Consider the snakes as they wind around the staff of Mercury. They are in eternal conflict. They represent the opposites that can be perceived. Life & Death. Science & Art. Any pair of opposites you can imagine. They cannot unite at their own level, as Jung described because they are in eternal conflict. But provided enough energy and focus, a transcendent third may appear, represented by the winged globe above. This is wholeness, or the synthesis which arises from thesis and antithesis.
“As opposites never unite at their own level, a supraordinate ‘third’ is always required, in which the two parts can come together. And since the symbol derives as much from the conscious as from the unconscious, it is able to unite them both, reconciling their conceptual polarity through its form and their emotional polarity through its numinosity.” Jung – Aion
Jung’s work was central in applying the ideas relating to uniting the opposites contained within the conscious and the unconscious for psychospiritual growth. However, the seeds of this concept were planted deep in history. Plato is often attributed to first raising the concept of thesis, antithesis, synthesis, although these were not his exact words.
Meister Eckhart brought Christian concepts to the German speaking people by considering God as the thesis, Christ as the antithesis in physical form, and the unifying concept as the Holy Spirit. His work was censured by the Catholic Church soon after his death.
Hegel described this in terms of his dialectic: two opposites which created a new whole. His usage was more along the line of the abstract as the first principle which would generate a form of its automatic opposite as it became concrete in the world. The opposing energy between the two would then generate a new level of understanding. Writers who later described Hegel’s work used the Thesis – Antithesis – Synthesis model to describe his thought.
Thomas Campbell, a physicist by training, has developed a clever and seemingly complete description of the development of consciousness in his book series My Big TOE [Theory of Everything]. He correctly criticizes current scientific views of the world as being unable to incorporate subjective experience into the predominant models. His response is to suggest that by using only two a priori assumptions he can accurately model the universe more accurately than mainstream scientific theory. Campbell’s only two assumptions are that the primary primordial “stuff” of the universe contains rudimentary consciousness, and that this primordial “stuff” could evolve. He is then able to weave together a detailed description of the forces within physics and the primacy of direct experience.
He chose to use the two simplest assumptions available that would provide for the derivation of a richness of both experience and of basic physical science. He does not necessarily suggest that this basic primordial consciousness is the actual description, only that even if this very basic definition is applied that the results of the evolution of consciousness can become staggeringly complex. What is highly relevant about the model is the use of consciousness at any level as essentially a primary building block of the universe both subjective and objective. He is clearly not a monistic idealist, but his underlying assumptions at least have similarities in some ways to the idealist perspective. The difference is that he uses his assumptions to support the existence of an objective scientific universe which exists independently of the idealist. Quite an intellectual tour de force.
One other subtle requirement of Godel’s Proof is a special use of numbers in which unique numbers are used to encode mathematical formulas and even other numbers. In this manner, numbers are used to describe themselves, a form of self reference. At one level the numbers are numbers, yet at the meta-level the numbers provide information about the truth or falsity of equations.
This use of self reference may in some ways have equivalence to our own mental representations making reference to our selves or the ability to observe mental states. Theoretically the electrical and chemical processes of the brain could be understood in a mechanistic way. Yet, the actual experience of being seems to elude the reductionistic approach.
The surprise of a new insight, perspective or understanding which was true but unknown may, in fact, be a rough equivalent of the true but unprovable Godel statement. These insights often come unbidden, or through self-reflection, or depth psychotherapy, but the surprise of the AHA moment creates a new whole of reality for the individual who experiences it. An interior depth of new views of a data set that is largely unchanged in detail, the meta-view of the self.
There is one key distinction to be made in this particular discussion regarding the concept of an infinite number of truths not provable within any formal system. Many post-modernists have taken Godel’s ideas to promote the primary tenet of post-modernism which is that all narratives [truths] are equally true. The corollary to their perspective is that various truths cannot be compared, especially if they arise from different cultures or worldviews.
From that disastrous series of errors, the post-modernist arrives at political correctness and other forms of idea restriction. The reason for this degeneration in communication is because truth is no longer the value that determines what can be argued since all truths are equal. The means the post-modernist then justifies is the emotional effect on the reader. Anything that potentially offends is forbidden under this schema.
As a logician, Godel would, I believe, have been horrified by this misuse of his proof. Godel would have easily known that there are actually infinitely more false statements than there are true statements in the universe of ideas. His proof does not proclaim false statements to be true, nor would he have ever endorsed the abandonment of logic itself. His proof only stated that there exist statements which are true, but not provable; he does not claim or endorse the concept that all statements are equally true.
One of Godel’s biographers, Dr. Wang, a rather conservative philosopher himself, concluded that the consequences of Godel’s Incompleteness Theorem for Mathematics included at least one of the following, if not all:
1. Mathematics is inexhaustible.
2. Any consistent formal theory of mathematics must contain undecidable propositions.
3. No theorem-proving computer (or program) can prove all and only the true propositions of mathematics.
4. No formal system of mathematics can be both consistent and complete.
5. Mathematics is mechanically (or algorithmically) inexhaustible (or incompletable)
Certainly if mathematics, as the foundation of science, is without limit, that at least suggests that other aspects of reality are also without limit, inexhaustible, and contain “undecidable propositions.” There is no reason that this limitlessness should be necessarily limited to mathematics. Godel actually believed that he had demonstrated the truth of Platonism, but neglected to publish that further proof. This proof certainly does imply that “truths” are discovered from a larger field of reality rather than merely created as an arbitrary convenience.
