In 1983, in an open letter to the journal Nature, Karl Popper and David Miller set forth a particularly strong critical argument which sought to demonstrate the impossibility of inductive probability. Since its publication the argument has faced many criticisms and we argue in this article that they do not reach their objectives. We will first reconstruct the demonstration made by Popper and Miller in their initial article and then try to evaluate the main arguments against it. Although it is (...) possible to conceptualize logically the idea of induction, it is shown that it is not possible on traditional Bayesian grounds. (shrink)

This note makes a contribution to the issue raised in a paper by Popper and Miller (1983) in which it was claimed that probabilistic support is purely deductive. Developing R. C. Jeffrey's remarks, a new general approach to the crucial concept of "going beyond" is here proposed. By means of it a quantitative measure of the inductive component of a probabilistic inference is reached. This proposal leads to vindicating the view that typical predictive probabilistic inferences by enumeration and analogy are (...) purely inductive. (shrink)

Wayne (1995) critiques the Bayesian explication of the confirmational significance of evidential diversity (CSED) offered by Horwich (1982). Presently, I argue that Wayne’s reconstruction of Horwich’s account of CSED is uncharitable. As a result, Wayne’s criticisms ultimately present no real problem for Horwich. I try to provide a more faithful and charitable rendition of Horwich’s account of CSED. Unfortunately, even when Horwich’s approach is charitably reconstructed, it is still not completely satisfying.

This paper aims to contribute to our understanding of the notion of coherence by explicating in probabilistic terms, step by step, what seem to be our most basic intuitions about that notion, to wit, that coherence is a matter of hanging or fitting together, and that coherence is a matter of degree. A qualitative theory of coherence will serve as a stepping stone to formulate a set of quantitative measures of coherence, each of which seems to capture well the aforementioned (...) intuitions. Subsequently it will be argued that one of those measures does better than the others in light of some more specific intuitions about coherence. This measure will be defended against two seemingly obvious objections. (shrink)

It is known that evidential support, on the Bayesian definition of this notion, is intransitive. According to some, however, the Bayesian definition is too weak to be materially adequate. This paper investigates whether evidential support is transitive on some plausible probabilistic strengthening of that definition. It is shown that the answer is negative. In fact, it will appear that even under conditions under which the Bayesian notion of evidential support is transitive, the most plausible candidate strengthenings are not.

Glymour’s theory of bootstrap confirmation is a purely qualitative account of confirmation; it allows us to say that the evidence confirms a given theory, but not that it confirms the theory to a certain degree. The present paper extends Glymour’s theory to a quantitative account and investigates the resulting theory in some detail. It also considers the question how bootstrap confirmation relates to justification.