Recently, in the debate about the ontology of quantum mechanics some authors have defended the view that quantum particles are individuals in a primitive sense, so that individuality should be preferred over non-individuality (the alternative option). Primitive individuality involves two main claims: (1) every item is identical with itself and (2) it is distinct from every other item. Non-relativistic quantum mechanics is said to provide positive evidence for that position, since in every situation comprising multiple particles there is a well-defined (...) number of them to begin with, and so they must be distinct from each other. We argue that the link between a well-defined number of items and the relation of identity that is being claimed to hold is not imposed by quantum mechanics, but rather by a metaphysical view. Formal evidence is advanced in favor of the thesis that counting may be performed for items without identity (non-individuals), so that quantum mechanics needs not be viewed as endorsing an ontology of individuals. (shrink)

We investigate the higher-order modal logic , which is a variant of the system presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like 'electron' have (...) no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory. (shrink)

This paper puts forward the hypothesis that the distinctive features of quantum statistics are exclusively determined by the nature of the properties it describes. In particular, all statistically relevant properties of identical quantum particles in many-particle systems are conjectured to be irreducible, ‘inherent’ properties only belonging to the whole system. This allows one to explain quantum statistics without endorsing the ‘Received View’ that particles are non-individuals, or postulating that quantum systems obey peculiar probability distributions, or assuming that there are primitive (...) restrictions on the range of states accessible to such systems. With this, the need for an unambiguously metaphysical explanation of certain physical facts is acknowledged and satisfied. (shrink)

Various forms of underdetermination that might threaten the realist stance are examined. That which holds between different 'formulations' of a theory (such as the Hamiltonian and Lagrangian formulations of classical mechanics) is considered in some detail, as is the 'metaphysical' underdetermination invoked to support 'ontic structural realism'. The problematic roles of heuristic fruitfulness and surplus structure in attempts to break these forms of underdetermination are discussed and an approach emphasizing the relevant structural commonalities is defended.

This thesis analyses the ontological nature of quantum particles. In it I argue that quantum particles, despite their indistinguishability, are objects in much the same way as classical particles. This similarity provides an important point of continuity between classical and quantum physics. I consider two notions of indistinguishability, that of indiscernibility and permutation symmetry. I argue that neither sort of indistinguishability undermines the identity of quantum particles. I further argue that, when we understand in distinguishability in terms of permutation symmetry, (...) classical particles are just as indistinguishable as quantum particles; for classical physics also possesses permutation symmetry. (shrink)

In this paper we argue that physical theories, including quantum mechanics, refer to some kind of ‘objects’, even if only implicitly. We raise questions about the logico-mathematical apparatuses commonly employed in such theories, bringing to light some metaphysical presuppositions underlying such apparatuses. We point out to some incongruities in the discourse holding that quantum objects would be entities of some ‘new kind’ while still adhering to the logico-mathematical framework we use to deal with classical objects. The use of such apparatus (...) would hinder us from being in complete agreement with the ontological novelties the theories of quanta seem to advance. Thus, we join those who try to investigate a ‘logic of quantum mechanics’, but from a different point of view: looking for a formal foundation for a supposed new ontology. As a consequence of this move, we can revisit Einstein’s ideas on physical reality and propose that, by considering a new kind of object traditionally termed ‘non-individuals’, it is possible to sustain that they still obey some of Einstein’s conditions for ‘physical realities’, so that it will be possible to talk of a ‘principle of separability’ in a sense which is not in complete disagreement with quantum mechanics. So, Einstein’s departure from quantum mechanics might be softened at least concerning a form of his realism, which sees separated physical objects as distinct ‘physical realities’. (shrink)

It has been suggested that quantum particles are genuinelyvague objects (Lowe 1994a). The present work explores thissuggestion in terms of the various metaphysical packages that areavailable for describing such particles. The formal frameworksunderpinning such packages are outlined and issues of identityand reference are considered from this overall perspective. Indoing so we hope to illuminate the diverse ways in whichvagueness can arise in the quantum context.

Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of counting, to them is (...) associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described. (shrink)

I modify and generalize Carnap’s notion of frameworks as a way of unpacking Goodman’s metaphor of “making worlds with symbols”. My frameworks provide, metaphorically, a way of making worlds out of symbols in as much as all our framework-bound access to the world is through frameworks that always stand to be improved in accuracy, precision, and usually both. Such improvement is characterized in pragmatist terms.

