The notion of a severe test has played an important methodological role in the history of science. But it has not until recently been analyzed in any detail. We develop a generally Bayesian analysis of the notion, compare it with Deborah Mayo’s error-statistical approach by way of sample diagnostic tests in the medical sciences, and consider various objections to both. At the core of our analysis is a distinction between evidence and confirmation or belief. These notions must be kept separate (...) if mistakes are to be avoided; combined in the right way, they provide an adequate understanding of severity. Those who think that the weight of the evidence always enables you to choose between hypotheses “ignore one of the factors (the prior probability) altogether, and treat the other (the likelihood) as though it ...meant something other than it actually does. This is the same mistake as is made by someone who has scruples about measuring the arms of a balance (having only a tape measure at his disposal ...), but is willing to assert that the heavier load will always tilt the balance (thereby implicitly assuming, although without admitting it, that the arms are of equal length!). (Bruno de Finetti, Theory of Probability)2. (shrink)

Epistemology and Inference was first published in 1983. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. Henry Kyburg has developed an original and important perspective on probabilistic and statistical inference. Unlike much contemporary writing by philosophers on these topics, Kyburg's work is informed by issues that have arisen in statistical theory and practice as well as issues familiar to professional philosophers. In two major (...) books and many articles, Kyberg has elaborated his technical proposals and explained their ramifications for epistemology, decision-making, and scientific inquiry. In this collection of published and unpublished essays, Kyburg presents his novel ideas and their applications in a manner that makes them accessible to philosophers and provides specialists in probability and induction with a concise exposition of his system. (shrink)

In introducing the papers of the symposiasts, I distinguish between statistical, physical, and evidential probability. The axioms of the probability calculus and so Bayes’s theorem can be expressed in terms of any of these kinds of probability. Sober questions the general utility of the theorem. Howson, Dawid, and Earman agree that it applies to the fields they discuss--statistics, assessment of guilt by juries, and miracles. Dawid and Earman consider that prior probabilities need to be supplied by empirical evidence, while Howson (...) considers that there are no objective constraints on prior probabilities. I argue that simplicity is a crucial determinant of prior probability. Miller discussed how Bayes’s theorem can be interpreted so as to apply to physical probability. (shrink)

This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

The Description for this book, Theory and Evidence, will be forthcoming.

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

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)

Several of these essays have been printed whole in journals; others are in varying degrees new. Two main themes run through them. One is the problem of meaning, particularly as involved in the notion of an analytic statement. The other is the notion of ontological, commitment, particularly as involved in the problem of universals.

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides a restricted equivalence between the two: where the Bayesian model for MAXENT inference uses an "a priori" probability that is uniform, and where all MAXENT constraints are limited to 0-1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result 2 established a sensitivity of (...) MAXENT inference to the choice of the algebra of possibilities even though all empirical constraints imposed on the MAXENT solution are satisfied in each measure space considered. The resulting MAXENT distribution is not invariant over the choice of measure space. Thus, old and familiar problems with the Laplacian principle of Insufficient Reason also plague MAXENT theory. Result 3 builds upon the findings of Friedman and Shimony (1971; 1973) and demonstrates the absence of an exchangeable, Bayesian model for predictive MAXENT distributions when the MAXENT constraints are interpreted according to Jaynes's (1978) prescription for his (1963) Brandeis Dice problem. Lastly, Result 4 generalizes the Friedman and Shimony objection to cross-entropy (Kullback-information) shifts subject to a constraint of a new odds-ratio for two disjoint events. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach (...) has shortcomings. We also discuss the relationship between Schwarz's Bayesian Information Criterion and BTC. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes’ theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory’s goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)

This is an introduction to a collected volume. It distinguishes between evidential, statistical, and physical probability, and between objective and subjective understandings of evidential probability, in the use of Bayes’s theorem. If Bayes’s theorem is to be used to assess an objective evidential probability, a priori criteria--mainly the criterion of simplicity--are required to determine prior probability. The five main contributors to the volume discuss the use of Bayes’s theorem to assess the evidential probability of scientific theories, statistical hypotheses, criminal guilt, (...) and miracles; and also its value for assessing physical probability. (shrink)

How should we reason with causal relationships? Much recent work on this question has been devoted to the theses (i) that Bayesian nets provide a calculus for causal reasoning and (ii) that we can learn causal relationships by the automated learning of Bayesian nets from observational data. The aim of this book is to..

_Epistemology and Inference _ was first published in 1983. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. Henry Kyburg has developed an original and important perspective on probabilistic and statistical inference. Unlike much contemporary writing by philosophers on these topics, Kyburg's work is informed by issues that have arisen in statistical theory and practice as well as issues familiar to professional philosophers. In two (...) major books and many articles, Kyberg has elaborated his technical proposals and explained their ramifications for epistemology, decision-making, and scientific inquiry. In this collection of published and unpublished essays, Kyburg presents his novel ideas and their applications in a manner that makes them accessible to philosophers and provides specialists in probability and induction with a concise exposition of his system. (shrink)

... Press for their editorial perspicacity, to the National Institutes of Health for the partial financial support they gave me while I was writing some of the chapters, and to Donald Michie for suggesting the title Good Thinking.

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)

This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.

Kyburg goes half-way towards objective Bayesianism. He accepts that frequencies constrain rational belief to an interval but stops short of isolating an optimal degree of belief within this interval. I examine the case for going the whole hog.