In this paper we discuss the relation of quantum theory to the problem of metaphysics.Based on metaphysical and anti-metaphysical stances, we put forward an 'interpretational map' of quantum mechanics in general and of the modal interpretation in particular.Thus, within the modal interpretation, we distinguish between: Modal Interpretations (which start from) the Mathematical Formalism (MIMF) and Modal Interpretations (which start from) Metaphysical Principles (MIMP).Finally, we argue for a middle path in between metaphysical principles and the formal conditions imposed on quantum mechanics.
In this paper we discuss the relation of quantum theory to the problem of metaphysics.Based on metaphysical and anti-metaphysical stances, we put forward an 'interpretational map' of quantum mechanics in general and of the modal interpretation in particular.Thus, within the modal interpretation, we distinguish between: Modal Interpretations (which start from) the Mathematical Formalism (MIMF) and Modal Interpretations (which start from) Metaphysical Principles (MIMP).Finally, we argue for a middle path in between metaphysical principles and the formal conditions imposed on quantum mechanics.
This doctoral dissertation contains four main elements: \n \n1. We put forward an interpretational map of quantum mechanics in general and of the modal interpretation in particular based on metaphysical and anti-metaphysical stances. \n \n2. In contraposition to what we characterize as the anti-metaphysical and classical metaphysical \n \nstances we collect arguments in favor of a constructive metaphysical stance. \n \n3. We analyze the meaning of contextuality and possibility in quantum theory in general, and in the modal interpretation in particular. \n \n4. Finally, we end up with a proposal for the development of a possible constructive metaphysical scheme based on the notion of potentiality. \n \nAlthough some of these problems are well known in the literature we attempt to cast new light on the discussion through the analysis of the concepts involved and their relation to the formalism. We attempt to make explicit the tension in between the theoretical conditions and the conceptual structure of the theory, in order to discuss and disclose the metaphysical ideas involved within the different interpretational problems of quantum mechanics. We believe that this analysis can help us to understand much of the implicit background of such theoretical conditions. \n \nThe dissertation centers itself on the modal and contextual character of quantum mechanics. On the one hand, we discuss the contextual character of quantum possibility through the development of a Modal Kochen-Specker theorem, and on the other hand, we analyze the contextual character of quantum correlations through the distinction of properties. In the last part we discuss some more speculative ideas related to the possible metaphysical developments of quantum mechanics based on the notion of potentiality.
According to scientific realism, science gives us an approximately true description of what the world is like. But what does it mean? In this chapter, we focus on the ontological and metaphysical aspects of this discussion. That is, we are concerned with the following questions: what there is, according to our best scientific theories? And how are these things that theories say exist? We start from the assumption that a genuine scientific realism must deal with these issues. Taking non-relativistic quantum mechanics as a case study, we discuss some of the challenges currently faced by a genuinely realistic stance. We argue, first, that in the ontological aspect, realists are in the same boat as science, that is, without sufficient epistemic justification to adopt the belief in the entities postulated by a single quantum theory, given that experience (currently) is not able to decide between rival theories; in the metaphysical aspect, realists also encounter problems with theory choice, given the possibility of associating more than one metaphysical theory with the description of the entities postulated by each quantum theory. The same goes for structuralist alternatives, since, even if we accept that scientific theories are committed to the existence of structures, but not objects, we still do not know what structures are, metaphysically. Finally, we move forward in the discussion with the meta-Popperian method, which serves to reduce the metaphysical alternatives associated with the ontological postulates of scientific theories. We may not know what the correct alternative is, but we have been able to progressively check which metaphysical alternatives are incompatible with each scientific theory.
In this paper, I address the problem regarding the physicality of Hilbert space in quantum mechanics, a topic brought into focus by Carcassi et al.'s paper "The unphysicality of Hilbert spaces" recently. I argue for the physicality of the Hilbert space in quantum mechanics, and demonstrate that there are inevitable ambiguity and arbitrariness if we want to identify the set of physical states with a proper subset of it. Moreover, I distinguish the ontological and modal reading of physicality from the pragmatic and operational reading of physicality, and then develop what I call the hierarchical view of physicality. According to this view, physicality is not a monolithic concept, but a layered one that admits degrees. I show the connection between the concept of physicality and modal metaphysics, and finally explain how it can be used to address the interpretational problem of quantum field theory brought by the existence of inequivalent representations.
We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics (QM) might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the semantic level, has severe difficulties when considering the syntactic level of the theory.
The measurement problem is one of the major philosophical problems in the Philosophy of Quantum Mechanics. Modal Interpretations of Quantum Mechanics aim to overcome the measurement problem, however, not always without a hitch: other problems arise. That is, some Modal Interpretations claim that a property Q, considered in a subsystem , is a di erent property while considered in the composite physical system , this while both situations are empirically indistinguishable: a non-empirical mismatch ensues. The mismatch, that seems to manifest at the metaphysical level, implies that empirically equivalent propositions like \\the left-hand side of the table is green" (subsystem) and \\the table is green at the left-hand side" (composite system) are metaphysically di erent. Although such a conclusion is clearly at odds with our everyday idea of properties, in my thesis, I question why metaphysical equivalence should (directly) ensue from empirical equivalence. The goal is to provide an explanation why the mismatch can been seen as a correct representation. Furthermore, I question what is exactly ment by metaphysical. As it turns out, under certain circumstances, by using an injective non-surjective function f that sends ordered pairs of operators to quantitative properties, in all possible worlds, the mismatch appears to be a correct representation. Nevertheless, since there are good reasons to renounce the mismatch, I question the level of activity and I invoke a more ne-grained version of metaphysics, i.e hyperintensional metaphysics. A relation between two entities is considered as hyperintensional from the very moment the relation is more ne-grained than necessary equivalence: beyond necessary equivalence. Finally, I claim that the mismatch must be understood in terms of beyond necessary equivalence and should be seen as a correct representation of the relation between language and reality in all hyperintensional worlds.