I am a liar. I know this to be true. Yet if it is true, then I am lying that I am a liar, thus I am not a liar. So it must be false. But if my statement is false, and I am not a liar, then my statement that I am a liar is a lie and I am lying.
So, maybe I am a liar, maybe I am not. But the statement itself can never prove or disprove that I am or am not.
This sentence is a variation on the liar’s paradox, which goes: “Epimenides is a Cretan who says, ‘All Cretans are liars.’ ” Just like my example above, if he is telling the truth, then all Cretans are liars, so he is lying – which is a contradiction. If he is lying, then all Cretans are not liars and he may be telling the truth – which is also a contradiction.
This seemingly simple sentence has created an infinite feedback loop that one cannot escape with logic. It just goes round and round ad infinitum. It is reminiscent of the drawings and paintings of M.C. Escher. For instance, in Escher’s painting Print Gallery, a young man inside a gallery is looking at a picture of a ship that is anchored in the harbor of a town. In this town is a print gallery in which there is a young man who is looking at a ship that is anchored in the harbor of a town. As you look at the painting, and you go through all the buildings of the town, the picture comes back to the original point where it starts, to begin its oscillation again. And there is no end to this oscillation, for it will go on forever, caught in its own inherent contradiction of logic.
It was Hegel who said, “All finite things are contradictory.” This statement would have been left for philosophical debate if it hadn’t been for the work of Kurt Godel, and his theorem of incompleteness that he put forth in the 1930’s. Of Godel’s work, the mathematician John von Neumann wrote, “Godel’s achievement in modern logic is singular and monumental…a landmark which will remain visible in space and time.”
Godel’s theorem demonstrated that any sufficiently rich deductive system – arithmetic, for example – will generate statements that are meaningful but unprovable, one way or the other, within the system. Mathematics, or any sufficiently developed system, cannot ever be complete. The proof is binding, because to deny the conclusion puts you in the position of trying to have it both ways. The conclusion is true if it is false and false if it is true. Thus, no rich system can be complete and closed. It must either be complete and inconsistent, or incomplete and consistent – as in the statement “I am a liar.”
A sufficiently rich system must be open-ended in order to find true meaning. Godel showed that the only way to solve a proposition was to go outside the system, in order to come up with new rules and axioms. Yet by doing so, you’ll only create a larger system with its own unprovable statements. The implication in all this is that all logical systems of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.
Theoretically and practically, then, you have to keep expanding the parameters to arrive at the answers within the system being studied; for, as Hegel said, within a finite system, things will begin to become contradictory. Putting it another way, Hegel said, “For anything to be finite, is just to suppress itself and put itself aside.” Thus, he added, “all that is determinate and finite is unstable.” And, Hegel believed, it was this incompleteness, this instability that drives the agitated movement of the entire finite and manifest universe: “Only insofar,” he said, “as something has contradiction in itself does it move, have impulse, or activity.”
Hegel lived and worked over a 100 years before the time of Godel, yet he understood this contradictory process quite well. Perhaps his writings had an influence on Godel. It is possible his philosophy also influenced Niels Bohr and the quantum physicists in regards to their theories of complementarianism, as the respective approaches have many parallels.
In Hegel’s view, existence is a dialectical process of thesis, antithesis, and synthesis, through which two contradictory forces are resolved in a higher, more rational state. He saw history as the progressive development of human understanding toward perfect knowledge; he believed civilization advances in stages, or “historical moments,” each of which is a necessary but incomplete step in the development of human consciousness, reason, and freedom. Since each stage is imperfect, he postulated, its flaws give rise to opposing ideas of forces, and out of the resulting conflict comes a new, higher, and temporarily more stable stage.
It’s like the story of the little old lady who comes to a meeting of cosmologists, insisting that the world rests on the back of a giant turtle. The contemptuous chairman asks her what this turtle stands on, and she snaps back that it stands on the back of still another turtle. “And what does that turtle stand on?” the chairman demands. The little old lady shakes her finger at him and replies, “You can’t fool me sonny; it’s turtles all the way down!”
