This essay presents some thoughts on an ontology of cybernetics. There is a very simple translation of the term "ontology". It is the theory of What There Is (Quine). But if this is the case, one rightly expects the discipline to represent a set of statements about "everything". This is just another way of saying that ontology provides us with such general and basic concepts that all aspects of Being or Reality are covered. Consequently all scientific disciplines find their guiding principles and operational maxims grounded in ontology and legitimized by it. Ontology decides whether our logical systems are empty plays with symbols or formal descriptions of what "really" is.

The following investigation arrives at the result that our present (classic) ontology does not cover "everything". It excludes certain phenomena of Being from scientific investigation declaring them to be of irrational or metaphysical nature. The ontologic situation of cybernetics, however, is characterized by the fact that the very aspect of Being that the ontologic tradition excludes from scientific treatment is the thematic core and center of this new discipline. Since it is impossible to deny the existence of novel methods and positive results produced by cybernetic research, we have no choice but to develop a new system of ontology together with a corresponding theory of logic The logical methods that are used faute de mieux in cybernetics belong to the old ontological tradition and are not powerful enough to analyze the fresh aspects of Reality that are beginning to emerge from a theory of automata.

The first section of this essay deals with classic ontology. The second is devoted to some perspectives of a trans-classic ontology. Sections three and four try to develop a new theory of logic capable of meeting the demands of cybernetics better than the two- or many-valued systems currently in use. In the first two sections the philosophical view-point dominates. In the last two, technical problems of logic are accentuated.

The author strongly suspects that a majority of readers will hold the opinion that it would have been amply sufficient to restrict the investigation to Section 3 and 4 and to forget about the ontologic prelude of Section 1 and 2. The consensus that basic "metaphysical" reflections about logic have little or no practical value at all is widely spread. There is even some justification for this belief and it may be safely said that, as far as our two-valued traditional logic is concerned, the cyberneticist will gain nothing by submitting his logical procedures to a renewed scrutiny of its fundamental presuppositions. This logic is in its basic features now more than two thousand years old. A long historical process has worked its ontology into the very marrow of our bones, so to speak. We use this ontology with reasonable precision without being in the least aware of doing so.

There seems to be no reason why this happy and comfortable state should not continue. Einstein's widely quoted exclamation: "Der liebe Gott spielt nicht mit Würfeln"+2) is a poignant expression of the deep-seated belief in classic ontology. And everything might be very well, indeed, except for the advent of transclassic calculi which demanded an ontologic interpretation. From then on, the logician was faced with an alternative. He could either try to interpret his new procedures in terms of the Aristotelian ontology or he could assume that a many-valued system is incompatible with the classic foundations of logic. This second part of the alternative involves, of course, a much greater risk. So it is understandable that Jan Lukasiewicz looked for ontological support in Aristotle's Organon when he introduced a third value into logic. It is important to know that he succeeded to a certain degree and that he was able to find a philosophic interpretation for a calculus with three values, and for another one with a denumerably infinite number of values. This happened between 1920 and 1930. It is quite significant, however, that after about ten years of research he was forced to admit that he could not find any ontologic significance for calculi between three and an infinite number of values. Since then hardly any progress has been made in this direction. Four- five- and other finite n-value systems have been used with practical applications but without any genuine insight into their basic ontologic significance. C. I. Lewis's sceptical statement with regard to many-valued systems, that "the attempt to include all modes of classification, and all resultant principles would produce, not a canon, but chaos" still stands unchallenged [31a]. For the first time the unity of logic is endangered! To preserve it, competent logicians have suggested that formal logic should be restricted to two values.

We are going to show that this suggestion is untenable. But so is the assumption that many-valued theories should be restricted to interpretation in terms of classic ontology. There is no doubt that this can be done within certain narrow limits and valuable results have been obtained with such procedures. Jack D. Cowan´s Many-valued Logics and Reliable Automata is a recent and notable example of this method[41b]. We should be very clear about the fact that the interpretation of many-valued systems on the basis of Aristotelian ontology is by no means "false". It is quite legitimate. In fact a vigorous continuation along this line is absolutely necessary.

