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.
Author(s): Polya G.
Publisher: Princeton
Year: 1968
Language: English
Pages: 240
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
