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)

The question of the relationship of the making of value judgments in a typically ethical sense to the methods and procedures of science has been discussed in the literature at least to that point which e. e. cummings somewhere refers to as “The Mystical Moment of Dullness.” Nevertheless, albeit with some trepidation, I feel that something more may fruitfully be said on the subject.

This comprehensive discussion of the problem of rational belief develops the subject on the pattern of Bayesian decision theory. The analogy with decision theory introduces philosophical issues not usually encountered in logical studies and suggests some promising new approaches to old problems."We owe Professor Levi a debt of gratitude for producing a book of such excellence. His own approach to inductive inference is not only original and profound, it also clarifies and transforms the work of his predecessors. In short, the (...) book deserves to become a classic....There is a great deal of interest in the book besides these basic matters [forumlating rules of acceptance]. Some of the most interesting chapters are those that examine the implications of such rules. The discussions of probability, generalization, and various forms of inference are brilliant and enlightening. Indeed, the problems and methods elaborated by Professor Levi in his book serve as a new foundation for the study of inductive inference."--Keith Lehrer, Nous"Levi's book is an extremely interesting report on 'tentative and speculative first steps' toward a decision-theoretic approach to inductive inference....Professor Levi is to be congratulated on his ingenious development and application of this approach...."--Richard C. Jeffrey, The Journal of Philosophy. (shrink)

The book was planned and written as a single, sustained argument. But earlier versions of a few parts of it have appeared separately. The object of this book is both to establish the existence of the paradoxes, and also to describe a non-Pascalian concept of probability in terms of which one can analyse the structure of forensic proof without giving rise to such typical signs of theoretical misfit. Neither the complementational principle for negation nor the multiplicative principle for conjunction applies (...) to the central core of any forensic proof in the Anglo-American legal system. There are four parts included in this book. Accordingly, these parts have been written in such a way that they may be read in different orders by different kinds of reader. (shrink)

1. I shall attempt in this paper to give a rounded, if schematic, account of the concept of probability. My central concern will be to clarify the sense in which law-like statements (including 'statistical' law-like statements) are made probable by observational data which, in a sense equally demanding analysis, 'accord' with them.

In past years, the traditional Bayesian theory of rational decision making, based on subjective calculations of expected utility, has faced powerful attack from philosophers such as David Lewis and Brian Skyrms, who advance an alternative causal decision theory. The test they present for the Bayesian is exemplified in the decision problem known as 'Newcomb's paradox' and in related decision problems and is held to support the prescriptions of the causal theory. As well as his conclusions, the concepts and methods of (...) Professor Eells introduces in the course of his analyses have extensive implications, not solely for probability theorists narrowly conceived, but for economists, statisticians and psychologists concerned with decision making and the employment of Bayesian principles. They and their students will, in addition, find the early chapters of great use as a background and introduction to the subject as a whole. (shrink)

First published in 1982, Ellery Eells' original work on rational decision making had extensive implications for probability theorists, economists, statisticians and psychologists concerned with decision making and the employment of Bayesian principles. His analysis of the philosophical and psychological significance of Bayesian decision theories, causal decision theories and Newcomb's paradox continues to be influential in philosophy of science. His book is now revived for a new generation of readers and presented in a fresh twenty-first-century series livery, including a specially commissioned (...) preface written by Brian Skyrms, illuminating its continuing importance and relevance to philosophical enquiry. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:137. PROBABILITY IN HUME'S SCIENCE OF MAN This paper is an attempt to make sense of a fragment of Hume's positive philosophy, namely his theory of how we apportion belief on the basis of ambiguous evidence. The topic is one that has received little critical attention from philosophers. One reason for this neglect is the belief that Hume's discussion of probable reasoning is not addressed to philosophical questions, but (...) rather is concerned merely to give a psychological theory of why we tend to make the inferences we do. Another is the view that Hume's psychology of probability is too obscure to merit serious study. I hope to show, however, that Hume's discussion of probable reasoning contains more philosophy, and more interesting psychology, than the prevalence of these attitudes would suggest. The main philosophical content that I see in Hume's account of probable reasoning is that it embodies a certain theory of belief, worked out in some detail. Here the central notion is the "belief-feeling", vivacity. After an initial discussion of Hume's use of this notion, I hazard the opinion that vivacities are related to probabilities by a simple subtraction formula (§1). The investigation of Hume's account of probable inference (§2) gives strong grounds for thinking that this conjecture is indeed correct. Finally, an examination of what Hume says about the influence of probability on the passions unearths a bold theory of the specific psychological mechanism by which the subtraction of probabilities is effected (§3).§1 Degrees of belief Hume's philosophy makes heavy use of the quality of perceptions which he referred to variously as "force", "liveliness", "violence", "vivacity", "strength", "firmness" and so on. As the variety of these terms indicates, Hume was not entirely happy with any of them. He says it is 138. impossible by words to describe this feeling, which every 2 one must be conscious of in his own breast (A19). But we need to use some word, and rather than emulate Hume's diverse usage it will be convenient to adhere uniformly to the single term 'vivacity'. The first use to which Hume puts vivacity is in distinguishing impressions from ideas. Intuitively, impressions are either sensations, passions or emotions, whereas ideas are the perceptions involved in thinking or reasoning. And Hume maintains that we can distinguish these two kinds of perceptions by their differing degrees of vivacity: all impressions have greater vivacity than any idea. Apparently Hume thinks that the difference in vivacity between impressions and ideas is normally quite considerable, although in a few instances there is only a small differential (T2). Vivacity is again used by Hume to distinguish between belief and conception. Although to have an idea of God, say, is not the same thing as to believe in God, Hume argues that what distinguishes the latter is only the manner of conception. In belief, the idea feels different to an idea that is entertained incredulously. And this difference in feeling is identified by Hume with a difference in vivacity (T96).3 In general, Hume thinks of beliefs as being ideas, not impressions (T86 being an exception). This is the natural view, if one thinks of the distinction between impressions and ideas as a distinction between feeling and thinking (T2, A9 ). What distinguishes beliefs then is a somewhat intermediate vivacity, inferior to the vivacity of an impression but superior to the vivacity of a mere conception. A third use to which Hume puts vivacity is in making the distinction between memory and other beliefs. Just as beliefs are distinguished from other conceptions by their greater vivacity, so likewise memories are distinguished from other beliefs by their greater vivacity (T153). 139. Each of these three applications of vivacity seems to be implausib^e. Introspection inevitably suggests that impressions are not always more vivacious or forceful, or whatever, than ideas. Similarly it seems that our beliefs, and even our memories, are often less vivid than our fancies, contrary to what Hume claims. A considerable part of Hume's appendix to the Treatise is concerned with such objections. Hume appears to allow that what we would naturally call the vivacity of ideas is not a quality... (shrink)