However, there is another aspect to the question of the relation between a formal logic and its ontology. Is it possible to exploit the immense capacities of many-valued systems if we use them only to analyze what the classic tradition calls Reality ? This author confesses that the present use of many-valued logic reminds him of a man who might spend a fortune on a Ferrari racer in order that his wife should have transportation to the super-market.

An ontologic analysis of many-valued structures shows that only a tiny, almost infinitesimal, part of them concides with the concept of Being or Reality that we have inherited from the Greeks. If we intend to use the full range of logical possibilities now available to us but still cling to ancient ontological concepts, the result will indeed not be a canon but logical chaos. The basic conceptual foundations with which a logic meets Reality are established as far as two-valued theories are concerned. But with regard to many-valuedness we have not even started to lay the proper foundation. An ontology is nothing but a very general prescription of how to use a logic in an existing world. It tells us how much of this world is approachable by exact scientific procedures. It is the aim of this essay to show which specific data of Reality that the classic ontology judged to be "irrational" or "transcendent" are within the grip of cybernetics if a certain type of many-valued logic is applied. For this very reason we claim that a careful analysis of the ontologic foundation of cybernetics is an eminently practical undertaking. The cyberneticist may find it useful to learn about a new way to interpret transclassic systems of logic. He should therefore not begrudge us the time and the effort to get acquainted with the contents of Sections 1 and 2.

This is a first attempt to outline an ontology for cybernetic logic. The author is aware of its considerable shortcomings. Among other things it is too abbreviated. But time was short and did not permit a more detailed analysis. The author hopes to make up for it in the second volume of his Idee und Grundriss einer nicht-Aristotelischen Logik which is in preparation.

The present essay deals only with one phenomenon, which will be called subjective self-reflection. Some of its elementary features are already recognizable in very primitive, inanimate systems. Nevertheless we shall focus our attention on its highest and richest representation, the self-awareness of Man. It may seem more reasonable to start with the simple manifestations of self-reflection in elementary models of self-organizing systems. Alas, this is not possible for a formal logic which claims general ontological validity for all structures of self-reflection. What will be valid for the self-awareness of man will also be valid for systems of lower reflective organization. But not vice versa. It is not possible to develop a new ontological theory of logic by starting at the bottom. Aristotle did not do so. The general principles of his theory of thinking which stood us in good stead till the advent of cybernetics were developed at the very outset of the evolution of Western science. Aristotle started with an answer to the primordial question: what is, "logically speaking", objective Being? We try to follow a great example if we pose and try to answer the question: what is "logically speaking" subjective self-awareness?


Philosophy has played a negligible part in the development of modern science since the times of Newton and Leibniz. The reasons are rather obvious and have frequently been stated. Descartes, Pascal, and Leibniz created the mathematics of their period out of the spirit of metaphysical problems. And Newton´s great work Philosophiae Naturalis Principia Mathematica not only carried the word philosophy in its title, but fully deserved this label because the transcendental problem of the relation between motion and time played a decisive part in the development of his theory of "fluxions". But then the ways of philosophy and exact science (including mathematics) begin to part. Kant´s philosophical speculations about the mutual relations of space and geometry on the one hand, and time and arithmetic on the other were actually refuted by Euler and d´Alembert even before they were stated in the Critique of Pure Reason[51]. For Hegel the mathematical type of thinking had nothing to do with philosophy. And Schopenhauer´s ideas about the exact sciences of his time show a complete lack of understanding of the very essence of mathematical or experimental reasoning. Since then the regrettable alienation between philosophy and science has progressed even further. What might be the most profound metaphysical investigation of our own time, the ontological thought analysis by Martin Heidegger, remains intrinsically incomprehensible to the exact scientist or mathematician. It is not the fault of either side. This alienation has unfortunately provoked indifference, contempt, or even outspoken enmity against philosophy in the scientific camp. Perhaps the strongest and most radical expression of the present discord between philosophy and science is represented by the following statement of a well known thinker in the scientific camp: "Es gibt keine Philosophie als Theorie, als System eigener Sätze neben denen der Wissenschaft". (There is no philosophy as theory, as a system of statements sui generis apart from those of science.[62]

