Individuals and Non-Individuals in Quantum Theory

Matteo Morganti

Jonas R. Becker Arenhart, Décio Krause

Décio Krause

The topics of identity, individuality and indiscernibility had already entered the domain of the philosophy of physics, mainly in what respects the philosophy of quantum theories. In this paper, I present the main ideas of an underlying metaphysics that considers the basic entities of quantum physics as non-individuals, that is, as entities to which the standard theory of identity of classical logic and standard mathematics (set theory) does not apply. Two things must be emphasized: the first is that we pursue Erwin Schrödinger’s ideas that the notion of identity (or sameness ) does not apply to quantum things; the second is to follow Heinz Post’s claim that the non-individuality of quantum entities ‘must be introduced right at the start’ and not by taking individuals and making them pretend to be non-individuals ‘by hand’, say by confining them to non-rigid structures. Thus, this paper should be regarded as an attempt to justify the metaphysics of non-individuals and the logical systems that cope with them, although these systems are here only referred to. We also answer some criticisms that have been directed to such a view. The paper is directed to an audience of both physicists interested in foundations and philosophers of physics. This article is part of the theme issue ‘Identity, individuality and indistinguishability in physics and mathematics’.

Valéria Gradinar

The non-relativistic quantum mechanics offers us conditions to consider at least two possible metaphysical packages, but incompatible between themselves: metaphysics of individuals, and metaphysics of non-individuals. In addition, the standard formalism is compatible with both the ontologies, without the theory being decided for either of them. From this particular kind of situation, the thesis of the underdetermination of metaphysics by physics can be established. Actually, it can be found, among scientists and philosophers, defenders of one, or another ontology, as well as those who do not address the issue, given that theory on its own does not decide. This means that if we make a choice for one of these packages, it will be happing in a metaphysical field, increasing a lot the philosophical discussions about individuality of quantic objects in quantum physics. From a naturalized methodological view, we present the issues from those defend the individuality of quantic objects, and from those, include us, defend non-individuality, focusing two approaches: (i) the ontological one, in which the fail of IIP as individuation principle is discussed; and, (ii) the logical one, in which non-reflexive logics, as well as a quasi-set theory became more suitable for representing the non-individuals. In this paper we stand for the choice of non-individuals ontology becomes more plausible, and should be taken in account seriously, opening up possibilities for ontological pluralism.

D�cio Krause, Steven French

Décio Krause

In this article we try to justify a way of looking for an alternative approach to quantum mechanics based on a non-classical logic. The main motivation is both to accommodate a metaphysical view according to which quantum objects are non-individuals and to introduce, so to say, these objects within the formalism, for as we know, the usual formalism treats of states of quantum systems and not (directly) of quantum systems properly speaking. We consider two specific questions related to quantum theory, namely, entanglement and the indiscernibility of quanta. Our way of looking to these concepts motivate us to construct a metaphysical view according to which quantum objects do not present identity criterion (they are ‘non-individuals’), and then we try to construct a quantum theory based on such a view, which is grounded on a non-classical logic, termed non-reflexive. From the formal point of view, the main motivation comes from the fact that in using classical logic and classical set theory (such as ZFC), we are necessarily committed to individuals, and non-individuals can be considered only by assuming ‘strong’ symmetry principles, which mask the basic idea involving non-individuality. In the core of the article, due to questions of space, only the main philosophical arguments are presented, but in two appendixes we outline, firstly, quasi-set theory, the non-reflexive mathematical framework that sustain our view, and a bottom-top construction of a quantum mechanics based on quasi-set theory.