Mathematics and plausible reasoning

Description

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. II, on Patterns of Plausible Inference, attempts to develop a logic of plausibility. What makes some evidence stronger and some weaker? How does one seek evidence that will make a suspected truth more probable? These questions involve philosophy and psychology as well as mathematics. Cover Title Page Copyright Page Preface Preface to Second Edition Hints to the Reader Table of Contents Chapter XII Some Conspicious Patterns 1. Verification of a Consequence 2. Successive verification of several consequences 3. Verification of an improbable consequence 4. Inference from Analogy 5. Deepening the Analogy 6. Shaded analogical inference Examples and Comments Chapter XII Chapter XIII Futher Patterns and First Links 1. Examining a Consequence 2. Examining a Possible Ground 3. Examining a Conflicting Conjecture 4. Logical Terms 5. Logical links between patterns of Plausible Inference 6. Shaded Inference 7. A Table 8. Combination of Simple Patterns 9. On Inference from Analogy 10. Qualified Inference 11. On Successive Verifications 12. On Rival Conjectures 13. On Judicial Proof Examples and Comments Chapter XIII First Part Second Part Chapter XIV Change, The Ever Present Rival Conjecture 1. Random Mass Phenomena 2. The Concept of Probability 3. Using the Bag and the Balls 4. The calculus of Probability, Statistical Hypothesis 5. Straightforward prediction of frequencies 6. Examination of Phenomena 7. Judging Statistical Hypothesis 8. Choosing between Statistical Hypothesis 9. Judging non-statistical conjectures 10. Judging mathematical conjectures Examples and Comments on Chapter XIV First Part Second Part Chapter XV The Calculus of Probability and The Logic of Plausible Reasoning 1. Rules of Plausible Reasoning? 2. An aspect of demonstrative reasoning 3. A corresponding aspect of Plausible reasoning 4. An aspect of calculus of probability. Difficulties 5. An aspect of calculus of probability. An Attempt 6. Examining a consequence 7. Examining a possible ground 8. Examining a conflicting conjecture 9. Examining several consequences in succession 10. On Circumstantial evidence Examples and Comments on Chapter XV Chapter XVI Plausible Reasoning in Invention and Instruction 1. Object of present chapter 2. The story of little discovery 3. The process of solution 4. Deus ex machina 5. Heuristic justification 6. The story of another discovery 7. Some typical indications 8. Induction in invention 9. A few words to the teacher Examples and Comments on Chapter XVI Solutions Chapter XII Chapter XIII Chapter XIV Chapter XV Chapter XVI Bibliography Appendix Heuristic Reasoning in Theory of Numbers Additional Comments, Problems and Solutions