It seems a rather hopeless task under the circumstances to recommend some philosophical considerations from the field of ontology to the present-day scientist. Yet the attempt has to be made; the radical developments that have taken place within Science during the last decades, have made us suspect that certain fundamental philosophical concepts and presuppositions on which all our scientific efforts are (more or less unconsciously) based are in dire need of a thorough reexamination. The recent arrival of the youngest member of the scientific family, cybernetics, has made this suspicion almost a certainty[73]. Moreover, there is a special reason why the ontologist is interested in this situation. Formal (symbolic) logic, which has so often served as the arbiter in scientific controversies, is at present unable to help: its explosive expansion since about the middle of the last century has made the security of its own foundations dubious. Today it is still impossible to evaluate the effects which such discoveries as those that have come to us from Kurt Gödel and others will have on the future development of this discipline. The ontological basis of logic itself is in question, proof of it is the impossibility of resolving the claims of Intuitionism against Formalism and Platonism at this juncture[84].

There is no escape! When the formal logical foundations of science and mathematics become doubtful, the issue automatically reverts back to the ontological sector of philosophy. But even now the ontologist hardly dares offer his services: he knows only too well how unwelcome his reflections are, even under the present mental tribulations. The shout of logical positivism that the metaphysician is a fictioneer still reverberates loudly in the Hall of Science. But lately events have taken an ironic twist. The scientists themselves have invaded ontology. W.Heisenberg did so some time ago with a very valuable essay Kausalgesetz und Quantenmechanik[95]. E. Schrödinger gave in his Tarner Lectures[106] a very competent exposition of the ontologic relations between consciousness and world. As far as cybernetics is concerned one has only to mention W. S. McCulloch, whose articles offer us quite concentrated doses of metaphysics[117] and Norbert Wiener´s essay on Newtonian and Bergsonian Time [128] which in our opinion refutes certain basic aspects of traditional metaphysics.

Since cybernetics is much younger than quantum mechanics and, ontologically speaking, less developed, the new ontological situation naturally is delineated most sharply in the statements of Heisenberg and Schrödinger. In the above-mentioned essay Heisenberg offers the following reflections: Kant introduces in his Critique of Pure Reason the law of causality as an a priori principle by demonstrating that without this principle we could never form the concept of an objective world that exists independently of the subjective thought-processes that take place within our consciousness. Kant poses precisely this question: what "mechanism" in our mind enables us to distinguish between a sequence of events that occurs exclusively in our psyche - for instance a sequence in a dream - and a sequence that takes place in the external world independent of our observation? It is evident, so the Critique of Pure Reason points out, that we need a formal criterion to make the desired distinction; for we are aware of objective reality, as well as of our dreams and fantasies, only as content of our consciousness[139]. Nevertheless, we obstinately believe that some of these impressions have their origin in a world outside the mind and others have not. The source of this conviction, Kant declares, is the category of causality, which makes us look at a specific series of impressions as a rigid temporal succession that our mind is powerless to alter or stop. And what our consciousness cannot modify and control must necessarily have an existence outside and independent of it. The law of causality appears thus as a criterion to distinguish between subject and object, between consciousness and world. If we look at our impressions without interpreting them as causally linked to each other, they can be understood only as "a play of imaginations with no reference to an object"[1410].

Heisenberg quotes the relevant passage (where Kant demonstrates that causality is our mental mechanism for the distinction between Subjectivity and external Reality) and admits that, if we use this interpretation, we have obtained a genuine a priori principle[1511]. As such it is, of course, irrefutable - for the very simple reason that this a priori principle does not make the slightest assumption about the factual contents of the external Reality. It only states that if we want to think of a Reality that exists independently of the subject who is aware of it, we cannot do so without using the category of causality. To put it differently: if we want to establish an absolutely objective natural science which completely describes Reality without reference to the subjective origins of our scientific terms and concepts then everything must be understood in terms of causality. Laplace´s famous Spirit would face in his differential equations a world devoid of any subjectivity whatsoever. This relation between subject and object depicts the classic ideal of scientific knowledge.

