In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (shrink)

In statistics, there are two main paradigms: classical and Bayesian statistics. The purpose of this article is to investigate the extent to which classicists and Bayesians can agree. My conclusion is that, in certain situations, they cannot. The upshot is that, if we assume that the classicist is not allowed to have a higher degree of belief in a null hypothesis after he has rejected it than before, then he has to either have trivial or incoherent credences to begin with (...) or fail to update his credences by conditionalization. (shrink)

It is notoriously difficult to spell out the norms of inductive reasoning in a neat set of rules. I explore the idea that explanatory considerations are the key to sorting out the good inductive inferences from the bad. After defending the crucial explanatory virtue of stability, I apply this approach to a range of inductive inferences, puzzles, and principles such as the Raven and Grue problems, and the significance of varied data and random sampling.

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

It would be difficult to overestimate the influence Hume’s problem of induction exercises on contemporary epistemology. At the same time, the problem of induction has not perceptibly slowed the progress of mathematics and science. This ironic state of affairs, immortalized by C. D. Broad’s description of induction as “the glory of science” and “the scandal of philosophy,” ought in all fairness to give both sides some pause. And on occasion, it does: the mathematicians stop to concede that Hume has not (...) yet been answered, the scientists worry about randomization of experiments, and inductive skeptics stir uneasily in their chairs at the mention of certain mathematical theorems that seem palpably to have bearing on the problem. (shrink)