On January 14, 1978, Austrian-born logician Kurt Godel died of starvation when his wife Adele had been hospitalized for six months and could no longer prepare his food. As it happens, Godel had an obsessive fear of being poisoned and would not trust anyone to make his food aside from his wife, and so when she was hospitalized, he wasted away, dying at the weight of about 65 pounds. His widow survived another three years and then died herself. When he died at Princeton Hospital, the cause of death was rather unkindly given as being of “malnutrition and inanition caused by personality disturbance .” How was it that a logician, someone who was skilled and immensely able in logical proofs and understanding the limits of rationality when it came to artificial intelligence and the coherence of mathematical systems, could be so ignorant of the limits of rationality when it came to his own mind, dying because of obsessive paranoia that someone wished to kill him, when in the end his death was a result of his own irrational fears.
As it happens, Godel’s work in mathematics was particularly notable in two areas of great importance to the very problem that ended his life. For one, in his mid-20’s he published his two incompleteness theorems as a post-doc researcher in mathematics at the University of Vienna. The first of these theorems stated that for any recursive, self-consistent systems of axioms, like that of Euclidian Geometry, there will be true propositions that cannot be proven by the axioms, but must be presupposed to be true. The implications of this view are rather intriguing, including the fact that what is true is always going to extend out some distance from what we can prove. As human beings, we all live our lives in that space between that which can be proven and certain and that which we know to be true and hold on faith, or presuppose as part of the foundation of our thinking and behavior. At times, our presuppositions can be good ones, and noble ones. At times, as was the case for the mathematician himself, our assumptions and presuppositions can kill us because it is impossible for the world to prove its innocence, and generally extremely difficult for people to prove that they mean no harm, because we can always infer evil if we desire to do so, simply because the ability to prove a negative is not always present. No one may have desired to poison Kurt Godel, but because he only trusted his wife, and because those who would have desired to see him live could not prove their innocence in the face of his insistent suspicions and pervasive mistrust, his death serves as a confirmation of his own theorem, that there are truths that cannot be proven, and that sometimes such obscure matters of mathematical theory are matters of life and death importance.
The second aspect of interest is that our theoretical understanding of set theory  does not preclude two radically different conceptions of how the universe operates, namely what are called the Global Continuum Hypothesis and the axiom of choice. Without wishing to be too technical about the matter, what this means is that questions such as whether mankind is free or whether we are determined are matters of assumption and not matters of proof. Based on what assumptions we make, certain conclusions follow, but those assumptions cannot be proven. The same general conventions of set theory, or of any particular realm of study, can be chosen, and based on the assumptions one makes, certain conclusions can be “proven” by the system, even if those proofs depend on assumptions that cannot be proven by the chosen system, or any other system that is purely rational in nature. At some fundamental level, human beings live by faith and not by proof . Whether or not that is a comforting thought depends on the sort of person one is, and one’s general approach and attitude towards life.
These sorts of mathematical matters have importance when it comes to the way that our minds work, and how we try to mimic human intelligence via computers. At present, Artificial Intelligence suffers from very strict limitations, in that human input is necessary whenever a decision moves beyond mere rote algorithm, which computers do far better than human beings. In the design of games and in participating in conversations, computers show clear limitations because they are chained to recursive steps and cannot make the leaps of fancy that come so naturally to human beings. What this means is that when video games are designed or when bots attempt to participate in conversations that they are easy to sniff out because their response has a clear pattern, and lacks the randomness and quirkiness of human behavior . In addition, the fact that artificial intelligence appears to have real structural limits as it is currently conceived means that there are aspects of our minds that go beyond machine code and programming, leaving space for problems that scientific naturalists would rather not want to deal with in their efforts to banish all conceptions of the immaterial or the spiritual from human existence.
This leaves us where we began. No matter how bright or intelligent we are, no matter how rigorously logical we are, there will be something beyond what we can prove, something that we have to take on faith. No matter our contributions to the rigorous testing and limitations of rationality, we may always find ourselves outside of the lines, subject to the same irrationality in our own lives that we seek to banish from our fields of study and practice. Our very survival may be dependent on whether or not we can trust others provisionally enough to provide for our needs when we are unable to take care of ourselves, and whether those people we are called upon to trust are worthy of that trust. In the end, whether we are mathematicians on the level of Kurt Godel, or more ordinary human beings, we are all faced with the same unanswerable questions when we stare out into the universe or when we try to deal with each other. There is much that is true that we cannot prove, and much that we assume to be true that is not true that cannot be disproven either. How then are we to live in the best way possible for ourselves and those around us?
 Toates, Frederick; Olga Coschug Toates (2002). Obsessive Compulsive Disorder: Practical Tried-and-Tested Strategies to Overcome OCD. Class Publishing. p. 221.
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