This ideal, however, Heisenberg points out, cannot be pursued since the advent of quantum mechanics. A radically objective system of physics, with a dichotomy of Reality into "thing" and "thought" is now impossible: "the radically isolated object has, on principle, no describable properties"[1612].

If Heisenberg´s claim remains valid, and there is overwhelming evidence that it will, an entirely new type of logic must be developed. However, the term New Logic has been grossly misused since the Cartesian Johannes Clauberg (1622-1665) first spoke of Logica Vetus et Nova [1713] ; it will therefore be necessary to state what should be understood if such an expression is used. A system of logic is a formalization of an ontology [1814]! If there seems to be a need for a new logic a new concept of ontology must be formed and vice versa In the present situation, outstanding representatives of the physical sciences express viewpoints which are de facto statements from a new ontology. A new concept of logic is consequently called for. But since such a new concept can only be developed in contrast to our classic tradition and theory of thought, it will be useful to offer a brief sketch of the reciprocity of traditional logic and ontology.

The correspondence theory of logical and ontological structures dates back at least to the dialogues of Plato, the Aristotelian Organon, and the logic of the Stoics. During this epoch the question was raised (and answered): what are the formal and ontological requisites for making verifiable and generally valid statements about the objective world ? It was found that such statements are possible only if we assume that the laws of Nature (Being) and the laws of Thought are essentially identical but differ in their formal aspects. This formal difference between a mathematical law in physics and the corresponding law in logic is due to the fact that, in the first case a description of the external world is intended, while in the second case the mirror image of this world, as it is repeated in our thought processes, is the motive and semantic theme of our representation.

Thus the set of natural laws (objectivity) and the inverse set of the rules and structures of logic together form an enantiomorphic system of rationality. The two subsets of this system constitute a symmetrical exchange relation which is as simple as our familiar distinction between left and right. This exchange relation is defined by our traditional operator of two-valued negation. Any datum of experience is either positive or negative, objective or subjective, and no third term (tertium non datur) is allowed. The disjunction is exclusive and total. The classic tradition, in a time-honored expression, speaks of the metaphysical identity of Thought and Being. In the realm of the ultimate, absolute Reality, Thought and Being are the same. They can be distinguished only on a relative empirical level where they appear as opposites. But our ontologic tradition insists that even in this opposition they express the same meaning and represent only two different aspects of the same "subject-matter" as our language profoundly says. However, it should never be forgotten that these two empirical aspects of Reality constitute a strict exchange relation of two sets or subsystems of a universal enantiomorphic structure which is, as such, indifferent to the distinction between subject and object (Cusanus´ coincidentia oppositorum).

However, this system of classic (two-valued) ontology, successful as it has proved for the development of Western science, suffers from an enormous drawback. The symmetrical exchange relation and the resulting ontological equivalence of subject and object governs only the mutual relations between the two subsets as inverse totalities. It is not applicable to any individual member of either set. In other words, the context of terms that describe the structure of our external objective world permits not the slightest penetration by concepts that refer to the epistemologic subject of cognizance that comprehends and is aware of objects. We may either discourse about objective reality (i.e. nature) in ontological terms or we may refer to the perceiving subject in logo-logical concepts, but we are absolutely not permitted to mix the two. If we ignore this prohibition we invariably get lost in a jungle of contradictions and paradoxes. The very fact that we nowadays possess an accurate science and base on it a vast technology is due to an ontologic tradition which was reasonably strict in adhering to the principle of dichotomy between matter and form and between subject and object.

