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 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 dissertation is ordered into three Parts. Part I is an investigation into identity, indiscernibility and individuality in logic and metaphysics. In Chapter 2, I investigate identity and discernibility in classical first-order logic. My aim will will be to define four different ways in which objects can be discerned from one another, and to relate these definitions: (i) to the idea of symmetry; and (ii) to the idea of individuality. In Chapter 3, the four kinds of discernibility are put to use in defining four rival metaphysical theses about indiscernibility and individuality. Part II sets up a philosophical framework for the work of Part III. In Chapter 4, I give an account of the rational reconstruction of concepts, inspired chiefly by Carnap and Haslanger. I also offer an account of the interpretation of physical theories. In Chapter 5, I turn to the specific problem of finding candidate concepts of particle. I present five desiderata that any putative explication ought to satisfy, in order that the proposed concept is a concept of particle at all. Part III surveys three rival proposals for the concept of particle in quantum mechanics. In Chapter 6, I define factorism and distinguish it from haecceitism. I then propose an amendment to recent work by Saunders, Muller and Seevinck, which seeks to show that factorist particles are all at least weakly discernible. I then present reasons for rejecting factorism. In Chapter 7, I investigate and build on recent heterodox proposals by Ghirardi, Marinatto and Weber about the most natural concept of entanglement, and by Zanardi about the idea of a natural decomposition of an assembly. In Chapter 8, I appraise the first of my two heterodox proposals for the concept of particle, varietism. I define varietism, and then compare its performance against the desiderata laid out in Chapter 5. I argue that, despite its many merits, varietism suffers a fatal ambiguity problem. In Chapter 9, I present the second heterodox proposal: emergentism. I argue that emergentism provides the best concept of particle, but that it is does so imperfectly; so there may be no concept of particle to be had in quantum mechanics. If emergentism is true, then particles are (higher-order) properties of the assembly, itself treated as the basic bearer of properties.
Abstract Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, this book explores two alternative metaphysical approaches to quantum particles. It asks if quantum particles can be regarded as individuals, just like books, tables, and people. Taking the first approach, the book argues that if quantum particles are regarded as individuals, then Leibniz’s famous Principle of the Identity of Indiscernibles is in fact violated. Recent discussions of this conclusion are analysed in detail and the costs involved in saving the Principle are carefully considered. For the second approach, the book considers recent work in non-standard logic and set theory to indicate how we can make sense of the idea that objects can be non-individuals. The concluding chapter suggests how these results might then be extended to quantum field theory.
Abstract This chapter discusses the concepts of indistinguishability, individuality, and non-individuality in the quantum context. It is argued that the above view of particles as non-individuals is not a necessary consequence of the physics, and that quantum particles can be taken to be individuals, subject to certain constraints. However, the sense of individuality here cannot be understood in terms of the Identity of Indiscernibles, since on a standard interpretation of quantum theory, Leibniz’s Principle is violated by both fermions and bosons. Criticisms of this argument are reviewed, as is Saunders’ recent attempt to defend a Quinean form of the Principle. The consequences of regarding quantum particles as individuals are considered in detail, and Teller’s account of entanglement in terms of non-supervenient relations is developed in this context. The conclusion is reached that quantum physics supports two alternative metaphysical packages of individuality and non-individuality, yielding a stronger form of underdetermination, which can be used to support a form of structuralism.
The notion of an individual and the related issues on individuation are topics that appear in the philosophical discussion ever since the antiquity. The idea of an individual thing is intuitively clear: an individual is something of a specific kind that is a unity, having its own identity, and being so that it is possible at least in principle to discern it from any other individual, even of similar species. But when we try to leave the intuitive realm and push this idea to a logical analysis, we find a cluster of problems that are difficult to overcome within standard logico-mathematical contexts. In this work, we shall be concerned with some aspects of this intuitive concept of an individual and on some related facts about individuation taken from recent discussions that arose ever since the inception of quantum theory, pushing the discussion to a “logical” view, which in our opinion is still lacking in the usual debates on such issues. In the final part of the paper, we propose a metaphysics where the notion of identity is substituted, for some objects, by a weaker notion of indiscernibility, and we try to justify such a move. In most of the uses of the expression “quantum theory”, we shall not make explicit the distinction between the non-relativistic and the relativistic approaches, although they of course are quite different, for we think that the problems as we shall present them appear in both versions. But, as the text goes, the context will distinguish between them and these questions will become clear to the reader.
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’.
In the non-reflexive formulation of quantum physics, attention is given to a metaphysical view of quantum objects (q-objects) as non-individuals, characterised as entities to which the standard notion of identity lacks sense. The reference to the nature of q-objects is usually omitted in other interpretations and the most we can find is some vague reference to “to each [quantum] system we associate a Hilbert space”, and nothing more is said about them; we need to infer from the theory their characteristics, and it gives us several alternatives. One of them, to be justified here in broad aspects, is the non-individual view. It is important to enlighten that we are not trying to just find a way to deal with quantum entities but to defend a possible ontology of non-individuals, which can be applied also to ‘particles’ arising from quantum fields. Our account is based on two assumptions: (i) the ‘classical theory of identity’ does not apply to q-objects, and (ii) their non-individuality must be attributed from the start, that is, as a primitive notion and not ‘made a posteriori’ say by assuming symmetry principles. The underlying logic is called non-reflexive because the reflexive law of identity ∀x(x=x) is supposed not to hold for q-objects. Since all the details demand a lot of space, here we only sketch and justify our view. The references provide a more detailed account.