Essential to Peirce's distinction among three kinds of reasoning, deduction, induction and abduction, is the claim that each is correlated to a unique species of validity irreducible to that of the others. In particular, abductive validity cannot be analyzed in either deductive or inductive terms, a consequence of considerable importance for the logical and epistemological scrutiny of scientific methods. But when the full structure of abductive argumentation — as viewed by the mature Peirce — is clarified, every inferential step in (...) the process can be seen to dissolve into familiar forms of deductive and inductive reasoning. Specifically, the final stage is a special type of practical inference which, if correct, is deductively valid, while the creative phase, surprisingly, is not inferential at all. In neither is abduction a type of inference to the best explanation. The result is a major reassessment of the relevance of Peirce's views to contemporary methodological studies. (shrink)

Like Leibniz, C. S. Peirce drew much of the inspiration for his philosophical work from a close study of logical and mathematical reasoning. Now what insights did this study reveal to Peirce? His own answer is formulated as follows: “My first real discovery about mathematical procedure was that there are two kinds of necessary reasoning, which I call the Corollarial and the Theorematic.…” The import of this discovery was lost on philosophers for a long time. The purpose of the present (...) paper is to show what Peirce's insight amounts to, to point out some of its applications, relate it to certain recent developments in the philosophy of logic, and thereby vindicate Peirce's distinction. This undoubtedly will also help to show its present day relevance. (shrink)

This volume represents an important contribution to Peirce’s work in mathematics and formal logic. An internationally recognized group of scholars explores and extends understandings of Peirce’s most advanced work. The stimulating depth and originality of Peirce’s thought and the continuing relevance of his ideas are brought out by this major book.

This monograph attempts to clarify one significant but much neglected aspect of Peirce's contribution to the philosophy of science. It was written in 1963 as my M. A. thesis at the Uni versity of Illinois. Since the topic is still neglected it is hoped that its pUblication will be of use to Peirce scholars. I should like to acknowledge my indebtedness to Dr. Max Fisch who broached this topic to me and who advised me con tinuously through its development, assisting (...) generously with his own insights and unpublished Peirce manuscripts. TABLE OF CONTENTS INTRODUCTION 1. A Current Issue in the Philosophy of Science 1 2. Peirce and His Theory of Abduction 5 3. The General Character of Abduction 7 PART I: THE EARLY THEORY 1. Peirce's Earliest Conception of Inference 11 2. Three Kinds of Inference and Three Figures of Syllogism 13 3. Ampliative Inference and Cognition 17 4. Induction and Hypothesis 20 5. The Method of Methods 23 PART II: THE LATER THEORY 1. The Transitional Period 28 2. Three Stages of Inquiry 31 3. Abduction and Guessing Instinct 35 4. Logic as a Normative Science 38 5. Hypothesis Construction and Selection 41 6. Abduction and Pragmatism 44 7. Economy of Research 47 8. Justification of Abduction 51 CONCLUSION 55 61 BIBLIOGRAPHY INTRODUCTION 1. (shrink)

Introduction 1 1 Inductive Inference: A New Approach 19 2 Luck, License, and Lingo 31 3 Natural Kinds 41 4 Concerning a Fiction about How Facts Are Forecast 57 5 Grue 79 6 Concepts of Projectibility and the Problems of Induction 97 7 Induction, Conceptual Spaces, and AI 117 8 The Projectibility Constraint 135 9 Simplicity as a Pragmatic Criterion for Deciding What Hypotheses to Take Seriously 153 10 A Grue Thought in a Bleen Shade: ’Grue’ as a Disjunctive Predicate (...) 173 11 Entrenchment 193 12 No Model, No Inference: A Bayesian Primer on the Grue Problem 225 13 Bayesian Projectibility 241 14 Learning and Projectibility 263 15 Selecting Variables and Getting to the Truth 273 Annotated Bibliography 281 Index 459. (shrink)

R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has (...) this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however. (shrink)

The roughly two and a half millennia over which we can trace the development of mathematics as a discipline have seen ups and downs in its study; the "ups" have involved varying emphases and interests depending on the problems and the temper of the time. The 19th Century may be characterized as a period of development of rigor and attention to the axiomatic method in mathematics. This focus on the deductive process in mathematics was accompanied by the application of mathematics (...) in the study of the deductive process itself. It is safe, I think, to say that the best-known and most influential of the lines of.. (shrink)