Conceptual Systems and Logical Analysis

In The Shadows of the Mind, Roger Penrose spends many pages discussing whether calculating machines (computers) can match human intelligence.  Penrose proposes to elucidate the nature of human consciousness through modern mathematical discoveries and quantum physics. He is working out the implications of Godel’s Theorem but in reverse, so to speak.  Since we cannot completely prove any axiomatic system in mathematics, when we do discover truth in mathematics […]

Joseph Weizenbaum , Computer Power and Human Reason (New York, W.H. Freeman and Company, 1976), pp 221-22. There was a time when physics dreamed of explaining the whole of physical reality in terms of one comprehensive formalism. Leibnitz taught that if we knew the position and velocity of every elementary particle in the universe, we could predict the universe’s whole future course. But then Werner Heisenberg proved that […]

One of the purposes of his site is to provide an overall view of Systems of Thought , ways of seeing and understanding things derivative from the work of David Hilbert and Alan Turing. Let us begin with the concept of RULE FOLLOWING SYSTEMS: Here is how it works: A machine is the best model of a Rule Following System. A Machine is not merely law abiding. A […]