In quantum mechanics the properties of a composite system can be divided into properties which are reducible to the properties of the subsystems of the composite and properties which are irreducible to those subsystem properties. The irreducible properties are called holistic and emerge when one describes the system as a whole. In this chapter I show that the bi and spectral modal interpretations can ascribe the holistic properties to composites but, in general, fail to reproduce the relations between the reducible properties of a composite and the properties of the subsystems. The atomic modal interpretation, on the other hand, fails to ascribe the holistic properties but is much more successful in reproducing the relations between the reducible properties and the subsystem properties. I discuss whether these failures harm the empirical adequacy and the metaphysical tenability of modal interpretations. Holistic properties of composite systems The basic principle of reductionism, that all the properties of composite systems are amalgamates of the properties of the subsystems of these composites, has triumphed so much in classical physics that I find it difficult to come up with a clear example of a classical property that cannot be taken as a complex of the subsystem properties. So, in order to make a case for the idea that composites can also possess, in addition to reducible properties, so-called holistic properties which cannot be reduced to the properties of the subsystems, one has to move outside physics or to draw upon some counterfactual development of physics.
In quantum mechanics the properties of a composite system can be divided into properties which are reducible to the properties of the subsystems of the composite and properties which are irreducible to those subsystem properties. The irreducible properties are called holistic and emerge when one describes the system as a whole. In this chapter I show that the bi and spectral modal interpretations can ascribe the holistic properties to composites but, in general, fail to reproduce the relations between the reducible properties of a composite and the properties of the subsystems. The atomic modal interpretation, on the other hand, fails to ascribe the holistic properties but is much more successful in reproducing the relations between the reducible properties and the subsystem properties. I discuss whether these failures harm the empirical adequacy and the metaphysical tenability of modal interpretations. Holistic properties of composite systems The basic principle of reductionism, that all the properties of composite systems are amalgamates of the properties of the subsystems of these composites, has triumphed so much in classical physics that I find it difficult to come up with a clear example of a classical property that cannot be taken as a complex of the subsystem properties. So, in order to make a case for the idea that composites can also possess, in addition to reducible properties, so-called holistic properties which cannot be reduced to the properties of the subsystems, one has to move outside physics or to draw upon some counterfactual development of physics.
In this final part I analyse the modal interpretations from a more philosophical point of view. In Chapter 12 I start by arguing that modal interpretations describe noumenal states of affairs and that therefore metaphysically tenable interpretations need only to meet the criteria of Consistency and Internal Completeness. Then I analyse the relations between properties, states and outcomes of measurements in the modal description of reality. I end by discussing how modal interpretations, when restricted to the description of measurement outcomes, recover the standard formulation of quantum mechanics. Chapter 13 concerns the relations between the properties ascribed to composite systems and subsystems. I show that the property ascriptions of the bi and spectral modal interpretations can be characterised as holistic and non-reductionistic, whereas the property ascription of the atomic modal interpretation is non-holistic and to a large extent reductionistic. I argue that notwithstanding the lack of reductionism, the bi and spectral modal interpretations are empirically adequate and metaphysically tenable. I also discuss the possibility of saving the metaphysical tenability of the atomic modal interpretation by taking holistic properties as dispositional properties. In Chapter 14 I give a survey of the possibilities and impossibilities of modal interpretations and in Chapter 15 I end with general conclusions.
A composite quantum system has properties that are incompatible with every property of its parts. The existence of such global properties incompatible with all local properties constitutes what I call "mereological holism"--the distinctive holism of Quantum Theory. Mereological holism has the dramatic conceptual consequence of making untenable the usual understanding of the "quantum system" as being a "physical object", since composed objects have properties compatible with those of its parts. The notion of "property" can be extended in a unique way to the whole class of operational probabilistic theories (shortly OPTs), of which the most relevant cases are Quantum Theory and Classical Theory. Whereas Classical Theory is not mereologically holistic, we can now search for other OPTs that are so. Within the OPT framework the role of the "system" is that of an input-output connection between two objective events. In non holistic theories, such as Classical Theory, the system can still be regarded as an "object". On the contrary, in holistic theories interpreting "system" as "object" constitutes an hypostatization of a theoretical notion.
Quantum mechanics is often credited for having clearly shown that the whole is something over and above the sum of its parts. We want to assess whether this is really the case, and if so, in what sense. We argue that there is indeed a sense in which this is true. Our argument is that even a weak realistic interpretation of quantum mechanics renders a particular metaphysical principle about property instantiation, that we label Property Compositional Determinateness, untenable. Yet there is another metaphysical principle about composition that is usually maintained to imply that composition of parts exhausts the whole they are part of, namely Mereological Extensionalism. In this case, contrary to widespread agreement, we argue that quantum mechanics does not provide any reason, either direct or indirect, to abandon such principle.
David Lewis is a natural target for those who believe that findings in quantum physics threaten the tenability of traditional metaphysical reductionism. Such philosophers point to allegedly holistic entities they take both to be the subjects of some claims of quantum mechanics and to be incompatible with Lewisian metaphysics. According to one popular argument, the non-separability argument from quantum entanglement, any realist interpretation of quantum theory is straightforwardly inconsistent with the reductive conviction that the complete physical state of the world supervenes on the intrinsic properties of and spatio-temporal relations between its point-sized constituents. Here I defend Lewis's metaphysical doctrine, and traditional reductionism more generally, against this alleged threat from quantum holism. After presenting the non-separability argument from entanglement, I show that Bohmian mechanics, an interpretation of quantum mechanics explicitly recognized as a realist one by proponents of the non-separability argument, plausibly rejects a key premise of that argument. Another holistic worry for Humeanism persists, however, the trouble being the apparently holistic character of the Bohmian pilot wave. I present a Humean strategy for addressing the holistic threat from the pilot wave by drawing on resources from the Humean best system account of laws.
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.
The pros and cons of various forms of atomism and holism that are applicable both in physical science and today’s philosophy of nature are evaluated. To this end, Lewis’ thesis of Humean supervenience is presented as an important case study of an atomistic doctrine in philosophical thought. It is shown that Lewis’ ontological doctrine of Humean supervenience incorporates at its foundation the so-called separability principle of classical physics. In view of the systematic violation of the latter within quantum mechanics, it is argued that contemporary physical science posits non-supervenient relations over and above the spatiotemporal ones. Depending on the mode of assignment of states to physical systems — unit state vectors versus statistical density operators — we distinguish between strongly and weakly non-supervenient relations. It is demonstrated that in either case the relations of quantum entanglement constitute prototypical examples of irreducible physical relations that do not supervene upon a spatiotemporal arrangement of Humean qualities, weakening, thereby, the thesis of Humean supervenience. It is examined, in this respect, the status of Lewis’ recombination principle, whereas his conception of lawhood is critically investigated. It is concluded that the assumption of ontological reductionism, as expressed in Lewis’ Humean doctrine, cannot be regarded as a reliable code of the nature of the physical world and its contents. It is proposed instead that due to the undeniable existence of non-supervenient relations a metaphysic of relations of a moderate kind ought to be acknowledged as an indispensable part of our understanding of the natural world at a fundamental level.