological dimension to the concept of Reality. Nature is an immense, inexhaustible source of the unknown which justifies the very existence of science. Reality is not only a social construction, the consensus of a collectivity, or some intersubjective agreement. It also has a trans-subjective dimension, to the extent that one simple experimental fact can ruin the most beautiful scientific theory.

By level of Reality [1] I intend to designate an ensemble of systems which are invariant under the action of certain general laws: for example, quantum entities are subordinate to quantum laws, which depart radically from the laws of the macrophysical world. That is to say that two levels of Reality are different if, while passing from one to the other, there is a break in the laws and a break in fundamental concepts (like, for example, causality). No one has succeeded in finding a mathematical formalism which permits the rigorous passage from one world to another. Semantic glosses, tautological definitions or approximations are unable to replace a rigorous mathematical formalism. There are even strong mathematical indications that the passage from the quantum world to the macrophysical world would never be possible. But there is nothing catastrophic about this. The discontinuity which is manifest in the quantum world is also manifest in the structure of the levels of Reality. That does not prevent the two worlds from co-existing. The proof: our own existence. Our bodies are at once a macrophysical structure and a quantum structure.

The levels of Reality are radically different from the levels of organization as these have been defined in systemic approaches [2]. Levels of organization do not presuppose a break with fundamental concepts: several levels of organization appear at one and the same level of Reality. The levels of organization correspond to different structurings of the same fundamental laws. For example, Marxist economy and classical physics belong to one and the same level of Reality.

The emergence of at least two different levels of Reality in the study of natural systems is a major event in the history of knowledge. It can lead us to reconsider our individual and social life, to give a new interpretation to old knowledge, to know ourselves in a different way, here and now.

The existence of different levels of Reality has been affirmed by different traditions and civilizations, but these affirmations were founded on religious dogma or on the exploration of the interior universe.

In our century, in their questioning of the foundations of science, Edmund Husserl [3] and other scholars have discovered the existence of different levels of perception of Reality by the subject-observer. But these thinkers have been marginalized by academic philosophers and misunderstood by physicists, enclosed in their respective specializations. In fact, they were pioneers in the exploration of a multi-dimensional and multi-referential reality, in which human beings are able to recover their place and their verticality.

2. The logic of the included middle

Knowledge of the coexistence of the quantum world and the macrophysical world and the development of quantum physics has led, on the level of theory and scientific experiment, to the upheaval of what were formerly considered to be pairs of mutually exclusive contradictories (A and non-A): wave and corpuscle, continuity and discontinuity, separability and nonseparability, local causality and global causality, symmetry and breaking of symmetry, reversibility and irreversibility of time, etc.

For example, equations of quantum physics are submitted to a group of symmetries, but their solutions break these symmetries. Similarly, a group of symmetry is supposed to describe the unification of all known physical interactions but the symmetry must be broken in order to describe the difference between strong, weak, electromagnetic and gravitational interactions.

The intellectual scandal provoked by quantum mechanics consists in the fact that the pairs of contradictories that it generates are actually mutually contradictory when they are analyzed through the interpretative filter of classical logic. This logic is founded on three axioms:

1. The axiom of identity : A is A.

2. The axiom of non-contradiction : A is not non-A.

3. The axiom of the excluded middle : There exists no third term T which is at the same time A and non-A.

According to the hypothesis of the existence of a single level of Reality, the second and third axioms are obviously equivalent. The dogma of a single level of Reality, arbitrary like all dogma, is so embedded in our consciousness that even professional logicians forget to say that these two axioms are in fact distinct and independent from each other.

If one nevertheless accepts this logic which, after all, has ruled for two millennia and continues to dominate thought today (particularly in the political, social, and economic spheres) one immediately arrives at the conclusion that the pairs of contradictories advanced by quantum physics are mutually exclusive, because one cannot affirm the validity of a thing and its opposite at the same time: A and non-A.

Since the definitive formulation of quantum mechanics around 1930 the founders of the new science have been acutely aware of the problem of formulating a new "quantum logic." Subsequent to the work of Birkhoff and van Neumann a veritable flourishing of quantum logics was not long in coming [4]. The aim of these new logics was to resolve the paradoxes which quantum mechanics had created and to attempt, to the extent possible, to arrive at a predictive power stronger than that afforded by classical logic.

