Realistic (non-associative) Logic and a Possible Explanations of 7 + 2 Law

摘要

When the subjective probabilities (degrees of belief) p1 and p2 of two statements S1 and S2 are known, and there is no information about the relationship between these statements, then the probability of S1 & S2 can take any value from the interval max(p1+p2- 1,0), min(p1,p2). If we must select a single number from thus interval, the natural idea is to take its midpoint. The corresponding 'and' operation p1 and p2(def) (1/2)(max(p1 + p2- 1,0)) + min(p1, p2) is not associative. However, since the largest possible nonassociativity degree.