Theory Of Induction
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The Material Theory of Induction
"The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference."--
Handbook of Mathematical Induction
Author: David S. Gunderson
language: en
Publisher: Chapman & Hall/CRC
Release Date: 2016-11-16
Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn's lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process.
Peirce’s and Lewis’s Theories of Induction
Author: Chung-ying Cheng
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book is based on my doctoral dissertation written at Harvard University in the year of 1963. My interest in Peirce was inspired by Professor D. C. Williams and that in Lewis by Professor Roderick Firth. To both of them lowe a great deal, not only in my study of Peirce and Lewis, but in my general approach toward the problems of knowledge and reality. Specifically, I wish to acknowledge Professor Williams for his patient and careful criticisms of the original manuscripts of this book. I also wish to thank Professor Firth and Professor Israel Scheffler for their many suggestive comments regarding my discussions of induc tion. However, any error in this study of Peirce and Lewis is completely due to myself. Chung-ying Cheng Honolulu, Hawaii March,1967 TABLE OF CONTENTS PREFACE V SUMMARY IX CHAPTER I: Introduction I I. Problem of Justifying Induction and Proposal for Its Dissolution I 2. Two Types of Recent Arguments for the Validity of Induction 3 Arguments from Paradigm Cases and Uses of Words 4 3.