Most quantum logics have modified the second axiom of classical logic -- the axiom of non-contradiction -- by introducing non-contradiction with several truth values in place of the binary pair (A, non-A). These multivalent logics, whose status with respect to their predictive power remains controversial, have not taken into account one other possibility: the modification of the third axiom -- the axiom of the excluded middle.

History will credit Stéphane Lupasco with having shown that the logic of the included middle is a true logic, formalizable and formalized, multivalent (with three values: A, non-A, and T) and non-contradictory [5]. Stéphane Lupasco, like Edmund Husserl, belongs to the race of pioneers. His philosophy, which takes quantum physics as its point of departure, has been marginalized by physicists and philosophers. Curiously, on the other hand, it has had a powerful albeit underground influence among psychologists, sociologists, artists, and historians of religions. Perhaps the absence of the notion of "levels of Reality" in his philosophy obscured its substance. Many persons believed that Lupasco's logic violated the principle of non-contradiction -- whence the rather unfortunate name "logic of contradiction" -- and that it entailed the risk of endless semantic glosses. Still more, the visceral fear of introducing the idea of the included middle , with its magical resonances, only helped to increase the distrust of such a logic.

Our understanding of the axiom of the included middle -- there exists a third term T which is at the same time A and non-A -- is completely clarified once the notion of "levels of Reality" is introduced.

In order to obtain a clear image of the meaning of the included middle, we can represent the three terms of the new logic -- A, non-A, and T -- and the dynamics associated with them by a triangle in which one of the vertices is situated at one level of Reality and the two other vertices at another level of Reality. If one remains at a single level of Reality, all manifestation appears as a struggle between two contradictory elements (example: wave A and corpuscle non-A). The third dynamic, that of the T-state, is exercised at another level of Reality, where that which appears to be disunited (wave or corpuscle) is in fact united (quanton), and that which appears contradictory is perceived as non-contradictory.

It is the projection of T on one and the same level of Reality which produces the appearance of mutually exclusive, antagonistic pairs (A and non-A). A single level of Reality can only create antagonistic oppositions. It is inherently self-destructive if it is completely separated from all the other levels of Reality. A third term, let us call it T', which is situated on the same level of Reality as that of the opposites A and non-A, can accomplish their reconciliation.

The entire difference between a triad of the included middle and an Hegelian triad is clarified by consideration of the role of time . In a triad of the included middle the three terms coexist at the same moment in time . On the contrary, each of the three terms of the Hegelian triad succeeds the former in time. This is why the Hegelian triad is incapable of accomplishing the reconciliation of opposites, whereas the triad of the included middle is capable of it. In the logic of the included middle the opposites are rather contradictories : the tension between contradictories builds a unity which includes and goes beyond the sum of the two terms.

One also sees the great dangers of misunderstanding engendered by the common enough confusion made between the axiom of the excluded middle and the axiom of non-contradiction [6]. The logic of the included middle is non-contradictory in the sense that the axiom of non-contradiction is thoroughly respected, a condition which enlarges the notions of "true" and "false" in such a way that the rules of logical implication no longer concerning two terms (A and non-A) but three terms (A, non-A and T), co-existing at the same moment in time. This is a formal logic, just as any other formal logic: its rules are derived by means of a relatively simple mathematical formalism.

One can see why the logic of the included middle is not simply a metaphor like some kind of arbitrary ornament for classical logic, which would permit adventurous incursions and passages into the domain of complexity. The logic of the included middle is perhaps the privileged logic of complexity, privileged in the sense that it allows us to cross the different areas of knowledge in a coherent way, by enabling a new kind of simplicity.

The logic of the included middle does not abolish the logic of the excluded middle: it only constrains its sphere of validity. The logic of the excluded middle is certainly valid for relatively simple situations. On the contrary, the logic of the excluded middle is harmful in complex, transdisciplinary cases.

3. The Gödelian unity of the world

The transdisciplinary approach [7] sets forth for consideration a multi-dimensional Reality, structured by multiple levels replacing the single level of classical thought -- one-dimensional reality. This proposal is not enough, by itself, to justify a new vision of the world. We must first of all answer many questions in the most rigorous possible way. What is the nature of the theory which can describe the passage from one level of Reality to another? Is there truly a coherence, a unity of the totality of levels of Reality? What is the role of the subject-observer of Reality in the dynamics of the possible unity of all the levels of Reality? Is there a level of Reality which is privileged in relation to all other levels? What is the role of reason in the dynamics of the possible unity of knowledge? What is the predictive power of the new model of Reality in the sphere of reflection and action? Finally, is understanding of the present world possible?