The two-valued character of our logical tradition from the time of the Greeks up to the present day[1915] testifies to the fact that our logic is a faithful attempt to formalize the ontology of the ultimate parity of form and matter, or subject and object as it was expressed in the ancient maxim of the metaphysical identity of Thought and Being. As long as our logical endeavors are orientated to this ontology we have no right to speak of a new logic, despite the enormous amount of detail that has been added to the older system in the course of the past century. But our logic still insists that it is meaningful to conceive the idea of a thought-object being fully identical with itself and therefore capable of isolation. The assumed metaphysical parity of Thought and Being permits a consistent system of formalization (logic) only if we regard these two primordial components of Reality as a symmetrical exchange relation. But such a relation isolates the two components completely from each other. Mind and Matter belong to different metaphysical dimensions; they do not mix. There is no such division between the energetic and the material state of the Universe. The Einstein equation E = mc2 states that energy may be converted into mass and vice versa. But there is no analogous formula for the conversion of thought into matter or meaning into energy. We know as an empirical fact that our brain is a physical system where certain largely unknown - but physical - events take place. These represent to the observer a combination of electrical and chemical data[2016] producing a mysterious phenomenon which we might call meaning, consciousness, or self-awareness. In view of this fact we must either retreat into theology and speak of a supernatural soul which only resides in this body as a guest, or assume that matter, energy and mind are elements of a transitive relation. In other words there should be a conversion formula which holds between energy and mind, and which is a strict analogy to the Einstein equation. From the view-point of our classic, two-valued logic (with its rigid dichotomy between subjectivity and objective events) the search for such a formula would seem hardly less than insanity. The common denominator between Mind and Matter is metaphysical and not physical according to a spiritual tradition of mankind that dates back several millenia. The very structure of our logic implies this metaphysical belief.

But if Heisenberg´s statements about the mathematical inseparability of subject and object in a quantum-mechanical description of the physical world are correct, then it becomes impossible to subscribe further to our traditional ontology and its consequences in formal logic. However, the mental step implied is enormous, and should not be taken on the testimony of a single witness no matter how great his scientific reputation. We shall, therefore, turn our attention to Erwin Schrödinger´s more elaborate discussion of the problem.

In the main, Schrödinger´s ideas take the same epistemological trend as those of Heisenberg. He discusses in detail the principle of objectivation which interprets objects as ontologically isolated identities. This has led to great successes. But the price we have paid for it is indicated by the fact that "we have not yet succeeded in elaborating a fairly understandable outlook on the world without retiring, our own mind, the producer of the world picture, from it º"[2117]. The principle of radical objectivation was undoubtedly necessary for the past period of scientific research and it will remain so for certain borderline cases.

However, since the advent of quantum mechanics in physics, of meta-theory in logic and mathematics, and, last but not least, since the emergence of cybernetics the scientific situation has changed so radically that a new appraisal of this principle is overdue. Schrödinger draws our attention to the fact that as long as our thinking objectivates without hindrance and inhibitions it "º has cut itself off from all adequate understanding of the subject of Cognizance, of the mind"[2218]. And he continues: "But I do believe that this is precisely the point where our present way of thinking does need to be amended º That will not be easy, we must beware of blunders º We do not wish to lose the logi-cal precision that our scientific thought has reached º"[18]. This is not a passing thought in the Tarner Lectures. On another page we find a similar statement where Schrödinger again admonishes us to give up "º the time-hallowed discrim-ination between subject and object. Though we have to accept it in everyday life for ´practical reference´ we ought, so I believe, to abandon it in philosophical thought"[2319].

