Solutions to Some Open Problems from Slaney

In response to a paper by Harris & Fitelson, Slaney states several open questions concerning possible strategies for proving distributivity in a wide class of positive sentential logics. In this note, I provide answers to all of Slaney's open questions. The result is a better understanding of the class of positive logics in which distributivity holds

Bayesians sometimes cannot ignore even very implausible theories (even ones that have not yet been thought of)

In applying Bayes’s theorem to the history of science, Bayesians sometimes assume – often without argument – that they can safely ignore very implausible theories. This assumption is false, both in that it can seriously distort the history of science as well as the mathematics and the applicability of Bayes’s theorem. There are intuitively very plausible counter-examples. In fact, one can ignore very implausible or unknown theories only if at least one of two conditions is satisfied: (i) one is certain that there are no unknown theories which explain the phenomenon in question, or (ii) the likelihood of at least one of the known theories used in the calculation of the posterior is reasonably large. Often in the history of science, a very surprising phenomenon is observed, and neither of these criteria is satisfied

Remarks on "Random Sequences"

We show that standard statistical tests for randomness of finite sequences are language-dependent in an inductively pernicious way

The Philosophical Significance of Stein's Paradox

Charles Stein discovered a paradox in 1955 that many statisticians think is of fundamental importance. Here we explore its philosophical implications. We outline the nature of Stein’s result and of subsequent work on shrinkage estimators; then we describe how these results are related to Bayesianism and to model selection criteria like the Akaike Information Criterion. We also discuss their bearing on scientific realism and instrumentalism. We argue that results concerning shrinkage estimators underwrite a surprising form of holistic pragmatism