According to our model, Reality comprises a certain number of levels [1,2]. The considerations which follow do not depend on whether or not this number is finite or infinite. For the sake of clarity, let us suppose that this number is infinite.

Two adjacent levels are connected by the logic of the included middle in the sense that the T-state present at a certain level is connected to a pair of contradictories (A and non-A) at the immediately adjacent level. The T-state operates the unification of contradictories A and non-A but this unification is operated at a level different from the one on which A and non-A are situated. The axiom of non-contradiction is thereby respected. Does this fact signify that we can obtain a complete theory, which will be able to account for all known and forthcoming results? The answer to this question is not merely theoretically interesting. After all, all ideology and all fanaticism which assert that their aim is to change the face of the world, are founded on a belief in the completeness of their approach. The ideologies and fanaticisms in question claim to be in possession of the truth, the whole truth.

There is certainly a coherence between different levels of Reality, at least in the natural world. In fact, an immense self-consistency -- a cosmic bootstrap -- seems to govern the evolution of the universe, from the infinitely small to the infinitely large, from the infinitely brief to the infinitely long [1]. For example, one very small variation of the coupling constant of the strong interactions between quantum particles would lead, at the level of the infinitely large -- our universe -- either to the conversion of all hydrogen into helium, or to the non-existence of the complex atoms such as carbon. Or else, a very small variation of the gravitational coupling constant would lead either to ephemeral planets, or to the impossibility of their formation. Still more, according to current cosmological theories, the universe seems capable of self-creating without any external intervention. A flow of information is transmitted in a coherent manner from one level of Reality to another level of Reality in our physical universe.

The logic of the included middle is capable of describing the coherence between the levels of Reality by an iterative process defined by the following stages: 1. A pair of contradictories (A, non-A) situated at a certain level of reality is unified by a T-state situated at a contiguous level of Reality; 2. In turn, this T-state is linked to a couple of contradictories (A', non-A'), situated at its own level; 3. The pair of contradictories (A', non-A') is, in its turn, unified by a T'-state situated at a different level of Reality, immediately contiguous to that where the ternary (A', non-A', T) is found. The iterative process continues indefinitely until all the levels of Reality, known or conceivable, are exhausted.

In other terms, the action of the logic of the included middle on the different levels of Reality induces an open, Gödelian structure of the unity of levels of Reality. This structure has considerable consequences for the theory of knowledge because it implies the impossibility of a complete theory, closed in upon itself.

In effect, in accordance with the axiom of non-contradiction, the T-state realizes the unification of a pair of contradictories (A, non-A) but it is associated, at the same time with another pair of contradictories (A', non-A'). This signifies that starting from a certain number of mutually exclusive pairs one can construct a new theory which eliminates contradictions at a certain level of Reality, but this theory is only temporary because it inevitably leads, under the joint pressure of theory and experience, to the discovery of new levels of contradictories, situated at a new level of Reality. In turn this theory will therefore be replaced by still more unified theories as new levels of Reality are discovered. This process will continue indefinitely without ever resulting in a completely unified theory. The axiom of non-contradiction is increasingly strengthened during this process. In this sense, without ever leading to an absolute non-contradiction, we can speak of an evolution of knowledge which encompasses all the levels of Reality: knowledge which is forever open . In the sphere of levels of Reality per se , that which is above is like that which is below, and that which is below is not like that which is above. Finer matter penetrates coarser matter, just as quantum matter penetrates macrophysical matter, but the reverse is not true. Degrees of materiality induce an orienting arrow for tracing the transmission of information from one level to the other. In this sense, that which is below is not like that which is above ; the words "high" and "low" here having no other signification (spatial or moral) than that which is topologically associated with the flow of transmission of information. In turn, this orienting arrow is associated with the discovery of more and more general, unifying, and encompassing laws.