Unfortunately, that seems to be easier said than done. Schrödinger himself draws our attention to a very peculiar relation between subject and object when he remarks: "the reason why our sentient, percipient, and thinking ego is met nowhere within our world picture can easily be indicated in seven words: because it is itself that world picture. It is identical with the whole and therefore cannot be contained in it as a part of it"[2420]. Yet common sense and daily experience tell us that our thinking ego is a content of this world which science describes as an utterly subjectless context of existence. The Tarner Lectures call this an "antinomy" and refer to it with the following remarks: "The thing that bewilders us is the curious double role that the conscious mind acquires. On the one hand it is the stage, and the only stage on which this whole world-process takes place, or the vessel and container that contains it all and outside which there is nothing. On the other hand we gather the impression, maybe the deceptive impression, that within this world-bustle the conscious mind is tied up with certain very peculiar organs (brains) º On the one hand, mind is the artist who has produced the whole; in the accomplished work, however, it is but an insignificant accessory that might be absent without detracting from the total effect"[2521].

If Schrödinger states that the phenomenon of consciousness or self-awareness has no legitimate place in our world picture because it is itself this very picture, he says in effect, that to be a subject means to be a mirror for an object. But since no subjects are to be found in this world this mirror must be an object too. The conclusion is unavoidable that if we use the term "subject" we actually mean a special class of objects which have the mysterious quality that they can reflect any other object in such a way that not only the object but the process of reflection is mirrored. Fichte significantly called the subject (ego) an "image of an image" and in another context "the image of a capacity" (to have images)[2622]. So there is nothing but objects and "images". And insofar as a subject "exists" it does so only as an object. Qua subject it simply isn´t there. In fact it is nowhere. No wonder classic ontology delivered a startling dictum through the person of William James who published, in 1904, an essay: "Does Consciousness Exist"?[2723] He first notes that Kant in the Critique of Pure Reason weakened the philosophic concept of "soul". He replaced it with his concept of the transcendental ego which in its turn attenuated itself to the "thoroughly ghostly condition" of a Bewusstsein-überhaupt (general consciousness) "of which in itself absolutely nothing can be said[2824]. James´ careful analysis finally leads to the assertion that consciousness does not exist! "That entity is fictitious, while thoughts in the concrete are fully real. But thoughts in the concrete are made of the same stuff as things are"[2925].

This conclusion may sound somewhat melodramatic, but it does not come as a surprise to the student of the history of Western science. He knows that all scientific endeavors of the past are based on the ontological proposition that every law that contributes to a verifiable description of Reality must be resolvable into statements about objects and objective events, because the terms that our cognitive mind forms as categories of mental comprehension are at the same time ontic properties of things and their modes of physical existence[3026]. This "metaphysical" identity of Thought and Being is, according to Aristotle, the fundamental prerequisite of any science that deserves the name. And we cannot deny that the faithful adherence to this ancient tradition has stood us in good stead.

However, this basic epistemologic attitude, which still dominates our thinking, entails, a fatal weakness. All our scientific terms - as they are developed on this Aristotelian ontological basis - retain a semantic ambiguity. They can, in their entirety, either be taken as a description of the Universe as the absolute Object or as the absolute Subject. In other words: there is nothing in our present theories of thinking to enable us to distinguish logically between a genuine object like a stone and a subject or center of consciousness that appears to us to be a pseudo-object if we locate it in the body of all animal or human and call it all ego. This is the relevant meaning in Schrödinger´s remark that the mysterious entity we are accustomed to call a subject is nothing but our world picture taken as a totality.

It is interesting to note that it has occurred to neither Heisenberg nor Schrödinger that this situation makes their suggested inclusion of subjectivity into our scientific world picture quite impossible. Our classic system of (two-valued) concepts represents an enantiomorphic structure of rationality where the object exhaustively mirrors the subject and vice versa. This system offers two and only two ways to provide us with an ontological description of the relation between subject and object. This relation may either be interpreted as a conjunction or as a disjunction. But these two interpretations are inextricably compounded. If we consider the relation between subject and object with regard to the totality of the world and define it as conjunctive, then both form a disjunction relative to any arbitrarily chosen part of the world. But if we take the opposite view and presume that their ultimate ontological relation is disjunctive, then their relation inside the world must necessarily be conjunctive. This is the law of duality of two-valued logic stated by the two DeMorgan expressions:
p q ½ ~(~p ~q)
p q ½ ~(~p ~q)

Since it does not matter from which angle we look at the situation we shall take our orientation in the following arguments mostly from the conjunctive viewpoint.

