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

Mathematics and Plausible Reasoning #2

by George Pólya

This is a guide to the practical art of plausible reasoning, particularly in mathematics but also in every field of human activity. Using mathematics as the example par excellence, Professor Polya shows how even that most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can even begin, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but not proved until much later. In the same way, solutions to problems can be guessed, and a good guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser." Professor Polya's deep understanding of the psychology of creative mathematics enables him to show the reader how to attack a new problem, how to get at the heart of it, what trains of thought may lead to a solution. There is no magic formula here, but there is much practical wisdom. Volumes I and II together make a coherent work on Mathematics and Plausible Reasoning. Volume I on Induction and Analogy stands by itself as an essential book for anyone interested in mathematical reasoning. Volume II on Patterns o f Plausible Inference builds on the examples of Volume I but is not otherwise dependent on it. A more sophisticated reader with some mathematical experience will have no difficulty in reading Volume II independently, though he will probably want to read Volume I afterward. Professor Polya's earlier more elementary book How to Solve It was closely related to Mathematics and Plausible Reasoning and furnished some background for it.

Genres: Mathematics, Science, Philosophy, Logic, Nonfiction

202 pages, Paperback

First published January 1, 1954

Reviews

[Eugene Shcherbinin · Rating 5 out of 5]

what a great book! Really enjoyed how it gives a very intuitive introduction to both frequentist and Bayesian approach to probability and applies it in a very wise manner to a diversity of problem-solving issues. I think I myself started thinking in categories of plausibility evaluating, for example, results I obtain in further mathematical methods problems

[Sarah Wise · Rating 5 out of 5]

In defense of subjective probability. I’ve been pondering the phenomenon, and it goes something like this: we go through university being taught a frequentist perspective, which involves deriving hypotheses from data collected, accepting or rejecting the null hypothesis, and accumulating information. But what if there is another perspective which does not deal with data as a prior, as a given set from which you deduct your hypothesis? This is the logic of plausible reasoning. It's uncomfortable from the frequentist point of view. How do you determine the priors? Who is to say if they are correct? biased? is it too subjective? . . . Here, Polya argues poetically for the potential for plausible reasoning to have rigour and leverage subjectivity. I think this is an incredible book. I highly recommend it if you are interested in Bayesianism or conditional probability.