The aim of this paper is modest. It is argued that if the nature of the “equivalence” between first-quantized particle theories and second-quantized (Fock Space) theories is examined closely, if the inadequacies of de Muynck's “indexed particle” version of Fock Space are recognized, and if the question is not begged against modal metaphysics, then van Fraassen's attempted deflation of ontological issues in quantum theory can be seen to fail.
The aim of this paper is modest. It is argued that if the nature of the “equivalence” between first-quantized particle theories and second-quantized (Fock Space) theories is examined closely, if the inadequacies of de Muynck's “indexed particle” version of Fock Space are recognized, and if the question is not begged against modal metaphysics, then van Fraassen's attempted deflation of ontological issues in quantum theory can be seen to fail.
This chapter aims to place the discussion of holism in quantum theory generally and of the problem of identical particles and quantum statistics specifically in the context of general philosophy. Various debates in metaphysics, both historical and current, broach related subjects and involve analyses of concepts currently used in the philosophy of quantum mechanics. These include concepts of identity, individuation, essence, form, necessity, possibility, modality, contingency, and universality. But this chapter also extends the previous one by introducing Fock space and the transition from elementary quantum mechanics to quantum field theory via 'second quantization’. For this formalism relates clearly to certain ’anti‐essentialist’ approaches in the metaphysics of modality. Finally, in keeping with the empiricism pursued in this book, the general enterprise of metaphysics pertaining to those topics is viewed here within an anti‐metaphysical stance, as having as its value the display of a plurality of interpretations whose very diversity enhances our understanding of the theory.
Philosophers of science commonly connect ontology and science, stating that these disciplines maintain a two-way relationship: on the one hand, we can extract ontology from scientific theories; on the other hand, ontology provides the realistic content of our scientific theories. In this article, we will critically examine the process of naturalizing ontology, i.e., confining the work of ontologists merely to the task of pointing out which entities certain theories commit themselves to. We will use non-relativistic quantum mechanics as a case study. We begin by distinguishing two roles for ontology: the first would be characterized by cataloging existing entities according to quantum mechanics; the second would be characterized by establishing more general ontological categories in which existing entities must be classified. We argue that only the first step is available for a naturalistic approach; the second step not being open for determination or anchoring in science. Finally, we also argue that metaphysics is still a step beyond ontology, not contained in either of the two tasks of ontology, being thus even farther from science.
This thesis examines the concepts of identity and individuality via scientifically-informed philosophical analysis. It has two parts. The first part deals with metaphysical claims that turn out to be, in effect, very general empirical claims extracted from our (supposed, but rationally-accredited) knowledge of the world. I here compare two approaches: a) the Leibniz-Quine view of identity as a derivative relation, and, relatedly, of individuality as dependent on the qualities of things; and b) the view that identity is a non-analysable primitive, and, relatedly, that the individuality of things is not reducible to anything else. The former position, based on the Principle of the Identity of the Indiscernibles as a criterion of individuation, might appear prima facie more plausible. However, I argue that it runs into difficulties both at the level of a priori analysis and in terms of 'fit' with the evidence described by our best science. It is, in fact, not even as compelling from the empiricist point of view as is commonly believed. I therefore argue that the position that identity and individuality are primitive may be preferred. In the second part of the thesis - under the assumption that the proper role of metaphysics is to characterise the best solutions to issues that are left open by current science - I deal with the question regarding whether and how the ultimate constituents of reality can actually be conceived of as primitive individuals. I argue in favour of an ontology of tropes, develop the view in detail and defend it against various criticisms. The fundamental tropes that constitute the basic 'building blocks' of reality are identified with the state-independent properties of elementary particles. The way in which these constitute complex particulars is described, and certain peculiarities having to do with quantum statistics are accounted for. I conclude by suggesting possible avenues for further research.
This paper compares two frameworks that confront “infinity” in sharply different ways: (i) Fock space, the graded Hilbert-space construction underlying second quantization and quantum field theory, which accommodates superpositions across particle-number sectors; and (ii) the Theory of Infinity (TOI), an ontological/computational program in which infinity is taken as a primitive and finite “contexts” are generated through iterative symmetry operations. We focus on three comparative axes: (a) how variable cardinality is represented, (b) how symmetry is implemented, and (c) how invariants constrain permissible structure and dynamics. Although the two frameworks are not mathematically equivalent, both employ a graded decomposition (particle-number sectors in Fock space versus a nested context lattice in TOI) and treat invariants as structuring constraints. We conclude by identifying robust analogies (graded structure, invariants, refinement) and the principal divergences (linear operator-algebraic versus nonlinear iterative dynamics; potential/sectoral versus ontological infinity).
While entanglement in the case of distinguishable particles is clearly understood, in the case of indistinguishable particles, there is still a wide debate regarding basic conceptual issues. Here, I will address two such issues. First, the debate almost always rests on a differentiated treatment of the cases of distinguishability and indistinguishability, even with respect to the definition of the concept of entanglement. Second, the fact that symmetrized and antisymmetrized states of indistinguishable particles are non-factorizable leads to certain perplexities about the very nature of entanglement. In the present work, both issues will be addressed from the perspective of an ontology of properties, which finds its natural expression in the algebraic formalism of quantum mechanics. The final goal will be to show that the proposed ontology allows a unified treatment of entanglement in the distinguishability and indistinguishability cases and offers a straightforward way out to perplexities. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.