The paper explores the disjunctive riddle for induction: If we know the sample Ks to be P, we also know that they are P or F. Assuming that we also know that the future Ks are non-P, we can conclude that they are F, if only we can inductively infer the evidentially supported P-or-F hypothesis. Yet this is absurd. We cannot predict that future Ks are F based on the knowledge that the samples, and only they, are P. The ensuing (...) challenge is to account for the unprojectibility of the disjunctive hypothesis. I provide an explanation in terms of epistemic dependence. The P-or-F hypothesis is unprojectible because the evidence supporting it depends epistemically on the evidence for the defeated P-hypothesis. The paper also shows that the disjunctive riddle covers the essence of Goodman's infamous grue-problem, which, therefore, can be resolved by the same means: In contrast to the green-hypothesis, the grue-hypothesis is unprojectible because the grue-evidence depends on the evidence for a defeated hypothesis. (shrink)

In a number of recent papers I have been developing the theory of "nomic probability," which is supposed to be the kind of probability involved in statistical laws of nature. One of the main principles of this theory is an acceptance rule explicitly designed to handle the lottery paradox. This paper shows that the rule can also handle the paradox of the preface. The solution proceeds in part by pointing out a surprising connection between the paradox of the preface and (...) the gambler's fallacy. (shrink)

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...) part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...) is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)