Mathematics and Plausible Reasoning. Vol. II: Patterns of Plausible Inference

George Polya Mathematics and Plausible Reasoning Vol. II: Patterns of Plausible Inference. (1954). I skipped Vol. I, which deals with mathematical induction. The two books are intended as texts, either for self-study or for a course. This purpose of this volume can be seen in this example. Given A -> B and B, what can be deduced? By formal logic, nothing; i.e., the truth of A cannot be inferred from the truth of the consequence. (However, if B is false, then A is false.) Polya shows that in fact the truth of A will be more or less credible depending on a number of relevant factors. For example, if the truth of B is less credible without the truth of A than with it, then B supports A. Or, if B is more credible, then A is more credible; and so on. IOW, the truth of A lies somewhere between 0 (false) and 1 (true).
     Polya notes that credibility of A depends in part on the judge's experience and background. He is very close to fuzzy logic here, but he doesn't take the next step because he can't see any supportable way to compute that value. Fuzzy logic formalises that personal judgement, and so can provide computations (which are used to control machines, e.g.) Polya uses probability theory, interpreting probability as credibility, and thus provides strong support for his POV. He's also interested in the use of plausible reasoning in mathematical research. An interesting book. I like its assumption that its subject is worth pursuing. Polya writes very clearly, and I was able to follow about half of the math. The general principles of plausible reasoning seem to me to be obvious. *** (1998) Update 2012-12: It seems to me that Polya was a pioneer of what became fuzzy logic, but I can’t recall any acknowledgement of this in the fuzzy logic text I read.