Gödel's Incompleteness Theorem, Consciousness, & Linguistic Place Holders*

Born in Czechoslovakia, in 1931 Kurt Gödel demonstrated that some propositions could not be mathematically proven true or false using the rules and axioms within a given mathematical system. Outside it, the system could be proved or disproved, but by doing so you would only create a larger system with its own unprovable statements.

So what?, you ask. Only this. Gödel undermines any belief that all complex logical systems are logically air-tight—that they contain undeniable truths within them so long as rules and axioms are observed. Instead, each system holds more true statements than it can possibly prove.

This has far-reaching implications.

His Theorem can be used against artificial intelligence as eventually somehow becoming as smart as people. A computer can never be, because its knowledge is limited by a fixed set of axioms.

For my purposes, it also applies to the realm of consciousness. Some neuro-scientists and philosophers of consciousness are bravely optimistic that the processes of consciousness can finally be explained. Gödel's Incompleteness Theorem offers a way to see this as unlikely. You can be sure of what consciousness knows only by relying on what it knows about itself. That which it knows is subjective. You must be somehow able to objectify it to explain it. The problem is that here is no molecular structure, no particles. If you say neurons, you say nothing about what it feels like to be you.

In a phrase, neuroscientists and philosophers will always depend on linguistic place holders. By that phrase, I refer to the use of words to stand for what is not understood. They range from the metaphysical (God) to the physical (dark energy). Mainly, though, I see them operative in the study of consciousness. Note the shift in neurophysiological parlance from matter to physical processes. Matter had once held a promise that it could be plumbed, that somewhere at its base, science would shout Eureka! after years of hard research. The discovery did not happen. Instead, matter behaved very strangely indeed and invited strange imaginings to explain its behavior. The Standard Model of quantum physics wouldn't cooperate with gravity in General Relativity. Now we have the wholly unverifiable excitation modes of String Theory. As quantum physicist Richard Feynman said in a different context, if a scientist isn't confused by it all, he doesn't understand it well enough.

Especially for the study of consciousness, the new linguistic place holder is physical processes, with its implication that matter has been discarded as a hopeless dead end. The new term does not insist on a basement order for physical things, which was the expectation of matter. Instead, processes occur, which are called physical. These processes will eventually be determined, so goes the belief.

Of course, that still leaves the question, What does physical mean? Sounds like a glib replacement for matter to me. The shift from matter to physical is intended to support the meta-paradigm of science—the overarching view that the real world is composed of space, time, and the physical. To slightly alter Hamlet, There are more things in heaven and earth, Horatio, than are dreamt of in your meta-paradigm.

The meta-paradigm holds that only the physical—or the material, if you want—is real. Real? Even if, by that, you mean physical reality, problems still occur. The European cuckoo never sees its parents. It is raised by birds of other species. Near summer’s end, its parents migrate southward to southern Africa, without even a goodbye to their offspring. A month later, the young cuckoo locates other youngsters, and together they also migrate. How can this be? Any answer is superficial if it merely asserts that the instinct is encoded in DNA or passed on through genetic chemicals. It still has not explained how the instinct works. It has resorted to physical processes with more specific words.**

The meta-paradigm does not allow for the existence of any non-physical, non-material, causal agency, nor should it, for--scientifically speaking--any other approach is useless. It's just that when research comes down to consciousness, more humility is in order.

The meta-paradigm allows that swimming around in the primordial soup, life began. Okay. Allow that physical reality has a wholly convincing explanation in this regard—it still would not explain the nature of life. Is that nature physical? This is a pointless question according to the meta-paradigm, which holds that this sense of the word nature is like the word God, simply a universal idea created by the human mind. Mechanical causation would be enough. Nature is described by what happens. Would this causation be enough? Enough for what? For scientific explanation? As far as it can go.

Science has serious problems with cause and effect. It operates predictably in the macro-world, but behaves quite oddly in the micro-world. Evidence for this behavior abounds at the quantum level. To use a classic example, how can a wave also be a particle? What about the so-called Observer’s Paradox? How can the wave function collapse as soon as it is recorded? Problems with consciousness occur at the quantum level. Consider Bell’s Theorem, which demonstrates what Einstein called spooky action at a distance. How does an electron here know what is happening to an electron a million miles over there? Quantum computers may be invented out of this entanglement, but that only means we know how to harness it, not that we understand it in a realm where our cause and effect become confused.

Erwin Schrödinger described the time-dependence of a quantum mechanical system with his equation, which today is fundamental in quantum mechanics as a description of the system. Among scientists, Schrödinger had a nimble mind with interests spanning numerous fields, which gave him versatility. This allowed him to see and think outside the box of science. In My View of the World, (Meine Weltansicht), he expressed an outlook rooted in the ancient Sanskrit teachings of the Vedanta. Written in 1961, his book reveals the culmination of his search for understanding of consciousness. In it he said, “the plurality of sensitive beings is mere appearance (maya); in reality they are all only aspects of the one being.” As a scientist he sought the physical processes of that unity; as an individual he had an understanding where science could not go. He saw deeply into the paradox of objectivity. Were his consciousness not part of the real world, and he must exclude it, then he must exclude objective manifestations of consciousness—his body, others’, as well as the objective manifestations (consciousness) of their brains. Were he to exclude his own manifestations, he would deny his own existence.