If we assume that subject and object are the inverse unit elements of an enantiomorph system, then it is possible to make empirically conjunctive statements about subjects and objects in a context where all terms are uniformly designated. We do that in our discourse daily and think nothing of it. But, of course, everything we say about subjects is expressed in terms that designate objects. We cannot help it because there are no other terms available owing to the collaboration between the principle of objectivation and two-valued logic. We are so accustomed to this epistomological deficiency in our language that we make automatically and unconsciously the necessary allowances when we receive information of this sort. If somebody told his friend to pick up his wife at the steps of the Lincoln Memorial and he reported afterwards: I could not pick "her" up because I located only her body standing on the steps, that would be considered a very stupid joke. However, in a strict ontological sense the friend would have been right. Subjectivity cannot be located in this manner. And what could have been picked up was merely an "it", not a "she".

But if Reality is actually the conjunction of the inverse components of subject and object, and we insist on a precise scientific language which does not permit the liberties of everyday speech, we arrive by logical necessity at a duality of interpretations for our system of objective terms. H. Reichen-bach has drawn our attention to the fact that this is what has actually happened in quantum mechanics. The Schrödinger wave equation guarantees logically a "strict duality of wave and cor-puscle interpretation for free particles"[3127]. This is the only way to obtain an "exhaustive" description of Reality in purely objective terms. The contraposition of subject and object is transposed into Bohr´s rule of complementarity. The two quantum mechanical concepts of corpuscle and wave still designate objective reality. But the degree of objectivation that is repre-sented by them is much lower than for corresponding terms of classic physics. What dilutes their ontological significance is their complementary contraposition[3228]. The degree of objec-tivity that was formerly represented by a single concept is now distributed over two. This property of distribution is the dis-guise under which the subjective component of our quantum- mechanical terms conceals itself.

Since we will later demonstrate that this element of distribution is the general logical criterion for determining whether a given theoretical system contains smaller or larger traces of subjectivity in its terms, it may be useful to explain a little further how it shows up in Bohr´s rule of complementarity. The so-called Copenhagen Interpretation of quantum theory starts from the fact that any experiment in physics must be described by using the two-valued classic terms of physical science. These terms cannot be replaced as an epistemological basis of our thinking because our consciousness assumes a two-valued structure whenever it contacts objective facts. Our classic theories of nature use these terms exclusively because they strive for that scientific "idealization in which we can speak about parts of the world without reference to ourselves"[3329]. Quantum mechanics on the other hand maintains that this radical dichotomy between subject and object is a purely formal concept. Subject and object constitute a clear-cut division of Reality only as long as we conceive the objective world as a self-contained totality and put it as such in contrast to subjectivity in general. But as soon as we want to observe part of the world the symmetrical character of our formal system of logic is affected and special provisions have to be taken to preserve it.

Heisenberg has described the epistemological imbalance of terms in quantum mechanics by making the statement that modern physics "starts from the division of the world into the ´object´ and the rest of the world". But dichotomy implies "already a reference to ourselves and insofar our description (of the world) is not completely objective"[3430]. It is important that we are fully aware of the ontologic consequences of this statement. If the dichotomy radically separates object and subject so that the first represents all of the world and the second only our description of it, then this description would be completely objective. Our set of descriptive terms and the corresponding set of objective properties of the external world would represent a structural equivalence and not an implicative relation. There would be no Reflexionsgefälle (gradient of reflection) between the subject and the object. But the division which Heisenberg proclaims is not such a simple one. He places the object on one side and the "rest of the world" on the other. But the rest of the world means a conjunction of object and subject! This is exactly his point.