The open structure of the unity of levels of Reality is in accord with one of the most important scientific results of the 20th century concerning arithmetic, the theorem of Kurt Gödel [8]. Gödel's theorem tells us that a sufficiently rich system of axioms inevitably lead to results which would be either undecidable or contradictory. The implications of Gödel's theorem have considerable importance for all modern theories of knowledge. First of all it does not only concern the field of arithmetic but also all mathematics which includes arithmetic. Now, obviously the mathematics which underlies theoretical physics include arithmetic. This means that all research for a complete physical theory is illusory. If this affirmation is true for the most rigorous fields of the study of natural systems how can one dream of a complete theory in an infinitely more complex sphere -- that of the human sciences?

In fact, the search for an axiomatic system leading to a complete theory (without undecidable or contradictory results) marks at once the apex and the starting point of the decline of classical thought. The axiomatic dream is unraveled by the verdict of the holy of holies of classical thought -- mathematical rigor.

The theorem that Kurt Gödel demonstrated in 1931 sounded only a faint echo beyond a very limited circle of specialists. The difficulty and extreme subtlety of its demonstration explains why this theorem has taken a certain time to be understood within the mathematical community. Today, it has scarcely begun to penetrate the world of physicists. Wolfgang Pauli, one of the founders of quantum mechanics, was one of the first physicists to understand the extreme importance Gödel's theorem has for the construction of physical theories [9].

The Gödelian structure of the unity of levels of Reality associated with the logic of the included middle implies that it is impossible to construct a complete theory for describing the passage from one level to the other and, a fortiori, for describing the unity of levels of Reality.

If it does exist, the unity linking all the levels of Reality must necessarily be an open unity .

To be sure, there is a coherence of the unity of levels of Reality, but we must remember that this coherence is oriented : there is an arrow associated with all transmission of information from one level to the other. As a consequence of this, if coherence is limited only to the levels of Reality, it is stopped at the "highest" level and at the "lowest" level. If we wish to posit the idea of a coherence which continues beyond these two limited levels so that there is an open unity, one must conceive the unity of levels of Reality as a unity which is extended by a zone of non-resistance to our experiences, representations, descriptions, images and mathematical formalizations. Within our model of Reality, this zone of non-resistance corresponds to the "veil" which Bernard d'Espagnat referred to as "the veil of the real" [10]. The "highest" level and the "lowest" level of the unity of levels of Reality are united across a zone of absolute transparence. But these two levels are different; from the point of view of our experiences, representations, descriptions, images, and mathematical formalizations, absolute transparence functions like a veil. In fact, the open unity of the world implies that that which is "below" is the same as that which is "above". The isomorphism between "above" and "below" is established by the zone of non-resistance.

Quite simply, the non-resistance of this zone of absolute transparence is due to the limitations of our bodies and of our sense organs, limitations which apply regardless of the instruments of measure used to extend these sense organs. To claim that there is an infinite human knowledge (which excludes any zone of non-resistance), while simultaneously affirming the limitations of our body and our sense organs, seems to us a feat of linguistic sleight of hand. The zone of non-resistance corresponds to the sacred , that is to say to that which does not submit to any rationalization. Proclamation of the existence of a single level of Reality eliminates the sacred, at the price of the self-destruction of that level.

The unity of levels of Reality and its complementary zone of non-resistance constitutes the transdisciplinary Object.

A new Principle of Relativity [7] emerges from the coexistence between complex plurality and open unity: no one level of Reality constitutes a privileged place from which one is able to understand all the other levels of Reality . A level of Reality is what it is because all the other levels exist at the same time. This Principle of Relativity is what originates a new perspective on religion, politics, art, education, and social life. And when our perspective on the world changes, the world changes. In the transdisciplinary vision, Reality is not only multi-dimensional, it is also multi-referential.

The different levels of Reality are accessible to human knowledge thanks to the existence of different levels of perception , which are in bi-univocal correspondence with levels of Reality. These levels of perception permit an increasingly general, unifying, encompassing vision of Reality, without ever entirely exhausting it.

As in the case of levels of Reality the coherence of levels of perception presupposes a zone of non-resistance to perception.

The unity of levels of perception and its complementary zone of non-resistance constitutes the transdisciplinary Subject .

