What Does Kurt Gödel’s Incompleteness Theorem Have to Do With Mental Health?


In 1931, Kurt Gödel, a brilliant mathematician, gained quite a bit of fame with his “Incompleteness Theorem.” What Gödel stated was the following (in non-technical terms thanks to a Wikipedia article):

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250).

Reading this, although directly applicable to mathematics, hit home as an analogy for mental health care and the quest for successful treatment of our conditions as patients.

The equation in our case, at its simplest expression is expressed as such:

whereas P = patient, D = Doctor, C = condition, and T = treatment. But we know all too well that it is not this simple, don’t we? No treatments for mental health are fully consistent nor are they anywhere near complete.

There are too many factors involved to arrive at a simple treatment for the more complex mental health problems. Too many unknowns or additional variables. These variables come in the form of emotional/situational issues with the patient, education/knowledge of the presenting symptoms by the doctor, the symptoms presented by the patient, and the available known data regarding the various symptom sets related to the potential condition diagnoses which is again, limited by the presenting patient and comprehension of said presentation by the attending physician. Therefore, with this equation, we have an infinite amount of possibilities which is essentially what Gödel’s theorem states – that there is an infinite amount of true possible answers but none of them are absolutely provable.

If we take this theory, this Gödel theorem of Incompleteness, we significantly address the reasoning behind the continuing stigma of treatment for mental health in the world today. For instance, let’s address cancer. Most cancers respond to radiation and various forms of chemotherapy, right? Granted, we still lose people to cancer but there is an accepted manner of treatment and no one seems to question that course. It is assumed if one is diagnosed with cancer, he or she will receive some form of radiation or chemotherapy to combat the disease within.

If one is struggling mentally, we hear everything from “suck it up” to “take the natural approach” to “go exercise more” to “take a pill” to “every kind of therapy under the sun” to “eat more chocolate” to “happy light” to “color therapy” to “hospitalization” to…. you get my point. I could keep going for quite some time. There is a sea of possibilities to treat the many various forms of mental health issues which have plagued mankind since the dawn of time.

Even the ancient Greek scholars studied these disorders of the mind and out of these studies, they developed equations which helped them further gain insight into the functioning of the brain we have today. Now, they may have referred to mental imbalance as “black bile” but they were aware that when the mind and body were not connected and in balance, there was something very awry in the state of man. For the Greeks, mental well-being was very closely associated with the health of the body which is why good health was important. As a group of voracious scholars, to be off balance was to fail to be the essence of what their very society represented.

Back to the equation at hand, however. While scholars today struggle to continue to understand the inner workings of the human mind and thereby the issues which cause mental disharmony, we are left with this Incomplete Theorem of care to combat the imbalance inside us.

Gödel’s Theorem in the application of mental health may seem hopeless in the face of stigma because it does not narrow down the understanding of the range of issues so many of us face but there is a silver lining. With the infinite possibilities available for care and those possibilities increasing in effectiveness every day, we are able to fine-tune the available treatments for each patient, thereby increasing the potential for a successful outcome, even if it is just one case at a time.

I am reminded at this time of the story of the hare and the turtle. The hare zooms off past the great oak tree at the top of the hill the beginning of the race while the turtle meanders along the dusty road because well, that’s what turtles do. The hare, winded halfway through the race, stopped to nestle himself among some clover for a quick rest, only to discover the turtle crossed the finish line while he slept. As those around us continue to sleep through the reality that is the challenge of mental health issues, unaware of the battle we fight every second of the day, it is up to those of us who are awake and trudging forward to bring them to the finish line and show them that we are capable of getting there too.

An infinite but unprovable amount of solutions is not a bad thing for us – in fact, it is a rainbow of hope shining across an otherwise dark and stormy sky. Don’t let it go.

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