Circlemath and Philosophy

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The Hegelian Dialectic

Immanuel Kant, Professor of Logic at the University of Konigsberg in the late 18th century, observed that no change had overtaken the teaching of logic since its inauguration by Aristotle some 2000 years earlier. His own work then began a sea change in philosophy that was to sweep through all subjects and the whole of knowledge. He did not manage, however, to consummate his vision, and it fell to Hegel to complete it in his dialectic, the motor we might say, of the ‘Kant to Hegel’ absolute philosophy in the 18th century.

 

We can now identify this dialectic, which has confounded so many scholars, as the mechanism at work in the EEG (electroencephalogram) trace of the brain, the wave or pulse that drives our conscious thinking. This identification, that the brain's electrical activity ‘drives’ the dialectic; conversely, that the dialectic lends recordable form to the brain's activity, is new. To pass judgement upon it requires an intimate knowledge of the Hegelian dialectic and neurology. It is not, therefore, something I would raise, were it not for the fact that in both its presentation and rebuttal, if this is to be the case, advantage will accrue to both subjects. The moment we give the dialectic an object, a locus and physical presence in our experience, it steadies in our appreciation.

 

For Hegel, the object of philosophy is the absolute or God. Shorn of all embellishment this is reality without qualification, which can be approached only negatively as that which is, and is as a whole, not finite, not a part. The medium of philosophy, that in which thought moves, Baillie calls a notion:

 

This has certain characteristics, negative and positive. Negatively, it is not derived from nor dependent on sensation or perception, and hence is not a mere general concept. It is not a purely formal “abstract” universal, and hence a notion has no rigid fixity of outline, empty of all specific content and applicable to any, and does not exclude all relationships with other notions. Positively characterized, a notion operates freely and independently within itself and under its own conditions. It is the ultimate principle controlling and penetrating all thought wherever it appears, whether in sensation, perception or abstract reflexion. It is universal, but is a concrete universal, that is, holds within itself the particular and is the organic unity of universality and particularity. It is a single identity in and through difference. And each notion directly refers to and connects itself intimately with other notions, so as to form an organically articulated system, a self-contained structure of notions.  Phen 22, Translator's Introduction.

The whole description cries out for the identity of its object. If it is to be the ultimate principle controlling thought, how are we to break out of this circle, so that it is not left a purely formal “abstract” universal? It is easier to understand, if we know that Hegel's notion is coincident with—another name for, the electronic pulse in the brain. This immediately gives us a sense of this pattern; the fact that it exists, and we are more comfortable about following the complexity of the described ‘notion’.

 

As Mendelian inheritance refers to the mechanism at work in DNA, Hegel's dialectic refers to the same, raised to a higher power; by which I mean, reflected through the neural organization of the brain. Notion, from Latin noscere to know, is a noun, but in Hegel's presentation it is the mind, or more specifically, thought at work.

 

From Hegel, step forward a hundred years, to the turn of the 19th century and the beginning of the 20th. Mendel’s work comes on stream (it is suitably published), while in another arena Planck, Einstein and others bring subatomic physics into view.

 

Now, this latter is an erudite subject, little known outside the enclaves of those who work in its relation, but its very name, subatomic physics, tells us that it is a discipline in foundation beneath ordinary physics. It bears the same relation to its mother subject, physics, as Hegel's dialectic bears to ordinary logic. Here is the pattern then, which now repeats in mathematics, wherein circlemath has emerged as the deep foundation of ordinary math.

 

Across all these subjects, one process is at work, one relation, which we can call interiorization. It is a folding in, the reverse of expression, much as a flower closes at night and the patterns of brain activity change on going to sleep.

 

Instead of standing apart and observing the logic, we are deducing its mechanism, getting mentally into its station. When we do this our subject alters. It is no longer logic, but the mind's operative procedure. It now becomes evident that this perspective lacks reality so long as its second step, the elucidation of the brain’s mechanism, remains unfulfilled. So long as we have no determinate conception of this, we cannot advance on this path. The most we can do is investigate the nature of mind in terms of religion, history and logic, which is the point reached in the Hegelian philosophy.

 

In likeness to subatomic physics, the Hegelian dialectic is the sublogical foundation of philosophy. Ending feudal causality, it lit the road ahead for modern research. For these words to bite we must realize that the change ending the feudal era went beyond the Copernican revolution, the relative motion of sun and earth. It also inverted our sense of the cause effect relation. For example, a question asking after the cause of wind, would draw the reply that in God's world it is to fill the sails of ships and dry clothes. Rain is to cool the land and provide streams. Everything, in circular fashion, found its reason in its result.

 

Empirical science had no purchase in this social environment. Authoritative opinion prevailed, as rigid as 2+2=4 taught to children. Those in power burned heretics and witches at the stake, and women, politically, did not exist. It took centuries for these attitudes to change, and heavy spadework in philosophy to bring the theoretical underpinning into line with the developing superstructure, that empirical science, freed of its chains, might advance.