The two zones of non-resistance of transdisciplinary Object and Subject must be identical in order that the transdisciplinary Subject can communicate with the transdisciplinary Object. A flow of consciousness crossing the different levels of perception in a coherent manner must correspond to the flow of information crossing the different levels of Reality in a coherent manner . The two flows are in a relation of isomorphism thanks to the existence of one and the same zone of non-resistance. Knowledge is neither exterior nor interior: it is at the same time exterior and interior. The study of the universe and the study of the human being sustain one another. The zone of non-resistance plays the role of the secretly included middle which permits the unification of the transdisciplinary Subject and the transdisciplinary Object while preserving their difference.

The role of the explicitly or secretly included middle in the new transdisciplinary model of Reality [7] is not so surprising after all. The words three and trans have the same etymological root: "three" signifies "the transgression of the two, that which goes beyond the two". Transdisciplinarity is the transgression of duality opposing binary pairs: subject/object, subjectivity/objectivity, matter/consciousness, nature/divine, simplicity/complexity, reductionism/holism, diversity/unity. This duality is transgressed by the open unity which encompasses both the universe and the human being.

The transdisciplinary model of Reality has, in particular, some important consequences in the study of complexity. Without its contradictory pole of simplicity, complexity appears as an increasingly enlarging distance between the human being and Reality which introduces a self-destructive alienation of the human being who is plunged into the absurdity of destiny. The infinite simplicity of the transdisciplinary Subject corresponds to the infinite complexity of the transdisciplinary Object, just as the terrifying complexity of a single level of Reality can signify the harmonious simplicity of another level of Reality.

The open unity between the transdisciplinary Object and the transdisciplinary Subject is conveyed by the coherent orientation of the flow of information which traverses the levels of Reality and the flow of consciousness which traverses the levels of perception. This coherent orientation gives a newly deepened meaning to the mere fact of the verticality of the human being in the world . In place of the verticality of the individual human being thanks to the law of universal gravitation, the transdisciplinary vision proposes the conscious and cosmic verticality of the crossing of different levels of Reality. In the transdisciplinary vision, it is this verticality which constitutes the foundation of every viable social project.

4. The death and the resurrection of Nature

Modernity is particularly deadly. It has invented all kinds of "deaths" and "ends": the death of God, the death of Man, the end of ideologies, the end of history. But, there is a death which is spoken of much less, on account of shame or ignorance: the death of Nature. In my view, this death of Nature is the source of all the other deadly concepts which were just invoked. In any case, the very word "Nature" has ended by disappearing from scientific vocabulary. Of course, the "man in the street", just as the scientist (in popularized works) still uses this word, but in a confused, sentimental way, reminiscent of magic. How have we arrived here?

Since the beginning of time we have not stopped modifying our vision of Nature [11]. Historians of science are in accord in saying that, despite all appearances to the contrary contrary, there is not only one vision of Nature across time. What can there be in common between the Nature of so-called "primitive" peoples, the Nature of the Greeks, the Nature in the time of Galileo, of the Marquis de Sade, of Laplace or of Novalis? Nothing, besides the fact of our humanness. The vision of Nature of a given period depends on the imaginary which predominates during that period; in turn, that vision depends on a multiplicity of parameters: the degree of development of science and technology, social organization, art, religion, etc. Once formed, an image of Nature exercises an influence on all areas of knowledge. The passage from one vision to another is not progressive, continuous -- it occurs by means of sharp, radical, discontinuous ruptures. Several contradictory visions can co-exist. The extraordinary diversity of visions of Nature explains why one cannot speak of Nature , but only of a certain nature in accord with the imaginary of a given period.

It is important to emphasize that the idea of a privileged, if not exclusive, relation between Nature and science is a recent prejudice, founded on the scientistic ideology of the 19th century. The historical reality is much more complex. The image of Nature has always had a multiform action: it has influenced not only science but also art, religion, and social life. This allows us to explain some strange synchronicities. Here I limit myself to but a single example: the simultaneous appearance of the theory of the end of history and of unified theories in particle physics at the end of this century. Unified theories in physics have as their aim the elaboration of a complete approach, founded on a unique interaction, which can predict everything (hence the name, "Theory of Everything"). It is quite obvious that if such a theory were formulated in the future, it would signify the end of fundamental physics, because there would be nothing left to look for. It is interesting to observe that both the idea of the end of history and of the end of physics have simultaneously emerged from the "end of the century" imaginary. Is this simply coincidence?

