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.
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.
Interviews with William Tiller Ph.D. describing the role of intention and consciousness.
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 suggests 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 a particular type of Zombie. 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: they lack all ability to actually experience anything, [which is termed qualia, the qualitative aspect of interacting with the world]. The Zombie acts just as a person would, but has no internal experience of pain, joy, love, beauty, or anything else.
Could such a Zombie exist, even in theory? Why or why not? If you think so, then you find some dualist perspectives persuasive. If not, you are clearly in the physicalist monist camp. If you’re in this latter category, then an additional question to ponder is: if a Zombie has no experience of qualia what leads it to act?
An interesting consequence of Chalmer’s theory is that any system which reaches adequate levels of complexity would cause an emergent quality of consciousness: including thermostats, computer programs, nations, etc. His theory is also consistent with a pan-psychic philosophy, although that is not the direction he argues to consider questions of consciousness. Pan-psychism will, interestingly, be quite compatible with several other theories to be discussed.