This paper is concerned with Wittgenstein's early doctrine of the independence of elementary propositions. Using the notion of a free generator for a logical calculus–a concept we claim was anticipated by Wittgenstein–we show precisely why certain difficulties associated with his doctrine cannot be overcome. We then show that Russell's version of logical atomism–with independent particulars instead of elementary propositions–avoids the same difficulties.

Quantum logic understood as a reconstruction program had real successes and genuine limitations. This paper offers a synopsis of both and suggests a way of seeing quantum logic in a larger, still thriving context.

My topics are two theses about quantum mechanics that are widely doubted but curiously tempting: value-definiteness and contextualism. Value-definiteness holds that every observable has a definite value; contextualism follows from value-definiteness, and claims that one Hermitian operator can represent many observables. In fact, contextualism is my deeper interest Although it is not a view with an army of defenders, it has a long history of discussion in the literature. (See, for example, Belinfante 1973, van Fraassen 1973, Shimony 1984, Redhead 1987). (...) The bulk of this paper will be concerned with a puzzle about degenerate operators that arises out of the standard accounts of contextualism. But before we get to the details, let us begin with a lurid example. (shrink)

One of the most interesting programs in the foundations of quantum mechanics is the realist quantum logic approach associated with Putnam, Bub, Demopoulos and Friedman (and which is the focus of my own research.) I believe that realist quantum logic is our best hope for making sense of quantum mechanics, but I have come to suspect that the usual version may not be the correct one. In this paper, I would like to say why and to propose an alternative.

Previous work has shown that the problem of measurement in quantum mechanics is not correctly seen as one of understanding some allegedly univocal process of measurement in nature which corresponds to the projection postulate. The present paper introduces a new perspective by showing that how we are to understand the nature of the change of quantum mechanical state on measurement depends very sensitively on the interpretation of the state function, and by showing how attention to this dependence can greatly sharpen (...) the problems and relations between them. In particular, the problems take a form resembling their traditional formulation only on an inexact value interpretation, according to which the state function attributes inexact values of quantities to systems. On other interpretations we can apply (with various drawbacks) the subensemble idea, according to which a discontinuous change of quantum mechanical description results on measurement simply because we need a new state function to describe a new object. (shrink)

Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather aims to complement that work.