Where E is the proposition that [If H and O were true, H would explain O], William Roche and Elliot Sober have argued that P(H|O&E) = P(H|O). In this paper I argue that not only is this equality not generally true, it is false in the very kinds of cases that Roche and Sober focus on, involving frequency data. In fact, in such cases O raises the probability of H only given that there is an explanatory connection between them.

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

Ockham's razor, the principle of parsimony, states that simpler theories are better than theories that are more complex. It has a history dating back to Aristotle and it plays an important role in current physics, biology, and psychology. The razor also gets used outside of science - in everyday life and in philosophy. This book evaluates the principle and discusses its many applications. Fascinating examples from different domains provide a rich basis for contemplating the principle's promises and perils. It is (...) obvious that simpler theories are beautiful and easy to understand; the hard problem is to figure out why the simplicity of a theory should be relevant to saying what the world is like. In this book, the ABCs of probability theory are succinctly developed and put to work to describe two 'parsimony paradigms' within which this problem can be solved. (shrink)

We argue elsewhere that explanatoriness is evidentially irrelevant . Let H be some hypothesis, O some observation, and E the proposition that H would explain O if H and O were true. Then O screens-off E from H: Pr = Pr. This thesis, hereafter “SOT” , is defended by appeal to a representative case. The case concerns smoking and lung cancer. McCain and Poston grant that SOT holds in cases, like our case concerning smoking and lung cancer, that involve frequency (...) data. However, McCain and Poston contend that there is a wider sense of evidential relevance—wider than the sense at play in SOT—on which explanatoriness is evidentially relevant even in cases involving frequency data. This is their main point, but they also contend that SOT does not hold in certain cases not involving frequency data. We reply to each of these points and conclude with some general remarks on screening-off as a test of evidential relevance. (shrink)

In the world of philosophy of science, the dominant theory of confirmation is Bayesian. In the wider philosophical world, the idea of inference to the best explanation exerts a considerable influence. Here we place the two worlds in collision, using Bayesian confirmation theory to argue that explanatoriness is evidentially irrelevant.

David Lewis (1941-2001) was Class of 1943 University Professor of Philosophy at Princeton University. His contributions spanned philosophical logic, philosophy of language, philosophy of mind, philosophy of science, metaphysics, and epistemology. In On the Plurality of Worlds, he defended his challenging metaphysical position, "modal realism." He was also the author of the books Convention, Counterfactuals, Parts of Classes, and several volumes of collected papers.

There is a de re modal truth that proves inconvenient for the canonical Lewisian theory of modality. For this truth requires on that theory, the existence of things (counterparts) that exist in distinct worlds but are also spatiotemporally related.

William Roche and Elliott Sober argue that explanatoriness is evidentially irrelevant. This conclusion is surprising since it conflicts with a plausible assumption—the fact that a hypothesis best explains a given set of data is evidence that the hypothesis is true. We argue that Roche and Sober's screening-off argument fails to account for a key aspect of evidential strength: the weight of a body of evidence. The weight of a body of evidence affects the resiliency of probabilities in the light of (...) new evidence. Thus, Roche and Sober are mistaken. Explanatoriness is evidentially relevant. (shrink)