Category Archives: Chapter 8: Deduction

   In mathematical logic, deduction is analyzed as a thing in itself, as an entity entirelyindependent from other mental processes. This point of view has led to dozens of beautiful ideas:Godel’s Incompleteness Theorem, the theory of logical types, model theory, … Continue reading →

   Let S be any set, and let I={I1, I2, …, In} be a subset of S, called the set of assumptions. LetSN denote the Cartesian product SxSxSx…xS, taken N times. And let T={T1,T2,…,Tn} be a set oftransformations; that is, … Continue reading →

    Contemporary mathematical logic is not the only conceivable deductive system. In fact, Isuggest that any deductive system which relies centrally upon Boolean algebra, withoutsignificant external constraints, is not even qualified for the purpose of general mentaldeduction. Boolean algebra is … Continue reading →

   When deduction is formulated in the abstract, in terms of assumptions and transformation, it isimmediately apparent that deductive reasoning is incapable of standing on its own. In isolation, itis useless. For why would there be intrinsic value in determining … Continue reading →