Notwithstanding the abundant and fascinating diversity of images of Nature one can nevertheless distinguish three main stages: Magic Nature, Nature as Machine, and the Death of Nature. Magical thought views nature as a living organism, endowed with intelligence and consciousness. The fundamental postulate of magical thought is that of universal interdependence: Nature cannot be conceived outside of its relations with us. Everything is sign, trace, signature, symbol. Science, in the modern sense of this word, is superfluous.

At the other extreme, the mechanistic thought of the 18th and above all the 19th century (which, by the way, still predominates today) conceives Nature not as an organism, but as a machine. It suffices to disassemble this machine piece by piece in order to possess it entirely. The fundamental postulate of mechanistic thought is that Nature can be known and conquered by scientific methodology, defined in a way which is completely independent of human beings and separate from us. The triumphant vision of "the conquest of Nature" is rooted in the formidable technical and technological efficiency of this postulate.

Certain scientists, artists and philosophers have been profoundly affected by the deadly danger of mechanistic thought. Hence, the antagonistic current of German Naturphilosophie [12], which revolved around the journal Athenaeum . One can cite important names like Schelling, Schlegel, Novalis, Ritter, and Goethe. The work of Jacob Boehme inspired Naturphilosophie [13]. Viewed from the perspective of our time, Naturphilosophie is liable to appear as a grotesque distortion, a crude manipulation of science, like a dead-end street, by virtue of what is considered a ridiculous attempt to return to magical thought and living Nature. But, how can one possibly hide the fact that this Philosophy of Nature generated at least two major scientific discoveries: cellular theory and electromagnetism? I believe that the true fault of Naturphilosophie was that it appeared two centuries too soon, thereby bypassing the threefold quantum, technological, and computer revolution.

The logical outcome of the mechanist vision is the Death of Nature, the disappearance of the concept of Nature from the scientific field. From the very beginning of the mechanistic vision, Nature as Machine, with or without the image of God as watchmaker, is split up into an ensemble of separate parts. From that moment on, there is no more need for a coherent whole, for a living organism, or even, for a machine which still kept the musty odor of finality. Nature is dead, but complexity remains. An astonishing complexity, which penetrates each and every field of knowledge. But this complexity is perceived as an accident; we ourselves are considered to be an accident of complexity -- an altogether joyful vision, which brings us to the world we live in today.

The Death of Nature is incompatible with a coherent interpretation of the results of contemporary science, in spite of the persistence of the neo-reductionistic attitude which accords exclusive importance to the fundamental building-blocks of matter and to the four known physical interactions. According to this neo-reductionist attitude, all recourse to Nature is superfluous and devoid of sense. But regardless of the origin of the resistance implied in such backward attitudes, the time for the resurrection of Nature has come. In truth, Nature is dead only for a certain vision of the world -- the classical vision.

The rigid objectivity of classical thought is only viable in the classical world. The idea of total separation between an observer and a Reality assumed to be completely independent from that observer brings us to the verge of insurmountable paradoxes. In fact, a far more subtle notion of objectivity characterizes the quantum world: objectivity depends on the level of Reality in question.

The empty vacuum of classical physics is replaced by the full vacuum of quantum physics. The smallest region of space is enlivened by astonishing activity, the sign of perpetual movement. The quantum fluctuations of the vacuum determine the sudden appearance of virtual particle/anti-particle pairs which are reciprocally annihilated in the course of extremely short intervals of time. Everything takes place as if the quanta of matter are created from out of nothing. A metaphysician might say that the quantum vacuum is a manifestation of one of the faces of God: God the Nothing . In any case, in the quantum vacuum, all is vibration, everything is a fluctuation between being and non-being. The quantum vacuum is full, full of all potentialities, from the particle to the universe.

By supplying energy to the quantum vacuum we can help it to actualize its potentialities. This is precisely what we do by constructing particle accelerators. It is precisely when certain threshold energies are attained that not virtual but real particles suddenly materialize, are literally drawn from out of nothing. These particles have an artificial character, in the true sense of that word. From our perspective our world, the macrophysical world, appears to be constructed in an extremely economical way: protons, neutrons, and electrons are enough to construct almost the totality of our visible universe. But we succeed in creating by drawing hundreds of other particles from nothingness: hadrons, leptons, and electro-weak bosons.

