This paper provides an algebraic reconstruction of Einstein’s argument for the incompleteness of quantum mechanics, in order to clarify the assumptions that underlie an understanding of Einstein completeness as categoricity.

There is confusion among scholars of Bohr as to whether he should be categorized as an instrumentalist (see Faye 1991) or a realist (see Folse 1985). I argue that Bohr is a realist, and that the confusion is due to the fact that he holds a very special view of realism, which did not coincide with the philosophers’ views. His approach was sometimes labelled instrumentalist and other times realist, because he was an instrumentalist on the theoretical level, but a realist (...) on the level of models. Such a realist position is what I call phenomenological realism. In this paper, and by taking Bohr’s debate with Einstein as a paradigm, I try to prove that Bohr was such a realist. (shrink)

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's (...) principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic. (shrink)

This three-part paper comprises: (i) a critique by Halvorson of Bell’s (1973) paper ‘Subject and Object’; (ii) a comment by Butterfield; (iii) a reply by Halvorson. An Appendix gives the passage from Bell that is the focus of Halvorson’s critique.

As the theory of the atom, quantum mechanics is perhaps the most successful theory in the history of science. It enables physicists, chemists, and technicians to calculate and predict the outcome of a vast number of experiments and to create new and advanced technology based on the insight into the behavior of atomic objects. But it is also a theory that challenges our imagination. It seems to violate some fundamental principles of classical physics, principles that eventually have become a part (...) of western common sense since the rise of the modern worldview in the Renaissance. So the aim of any metaphysical interpretation of quantum mechanics is to account for these violations. (shrink)

We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining (...) these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our "Principle of general tovariance" states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our "Equivalence principle" states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos. (shrink)

I argue that instead of a rather narrow focus on N. Bohr's account of complementarity as a particular and perhaps obscure metaphysical or epistemological concept (or as being motivated by such a concept), we should consider it to result from pursuing a particular method of studying physical phenomena. More precisely, I identify a strong undercurrent of Baconian method of induction in Bohr's work that likely emerged during his experimental training and practice. When its development is analyzed in light of Baconian (...) induction, complementarity emerges as a levelheaded rather than a controversial account, carefully elicited from a comprehensive grasp of the available experimental basis, shunning hasty metaphysically motivated generalizations based on partial experimental evidence. In fact, Bohr's insistence on the “classical” nature of observations in experiments, as well as the counterintuitive synthesis of wave and particle concepts that have puzzled scholars, seem a natural outcome (an updated instance) of the inductive method. Such analysis clarifies the intricacies of early Schrödinger's critique of the account as well as Bohr's response, which have been misinterpreted in the literature. If adequate, the analysis may lend considerable support to the view that Bacon explicated the general terms of an experimentally minded strand of the scientific method, developed and refined by scientists in the following three centuries. (shrink)

Bell correlations are the hallmark of quantum non-locality, and a rich context for analysing them is provided by the algebraic approach to quantum field theory : the basic idea is to associate with each bounded region O of Minkowski spacetime an algebra A of operators, of which a self-adjoint element P ∈ A represents a physical quantity pertaining to that part of the field system lying in O, that is measurable by a procedure confined to O. The violation of Bell (...) inequalities in AQFT is known to be "generic", as regards the choices of regions O, and of quantities P, and of states. Furthermore, they are typically "maximal" and "indestructible" in a sense that can be made mathematically precise. The prospects for “peaceful coexistence” between quantum non-locality and relativity theory’s requirement of no action-at-a-distance are also explored. The purpose of this Essay is to review the developments in these areas. (shrink)