Re P1: Jaynes presented his work as a method for science and engineering but throughout his work stated that the method was general. AR said that mathematics is

Re P1: Jaynes presented his work as a method for science and engineering but throughout his work stated that the method was general. AR said that mathematics is an abstracted form of conceptualization and logic which is why she was studying higher math to understand induction. Jaynes was not an epistemologist (nor an Objectivist) so the failure to distinguish or explain the exact relation between "A is A" from "A = A" is understandable especially in light of his explicit goal of targeting science and engineering. I did not claim that Jaynes solved the problem of induction nor that his theories were perfect, just that I think he was on the right track and made some significant contributions. Re P2: Jaynes' claim was that the laws of probability reduce to Aristotelian rules of deductive logic when the Pr=1. I do not agree that this makes logic subordinate to a mathematical process -- no more than AR's theory of concepts makes concept formation subordinate to algebra. In any case, the claim is mathematically true (given Jaynes' system which I admit may need revision) but it is also a fact that deduction is dependent on induction which is consistent. So to clarify the exact relations (without violating identity or inverting hierarchy, etc) requires AR's theory of concepts which Jaynes did not have. Moreover, to define the principles of when it is valid (without enumerating all cases) to go from Pr<1 to Pr=1 IS the problem of induction which Jaynes did not specifically address. Re P3: Jaynes completely rejects the the counting and ratio arguments for induction. Unfortunately he flips over to the subjectivist and vague "degrees of belief" view of probability and is unable to define it (which is why he needed a theory of concepts). This failure is hardly surprising given that every field today is split on intrinsic versus subjectivist premises.