Sebastian Horvat

Quantum theory implies, and empirical evidence confirms, that while particles can exhibit wave-like behavior in interferometric experiments, this behavior is so limited as not to allow for third- and higher-order interference. The article at hand shows that this possibility-impossibility structure suggests the universal validity of a principle that regulates statistical correlations between spatiotemporally localized events, independently of the nature of the objects that may or may not partake in these events. Roughly, the said principle mandates that any joint influence of m mutually spacelike separated events on another event, be such, that it can be separated by at least m/2 mediating events, and in some cases, by no more than m/2 mediating events. The structure of quantum interference thus teaches us that events can influence each other in a non-separable fashion, but that this non-separability has a certain exactly quantifiable limit.

Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first reconstruct his argument and present its restriction to the case of quantum logic (QL). Then we show that there is no problematic tension between the applicability of classical mathematical models to quantum phenomena and the endorsement of QL in the reasoning about the latter. Once we identify the premise in Williamson’s argument that turns out to be false when restricted to QL, we argue that the same premise fails for a wider variety of non-classical logics. In the end, we use our discussion to draw some general lessons concerning the relationship between applied logic and applied mathematics.

This essay is a two-step reflection on the question 'Which events (can be said to) occur in quantum phenomena?' The first step regiments the ontological category of statistical phenomena and studies the adequacy of probabilistic event models as descriptions thereof. Guided by the conviction that quantum phenomena are to be circumscribed within this same ontological category, the second step highlights the peculiarities of probabilistic event models of some non-relativistic quantum phenomena, and thereby of what appear to be some plausible answers to our initial question. The reflection ends in an aporetic state, as it is by now usual in encounters between ontology and the quantum.

Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first reconstruct his argument and present its restriction to the case of quantum logic (QL). Then we show that there is no problematic tension between the applicability of classical mathematical models to quantum phenomena and the endorsement of QL in the reasoning about the latter. Once we identify the premise in Williamson’s argument that turns out to be false when restricted to QL, we argue that the same premise fails for a wider variety of non-classical logics. In the end, we use our discussion to draw some general lessons concerning the relationship between applied logic and applied mathematics.

This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (2001). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical counterparts, thereby showing that the truth-functional status of classical and quantum connectives is not as different as usually thought. Then it points out that bivalent semantics for quantum logic – compatible with realism about quantum mechanics – can be maintained, albeit at the price of truth-functionality. Finally, the paper critically addresses Geoffrey Hellman’s argument (1980) that this lack of truth-functionality entails a change of meaning between classical and quantum connectives.