Program + Talks

Jonas Becker (Universidade Federal de Santa Catarina, Brasil)

Individuation without individuality

Abstract: The Received View for quantum entities is, in general terms, the claim that quantum particles are not individuals. Typical articulations of the view involve uses of the logical relation of identity and of the metaphysical notion of individuality, along with restrictions of such notions when it comes to deal with quantum entities. In this talk, I shall first suggest that the Received View may be understood in many different terms, depending on how one decides to disambiguate ‘individuality’. In the sequence, I shall argue that one particular understanding of the idea is in terms less metaphysically loaded than the usual ones, involving only an epistemic notion of individuation, which does not depend on metaphysical views on principles of individuality neither on restrictions of the relation of identity. Besides presenting the view, I shall argue that it has advantages over competing articulations, by being a more naturalistic approach to the problem and by being less revisionary than current proposals.

Tomasz Bigaj (University of Warsaw, Poland)

On some problems with discerning same-type particles using symmetric operators

Abstract: In quantum mechanics systems of particles of the same type are described by states possessing certain types of symmetries only. The restriction of the available states to the symmetric or antisymmetric section of the product Hilbert space has a well-known consequence in the form of the Indiscernibility Thesis, which states that the expectation values for single-particle operators are identical for all particles involved. I will discuss an alternative approach to the problem of the individuation and discernibility of same-type particles, based on the use of certain symmetric projector operators, following G. Ghirardi et al, S. Saunders and A. Caulton. I’ll present an ‘inductive’ argument in favor of the claim that being in an eigenstate of these projectors implies that the involved particles are discernible by some orthogonal single-particle projectors (exclusive properties). The main focus of the talk will be on an apparent conflict of this approach with the well-established facts regarding entangled states, such as the singlet-spin state. I will show how to avoid this problem by introducing spatial degrees of freedom. I will modify the formal description of single-particle quantum measurements accordingly, in order to exclude the non-physical concept of measurements performed on particles distinguished by labels in favor of measurements associated with well-defined locations in space.

Denis Dieks (Utrecht University, The Netherlands)

Identical quantum particles as distinguishable objects.

Abstract: Particles in classical physics are individuals that can be distinguished via their identifying physical properties. By contrast, in quantum mechanics the “received view” says that particles of the same kind (``identical particles'') cannot be distinguished in this way. This standard view is problematic, though: not only is it at odds with the very meaning of the term ``particle'' in ordinary language, but it also conflicts with how the term “particle” is actually used in the practice of present-day physics. Moreover, the indistinguishability doctrine prevents a smooth transition from quantum to classical particles (in the classical limit). We will discuss an alternative to the standard view that avoids these and similar problems. According to this proposal, a particle picture is not always appropriate to represent what is usually called an “identical particle system”; but when such a picture is applicable, identical quantum particles are distinguishable no less than classical particles. This alternative approach connects to recent discussions concerning the question of when identical particle states should be called entangled.

F. Holik & J.A. de Barros (CONICET, Argentina & San Francisco State University, US)

Indistinguishability at the heart of quantum phenomena

Abstract: In this talk we discuss the different ways in which the notion of indistinguishability appears in quantum theory. After reviewing its standard use in quantum statistics, we turn into interference and contextuality. We pose the problem of finding a unifying ontological principle for quantum theory, based on the notion of indistinguishability.

Ruth E. Kastner (University of Maryland, College Park, US)

The Advent of Individuality as the Quantum/Classical Threshold: A Transactional Account

Abstract: I discuss some approaches to understanding the requirement for symmetrization of fermionic and bosonic states in terms of various types of individuation of quantum degrees of freedom. I suggest that we need a new kind of haecceity, quantum haecceity, which differs from the usual classical notion of haecceity in key respects. I argue that we need quantum haecceity in order to account for the observed effects of symmetrization (such as entanglement and so-called ‘exchange forces’). Finally, I show that a transactional account of measurement transforms quantum haecceity into the full-fledged individuality characterized by classical haecceity.

