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Epistemology and Inference

Epistemology and Inference

Henry E. Kyburg
Copyright Date: 1983
Edition: NED - New edition
Pages: 336
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  • Book Info
    Epistemology and Inference
    Book Description:

    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 In this collection of published and unpublished essays, Kyburg presents his novel ideas and their applications in a manner that makes them accessible to philosophers and provides specialists in probability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.

    eISBN: 978-0-8166-5558-8
    Subjects: Philosophy

Table of Contents

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  1. Front Matter
    (pp. i-vi)
  2. Preface
    (pp. vii-x)
    Henry E. Kyburg Jr.
  3. Acknowledgments
    (pp. xi-xii)
  4. Table of Contents
    (pp. xiii-xiv)
  5. Part I. General

    • 1 Prophecies and Pretensions
      (pp. 3-17)

      There have always been prophets, and generally they have prophesied doom. The prophets of the Old Testament foretold, over and over, and in relished detail, the punishments the Lord had in store for stiff-necked and sinful Israel. No doubt there was no lack of cranks and crackpots foretelling the collapse of the Roman Empire. In recent decades we have been threatened with the exhaustion of resources, the explosion of population, the outbreak of global nuclear war, the disaster of widespread starvation, the depletion of our fuel and energy supplies, and an ignominious and final collapse of our collective moral fiber....

    • 2 Two World Views
      (pp. 18-27)

      1.There is a classical distinction, which has now and then been raised into a metaphysical principle, between two human attitudes toward the world. The distinction is that between the contemplative and the active. Often these poles are personified: Socrates, the seeker after truth; Alexander, the man of action. In more contemporary terms, the contrast is between Thought and Action. It is of course true that we all partake of both these principles, the contemplative and the active. Nevertheless, there are times and places when they can be encountered in fairly pure form. The mathematician in his study devising the proof...

    • 3 Tyche and Athena
      (pp. 28-46)

      The study of the foundations of probability and statistical inference seems to be about as technical and abstract a topic as one can imagine. Even for a philsopher, in this age of technocracy and specialization, it seems a narrow specialized field, connected perhaps to the philosophy of science or perhaps to that somewhat disreputable poor relation of real logic, inductive logic. I think, however, that in reality this study is fundamental to a very wide variety of topics in philosophy, and that indeed many philosophical problems have been rendered nearly insoluble only by the lack of an adequate treatment of...

  6. Part II. Critical Probability Papers

    • 4 Probability and Decision
      (pp. 49-62)

      There is a double-barreled thesis I want to defend here: it is that on the one hand the theory of statistical inference gives us a great deal of knowledge about the process of drawing conclusions from evidence; and that on the other hand, the conclusions that one draws depend to a large extent on the philosophical conception of probability with which one starts. I shall conduct my argument on the supposition that a behavioristic analysis of believing and conclusion-drawing is appropriate. I’m not at all sure that this is the case; indeed, I’m pretty sure that with respect to believing,...

    • 5 Bets and Beliefs
      (pp. 63-78)

      The subjectivistic or personalistic interpretation of probability is playing a larger and larger role both in statistics and in philosophy these days. In statistics it is associated with the recent resurgence¹ of Bayesian techniques which began with the work of Bruno de Finetti,² and which has been enthusiastically championed in English-speaking statistical circles by L. J. Savage.³ In philosophy the importance of this interpretation of probability has been felt in certain problems concerning induction, rationality, and decision-making, into which it has injected new spirit. It also has important connections with the (now) traditional logical approach of Carnap⁴ and his followers....

    • 6 Subjective Probability: Criticisms, Reflections, and Problems
      (pp. 79-98)

      The theory of subjective probability is certainly one of the most pervasively influential theories of anything to have arisen in many decades. It was developed first by probability theorists and philosophers (Koopman [12] and Ramsey [21], primarily), then by a few somewhat unconventional statisticians (De Finetti [4] and Savage [22]). Growth in interest in the topic among statisticians was slow at first, but turned out to be (it seems) exponential in character. From statistics it spread to economics, political science, and the social sciences in general. From philosophy it spread to psychology and decision theory, and thence again to economics...

    • 7 Chance
      (pp. 99-131)

      In a number of bodies of scientific knowledge there are laws and theories which, when applied in particular circumstances, give rise to statements that are not categorical but stochastic in character. In physics: quantum theory, statistical mechanics. In biology: genetic theory. In sociology and psychology: laws that express not an invariable relation between quantities, but a variable stochastic relation. This fact has called forth in recent years a variety of what purport to be analyses of the ‘use of probability in scientific theories’. These analyses are usually expressed in terms of ‘chance’ or ‘propensity’. It is argued (or, anyway, stated)...

    • 8 Logical and Fiducial Probability
      (pp. 132-150)

      Of most intellectual disciplines it is possible to take a very optimistic view: where there is agreement we may congratulate ourselves on the fact that we have discovered something that approaches truth, and where there is controversy we may remind ourselves that it is only through the conflict of ideas that people are stimulated to create new approaches, to invent new concepts, and thus, eventually, to approach a new state of agreement. The Foundations of Statistical Inference is a field in which there has for some time been more controversy than unanimity. That this controversy has been productive can hardly...

  7. Part III. Constructive Probability Papers

    • 9 The Nature of Epistemological Probability
      (pp. 153-157)

      A number of people have asked about the nature of epistemological probability. Since presentations of epistemological probability involve a fair amount of technical complexity, it is natural to want a description of what it is all about to serve as a basis for making the decision about whether or not to invest the time and effort required to go into the system in detail. These notes are designed to provide that description.

      NOT empirical: Probabilities are not frequencies, measures on events or sets of events or sequences; they are not propensities or chances.