Make no mistake. I carry no brief for obscurantism, for mystery. Perhaps consciousness does have a “physical” basis. Maybe consciousness is a feature of certain elementary particles. (That still leaves the door open for God—or the Gaia hypothesis, if you prefer.) The Observer Paradox and other phenomena suggest that some particles have potential for consciousness, just as particles have potential for an electrical charge. (Indian guru Ramesh Balsekar tells his many disciples that Consciousness is all. Sorry Ramesh. In this view, Consciousness is not all. All carry the potential for it while only some are.)

It's just that we are part of the system trying to find out what we are. That's where Gödel's Incompleteness Theorem comes into play. We are what we are looking for, as St Francis of Assisi is alleged to have said. Or, the eye cannot see itself, nor can consciousness. In our long evolution we developed the smarts to understand, describe, and predict much of the three dimensional world. This ability accelerated with the rise of modern science. I find it likely that we just do not have the right kind of intelligence to understand consciousness, somehow entangled with what we call time. (Try to explain time.) To be sure, linguistic analogs for consciousness processes will be developed and they will provide models for thinking about consciousness. They will remain only that—models, and with large areas of theory unavailable for verification or a Unified Theory of Consciousness. I cannot muster any enthusiasm for the optimism of those who hold that consciousness can be fully explained, although I believe their thinking and research is valuable. They and others have enabled a discussion that was long overdue.

I grant that Gödel's is a mathematical system, and can only be used as a metaphor of consciousness. He only served my introduction. My point is that, given my explanations, at the intersection of mind with matter I cannot foresee anything but more linguistic place holders for investigators of consciousness processes. Because the neuroscientific community has not questioned the meta-paradigm of science, that model remains as Holy Mother Church for the belief that the intersection of consciousness with matter can be adequately explained.

Look at it this way. When you see a tree, light is transmitted onto the retina of your eye where the tree image is inverted. Traveling to the back of your brain on electrical impulse through neurons, the image is turned right side up, and the tree is experienced—not necessarily as what is "out there," but as what your hard-wiring transmits. (Not only that, but you are unaware that the tree was ever upside down or that the length of your brain intervened between you and the tree. To pun, matter is immaterial.)

How does the matter of the brain give rise to the experience? The tree is an image in your mind. Touch the tree. Is it now proved as directly real in and of itself? No. It remains a construct of consciousness. Your fingers transmit a sensation to your mind. The physical process of the transmission can be explained, but how does it give rise to the experience? This involves the hard problem of consciousness, according to David Chalmers.***

What about this. Are you the experience or the experiencer? Both? Find yourself in both. You can not, except as consciousness interacting with the experience. Find yourself as experiencer. When you try, you locate thoughts and images, also experiences. Name the experiencer and you have only another linguistic place holder. You just cannot succeed, although your consciousness is the most obvious thing about you.

This obviousness is what you are and for a name it has only a linguistic place holder. In other words, the obviousness has no name. That is your most factual feature and it is beyond the ability of mental concepts or words to describe it. Thomas Nagel put it this way: "We can be compelled to recognize the existence of such facts without being able to state or comprehend them." ****
__________________________________
* The concept for this article originally appeared in Inveterate Bystander on 2 July 2004, and was titled Long-Legged Fly, Linguistic Place Holders, & The Tenth Man. That article will be republished after I revise its contents.
** “But if there is a process, there must be something—an object or substance—in which it goes on. If something happens, there must be something to which it happens, something which is not just the happening itself.” This expresses our ordinary understanding of things, but physicists are increasingly content with the view that physical reality is itself a kind of pure process—even if it remains hard to know exactly what this idea amounts to. The view that there is some ultimate stuff to which things happen has increasingly ceded to the idea that the existence of anything worthy of the name ‘ultimate stuff’ consists in the existence of fields of energy—consists, in other words, in the existence of a kind of pure process which is not usefully thought of as something which is happening to a thing distinct from it. Found in Galen Strawson.
*** The question is how does the flux of ions in little bits of jelly in my brain give rise to the redness of red, the flavour of marmite or mattar paneer, or wine. Matter and mind seem so utterly unlike each other. Well, one way out of this dilemma is to think of them really as two different ways of describing the world, each of which is complete in itself. Just as we can describe light as made up of particles or waves—and there's no point in asking which is correct, because they're both correct and yet utterly unlike each other. And the same may be true of mental events and physical events in the brain. (V.S. Ramachandran, 2003 Reith Lectures)
**** In this essay, I do not address the functional self, as I do in Of Cars and Selves, 6 January 2006. In the earlier piece, I simply point out the misguided thinking of those who—in search for the basis of consciousness—fail to see that a functional self does exist for survival purposes.

