One hears increasingly from philosophers that statistical inference is a technical study that is well in control by statisticians and should be left to them; and one hears, increasingly, from mathematical statisticians that all this talk about interpretations of probability is so much philosophical frosting that is utterly irrelevant to the serious business of producing mathematical statistics. "The more interpretations of probability there are, the wider the scope of applications of our purely mathematical theories." The point of this paper is (...) to present, in detail, a situation in which an individual with given degrees of belief, given evidence, and given values, will have three different and contrary courses of action recommended to him, each according to one of the three most popular interpretations of probability. (shrink)

One hears increasingly from philosophers that statistical inference is a technical study that is well in control by statisticians and should be left to them; and one hears, increasingly, from mathematical statisticians that all this talk about interpretations of probability is so much philosophical frosting that is utterly irrelevant to the serious business of producing mathematical statistics. “The more interpretations of probability there are, the wider the scope of applications of our purely mathematical theories.” The point of this paper is (...) to present, in detail, a situation in which an individual withgivendegrees of belief,givenevidence, andgivenvalues, will have three differentand contrarycourses of action recommended to him, each according to one of the three most popular interpretations of probability. (shrink)

This collection represents the best recent work on the subject and includes essays by Clark Glymour, James H. Fetzer, and Wesley C. Salmon.

Papers collected in this volume were originally presented at a symposium held at the University of Pennsylvania in December, 1968 and revised in the light of discussion at the symposium for publication. The contributors hold different views about the role played by induction in theories of knowledge and rational belief but many of the papers are conciliatory, reflecting no doubt a good deal of helpful communication at the symposium. For example, Frederic Schick's clearly written and informative lead article considers subjectivist, (...) empiricist, and pragmatist theories of rational belief, arguing that they are compatible theories relevant to different types of issues. Marshall Swain follows with an article which presents a general framework within which rules of rational acceptance can be constructed. An exchange between Isaac Levi and Richard Jeffrey shows that advocates of theories of acceptance and theories of partial belief may be defending complementary and not mutually exclusive theories. In the remaining three essays Henry Kyburg Jr., Gilbert Harman, and Keith Lehrer defend their own distinctive views about the nature of inductive inference and rational belief. Kyburg traces difficulties in some theories to the acceptance of the principle of conjunction which he rejects. Harman and Lehrer both see the relation of inductive inference to explanation as crucial to understanding the former and they develop theories along different lines which make use of this relation. A long and useful bibliography was prepared for the symposium by Ralph L. Slaght and revised for publication in the volume.--R. H. K. (shrink)

For a helpful presentation of the various views on probability and inductive logic as well as a thorough survey of the present literature on these topics, one could hardly do better than this work. Kyburg presents, in separate chapters, classical, frequency, logical, subjectivist and epistemological theories of probability, referring to major classical and contemporary works where each of these views is defended. He presents the common criticisms of each view as well as some criticisms of his own and brings (...) out what he takes to be of value in each view. These chapters are preceded by a brief but clear presentation of the probability calculus and a chapter on informal interpretations of probability in ordinary language. A descriptive bibliography follows each chapter in which Kyburg comments on the leading works in each area. The same format applies to his discussion of inductive logic in part II. Inductive inference is discussed in ordinary language and in formal contexts. Statistical inference, confirmation theories, acceptance theories, and demonstrative induction are discussed in separate chapters. There are also discussions of the role of simplicity in inductive inference and the problem of justifying induction. Exercises are added to each chapter and the work might serve well as a text in this field. A forty-eight page bibliography at the end of the book is another one of its assets.--R. H. K. (shrink)

Quantities are naturally viewed as functions, whose arguments may be construed as situations, events, objects, etc. We explore the question of the range of these functions: should it be construed as the real numbers (or some subset thereof)? This is Carnap's view. It has attractive features, specifically, what Carnap views as ontological economy. Or should the range of a quantity be a set of magnitudes? This may have been Helmholtz's view, and it, too, has attractive features. It reveals the close (...) connection between measurement and natural law, it makes dimensional analysis intelligible, and explains the concern of scientists and engineers with units in equations. It leaves the philosophical problem of the relation between the structure of magnitudes and the structure of the reals. What explains it? And is it always the same? We will argue that on the whole, construing the values of quantities as magnitudes has some advantages, and that (as Helmholtz seems to suggest in "Numbering and Measuring from an Epistemological Viewpoint") the relation between magnitudes and real numbers can be based on foundational similarities of structure. (shrink)

Two distinct issues are sometimes confused in the base rate literature: Why do people make logical mistakes in the assessment of probabilities? and why do subjects not use base rates the way experimenters do? The latter problem may often reflect differences in an implicit reference class rather than a disinclination to update a base rate by Bayes' theorem. Also important are considerations concerning the interaction of several potentially relevant base rates.

Charles Morgan has argued that nonmonotonic logic is ``impossible''. We show here that those arguments are mistaken, and that Morgan's preferred alternative, the representation of nonmonotonic reasoning by ``presuppositions'' fails to provide a framework in which nonmonotonic reasoning can be constructively criticised. We argue that an inductive logic, based on probabilistic acceptance, offers more than Morgan's approach through presuppositions.

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.

The system presented by the author in The Logical Foundations of Statistical Inference suffered from certain technical difficulties, and from a major practical difficulty; it was hard to be sure, in discussing examples and applications, when you had got hold of the right reference class. The present paper, concerned mainly with the characterization of randomness, resolves the technical difficulties and provides a well structured framework for the choice of a reference class. The definition of randomness that leads to this framework (...) is simplified and clarified in a number of respects. It resolves certain puzzles raised by S. Spielman and W. Harper in their contributions to Profiles: Henry E. Kyburg, Jr. and Isaac Levi 1982). (shrink)

Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book (...) will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science. (shrink)

First, a comment on a pessimistic note: Salmon says we can't be sure there is any such thing as inductive inference: in demanding that some explanations have the form of correct inductive inferences, “we may be laying down a requirement which cannot be fulfilled.” To doubt that we can fulfill that requirement is to doubt that we can formalize inductive logic. It may be true, but why begin the fight by throwing in the sponge? It is also true that there (...) are difficulties involved in formalizing acceptance rules for inductive conclusions, but these difficulties may be overcome. It is false to claim that we ‘cannot claim to know exactly’ what these acceptance rules are. Only two years ago I did just that. It was true that my claim was shown to be erroneous a year later, but that fate can befall almost any worthwhile claim. (shrink)