These are the introduction chapters to the forthcoming collection of essays published by Springer (Synthese Library) and entitled Probabilities, Causes and Propensities in Physics.

A “stopping rule” in a sequential experiment is a rule or procedure for deciding when that experiment should end. Accordingly, the “stopping rule principle” states that, in a sequential experiment, the evidential relationship between the final data and an hypothesis under consideration does not depend on the experiment’s stopping rule: the same data should yield the same evidence, regardless of which stopping rule was used. In this essay, I reconstruct and rebut five independent arguments for the SRP. Reminding oneself that (...) the stopping rule is a part of an experiment’s design and is no more mysterious than many other design aspects helps elucidate why some of these arguments for the SRP are unsound. (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)