The Biological Revolution

Hegel's thought was biologically motivated, but he had little means of bringing this to fruition. ‘In itself’, according to Hegel, refers to an indwelling potentia or power, which exists in a seed or undeveloped form. We call this seed—the fertilized cell from which an independent life will spring—a zygote. Within this is the chromosomal apparatus whose structure and function we are beginning to understand quite well. It is Hegel's potentia. Keep this biological analogy in sight, and Kant's thing-in-itself, along with Hegel's in-itself, falls into place. They refer to inheritance within expression, the genotype as the in-itself of the phenotype.

 

Hegel saw the diversity in philosophical expressions, not as true and false, but as relation and development. Thus, he wrote:

 

The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another. But the ceaseless activity of their own inherent nature makes them at the same time moments of an organic unity, where they not merely do not contradict one another, but where one is as necessary as the other; and this equal necessity of all moments constitutes alone and thereby the life of the whole.  Phen 68

This quotation from the second page of his Preface sets forth the model for his system. His object is not the development of a tree, but the mind in consciousness. A little further on, he approaches it more closely, saying:

 

Our epoch is a birth-time, and a period of transition. … as in the case of the birth of a child; after a long period of nutrition in silence, the continuity of the gradual growth in size, of quantitative change, is suddenly cut short by the first breath drawn—there is a break in the process, a qualitative change—and the child is born.

His idea is right but bland, drawn from the knowledge of a pre-technical age. We can neither rely upon nor dismiss it, but must endeavor to understand it as belonging to the very period of transition he mentions. He is looking from his vantage point to the past. We can look from that same point to his future, for the two hundred years that followed is now in our past. To take advantage of his philosophy we must determine what, in it, is valid, what is his decisive contribution; and this is his dialectic.

 

The question is, how does the mind relate to objective things, such as houses curtains trees wind, —the infinity of finite entities? These, in consciousness, are as much in the mind as in the world. We may speak of a thing as being in itself and also for us, and these two references encompass its being. Hegel studies these relationships in detail (the first three chapters of his Phenomenology). Things exist initially for us, he points out, at the level of sense-certainty. Objectively, sense-certainty is immediate, and this immediacy is undeveloped, as in first childhood. Hegel does not make this connection, now obvious to us. He describes our comprehension as an ever-more-complete development of the Notion, which he defines as the combination of the objectively sensed and the subjectively known. This notion, at the level of sense-certainty, is but a mere potential. We have to develop it to the stage where we see the thing as a reflection of our viewpoint, and this development is the beginning of his notion and philosophy.

 

The source of what he describes is life; his intention is to describe mind. His journey, from thing to cognitive understanding is a process of development within the framework of classical logic, which in the process will undergo a metamorphosis, becoming the notion and dialectic of his philosophy.

 

We, now, two hundred years later, cannot rest content with his account. He developed it upon a biological foundation, whose detail is now familiar to us. We must take it and develop it forward, filling in the lacunae, the gaps where it begs clarification. The areas calling for attention are (1) the mind's genesis in (a) evolution, and (b) in the life cycle, birth and mother-infant bonding, and (2), the philosophy's mathematical ground, which will relieve the problem of its exposition.

 

Babies imprint to their mother or mother surrogate. This we owe to Konrad Lorenz (1903-89). What we seem to have missed is the meaning of imprinting in nature's overall plan, that it is the species foundation of mind, that it is particularly prominent in the human, and that, mediating between the unconscious and the conscious, it equates to, and founds the subconscious, which in turn is the heart of mind.

 

Using analogies, the imprint falls upon the newborn's brain, much like an image upon a photographic plate. It then acts similar to the source program in a computer, the keel upon which every subsequent mental construction builds. It is an unconscious uptake, but subconscious in placement, for it ferries serves or mediates between the inherited DNA process of being, and the sense-fed cortex of the new brain or neocortex.

 

After weeks and months have passed, imprinting completes as an inversion, ushering in infancy in the mutual generation of an embryonic ego and a sense of externality. The inversion internalizes the mother, who then appears in the ego’s externality as the first known or prototype object. Such are the steps in the generation of every mind. The onset of infancy corresponds to Hegel's immediate sense-certainty, and when, at about thirty-eight months this stage matures, childhood begins. The child steps from immediacy to looking at things perceptively and associating words with entities. The first three chapters of Hegel’s Phenomenology of Mind map to this setting, but he was no more able to refer to this association than Mendel could refer to DNA.

 

This sequence in the development of mind in every individual recapitulates the genesis of mind in the race portrayed in ancient mythology. Leaving infancy behind, associating words with objects, perceiving and understanding corresponds to ‘eating of the fruit of the tree of good and evil’. In consequence, God drove the new Adamic (earthy) race out of the Garden of Eden. We read in Genesis 3:7: “And the eyes of them both were opened, and they knew that they were naked.” This describes the childhood of the human race, something we can understand, because each of us, in our own development, will have necessarily passed through it.

 

Finally, we come to philosophy's mathematical ground. This is Circlemath, which tracks with, and so supports the philosophy's exposition, as well as permitting a direct application of the dialectic to the mind in terms of neural function. For more details in this relation, see ‘ATOM, A Theory of Mind’.

 

As the parts of the jigsaw puzzle fall into place, the picture of the governing whole begins to reveal itself.

 

Copyright © Stephen W. Taylor 030303        email: stetay at bigpond.net.au

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