Godel certainly believed that although brain states might be mathematically determined as measured by such things as electo-encephalograms or brain imaging techniques, nevertheless, neither of those techniques nor any other mathematically based technique could [even in theory] predict or determine the richness of consciousness. He was certainly accurate regarding the limitations of the abilities of digital systems like computers to emulate consciousness, and was a consultant to the Artificial Intelligence community until his death.
So what is this Incompleteness Theorem?
At the beginning of the twentieth century, mathematicians assumed that all of mathematics was a created form [Constructivism] simply utilized to express relations between things, whether or not those things were present in reality. On that basis, it was further believed that if all of the rules of this creative form could be fully expressed that all of mathematics could be known, and all future assertions in mathematics could be determined true or false based upon the formal system developed to do such. An amazing attempt at this process was completely by Russell and Whitehead in the three volume set, the Principia Mathematica. Formalism or Constructivism was assumed to be reasonable, true, and the future of mathematics, and to some degree logic. For the formal system to be functional, it would have to correctly identify all true statements accurately, and create no contradictions
Kurt Godel shocked the mathematical world be creating a short Proof, which demonstrated beyond doubt that all formal systems are necessarily incomplete. That in some manner a true statement can be introduced into the formal system, which the formal system could not identify as true. As it turns out, this Godel Phrase actually creates an infinite number of true statements that the formal system cannot identify as true, making any formal system necessarily incomplete, because, once the first Godel number/phrase is inserted, another [G’] is created, which continues without ceasing. Godel’s intense introversion led his announcement of the proof to be less than overwhelming, but other mathematicians of the day made the findings more public within the mathematics community.
Godel’s original proof made the concept of a formal system quite strict, such as the Principia Mathematica level of formalism. Perhaps had he stopped at that point, his work would be non-relevant to the questions of consciousness, but in a later version of his proof, he was able to so simplify the definition of a formal system, while retaining the result of the proof, that this otherwise esoteric bit of mathematics suddenly becomes substantial in a whole host of other intellectual inquiries. These true but unprovable statements, and their existence, have, in Nagel and Hoffstader’s words, forever separated the concepts of “true” and “provable.” That is an amazing paradigm shifter for any of us.
Consider: is it not the case that a creative idea which in every way seems fresh, intriguing and true after receiving the insight, would not have been necessarily identified as “true” by your mind prior to that creative insight?
Kurt Godel was born in 1906, and was such a tenacious child that his family referred to him as “Mr. Why” by the time he entered grade school. He made rather amazing contributions to the field of logic and mathematics over the course of his career. Einstein remarked that his greatest pleasures late in life were the daily conversations he shared with Godel, someone, it appears, he considered an intellectual equal. Godel provided Einstein with a mathematical solution to the field equations of general relatively, which he gave to Einstein at his 70th birthday. It was Einstein who helped him obtain a position at the Institute for Advanced Study.
Godel believed that his proofs confirmed Platonism, according his biographer, Wang, but he never published a formal proof of that assertion. He was known as an idiosyncratic person, and appeared to have starved himself to death in 1978 over a general paranoia of food. Irrespective of his personal oddities, his genius at logic has earned accolades that he was the greatest logician since Aristotle. The most relevant of his proofs for this discussion are the Incompleteness Theorems, which will be the subject of the next entries. These theorems, and indeed Godel and his work in general, were made part of public knowledge with Hoffstadter’s “Godel, Escher & Bach.”
Many of the cutting edge thinkers in consciousness studies refer back to Logician and Mathematician Kurt Godel. Examples include Douglas Hoffstadter, in his epic “Godel, Escher & Bach: an Eternal Golden Braid.” David Chalmers in his “The Conscious Mind.” Roger Penrose in his trilogy of works on mind brain interaction. These three alone account for some of the most intriguing concepts in advanced ideas related to consciousness.
Each of them note that based upon Godel’s Theorem [subject of an upcoming entry], it is not possible, even theoretically, for the mechanical predictable aspects of the electical/chemical brain to account for all the qualities associated with “mind.” Godel predicted the limitations of artificial intelligence in digital computing that have proved to be quite accurate, at least to date. The limitations he suggested have remained solid for the nearly fifty years since his death.
The three above authors all attempt to restore as reductionistic and physically based a theory of concsiousness as possible, given the constraints of Godel’s Theorem. Chalmers and Penrose actually wrote that the limitations provided by Godel’s Theorem could imply a more idealistic or mystical philosophy, but they specifically chose to limit themselves to a more reductionistic explanation. I would support a more radical approach, approximating that of Amit Goswami, a physicist who wrote the rather stunning “The Self Aware Universe.”
More to come in the next series of posts.