Gödel vs. aristotle: Algorithmic complexity, models of the Mind, and top representations

Abstract

Brains learn much better than computers. But why? Is there a fundamental reason behind computers being slow learners? Often slow learning is described as computational complexity. This paper discusses that complexity of algorithms is as fundamental as Gödelian incompleteness of logic. Although the Gödel's theory is well recognized, its significance for engineering and modeling of the mind has not been appreciated. The mind-brain overcomes this fundamental difficulty, why computers cannot? I emphasize here that the reason is logical bases of machine learning. Aristotle explained that mind is not logical. The paper discusses that most neural networks and fuzzy systems require logical steps. A “nonlogical” mathematical theory overcoming computational complexity is described. It turns out to closely follow Aristotle's ideas. The new theory explains contents of the highest representations in the mind hierarchy, and related aesthetic emotions revealing the nature of the beautiful and the meaning of life. I discuss how it is possible that a non-logical mathematical technique can be computable, the function of logic in the mind, its relation to consciousness, and difficulties of understanding unconscious mechanisms.