Chaotic Logic by B. Goertzel
By B. Goertzel
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The purpose of each cluster in the dual network is to instruct its subservient clusters in the way that it estimates will best fulfill the task given to it by its master cluster -- and this estimation is based on reasoning analogically with respect to the information stored in its memory bank. Let's get a little more concrete. The brain is modeled as a dual network of neural networks. It is considered to consist of "level k clusters" of autonomous neural networks, each one of which consists of 1) a number of level k-1 clusters, all related to each other, 2) some networks that monitor and control these level k-1clusters.
In finite field theory there is something called the "discrete logarithm" of a number, written dlogb(n). The discrete logarithm is defined just like the ordinary logarithm, as the inverse of exponentiation. But in a finite field, exponentiation must be defined in terms of the "wraparound" arithmetic illustrated in the previous paragraph. For instance, in the field of size 7, 34 = 4. Thus one has dlog3(4) = 4. But how could one compute the log base 3 of 4, without knowing what it was? The powers of 3 can wrap around the value 7 again and again -- they could wrap around many times before hitting on the correct value, 4.
In sum, psychologists ignored those few voices which insisted on associating everyday mental processes with mathematical logic. And, on the other hand, logicians actively rebelled against the idea that the rules of mathematical logic must relate to rules of mental process. Psychology benefited from avoiding logism, and logic gained greatly from repudiating psychologism. 1. The Rebirth of Logism But, of course, that wasn't the end of the story. Although contemporary psychology and logic have few direct relations with one another, in the century since Frege there has arisen a brand new discipline, one that attempts to bring psychology and logic closer together than they ever have been before.