Single-case and long-run propensity theories are among the main objective interpretations of probability. There have been various objections to these theories, e.g. that it is difficult to explain why propensities should satisfy the probability axioms and, worse, that propensities are at odds with these axioms, that the explication of propensities is circular and accordingly not informative, and that single-case propensities are metaphysical and accordingly non-scientific. We consider various propensity theories of probability and their prospects in light of these objections. We (...) argue that while propensity theories face challenges, these challenges do not undermine their validity as prospective interpretations of probability in science. (shrink)

In this paper I attempt to tie together a longstanding dispute between Henry Kyburg and Isaac Levi concerning statistical inferences. The debate, which centers around the example of Petersen the Swede, concerns Kyburg's and Levi's accounts of randomness and choosing reference classes. I argue that both Kyburg and Levi have missed the real significance of their dispute, that Levi's claim that Kyburg violates Confirmational Conditionalization is insufficient, and that Kyburg has failed to show that Levi's criteria for choosing reference class (...) are problematic. Rather, the significance of the Petersen case is to show that other aspects of their respective systems are defective: for Levi his account of credal judgments other than direct inference, and for Kyburg his explanation of how indexes are associated with a body of knowledge. (shrink)

Can there be good reasons for judging one set of probabilistic assertions more reliable than a second? There are many candidates for measuring "goodness" of probabilistic forecasts. Here, I focus on one such aspirant: calibration. Calibration requires an alignment of announced probabilities and observed relative frequency, e.g., 50 percent of forecasts made with the announced probability of.5 occur, 70 percent of forecasts made with probability.7 occur, etc. To summarize the conclusions: (i) Surveys designed to display calibration curves, from which a (...) recalibration is to be calculated, are useless without due consideration for the interconnections between questions (forecasts) in the survey. (ii) Subject to feedback, calibration in the long run is otiose. It gives no ground for validating one coherent opinion over another as each coherent forecaster is (almost) sure of his own long-run calibration. (iii) Calibration in the short run is an inducement to hedge forecasts. A calibration score, in the short run, is improper. It gives the forecaster reason to feign violation of total evidence by enticing him to use the more predictable frequencies in a larger finite reference class than that directly relevant. (shrink)

The article responds to some of the points raised by B. van Fraassen concerning probability kinematics and direct inference within the framework of the approach to the revision of probability judgment proposed by Levi in The Enterprise of Knowledge. In particular, the critical importance of the question of direct inference is emphasized and explained.

R.A.Fisher introduced the fiducial argument as a means for obtaining something from nothing. He thought that on some occasions it was legitimate to obtain a posterior probability distribution over a range of simple statistical hypotheses without commitment to a prior distribution [4].H.Jeffreys thought he could tame Fisher by casting his argument in a Bayesian mold through a derivation of the fiducial posterior from a suitably constructed ignorance prior via Bayes’ theorem and conditionalization on the data of experimentation. According to Jeffreys, (...) Fisher was using something to obtain something after all ([7],pp.381-383).D.V.Lindley furthered the process of taming by specifying allegedly necessary and sufficient conditions for the consistency of fiducial reasoning in contexts of one parameter estimation with Bayesian requirements [14]. I. Hacking exploited Lindley’s result to supply his own ingenious method for taming Fisher([5],ch. 9).T.Seidenfeld has recently demonstrated that Lindley’s conditions are insufficient for consistency and that reconstructions like Jeffreys’ or Hacking’s lead to contradiction ([15], PP. 721-727). (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)

Evidentialists say that a necessary condition of sound epistemic reasoning is that our beliefs reflect only our evidence. This thesis arguably conflicts with standard Bayesianism, due to the importance of prior probabilities in the latter. Some evidentialists have responded by modelling belief-states using imprecise probabilities (Joyce 2005). However, Roger White (2010) and Aron Vallinder (2018) argue that this Imprecise Bayesianism is incompatible with evidentialism due to “inertia”, where Imprecise Bayesian agents become stuck in a state of ambivalence towards hypotheses. Additionally, (...) escapes from inertia apparently only create further conflicts with evidentialism. This dilemma gives a reason for evidentialist imprecise probabilists to look for alternatives without inertia. I shall argue that Henry E. Kyburg’s approach offers an evidentialist-friendly imprecise probability theory without inertia, and that its relevant anti-inertia features are independently justified. I also connect the traditional epistemological debates concerning the “ethics of belief” more systematically with formal epistemology than has been hitherto done. (shrink)