Ultimately, in the kind of universe that Hegel, Godel, and many others have postulated, you have to keep expanding the set infinitely, continually going beyond the system, in order to find the truth of how many turtles there really are. Godel’s theorem seems to say that rational thought can never penetrate to the final ultimate truth.
Each time scientists feel they are closer to the ultimate answers, all they find is that there are further layers to dig into, more turtles down the line. For instance, as particle physicists explore the heart of matter – the subatomic particle – they have found there is virtually no end to the limit of particles to be discovered. At last count hundreds of different particles have been found or postulated – with such names as pions, mesons, muons, leptons, neutrinos, quarks, antiquarks, tauans, tau neutrinos, gluons, baryons, neutralinos, wimps, champs, fermions, and bosons – some having life spans of 10[-24] seconds. About this, Enrico Fermi said, “If I could remember the names of all these particles, I would have been a botanist.”
We may never know everything, a theory of everything notwithstanding, because the universe is endless and infinite: there will always be new emergent systems and laws that will present themselves. There are many examples of emergent laws in science – laws that emerge from regularities in the collective behavior of fundamental particles or molecules. The science of emergent properties will never be exhausted, because, as Hegel and Godel have suggested, emergence is about continually expanding beyond the set. And it may not be so much that the behavior of the particles or molecules changes as much as it is our comprehension of their movement that expands, enabling us to better understand the depth and breadth of their scope.
Another way to look at it is to question whether it is nature that is going through the transition, or if it is our perception of the event that is evolving. Nature continually evolves, but even more importantly, so does the mind of man. Indeed, it may be that the most important emergent property of all is Mind; we are barely scratching the surface in our understanding of Mind.
Even if all the most basic, irreducible laws of physics were known, we would still face the great challenge of learning their consequences. The late physicist Richard Feynman put it well:
The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations…Today we cannot see whether Schrodinger’s equation contains frogs, musical composers, or morality – or whether it does not. We cannot say whether something beyond it like God is needed or not.
Physicist Frank Wilczek, writing in Discover magazine, added his thoughts to Feynmann’s. He said:
I would add that not one of these fascinating questions is likely to depend on the latest wrinkles in particle physics or early-universe cosmology. When and if we have found the complete irreducible laws of physics, we certainly shall not thereby know the mind of God (Hawking to the contrary). We will not even get much help in understanding the minds of slugs, which is about the current frontier of neuroscience.
The concept of mind, and consciousness, whether of slugs or humans, is one that remains one of the biggest mysteries in science; it is a topic that can be the subject of heated debates between the various, and often competing, theories. There is good reason to believe that consciousness arises from physical systems such as brains, but there is little idea how it arises, or why it arises at all. Most of the research on consciousness leaves the hardest problems untouched, opting instead for the “easier” problems of consciousness: How does the brain process environmental stimulation? How does it integrate information? How do we produce reports on internal states? These are important questions, but to answer them is not to solve the hard problem: Why is all this processing accompanied by an experienced inner life?
It stands that most probably consciousness and mind cannot be explained purely in physical terms. Ken Wilber, in his essay “How Big is Our Umbrella?” in the Winter 1996 edition of the Noetic Sciences Review, outlines what he believes are the 12 different schools of consciousness theory. He summarizes them as:
- Cognitive Science – views consciousness as anchored in functional schemas of the brain-mind
- Introspectionism – maintains that consciousness is best understood in terms of intentionality, anchored in first person accounts
- Neuropsychology – views consciousness as anchored in neural systems, neurotransmitters, and organic brain mechanisms
- Individual Psychotherapy – views consciousness as primarily anchored in an individual organism’s adaptive capacities
- Social Psychology – views consciousness as embedded in networks of cultural meaning or as a byproduct of the social system itself
- Clinical Psychiatry – views consciousness in strictly neurophysiological and biological terms
- Developmental Psychology – views consciousness not as a single entity but as a developmentally unfolding process
- Psychosomatic Medicine – views consciousness as strongly and intrinsically interactive with organic bodily processes
- Nonordinary States of Consciousness – views consciousness as a realm that encompasses states outside our everyday, waking realm
- Eastern and Contemplative Traditions – views consciousness as a spectrum in which ordinary consciousness is but a narrow and restricted version of deeper or higher modes of awareness
- Quantum Consciousness – views consciousness as capable of interacting and altering the physical world, through quantum interactions at the intracellular level and in the material world at large
- Subtle Energies Research – believes there are subtler types of bioenergies beyond the four recognized forces of physics, and these play an intrinsic role in consciousness and its activity
In mapping out these various schools of thought, Wilber attempts to find a common ground, a unifying theme for the inherent contradictions that some pose on the others. In attempting to answer how to unite them, he speaks in Hegelian, and Godelian, logic. In this regard, he allows for a higher ground in which a theory of consciousness could find a new synthesis, a new rational discourse, and a way of allowing for Mind to take a place in the equation.