But if we accept this second dichotomy, and there is no reason why we should not, we will have to remember that in any description of objective Reality the two terms "object" and "subject" are inversely equivalent. This means: Heisenberg´s dichotomy is only acceptable if it is supplemented by a corresponding dimension which separates the subject from "the rest of the world". In this way we arrive at three ontologic dichotomies as the following table demonstrates:
object (OO)
subject (SS)
object (OO)
object (OO) < subject (SO)
object (OS) < subject (SS)
subject (SS)

The indices refer to the "als" (as if) category of transcendental logic. Something is thought of as having reference only to itself or as referring to something else. The distinction corresponds roughly to that of world in itself (an sich) and "world" as content of our awareness, and to that of consciousness as inner subjective awareness and consciousness as objective event in the external world. Heisenberg´s dichotomy implies that distinction, but it seems that he is not aware of what his "rest of the world" means. The division above the horizontal line refers to the "absolute" dichotomy of the classic tradition of logic which believed in the ideal of a radically objective description of Reality. The Copenhagen interpretation of quantum mechanics is represented directly below and further down its necessary corollary. If we represent the possible formal relations between O and S in symbolic form we obtain

OO ½ SS ( 1 )
OO ... ( OS < SS ) ( 2 )
( OO SO ) Ã SS ( 3 )

Formula (1) is always true if OO and SS have the same value and it is always false if their values differ. Formula (2) is invalid if and only if OS is true and the conjunction of OS and SS does not hold. In Formula (3) this situation is reversed. This time the implication is not valid if SS is true and again the conjunction does not hold. It is obvious that if Formula (1) holds then Formula (2) cannot stand alone. It must be complemented by Formula (3). Otherwise the value symmetry which the Copenhagen Interpretation expressly demands is destroyed. It is significant that a two-valued calculus of logic (as applied in quantum mechanics) cannot assign different values to SS and SO or to OO and OS. In other words: although the Copenhagen Interpretation acknowledges epistemological differences between SS and SO or between OO and OS, from the view-point of a formal classic calculus the indices are redundant.

This co-validity of the Formulas (2) and (3) points at two distinct phenomena of distribution of terms in quantum mechanics. There must be one type of distribution concerning the OO-range describing the object) and another one in the SS-range (developing the logical theory). We have already taken notice of Bohr´s rule of complementarity in this context and observed that the duality of corpuscle and wave indicates a distribution of subjectivity over two sets of objective terms. The second feature of distributivity shall be mentioned three paragraphs below. Whatever the epistemologic frame of a scientific discipline, the thinking that is done in it is nothing else but the mapping of a set of conceptual terms onto a field of objective data. The simplest case is represented by Formula (1). Here the set of S-terms corresponds one-to-one with the set of O-terms. But in order to give this two-valued system ontological significance either "S" or "O" must be declared as designated value. If we choose "O" we are entitled to state that our formulas provide us with an abstract picture of the objective world. But the subject as the onlooker, who has this image, remains an unknown x because "S" was not the designated value. In other words, the procedure of designation implies that the ontological character of either "S" or "O" must remain unknown. If "O" is the designated value, then we assume a mysterious "soul" that perceives a real world and knows about it in genuine objective terms. If, however, the designation favors "S" as for instance Fichte´s and Hegel´s logic does, then the resulting philosophy seems to know all about the subject but the genuine object, the thing-in-itself, disappears. Kant still admits its existence in the Critique of Pure Reason but emphasizes that we will never know anything about it. His successors Fichte and Hegel are not even satisfied with that. They demonstrate rather convincingly that the very concept of an isolated object-in-itself is a logical contradiction. That means we cannot even make meaningful statements which assert the radical objective existence of such things.

We have gone in such detail about this ontological issue because it is of overriding importance to understand why a two-valued theory of thought can never describe an order of Reality in which subject qua subject and object qua object co-exist. A logic in the usual sense of the word cannot be applied at all unless we designate a value. But as soon as we have done this we are committed. We cannot have it both ways. If we use our logic to describe the object, then the context of our terms is never applicable to the subject. But if our theory aims at describing the relations between our mental (subjective) concepts, then we do not obtain a picture of the objective world, only of its reflected image, with typical properties of reflection that the objects do not possess.
<div style="color: #00