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, I (...) believe, that we consider how space itself relates to reality, and how other so-called "spaces" used in physics relate to reality. In chapter 2, I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the "property view" of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter 3, prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman. In chapter 4, some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the "measurement problem" of quantum mechanics: this problem and its proposed solution are the primary subjects of chapter 4. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber. Finally, in chapters 5 and 6, I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time. (shrink)

There have been attempts to derive anti-haeccetistic conclusions from the fact that quantum mechanics (QM) appeals to non-standard statistics. Since in fact QM acknowledges two kinds of such statistics, Bose-Einstein and Fermi-Dirac, I argue that we could in the same vein derive the sharper anti-haeccetistic conclusion that bosons are bundles of tropes and fermions are bundles of universals. Moreover, since standard statistics is still appropriate at the macrolevel, we could also venture to say that no anti-haecceitistic conclusion is warranted for (...) ordinary objects, which could then tentatively be identified with substrates. In contrast to this, however, there has been so far no acknowledgement of the possibility of inclusivism, according to which ontological accounts of particulars as widely different as those can possibly coexist in one world picture. The success of the different statistics in physics at least calls for a revision in this respect. (shrink)

It has frequently been suggested that quantum mechanics may provide a genuine case of ontic vagueness or metaphysical indeterminacy. However, discussions of quantum theory in the vagueness literature are often cursory and, as I shall argue, have in some respects been misguided. Hitherto much of the debate over ontic vagueness and quantum theory has centered on the “indeterminate identity” construal of ontic vagueness, and whether the quantum phenomenon of entanglement produces particles whose identity is indeterminate. I argue that this way (...) of framing the debate is mistaken. A more thorough examination of quantum theory and the phenomenon of entanglement reveals that quantum mechanics is best interpreted as supporting what I call the “vague property” construal of ontic vagueness, where vague properties are understood in terms of determinable properties without the corresponding determinates. (shrink)

Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve central difficulties faced by standard versions of scientific realism. Structures are invoked to respond to two important challenges: one posed by the pessimist meta-induction and the other by the underdetermination of metaphysics by physics, which arises in non-relativistic quantum mechanics. We argue that difficulties in the proper understanding of what a structure is (...) undermines the realist component of the view. Given the difficulties, either realism should be dropped or additional metaphysical components not fully endorsed by science should be incorporated. (shrink)

We consider the claim by Dorato and Morganti 591–610) that primitive individuality should be attributed to the entities dealt with by non-relativistic quantum mechanics. There are two central ingredients in the proposal: in the case of non-relativistic quantum mechanics, individuality should be taken as a primitive notion and primitive individuality is naturalistically acceptable. We argue that, strictly understood, naturalism faces difficulties in helping to provide a theory with a unique principle of individuation. We also hold that even when taken in (...) a loose sense, naturalism does not provide any sense in which one could hold that quantum mechanics endorses primitive individuality over non-individuality. Rather, we argue that non-individuality should be preferred based on the grounds that such a view fits better the claims of the theory. (shrink)

Although there have been several attempts to resist this conclusion, it is commonly held that the peculiar statistical behaviour of quantum particles is due to their non-individuality. In this paper, a new suggestion is put forward: quantum particles are individuals, and the distinctive features of quantum statistics are determined by the fact that all the state-dependent properties described by quantum statistics are emergent relations.

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build (...) a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. (shrink)

Despite the discrepancies between quantum objects and `classical' ones, mainly with regard to the fact that the latter may be thought of as `individuals', contrary to the former, we still regard the quanta as `things' in our ordinary discourse as well as in the logico-mathematical basis of quantum theories. This paper considers some possibilities for accomodating the logico-mathematical framework of the theories which deal with such a strange ontology where the inhabitants are things devoid of identity and both having and (...) not having certain properties.``All right'', said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone. (shrink)

In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a case-study and argue that if a certain metaphysical view of quantum objects is adopted, one seeing them as non-individuals, then there would be strong reasons (...) to ask for a different mathematical framework for describing the structures that would be the models of the corresponding theory. In departing from the standard frameworks (those worked on within standard mathematics), we hope to bring to the scene, within the scope of the semantic approach, the importance of paying attention to some fundamental concepts usually only superficially touched by philosophers of science (if touched). (shrink)

H. Post's conception of quantal particles as non-individuals is set in a formal logico-mathematical framework. By means of this approach certain metaphysical implications of quantum mechanics can be further explored.

The Mass Density approach to GRW (GRWm for short) has been widely discussed in the quantum foundations literature. A crucial feature of GRWm is the introduction of a Criterion of Accessibility for mass, which allows to explain the determinacy of experimental outcomes thus also addressing the tails problem of GRW. However, the Criterion of Accessibility leaves the ontological meaning of the non-accessible portion of mass utterly unexplained. In this paper I discuss two viable approaches to non-accessible mass, which I call (...) anti-realist and realist, and will defend the latter. First, I show that the anti-realist approach suffers from various objections. Second, I develop an account of non-accessible mass density states as objectively indeterminate states of affairs. (shrink)

This volume collects papers presented at the Founding Conference of the European Philosophy of Science Association meeting, held November 2007. It provides an excellent overview of the state of the art in philosophy of science in different European countries.