Décio Krause (Federal University of Santa Catarina, Brazil)

Consequences of the classical theory of identity or: why this theory doesn’t fit quantum physics

Abstract: Quantum logicians have been insistent in that quantum logical connectives would be different from the corresponding classical ones. Standard properties like the Lindenbaum Lemma has also limitations, so as the notions of sets of quantum objects and the use of quantifiers. Here we enlarge this discussion by arguing that also the standard theory of identity is problematic when associated to the usual ways we consider quantum systems. Concerning quantum entities, the better way would be do not consider them as individuals, namely, entities endowed with identity conditions, but speak just of kinds and cardinals, that is, of quantities of entities of certain kinds, without individuation.

James Ladyman (University of Bristol, UK)

Identity, Intension and Isomorphism

Abstract: TBA.

Olimpia Lombardi (CONICET – University of Buenos Aires)

What does ‘indistinguishability’ mean in an ontology without individuals?

Abstract: By contrast to the Hilbert space formalism of quantum mechanics, in the algebraic formalism a quantum system is represented by an algebra of observables, and states are functionals on that algebra. If this mathematical priority of observables on states is transposed to the ontological domain, the result is an ontology whose primary items are properties and relations, and systems are bundles of properties. This kind of ontology has been proposed, underlining the advantages of this picture to deal with the main ontological challenges of quantum mechanics: contextuality, non-locality, and indistinguishability.

In this talk I will focus only on indistinguishability in order to show that, in an ontology without individuals, indistinguishability is not a relation between particles, but an internal symmetry of a single composite system. Moreover, in such an ontology, the Indistinguishability Principle is not an ad hoc postulate of the theory, but turns out to be a consequence of the ontologically motivated symmetry of the observables of the composite system.

Jean-Pierre Marquis (Université de Montreal)

The I^3 and Abstract Mathematical Structuralism

Abstract: Contemporary mathematical practice of pure mathematics rests on abstract structures, where the term ‘abstract’ is used in a sense that is different from the traditional metaphysical distinction. The notion of abstract structure that permeates contemporary pure mathematics forces us to rearticulate identity, individuality and indistinguishability in the foundations of mathematics, in as much as the latter ought to capture fundamental features of the practice of mathematics. In this talk, we will look at one of these articulations, namely the one that emerges from category theory, in its higher-dimensional disguise. My concern will be first and foremost philosophical, although it is informed by Michael Makkai’s work on FOLDS (First-Order Logic with Dependent Sorts) as a framework for a Structuralist Foundation for Abstract Mathematics.

Simon Saunders (University of Oxford, UK)

When particle labels matter: a reply to Dieks

Abstract: TBA.

Stewart Shapiro

The semantics of indiscernibility

Abstract: Some critics of my ante rem structuralism (Philosophy of mathematics: structure and ontology) took me to task over structures that have indiscernible places. This generated a lively discussion on the topic of indiscernibility. There is a related and, I think, more interesting issue concerning the semantics and pragmatics of mathematical languages, and perhaps languages generally.

To take one example, the informal language of complex analysis has a term ‘i’ which is supposed to denote one of the square roots of -1. At least grammatically, ‘i’ is a constant, a proper name. And, of course, the role of a constant is to denote a single object—at least in a sufficiently regimented language. But which of the square roots does ‘i’ pick out? Is it not as if the mathematical community has managed to single out one of the roots, in order to baptize it with the name ‘i’. It seems that they cannot do so, as the two roots are indiscernbile—at least in the language of pure complex analysis. Complex analysis is just one, philosophically salient, example of this phenomenon. It occurs throughout mathematics. The language of category theory, for example, is rampant with indiscernibility.

In this talk, I will briefly outline the problem, and a suggested solution, formulated in terms of what may be called “parameters” in natural deduction. This raises some interesting questions concerning the truthconditions of sentences that contain parameters, and those questions have ramifications for linguistic theory generally and, surprisingly, logic. I address those