Space-time itself no longer rests on a fixed concept. Our space-time which proceeds in four dimensions is not the only conceivable space-time. According to certain physical theories, it appears more an approximation, like a part of a space-time all the more rich for being the generator of possible phenomena. Supplementary dimensions are not the result of mere intellectual speculation. On the one hand, these dimensions are necessary to insure the self-consistency of the theory and the elimination of certain undesirable aspects. On the other hand, they do not have a purely formal character -- they have physical consequences for our own scale. For example, according to certain cosmological theories, if the universe had been associated from the "beginning" of the big bang in a multi-dimensional space-time, supplementary dimensions would have remained forever hidden, unobservable; rather, their vestiges would be precisely the known physical interactions. By means of generalizing the example provided by particle physics, it becomes conceivable that certain levels of Reality correspond to a space-time different than that characterizing our own level. Moreover, complexity itself would depend on the nature of space-time as well.

According to present scientific conceptions, matter is far from being identical with substance. In the quantum world, we observe a perpetual energy-substance-information transformation; the concept of energy appears like a unifying concept: information is coded energy, while substance is concretized energy. In contemporary physics, space-time itself does not appear to be like a receptacle into which material objects are plunged: it is a consequence of the presence of matter. Matter is associated with a substance-energy-information-space-time. The degree of quantum materiality is, of course, different from the degree of materiality considered by classical physics.

The nature of complexity changes. It is no longer a complexity directly reducible to simplicity. Different degrees of materiality correspond to different degrees of complexity : extreme complexity can be conceived from the perspective of one level of Reality as simplicity relative to another level of Reality, but exploration of this second level reveals that this simplicity corresponds to extreme complexity relative to its own laws. This structure of degrees of complexity [2] is intimately tied to the Gödelian structure of Nature and of knowledge, which is induced by the existence of different levels of Reality.

The same notion of laws of Nature completely changes its contents when compared with that of the classical vision. This situation can be summed up by three theses formulated by the physicist Walter Thirring [14] :

1. The laws of any inferior level are not completely determined by the laws of a superior level . Thus, notions well anchored in classical physics, like "fundamental" and "accidental," must be re-examined. That which is considered to be fundamental on one level can appear to be accidental on a superior level and that which is considered to be accidental or incomprehensible on a certain level can appear to be fundamental on a superior level.

2. The laws of an inferior level depend more on the circumstances of their emergence than on the laws of a superior level . The laws of a certain level depend essentially on the local configuration to which these laws refer. There is therefore a kind of local autonomy of respective levels of Reality; however, certain internal ambiguities concerning laws of an inferior level of Reality are resolved by taking into account the laws of a superior level. It is the internal consistency of laws which reduces the ambiguity of laws.

3. The hierarchy of laws evolves at the same time as the universe itself . In other words, the birth of laws occurs simultaneously with the evolution of the universe. These laws pre-exist at the "beginning" of the universe as potentialities. It is the evolution of the universe which actualizes these laws and their hierarchy. A transdisciplinary model of Nature must integrate all this new knowledge of the emergent characteristics of the physical universe.

We can distinguish three major aspects of Nature in accordance with the transdisciplinary model of Reality:

(1) Objective Nature , which is connected with the natural properties of the transdisciplinary Object; objective Nature is subject to subjective objectivity. This objectivity is subjective to the extent that the levels of Reality are connected to levels of perception. Nevertheless emphasis here is on objectivity, to the extent to which the methodology employed is that of science.

2) Subjective Nature , which is connected with the natural properties of the transdisciplinary Subject; subjective Nature is subject to objective subjectivity . This subjectivity is objective to the extent that the levels of perception are connected to levels of Reality. Nevertheless, emphasis here is on subjectivity, to the extent to which the methodology is employed is that of the ancient science of being, which crosses all the traditions and religions of the world.

3) Trans-Nature , which is connected with a similarity in Nature -- a veritable communion -- which exists between the transdisciplinary Object and the transdisciplinary Subject. Trans-Nature concerns the domain of the sacred. It cannot be approached without considering the other two aspects of Nature at the same time.