The paper addresses a problem for the unification of quantum physics with the new Aristotelianism: the identification of the members of the category of substance. I outline briefly the role that substance plays in Aristotelian metaphysics, leading to the postulating of the Tiling Constraint. I then turn to the question of which entities in quantum physics can qualify as Aristotelian substances. I offer an answer: the theory of thermal substances, and I construct a fivefold case for thermal substances, based on (...) the irreversibility of time, the definition of thermodynamic concepts, spontaneous symmetry breaking, phase transitions, and chemical form. (shrink)

According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, which degeneracy (...) allegedly arises from the fact that “large” (but not “small”) local gauge transformations connect physically distinct states of zero field energy. If that is right, then some local gauge transformations do generate empirical symmetries. In defending conventional wisdom against this challenge I hope to clarify the meaning of empirical symmetry while deepening our understanding of gauge transformations. I distinguish empirical from theoretical symmetries. Using Galileo’s ship and Faraday’s cube as illustrations, I say when an empirical symmetry is implied by a theoretical symmetry. I explain how the theta-vacuum arises, and how “large” gauge transformations differ from “small” ones. I then present two analogies from elementary quantum mechanics. By applying my analysis of the relation between empirical and theoretical symmetries, I show which analogy faithfully portrays the character of the vacuum state of a classical non-Abelian Yang-Mills gauge theory. The upshot is that “large” as well as “small” gauge transformations are purely formal symmetries of non-Abelian Yang-Mills gauge theories, whether classical or quantized. It is still worth distinguishing between these kinds of symmetries. An analysis of gauge within the constrained-Hamiltonian formalism yields the result that “large” gauge transformations should not be classified as gauge transformations; indeed, nor should “global” gauge transformations. In a theory in which boundary conditions are modeled dynamically, “global” gauge transformations may be associated with physical symmetries, corresponding to translations of these extra dynamical variables. Such translations are symmetries if and only if charge is conserved. But it is hard to argue that these symmetries are empirical, and in any case they do not correspond to any constant phase change in a quantum state. (shrink)

In this basically expository paper we discuss the role oflogic and mathematics in researches concerning the ontology of scientific theories, and we consider the particular case of quantum mechanics. We argue that systems of logic in general, and classical logic in particular, may contribute substantially with the ontology of any theory that has this logic in its base. In the case of quantum mechanics, however, from the point of view of philosophical discussions conceming identity and individuality, those contributions may not (...) be welcome for a specific interpretation, and an altemative system of logic perhaps could be used instead of a classical system. In this sense, we argue that the logic and ontology of a scientific theory may be seen as mutually inftuencing each other. On the one hand, logic contributes to shape the general features of the ontology of a theory; on the other hand, the theory also puts constraints on the possible understanding of ontology and, respectively, on possible systems of logic that may be the underlying logic ofthe theory. (shrink)

In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a case-study and argue that if a certain metaphysical view of quantum objects is adopted, namely, that which sees them as non-individuals, then there would be (...) strong reasons to ask for a different mathematical framework for describing the structures that would be the models of the corresponding theory. In departing from the standard frameworks, we hope to bring to the scene, within the scope of the semantic approach, the importance of paying attention to some fundamental concepts usually only superficially touched by philosophers of science. (shrink)

In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosophical implications. We also review some proposals available in the literature (...) which may be considered within the framework of the quantum logical tradition regarding the problem of indistinguishability. Besides these discussions and constructions, we advance novel technical results, namely, a lattice theoretical structure for identical particles for the finite dimensional case. This kind of approach was not present in the scarcely literature of quantum logic and indistinguishable particles. (shrink)

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...) solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

Huggett and Weingard's critical review provides an opportunity to continue the interpretive examination of quantum field theory in terms of some specific issues as well as comparison of alternative approaches to the subject. This note recasts their example of inequivalent Fock spaces in an effort to further clarify what it illustrates. Questions are addressed about the role of analogy in developing quantum field theory and about the conflict between formal vs. concrete methods in both physics and its interpretation, continuing the (...) well-known historical debate between Pierre Duhem and Clark Maxwell. Huggett and Weingard's examination very usefully occasions clarification on some points of exposition which, it is hoped, will make An Interpretive Introduction to Quantum Field Theory a more useful resource for understanding this subject. (shrink)

The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin-statistics connection and the Symmetrization Postulate. In light of recent theories (such as q-deformed commutators) that allow for ‘small’ violations of the spin-statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that permutation (...) symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles. 1 Introduction 2 Philosophical background 2.1 Important terminology 2.1.1 Identity 2.1.2 Indistinguishability 2.1.3 Indiscernibility 2.2 When are particles indistinguishable? 2.3 The Principle of the Identity of Indiscernibles and quantum mechanics 2.4 The Principle of the Identity of Indiscernibles and logic 2.5 Particle history 2.6 Transcendental individuality 3 Some quantum formalism 3.1 The Principle of Permutation Invariance and the Symmetrization Postulate 3.2 The configuration-space approach 3.3 Commutators and anticommutators, and identical particle statistics 3.4 Q-mutators 4 Identical particle statistics: a holistic point of view 5 Conclusions. (shrink)

Quasi-set theory is a theory for dealing with collections of indistinguishable objects. In this paper we discuss some logical and philosophical questions involved with such a theory. The analysis of these questions enable us to provide the first grounds of a possible new view of physical reality, founded on an ontology of non-individuals, to which quasi-set theory may constitute the logical basis.

This chapter (in French) compares the ways to access to events in science and in art. In particular, the Déotte's concept of "appareil" is discussed. To be published in Jean-Louis Déotte and Sylvestra Mariniello (ed.), Appareil et Intermédialité, L'Harmattan, 2007.