APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

In his new foreword to this edition, Hilary Putnam forcefully rejects these nativist claims.

This definitive survey of the hottest issues in inductive logic sets the stage for further classroom discussion.

Preface. I. BASICS OF LOGIC. Introduction. The Structure of Simple Statements. The Structure of Complex Statements. Simple and Complex Properties. Validity. 2. PROBABILITY AND INDUCTIVE LOGIC. Introduction. Arguments. Logic. Inductive versus Deductive Logic. Epistemic Probability. Probability and the Problems of Inductive Logic. 3. THE TRADITIONAL PROBLEM OF INDUCTION. Introduction. Hume’s Argument. The Inductive Justification of Induction. The Pragmatic Justification of Induction. Summary. IV. THE GOODMAN PARADOX AND THE NEW RIDDLE OF INDUCTION. Introduction. Regularities and Projection. The Goodman Paradox. The Goodman (...) Paradox, Regularity, and the Principle of the Uniformity of Nature. Summary. 5. MILL’S METHODS OF EXPERIMENTAL INQUIRY AND THE NATURE OF CAUSALITY. Introduction. Causality and Necessary and Sufficient Conditions. Mill’s Methods. The Direct Method of Agreement. The Inverse Method of Agreement. The Method of Difference. The Combined Methods. The Application of Mill’s Methods. Sufficient Conditions and Functional Relationships. Lawlike and Accidental Conditions. 6. THE PROBABILITY CALCULUS. Introduction. Probability, Arguments, Statements, and Properties. Disjunction and Negation Rules. Conjunction Rules and Conditional Probability. Expected Value of a Gamble. Bayes’ Theorem. Probability and Causality. 7. KINDS OF PROBABILITY. Introduction. Rational Degree of Belief. Utility. Ramsey. Relative Frequency. Chance. 8. PROBABILITY AND SCIENTIFIC INDUCTIVE LOGIC. Introduction. Hypothesis and Deduction. Quantity and Variety of Evidence. Total Evidence. Convergence to the Truth. ANSWERS TO SELECTED EXERCISES. INDEX. (shrink)

According to Williamson, your evidence consists of all and only what you know (E = K). According to his critics, it doesn’t. While E = K calls for revision, the revisions it calls for are minor. E = K gets this much right. Only true propositions can constitute evidence and anything you know non-inferentially is part of your evidence. In this paper, I defend these two theses about evidence and its possession from Williamson’s critics who think we should break more (...) radically from E = K. (shrink)

Israel 2004 claims that numerous philosophers have misinterpreted Goodman’s original ‘New Riddle of Induction’, and weakened it in the process, because they do not define ‘grue’ as referring to past observations. Both claims are false: Goodman clearly took the riddle to concern the maximally general problem of “projecting” any type of characteristic from a given realm of objects into another, and since this problem subsumes Israel’s, Goodman formulated a stronger philosophical challenge than the latter surmises.

First, a brief historical trace of the developments in confirmation theory leading up to Goodman's infamous "grue" paradox is presented. Then, Goodman's argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman's "grue" argument against classical inductive logic. The upshot of this analogy is that the "New Riddle" is not as vexing as many commentators have claimed. Specifically, the analogy reveals an intimate connection between Goodman's problem, and (...) the "problem of old evidence". Several other novel aspects of Goodman's argument are also discussed. (shrink)

A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

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)