Logic and Metaphysics of Discernibility

Bartłomiej Błesznowski, Cezary Rudnicki, Michelle Granas

Jonas R. Becker Arenhart

Two entities are weakly discernible when an irreflexive and symmetric relation holds between them. That weak discernibility holds in quantum mechanics is fairly uncontroversial nowadays. The ontological consequences of weak discernibility, however, are far from clear. Part of the literature seems to imply that weak discernibility points to a definite metaphysics to quantum mechanics. In this paper we shall discuss the metaphysical contribution of weak discernibility to quantum mechanics and argue that, contrary to part of current literature, it does not provide for a fully naturalistic determination of metaphysics. Underdetermination of the metaphysics still plagues the way of the naturalist.

Tomasz Bigaj

Thomas Møller-Nielsen

In this paper I argue that the focus of much contemporary discussion concerning the proper role and philosophical significance of weak discernibility in the context of quantum mechanics (and other physical theories) is misplaced.In particular, I claim that metaphysicians' criticism of weak discernibility on the basis of its alleged inability to ground objects' numerical distinctness is orthogonal to Saunders's (2003a) main concern in his original paper, which is to use the notion of weak discernibility as part of a broader "logical aid" for interpreting physical theories.How exactly this "methodological" (as opposed to "metaphysical") construal of weak discernibility is supposed to work, however, is not immediately transparent.This paper therefore serves both as an attempt to gain a better understanding of Saunders's interpretational program, and also seeks to encourage a renewed emphasis on the set of issues and questions that such a program-at least on my understanding of it-would appear to raise.

Alexandre Koyré

Décio Krause, Jonas R. Becker Arenhart

Intuitively, an individual is a unity, having identity and being such that it is possible at least in principle to discern it from any other individual. But when we leave the intuitive realm and attempt a logical analysis, we find a cluster of problems that are difficult to overcome within standard logico-mathematical apparatuses. This chapter is concerned with some aspects of this intuitive concept of an individual and some related facts about individuation taken from recent discussions that arise in quantum theory, pushing the discussion to a “logical” view. It characterizes individuals by means of invariance by automorphisms. The final part of the chapter proposes a metaphysics where the notion of identity is substituted, for some objects, by a weaker notion of indiscernibility, and the chapter tries to motivate and justify such a move.