Godel 3

July 27th, 2009

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 [it would have to be both complete and consistent otherwise it would logically fail its purpose.]

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?

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Godel 2

June 27th, 2009

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 provided 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.”

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Godel 1

May 26th, 2009

Some of the cutting edge thinkers in consciousness studies all 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 rather famous “The Conscious Mind.” Roger Penrose in his trilogy of works on mind brain interaction.

Each of these three 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 three above authors all attempt to restore as reductionistic and physically based theory as possible, given the constraints of Godel’s Theorem. Chalmers and Penrose actually stated that the limitations provided by Godel’s Theorem could imply a more idealistic or mystical philosophy, but they specifically chose to stick to a more reductionistic explanation. I plan to take a more radical approach, approximating that of Amit Goswami, a physicist who wrote the rather stunning “The Self Aware Universe.”

More about Godel’s actual theorem next.

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Neuroplasticity

April 26th, 2009

Although epiphenomenalism may be nearly assumed by many doctors and patients alike since it seems to match data related to impaired neurological function, some of the research in neuroplasticity likely refutes the entire concept of epiphenomenalism. Early research demonstrated that when people learn new skills, such as typing or piano, that areas of the motor cortex of the brain actually increase in size to match. Later research demonstrated new brain connections, after some forms of brain injury, sometimes form to areas of the brain which would otherwise have processed information from different areas of function. This process actually restores the lost functioning, even with different areas of the brain processing the information.

Although these studies were fascinating as they showed the neuronal connections and biological functioning of the brain changed as a result of essentially newly learned tasks, some researchers minimized the results with arguments that this was largely a unique ability for repair following injury. One of the more recent studies was a true paradigm changer. In this research, Tibetan Buddhist monks participated in functional brain imaging studies while practicing a compassion based meditation technique. The finding was astounding: monks showed a novel Gamma brainwave pattern in the frontal lobe, which correlated with the subjective sense of blissfulness. This brainwave pattern had never been seen in any non-pathological state before, and its presence and strength was only related to the number of hours of meditative practice. No other demographic factors correlated with the finding, which suggested a clear circumstance in which willed meditative practice altered brain function over extended practice.

Since epiphenomenalism requires that mental process is only an accidental byproduct of neuronal firing, there is no conceivable way that mental process could actually effect the biological structure. This latest research proves just the opposite: that mental process changes the biology of the brain. Clearly then, any form of biological monism cannot account for this research finding. A different model is needed which accounts for the research data.

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Epiphenomenalism

April 6th, 2009

The version of mind brain interaction most popular in neuroscience these days is a version of physical monism called epiphenomenalism. Some form of epiphenomenalism is essentially required from a physical monist perspective to account for anything resembling mind or qualia. This perspective describes an emergence of consciousness or mind from the biological complexity of the neuronal net. Hoffstadter and others assume this perspective, and argue that new phenomenon arise from complexity in many physical systems. Examples often given include the complexity of fluid motion not being clearly predictable from the observation of a single water molecule. Other philosophers find the concept so revolting that they don’t even dignify it as a legitimate perspective at all.

Arguments from complexity do create interesting an interesting delimma, however. If the number of molecules in the Empire State Building meet a critical number, could they interact in a manner analogous to consciousness? If the number of Chinese in China reach a critical mass, does the country itself gain the quality of consciousness? Chalmers and others argue that, in fact, China would become a conscious being at the level of a nation due only to complexity itself. Each person would have at least the interactivity of a neuron, and if enough interacted that would mirror neural nets, and if the total reached a critical mass then “consciousness” would arise. Although the experts who defend the complexity argument are forced to this position in order to maintain a coherent perspective, it is an increasingly difficult position to reasonably defend, in my opinion. What might be defined as the consciousness of a country or other large aggregate of interacting materials seems woefully different than what each of us experience as consciousness on a day to day basis, largely based upon the difficulty of defining who or what might actually experience that form of consciousness.

A key foundation of the principle of epiphenomenalism is the assumption that consciousness is an unintended byproduct of neuronal complexity. The corollary of this assumption is that consciousness, or perhaps mind, flows from the biology of the system, and could not even in theory control or alter the biological system itself, given that it is an unintended byproduct. Recent studies employing brain scanning technology bring this a priori assumption into clear debate.

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Monism

March 5th, 2009

The more popular perspective amongst neuroscientists today is a physical monism which assumes that the entirety of conscious experience arises from the complexity of neuronal structure and connections. This provides a very simple solution to the challenge of dualism, but at a rather high price. The issue Chalmers raised regarding qualia become a central weakness of physical monist views. In addition, it is only an assumption that the complexity of the neural net creates some new emergent property called consciousness, an entirely untestable assumption.

Various versions of physical monism have been posited including analytic behaviorism, interactionism, and purely neurological models. Each of them basically requires the emergence of consciousness from a mass of non-conscious building blocks in a manner almost as mysterious as the elusive connection between mind and brain that is the weakness of dualistic theory. This curious leap of organization is typically referred to epiphenomenalism [consciousness arising as an incidental output of a complex neural net], which will be the topic of multiple future posts.

Bishop Berkeley, in a reaction to his disdain for a materialistic version of monism described a mental form of monism which suggested that only thought was real, and the physical was an illusion. This philosophy, called idealism, was never considered seriously by the scientific community, but it does raise significant questions. In a truly monistic perspective, as physical and mental must at some level be identical, it would be actually quite difficult to fully discount the idealistic version of monism over the physical version.