Transdisciplinary Nature has a ternary structure (objective Nature, subjective Nature, trans-Nature), which defines living Nature. This Nature is living because it is there that life is present in all its degrees and because its study demands the integration of lived experience . The three aspects of Nature must be considered simultaneously in terms of their inter-relation and their conjunction within all the phenomena of living Nature. The study of living Nature asks for a new methodology -- transdisciplinary methodology [7] -- which is different from the methodology of modern science and the methodology of the ancient science of being. It is the co-evolution of the human being and of the universe which asks for a new methodology.

An attempt to elaborate a new Philosophy of Nature, a privileged mediator of a dialogue between all the areas of knowledge, is one of the highest priorities of transdisciplinarity.

The definition of Nature which I propose neither signifies a return to magical thought nor a return to mechanistic thought, because it rests on a twofold affirmation: 1) the human being can study Nature by means of science; 2) Nature cannot be conceived except in terms of its relation to the human being.

In fact the term "living Nature" is a pleonasm, because the word "Nature" is intimately linked to that of "birth." The root of the Latin word, natura is nasci and designates the action of giving birth as well as the feminine organs of generation. Living Nature is the matrix of the self-engendering of the human being.

Galileo had a vision of Nature as being like a text written in mathematical language which it suffices to decipher and to read. This vision, which has come down to us over the centuries, has shown itself to be one of enormous efficacy. However, today we know that the situation is far more complex. Nature appears to us more as a pretext: the book of Nature is therefore not be read, but to be written .


*   Translated from French by Karen-Claire Voss ; published in Systems : New Paradigms for the Human Sciences , edited by G. Altmann and W. Koch, de Gruyter Verlag, Berlin - New York, 1998, pp. 385-403.


[1] Basarab Nicolescu, Nous, la particule et le monde , Le Mail, Paris, 1985.

[2] Basarab Nicolescu, Levels of complexity and levels of Reality : Nature as trans-Nature , in Proceedings of the Plenary Session of the Pontifical Academy of Sciences on The emergence of complexity in mathematics, physics, chemistry and biology , edited by Bernard Pullman, Pontificia Academia Scientiarum and Princeton University Press, USA, 1996.

[3] Edmund Husserl, Méditations cartésiennes , translated form German by Gabrielle Peiffer and Emmanuel Levinas, Vrin, Paris, 1966.

[4] T.A. Brody, On Quantum Logic , in Foundation of Physics , vol. 14, n° 5, 1984, pp. 409-430.

[5] Stéphane Lupasco, Le principe d'antagonisme et la logique de l'énergie , Le Rocher, Paris, 1987 (2nd edition), foreword by Basarab Nicolescu.

[6] As, for example, by Umberto Eco in Les limites de l'interprétation, translated from Italian by Myriem Bouzaher, Grasset, Paris, 1992, in particular in chapter IV.6.

[7] Basarab Nicolescu, La transdisciplinarité , manifeste, Le Rocher, Paris, coll. "Transdisciplinarité", 1996.

[8] See, for example, Ernest Nagel and James R. Newman, Gödel's Proof , New York University Press, New York, 1958.

[9] K.V. Laurikainen, Beyond the Atom - The Philosophical Thought of Wolfgang Pauli , Springer - Verlag, Berlin - Heidelberg, 1988.

[10] Bernard d'Espagnat, Le réel voilé - Analyse des concepts quantiques , Fayard, Paris, 1994.

[11] Robert Lenoble, Histoire de l'idée de Nature , Albin Michel, Paris, coll. "L'évolution de l'humanité", 1990.

[12] Georges Gusdorf, Le savoir romantique de la Nature , Payot, Paris, 1985;

Ph. Lacoue - Labarthe et J.L. Nancy, L'absolu littéraire - Théorie de la littérature du romantisme allemand , Seuil, Paris, 1978;

Pierre Thuillier, De la philosophie à l'électromagnétisme : le cas Oersted , La Recherche, Paris, n° 215, mars 1990, pp. 344-351;

Antoine Faivre, Philosophie de la Nature , Albin Michel, 1996.

[13] Basarab Nicolescu, Science, meaning and evolution - The cosmology of Jakob Boehme , Parabola Books, New York, 1991, foreword by Joscelyn Godwin.

[14] Walter Thirring, Do the laws of Nature evolve ? , in Proceedings of the Study Week of the Pontificia Academia Scientiarum on Understanding Reality : the Role of Culture and Science , 1991.

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Bulletin Interactif du Centre International de Recherches et Études transdisciplinaires n° 12 - Février 1998

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