If we follow this type of thinking, we may be able to allow for consciousness to be seen as a natural phenomenon, falling under the sway of natural laws. And these natural laws concerning consciousness may not be like laws in other domains, nor may they be physical laws. They may be quite different in kind.
If, as Godel showed, any sufficiently rich system is ultimately open-ended; and, we accept that the mind is a sufficiently rich system; then it goes to show that the mind is also, ultimately, open-ended. Given this, there may be a link between mind, nature, and the universe; this may be an aspect of the principle of non-locality that physics has uncovered.
In a recent book on Godel by John L. Casti and Werner DePauli, the authors state that “understanding the logic underlying Godel’s magnificent achievement has been described by some as being akin to a religious or mystical experience.” It may be that Godelian logic has opened the door to new pathways of understanding, of which we are just discovering the significance of its meaning. How far does an emergent mind go – to infinity? And what would it see there? Turtles all the way down?
An emerging science that is attempting to tackle that question is neurotheology, which is exploring the links between spirituality and the brain, and by doing so, trying to answer both the hard and easy questions of consciousness. Scientists in this field have been able to map out and observe brain states that correlate to moments when a subject has reached an intense spiritual peak. In this state, the orientation association area of the brain becomes virtually blacked out, which deprives the subject of information needed to draw the line between the self and the world. In this state the subject would experience a sense of a limitless awareness melting into infinite space.
What these brain patterns show is that the person’s sense of a separate self is being swept aside, and the mind’s awareness is growing broader and more unified. When asked if this means that God is just a perception generated by the brain, or if the brain has been wired to experience the reality of God, one researcher in the field replied, “The best and most rational answer I can give to both questions is yes.”
Calling the experience God is obviously open to interpretation. Different religions and philosophies have different terminologies, while scientists may look for their own syntax. But this type of research suggests that the mind has the capability of perceiving the universe in a way far different than what we have been taught to believe, a way that fits into the Hegelian and Godelian interpretation of the universe.
This also corresponds with the concept of nous, a word that the Greek philosophers Plato, Hermes, and Plotinus used to signify a Higher Intelligence, a mind capable of thinking and conceiving via creative reveries. Although our world is predicated on a rational and logical methodology, it is the creative impulse, which lies at the root of the manifestation of new ideas, that often is the foundation of progress. David Bohm said that creativity was a fundamental principle of the Cosmos and what needed to be explained were the processes that were not creative.
And it was Albert Einstein who said: The most beautiful emotion we can experience is the mystical. It is the power of all true art and science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead. To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and most radiant beauty, which our dull faculties can comprehend only in their most primitive forms – this knowledge, this feeling, is at the center of true religiousness. In this sense, and in this sense only, I belong to the rank of devoutly religious men.
It’s like the story that comes from the Sufi tradition. One day the Sufi master Mulla Nasruddin was found on his knees adding yogurt to the water in a pond. A passerby asked, “What are you doing, Nasruddin?’ “I’m trying to make yogurt,” answered the mulla. “But you can’t make yogurt that way!” “But suppose it takes,” the mulla said optimistically.