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Softer Dualism

February 22nd, 2009

David Chalmers provides an alternative to the more radical dualism of Descartes. He is known for the clear explication of the “hard problem” of consciousness, that being examining the question of why physical substrates [such as a brain] would give rise to subjective conscious experience [mind]. He does suggest that the physical is necessary for conscious experience, but that the presence of consciousness is an emergent property that is of a higher level than the physical and, additionally, at least to some degree independent of it.

The famous thought experiment he devised to argue this perspective was that of Zombies. These special Zombie creatures are exactly like you or I, and their behavior would be indistinguishable from ours. However, these Zombies lack one quality which we each possess: the ability to feel experience, or qualia. The Zombie acts just as a person would, but has no internal experience of pain, joy, love, beauty, or anything else.

Could such a thing exist? Why or why not? If you think so, then you find some dualist perspectives persuasive. If not, you are clearly in the monist camp. If the Zombie has no experience of qualia what leads it to act?

An interesting consequence of this theory is that any system which reaches adequate levels of complexity would cause an emergent quality of consciousness: including thermostats, and even countries of individual people. His theory is also consistent with a pan-psychic philosophy, although that is not the direction he takes to consider questions of consciousness. Pan-psychism will, interestingly, be quite compatible with several other theories to be discussed.

 

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Mind Stuff, Brain Stuff, or Both?

February 9th, 2009

Western thought has wrestled with the concept of whether such things as brains and minds are one in the same, some version of monism, or whether they are distinct and separate, some version of dualism.

Rene Descartes a prominent French philosopher was an intellectual giant in his day, credited with creating the “cartesian plane” which bears his name. He started a philosophical enquiry into the nature of reality by starting from a position of extreme skepticism, eliminating all dogma and trying to begin a system of belief with only that which was self evident. He arrived at the famous phrase, often quoted, of “I think, therefore I am.” A brief series of other “self-evident” statements led to his suggesting a strong form of dualism, suggesting that physical reality and mental [spiritual] reality were entirely separate things. The social ramifications of this conclusion freed science from the chains of church mediated versions of pseudo-science. Freeing scientific inquiry from religious dogma led to the technological and scientific revolutions, the fruits of which we enjoy today. From a practical standpoint, this dualistic philosophy of Descartes allowed science control over the study of the measurable and physical, but left religious authorities in control of matters related to the spirit.

Intuitively, dualism, at least in the West, feels so natural and experientially real: we experience sensations, emotions, and ideas, we don’t experience brain waves or brain chemicals in a direct way. It is so intuitively appealing, that although this strict form of dualism has substantial problems, it is often the manner in which people often live.

Yet, the dualism of Descartes left one giant and probably insurmountable question: how does an immaterial mind affect the physical brain [and the reverse]? That difficult, if not impossible question, led many more recent theorists to propose some version of monism: mind and brain as identical. Various models of biological monism remain in vogue with neuroscientists. The most radical version of this espoused by Daniel Dennett even suggests that subjective experience does not even exist, and likens it to an illusion of subjective experience. That seems a rather high price to pay for an answer to dualism’s problems.

Mental monism was suggested by Bishop Berkeley, and known as Idealism. Mental monism declares the entire physical world a complete illusion with the only truly real being the thought or idea. Berkeley suggested this theory in response to what he perceived as the inappropriate emphasis on physical reductionism.

There is rather amazingly no experiment which could be performed, even in theory, that can actually refute the claims of any of these three perspectives: neuroscience tends to make the assumption of biological reductionism, but the a priori assumption does not prove truth. An open mind, therefore, is a prerequisite to exploring the more insightful questions.

Eastern philosophy largely escapes the questions of dualism versus monism, in that it assumes that the level of physical reality is distorted by the Veil of Maya. In that model, everything is the result of a monism of consciousness being interpreted as a dualistic universe by instruments as primitive as the five senses, the brain and general awareness. Such a solution is inherent in interpretations of the Qabalah as well, with monism implied the highest levels, but dualism required in lower physical realms.

 

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Psychiatry and Consciousness

January 24th, 2009

One of the most amazing questions I’ve found is the mystery of consciousness. The quest to explore it drove me towards the study of psychology as an undergraduate, and towards psychiatry after medical training. Psychiatry, at least historically, had a depth and breadth that seemed to allow real exploration of questions of consciousness. After more than a decade in the field, and experience in academic and clinical psychiatry, it is truly peculiar to observe the minimal interest of my field in even asking the relatively hard questions. Many colleagues comfortably assume that all the questions of relevance have already been answered in the form of biology.

Until quite recently, consciousness was considered a taboo subject for research or consideration in mainstream academia. Not only ignored or defined into non-existence, the topic was considered quite dead until several authors began raising the timeless questions with new and serious discussion: authors such as David Chalmers, Roger Penrose, and Daniel Denett. The first two of whom used Godel’s Theorem as the starting point of their discussion on mind, brain, and consciousness. The discussion of the forbidden “C” word re-entered both public and academic life for the first time in decades.

David Chalmers has been credited with formulating the “hard question,” which is essentially the question of why is there mental experience at all. Or, how does the physical presence of a brain actually lead to subjective awareness, which he terms “qualia.”

Much more on Godel, Chalmers, Penrose and others later, but this essential question that Chalmers so perfectly framed remains the focus. Why indeed would a complicated physical system, such as a brain, necessarily result in subjective experience for you or for me? Answers to this question range from monistic versions of reality to dualism of various sorts. We’ll start this exploration looking at those two general models and later consider the limitations implied by Godel.

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Welcome to the Blog

January 11th, 2009

Welcome to the new site. I hope this will be a place for the open discussion of all things related to consciousness, consciousness studies, philosophical and mystical considerations including implications of quantum physics and Godel’s Incompleteness Theorem.

Depending on how consciousness is defined, the overall scope of discussion here could be quite large.

Comments and ideas from readers are most welcome!

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