Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a “protective belt” of auxiliary statements around reasonably successful theories is explicated. (3) The Bayesian approach to understanding the superiority of variety of evidence is pursued; a recent challenge (by Wayne) is converted into a positive result on behalf of the Bayesian analysis, potentially with far-reaching consequences. (4) The condition for applying the merger-of-opinion results and the thesis of underdetermination of theories are compared, revealing significant limitations in applicability of the former. (5) Implications concerning “diachronic Dutch Book” arguments and “non-Bayesian shifts” are drawn, highlighting the incompleteness, but not incorrectness, of Bayesian analysis.

I argue that the Bayesian Way of reconstructing Duhem's problem fails to advance a solution to the problem of which of a group of hypotheses ought to be rejected or “blamed” when experiment disagrees with prediction. But scientists do regularly tackle and often enough solve Duhemian problems. When they do, they employ a logic and methodology which may be called error statistics. I discuss the key properties of this approach which enable it to split off the task of testing auxiliary hypotheses from that of appraising a primary hypothesis. By discriminating patterns of error, this approach can at least block, if not also severely test, attempted explanations of an anomaly. I illustrate how this approach directs progress with Duhemian problems and explains how scientists actually grapple with them.

This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.

1. Probabilism. Statistics is probably the last discipline the ordinary person would associate with ideological wars, but one has been raging there for the last thirty years and more. Until recently the Classical, also known as Frequentist, theory of statistical inference dominated. But gradually a quite different approach has attracted adherents. This, named the Bayesian theory after the eighteenth-century English clergyman, Thomas Bayes, is a phoenix, reborn from the theory of inductive inference dominant from the mid-eighteenth to the late nineteenth century, which said that the measure of confidence proper to employ in an uncertain proposition is its probability (the idea goes back well beyond Bayes; in his great Ars Conjectandi, published posthumously in 1715, James Bernoulli stated that probability is degree of certainty (Part IV, Chapter II)).

Recently a number of authors have tried to avoid the failures of traditional Dutch book arguments by separating them from pragmatic concerns of avoiding a sure loss. In this paper I examine defenses of this kind by Howson and Urbach, Hellman, and Christensen. I construct rigorous explications of their arguments and show that they are not cogent. I advocate abandoning Dutch book arguments in favor of a representation theorem.

1. Introduction. The papers by Hellman and Mayo offer up a rich menu of problems and proposed solutions, so there is much here for a friendly critic to fasten on. In order to bring a modicum of focus to my commentary, I shall limit my remarks to the Duhem problem and its radiations in epistemology and methodology. Both Mayo and Hellman claim to have solutions to that hoary old problem and they tout these solutions as key indicators of the explanatory power of their respective technical epistemologies, whether Bayesian or Neyman/Pearsonian. Like Mayo, I shall be arguing that the Bayesian treatment of Duhem's problem is no solution at all; that, indeed, it fails to grapple with the core challenges posed by the purported ambiguities of falsification. My response to Mayo's more detailed, and I think more right-headed, treatment of the Duhem problem will be more complex. While I believe that she is moving in the right direction in many respects, I think that she fails to see one key dimension of the Duhemian conundrum. Indeed, she risks solving not Duhem's problem but quite a different one. I shall gently try to encourage her to steer her way back towards the central task.

Preface. Almost fifty years ago, in 1948, when I was an undergraduate at Queens College in New York and a student of Carl G. Hempel's, I received from his hands an offprint of his now-classic but then just-published paper “Studies in the Logic of Explanation”, written in collaboration with Paul Oppenheim and then just published in Philosophy of Science (15[1948], pp. 135–75).1 This paper greatly impressed me—and I was not alone. We have here one of those unusual publications that sets the agenda for a whole generation of investigators. It set in train an enormous body of discussions and publications which shaped the course of deliberations about scientific explanation over the next decades—an effort to which my own work also made some contributions. (This literature and its inherent dialectic has been examined and analyzed in close and interesting detail in Wesley Salmon's fine survey of Four Decades of Scientific Explanation.2) However my present aim is not to consider what came out of the Hempel-Oppenheim paper but what went into it. I want, in sum, to consider the prehistory of that era of scientific explanation studies—and to look more closely at the background ramifications of this paper that launched a thousand others.

Thomas S. Kuhn's singular voice was stilled by cancer on June 17, 1996, some 49 years after his initial encounters with past science had drawn him into a career in the history and philosophy of science. One of the most widely-read and influential academics of the 20th century, Kuhn was educated at Harvard University, where he received an S.B. (summa cum laude) in Physics in 1943 and a Ph.D. in the subject in 1949. He remained there until 1956, first as a Junior Fellow in the Society of Fellows from 1948 to 1951, when he in effect retrained himself as a historian of science, and then as an Assistant Professor of General Education and History of Science. He joined the faculty of the University of California, Berkeley, in 1956, becoming Professor of History of Science in 1961. From 1964 to 1979 he was on the faculty of the History of Science Program of Princeton University, and from 1972 to 1979 also a member of the Institute for Advanced Study. He moved to the Department of Linguistics and Philosophy of Massachusetts Institute of Technology in 1979, where he became Professor Emeritus in 1991. He was President of the History of Science Society in 1968—70 and of the Philosophy of Science Association in 1988–90. He received the George Sarton Medal of the History of Science Society in 1982 and the John Desmond Bernal Award of the Society for the Social Studies of Science in 1983.