There is a tension between normative and descriptive elements in the theory of rational belief. This tension has been reflected in work in psychology and decision theory as well as in philosophy. Canons of rationality should be tailored to what is humanly feasible. But rationality has normative content as well as descriptive content.A number of issues related to both deductive and inductive logic can be raised. Are there full beliefs – statements that are categorically accepted? Should statements be accepted when (...) they become overwhelmingly probable? What is the structure imposed on these beliefs by rationality? Are they consistent? Are they deductively closed? What parameters, if any, does rational acceptance depend on? How can accepted statements come to be rejected on new evidenceShould degrees of belief satisfy the probability calculus? Does conformity to the probability calculus exhaust the rational constraints that can be imposed on partial beliefs? With the acquisition of new evidence, should beliefs change in accord with Bayes' theorem? Are decisions made in accord with the principle of maximizing expected utility? Should they be?A systematic set of answers to these questions is developed on the basis of a probabilistic rule of acceptance and a conception of interval-valued logical probability according to which probabilities are based onknownfrequencies. This leads to limited deductive closure, a demand for only limited consistency, and the rejection of Bayes' theorem as universally applicable to changes of belief. It also becomes possible, given new evidence, to reject previously accepted statements. (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 In this collection of published and unpublished essays, Kyburg presents his novel ideas and their applications in a manner that makes them accessible to philosophers and provides specialists in probability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)

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)

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)

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)

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.

Since Ramsey, much discussion of the relation between probability and belief has taken for granted that there are degrees of belief, i.e., that there is a real-valued function, B, that characterizes the degree of belief that an agent has in each statement of his language. It is then supposed that B is a probability. It is then often supposed that as the agent accumulates evidence, this function should be updated by conditioning: BE(·) should be B(·E)/B(E). Probability is also important in (...) classical statistics, where it is generally supposed that probabilities are frequencies, and that inference proceeds by controlling error and not by conditioning. I will focus on the tension between these two approaches to probability, and in the main part of the paper show where and when Bayesian conditioning conflicts with error based statistics and how to resolve these conflicts. (shrink)

The dominant argument for the introduction of propensities or chances as an interpretation of probability depends on the difficulty of accounting for single case probabilities. We argue that in almost all cases, the``single case'' application of probability can be accounted for otherwise. ``Propensities'' are needed only intheoretical contexts, and even there applications of probability need only depend on propensities indirectly.

It has been manifested over the past few centuries that science provides superbly powerful tools and methods for modifying the natural world. Many people would agree that it has also offered explanation and understanding. But it is still unclear that these tools and methodology can propel us to solve all of the cognitive dilemmas that exist. It has been assumed, for example, that scientific knowledge and religious knowledge are so different that they cannot even clash with one another. But the (...) recent arguments about creation and evolution show that perhaps they can come into conflict after all. (shrink)

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.

There are a number of reasons for being interested in uncertainty, and there are also a number of uncertainty formalisms. These formalisms are not unrelated. It is argued that they can all be reflected as special cases of the approach of taking probabilities to be determined by sets of probability functions defined on an algebra of statements. Thus, interval probabilities should be construed as maximum and minimum probabilities within a set of distributions, Glenn Shafer's belief functions should be construed as (...) lower probabilities, etc. Updating probabilities introduces new considerations, and it is shown that the representation of belief as a set of probabilities conflicts in this regard with the updating procedures advocated by Shafer. The attempt to make subjectivistic probability plausible as a doctrine of rational belief by making it more flowery — i.e., by adding new dimensions — does not succeed. But, if one is going to represent beliefs by sets of distributions, those sets of distributions might as well be based in statistical knowledge, as they are in epistemological or evidential probability. (shrink)

Bishop Butler, [Butler, 1736], said that probability was the very guide of life. But what interpretations of probability can serve this function? It isn’t hard to see that empirical (frequency) views won’t do, and many recent writers-for example John Earman, who has said that Bayesianism is “the only game in town”-have been persuaded by various dutch book arguments that only subjective probability will perform the function required. We will defend the thesis that probability construed in this way offers very little (...) guidance, dutch book arguments notwithstanding. We will sketch a way out of the impasse. (shrink)

In, Levi has laid out the issues involving chances, frequencies, and direct inference with admirable precision. Nevertheless, puzzles remain. The chief puzzle to which I wish to draw attention is this: Under certain circumstances, we can combine knowledge of chances and knowledge of frequencies to yield new knowledge of chances. If Petersen is “drawn at random” from among Swedes, and we also know that the proportion of Protestants among Swedes is 0.9, then we can say that the chance that Petersen (...) is a Protestant is 0.9. But if we apply this principle generally, we are led to generally trivial results: direct inference yields probabilities constrained only to lie in a broad interval like [0, 1]. On the other hand, if we can't always combine knowledge of chances and knowledge of frequencies to get new knowledge of chances, or if this knowledge can be overridden by other considerations, how do we know when we can usefully apply direct inference? (shrink)

Reviewed Works:Newton C. A. da Costa, On the Theory of Inconsistent Formal Systems.Newton C. A. da Costa, The Philosophical Import of Paraconsistent Logic.Newton C. A. da Costa, On Paraconsistent Set Theory.Newton C. A. da Costa, Jean-Yves Beziau, Otavio Bueno, Paraconsistent Logic in a Historical Perspective.

The Bayesian view of inference has become popular in philosophy in recent years. Scientific Reasoning: a Bayesian Approach, by Colin Howson and Peter Urbach, represents an articulate and persuasive defense of the Bayesian view. We focus on the theme of that book, and argue that there are difficulties with Bayesianism, and alternatives worth considering. One of the most serious drawbacks to Bayesianism is the subjectivity that pervades most versions of it. We argue that this is an instance of a more (...) general contemporary tendency to move away from claims of objectivity, and toward frankly subjective views. This results from a desire to find a deductive, incorrigible, basis for scientific inference. We claim that such a desire is doomed to frustration, but that does not spell the end of efforts to formalize inductive reasoning. (shrink)

Kyburg proposes the following test for the simplicity of a theory: the complexity of a theory is measured by the number of quantifiers that occur in the set of statements comprising the theory. (staff).