Mathematics and Plausible Reasoning, Volume 2

Name: Mathematics and Plausible Reasoning, Volume 2 | Logic, Symbolic and mathematical
Brand: Princeton University Press
Price: 45.99 EUR
Availability: OnlineOnly

Logic, Symbolic and mathematical

George Polya(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 10. August 2021

240 Seiten

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978-1-4008-2372-7 (ISBN)

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Beschreibung

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Inhalt

Cover Page
Half-title Page
Title Page
Copyright Page
Preface
Hints to the Reader
Contents
Chapter XII. Some Conspicuous 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 on Chapter XII
Chapter XIII. Further 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 on Chapter XIII
Chapter XIV. Chance, 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 hypotheses
5. Straightforward prediction of frequencies
6. Explanation of phenomena
7. Judging statistical hypotheses
8. Choosing between statistical hypotheses
9. Judging non-statistical conjectures
10. Judging mathematical conjectures
Examples and Comments on Chapter XIV
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 the calculus of probability. Difficulties
5. An aspect of the 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 the present chapter
2. The story of a 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 to Problems
Bibliography
Appendix
I. Heuristic Reasoning in the Theory of Numbers
II. Additional Comments, Problems, and Solutions

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