Of Selves and Cars

In the 1 January 2006 article below, John Allen Paulos asserts that a major shift in society and culture would occur once the public widely understood that the self is non-existent. That is one view of the self. Only one.

For thousands of years Buddhists and Hindus have asserted that the self does not exist. Disciples are taught to look for the self. The simplest Zen koan can be, Who am I? Once the disciple learns that the question cannot be answered in terms of a locus for the "I," he is on the road to enlightenment. Basically, the finding is supposed to be that the "I" cannot be found. Instead, there are various forms of sense impressions--thoughts, feelings, perceptions. The absence of solid evidence for self becomes hitched to a belief--that if nothing can be found, the self is an illusion and does not exist.

Not necessarily so.

Consciousness research has determined that, yes, self cannot be located in a single place. It does appear, but not as an objective unity. Several areas of the brain can produce several events, none of which coalesce into a single objective presence on, say, an fMRI brain scan. Still, we feel only one.

The point: because a central, guiding self cannot be found does not mean that it is merely an illusion. When we look inwardly for the colonies of bacteria that digest our food we cannot find them. That does not mean they are illusory. Their presence is manifested by the fact of digestion. So, too, the self’s presence is manifested by its role in monitoring our activities. Even if we deny free will, we cannot deny the sense that something oversees our conscious affairs; this something can even participate in lucid dreaming.* We call it the self. It is part of the space that we call consciousness inside our head. Yet, if we looked inside the head, we would see only densely compacted grey matter, and no space. It and consciousness cannot be located but we believe both to be there.

Black holes provide an analogy. We cannot see them, but can infer their presence by their affects on nearby space.

As one example of the Eastern approach, advaita disciples learn that they cannot find the self by introspecting for it. Still, its absence does not imply that it is a creature of illusion. The inability to find it can be explained otherwise. It disappears under the flashlight of conscious focus. Try an experiment in perception. Stare at a blue dot lit against a yellow background. After a few minutes of focus the blue merges with the yellow. In Buddhist or Hindu meditation, the self dissolves into the background of consciousness. In Zen, this dissolution can initiate the experience of Big Mind, that one is a larger consciousness. But after the experience, self returns. Its earlier absence does not mean that it is illusory. In deep sleep, consciousness fades and self disappears but later returns.

Were self a tag-along phenomenon, a chimera, it would not have evolved through natural selection to play its prominent role in our minds. It has survival value, whether as a monitor of activities, their agent, or both. This does not mean it has independent "reality"--only that it has a function as do eyes, fingers, and orgasms.

Think of it this way. A tire is not a car. The steering wheel is not. Pistons are not. Put them all together and you have a car. You do not think of it as an illusion. Now imagine another situation. You sit on the couch. Drowsy, you dream a little. Then you awaken. You feel deep satisfaction at Mozart on the radio. You notice the cat purring on your lap. You think about a shopping list. You recall your boss's memo. With each of these, a different part of the brain "lights up," although if you had deliberately looked for a self you would not have found it. Yet you are aware of each event. Somehow, they harmonize into an "I" that is composed of them all. Although self is subjective, it gains explanations through comparison to a car. Even though the car is tangible as an object and self is intangible, the analogy is instructive once we allow that, for example, force at a distance (gravity) has an intangible "source," yet we recognize its affects.
______________________________
*(Yes, the word is "sense," and sensations do not prove reality. Nor do they disprove it. You can look at your chair. Your view, your skin, and the weight of your body against the chair are only perceptions/sensations which may be only that, with nothing "beyond" them, not even the chair, but you assume the chair to have shaped them. You can disclaim the objective reality of the chair if you want, but that is another argument.)

The Self Is A Conceptual Chimera

John Allen Paulos says this about the self: "Doubt that a supernatural being exists is banal, but the more radical doubt that we exist, at least as anything more than nominal, marginally integrated entities having convenient labels like "Myrtle" and "Oscar," is my candidate for Dangerous Idea. This is, of course, Hume's idea — and Buddha's as well — that the self is an ever-changing collection of beliefs, perceptions, and attitudes, that it is not an essential and persistent entity, but rather a conceptual chimera. If this belief ever became widely and viscerally felt throughout a society — whether because of advances in neurobiology, cognitive science, philosophical insights, or whatever — its effects on that society would be incalculable. (Or so this assemblage of beliefs perceptions, and attitudes sometimes thinks.)"

This is his answer to the annual question posed by Edge. For 2006 it is, What is the most dangerous idea of the year?

Paulos is Professor of Mathematics, Temple University, Philadelphia and authored A Mathematician Plays the Stock Market, among other works.