In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate meta-language to speak of the proposed ontology of properties and its structure.

In this paper, we introduce a quasi-set theory without atoms. The quasi-sets (qsets) can have as elements completely indiscernible things which do not turn out to be the very same thing as it would be implied if its underlying logic was classical logic. A quasi-set can have a cardinal, called its quasi-cardinal, but this is made so that, at least for the finite case, the quasi-cardinal is not an ordinal, and hence the indistinguishable elements of a quasi-set cannot be ordered. (...) In the last sections, we show how the theory can be used to ground a quantum metaphysics of properties, which sees the quantum entities as bundles of properties, and we also introduce a new approach for the use of quantifiers in quantum physics. (shrink)

This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in non-relativistic quantum mechanics. Section presents the traditional discussion of metaphysical underdetermination regarding the individuality and non-individuality of quantum particles. Section discusses three reactions to it found in the literature: eliminativism about individuality; conservatism about individuality; eliminativism about objects. Section wraps it all up with metametaphysical considerations regarding the epistemology of metaphysics of science.

This paper introduces the theory QST of quasets as a formal basis for the Nmatrices. The main aim is to construct a system of Nmatrices by substituting standard sets by quasets. Since QST is a conservative extension of ZFA (the Zermelo-Fraenkel set theory with Atoms), it is possible to obtain generalized Nmatrices (Q-Nmatrices). Since the original formulation of QST is not completely adequate for the developments we advance here, some possible amendments to the theory are also considered. One of the (...) most interesting traits of such an extension is the existence of complementary quasets which admit elements with undetermined membership. Such elements can be interpreted as quantum systems in superposed states. We also present a relationship of QST with the theory of Rough Sets RST, which grants the existence of models for SQT formed by rough sets. Some consequences of the given formalism for the relation of logical consequence are also analysed. (shrink)

In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This framework allows us to consider a new ontology (...) in order to study the properties of quantum systems. (shrink)

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default, sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties (...) can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality. (shrink)