      NOT subjective: Probabilities are not opinions, or...

    • 10 Probability and Randomness
      (pp. 158-179)

      1. The difficulties that surround the notion of randomness are becoming quite well known.¹ Most contemporary treatments of probability attempt to define randomness in terms of probability, and most of them fail. Most contemporary treatments of probability have other shortcomings as well.² This paper is an attempt to support the conjecture that the horse has been put behind the cart; that the best notion to take as primitive is that of randomness; and that it may even be possible to define the notion of randomness first, and then that of probability in terms of randomness.

      The paper is divided into...

    • 11 Probability and Informative Inference
      (pp. 180-203)

      There are a lot of ways of skinning the statistical cat and there are a lot of ways of classifying those techniques. One way is to distinguish between those approaches which stem from an epistemological stance and those approaches which are pragmatic in character. Alan Birnbaum¹ has characterized the problem with which the epistemological approach has been concerned as the problem ofinformative inference. The kind of problem with which the pragmatic approach is concerned might be characterized as a decision problem; but if we so characterize it, we must beware of supposing that decision theory is concerned merely with...

    • 12 Epistemological Probability
      (pp. 204-218)

      This paper is polemical, programmatic, and informal. In considering various interpretations of probability, I shall make no effort to consider all conceivable ways in which these interpretations can be applied; I shall consider only the most obvious ones. What I shall offer will be no solution to the problems examined, but merely a program which I believe will yield a solution. Finally, in view of the character of the paper, I shall allow myself to be utterly irresponsible with respect to quotes and quasi-quotes, use and mention, terms and objects, statements, sentences, propositions, and facts. In any full treatment these...

  8. Part IV. Epistemology

    • 13 Epistemology and Induction
      (pp. 221-231)

      1. There are a lot of things we may properly claim to know: what we like and dislike, what is right and wrong in behavior, what is virtuous or sinful, mathematical truths, what is beautiful and what is ugly. But the kinds of things that have most often attracted the attention of epistemologists are things like perceptions, observations, empirical generalizations, scientific theories, and the like. It is the latter sort of knowledge with which I shall be concerned, primarily, and in a very secondary way, with mathematical and logical knowledge. We may loosely characterize these items of knowledge as matters...

    • 14 Conjunctivitis
      (pp. 232-254)

      Consider a set S of statements that may be taken to represent an idealized body of scientific knowledge. Let s₁ and s₂ be members of S. Should we regard the conjunction of s₁ and s₂, also as a member of S? It is tempting to answer in the affirmative, and a number of writers, whose systems we shall consider below, have indeed answered this way. An affirmative answer is conjunctivitis, which may be expressed by the following principle:

      The Conjunction Principle: If S is a body of reasonably accepted statements, and s₁ belongs to S and s₂ belongs to S,...

    • 15 Probability, Rationality, and a Rule of Detachment
      (pp. 255-263)

      Carnap and many other writers on induction and probability deny that there is a rule of detachment in inductive logic. According to their view the relation among evidence, hypothesis, belief, and action is the following: A scientific hypothesisHis rendered probable to such and such a degree by evidenceE. Eis understood to include all of the relevant information we have concerningH.Weoughtto have a degree of belief inHcorresponding to its probability. We should neveraccept H—not even provisionally. We mayactin accordance withH, but the basis for our action...

    • 16 Local and Global Induction
      (pp. 264-284)

      In 1967 Isaac Levi introduced a distinction which has had a serious impact on the direction of research into inductive problems. The distinction itself was not new in principle; people for years had been aware that the problem of justifying a particular inductive conclusion in a practical scientific context was quite different from the general problem of justifying inductive conclusions wholesale. But Levi made the distinction sharper, and, more important, turned what had been taken to be the philosophical point of the distinction on its head. Traditionally, the point of the distinction was this: as philosophers we are not concerned...

  9. Part V. Theory and Generalization

    • 17 How to Make Up a Theory
      (pp. 287-290)

      It is now a commonplace that if you begin with a theory meeting certain requirements of explicitness, you can replace it by another theory which has precisely the same observational consequences as the original theory, but which avoids reference to any ‘theoretical’ terms. Like all commonplaces, this one deserves to be challenged once in a while. How do you go about getting this “other” theory, it may be asked? It is perfectly true, one may admit, that Craig’s interpolation theorem shows how to replace atheory,with a set of theoretical terms, with internal structure, with mixed sentences containing both...

    • 18 An Interpolation Theorem for Inductive Relations
      (pp. 291-295)

      Theorem: LetLbe a language with a theoretical vocabularyVTand an observational vocabularyVB; letPbe a conditional logical probability function defined on pairs of sentences ofL. LetTbe a conjunction of theoretical axioms and correspondence statements (or an interpretive system), and letO₁,O₂, andEbe statements employing only the observational vocabulary. Then, if the probability ofO₂is high relative toO₁,E, andT, and ifO₁does not undermine the acceptance or high probability ofT, the probability ofO₂relative to accepted evidential statementsin the observational vocabulary alone...

    • 19 All Acceptable Generalizations Are Analytic
      (pp. 296-312)

      According to my data, the probability is the interval (0.99, 1.0) that between 95% and 98% of introductory philosophy courses mention the statement “All generalizations are false.” So far as I know, relatively few people have observed that all general truths are analytic, including that one. (That is, non-observational generalizations: “There are no elephants in this room,” need not be taken as analytic.) But it is a thesis that has interesting consequences; among other things it entails that all our fancy theories in physics, biology, chemistry, sociology, psychology, if they are construed as universal generalizations, are completely without content: without...

  10. Index
    (pp. 315-318)
  11. Back Matter
    (pp. 319-319)