In this paper I consider the question of whether absolute discernibility is attainable in symmetric languages. Simon Saunders has proven that all facts expressible in first-order language with identity can be equivalently stated within its symmetric sublanguage. I use this result to show specifically how particles of the same type can be absolutely discerned in the permutation-invariant language of the quantum theory of many particles.

Reply in Book Symposium on James Ladyman, Don Ross: 'Everything must go: metaphysics naturalized', Oxford: Oxford University Press, 2007.

The concept of indistinguishable particles in quantum theory is fundamental to questions of ontology. All ordinary matter is made of electrons, protons, neutrons, and photons and they are all indistinguishable particles. Yet the concept itself has proved elusive, in part because of the interpretational difficulties that afflict quantum theory quite generally, and in part because the concept was so central to the discovery of the quantum itself, by Planck in 1900; it came encumbered with revolution. I offer a deflationary reading (...) of the concept ‘indistinguishable’ that is identical to Gibbs’ concept ‘generic phase’, save that it is defined for state spaces with only finitely-many states of bounded volume and energy. That, and that alone, makes for the difference between the quantum and Gibbs concepts of indistinguishability. This claim is heretical on several counts, but here we consider only the content of the claim itself, and its bearing on the early history of quantum theory rather than in relation to contemporary debates about particle indistinguishability and permutation symmetry. It powerfully illuminates that history. (shrink)

We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz's Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical relations, i.e. relations independent of the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as well, we argue that similar bosons can also be discerned in all (...) their admissible states; but their categorical discernibility turns out to be a state-dependent matter. In all demonstrated cases of discernibility, the fermions and the bosons are discerned (i) with only minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian transcendental individuality or Adamsian primitive thisness; and (iii) without revising the general framework of classical elementary predicate logic and standard set theory, thus without revising standard mathematics. This confutes: (a) the currently dominant view that, provided (i) and (ii), the quantum-mechanical description of such composite physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only way to do it is by adopting one or other of the thick metaphysical notions mentioned above. Among the most general and influential arguments for the currently dominant view are those due to Schrodinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett. We review them succinctly and critically as well as related arguments by van Fraassen and Massimi. (shrink)

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

Philosophers of science have often favoured reductive approaches to how-possibly explanation. This article identifies three alternative conceptions making how-possibly explanation an interesting phenomenon in its own right. The first variety approaches “how possibly X?” by showing that X is not epistemically impossible. This can sometimes be achieved by removing misunderstandings concerning the implications of one’s current belief system but involves characteristically a modification of this belief system so that acceptance of X does not result in contradiction. The second variety offers (...) a potential how-explanation of X. It is usually followed by a range of further potential how-explanations of the same phenomenon. In recent literature the factual claims implied by the second variety have been downplayed whereas the heuristic role of mapping the space of conceptual possibilities has been emphasized. I will focus especially on this truth-bracketing sense of potentiality when looking closer at the second variety in the paper. The third variety has attracted less interest. It presents a partial how-explanation of X. Typically it aims to establish the existence of a mechanism by which X could be and was generated. The third conception stands out as the natural alternative for the advocate of ontic how-possibly explanations. This article transfers Salmon’s view that explanation-concepts can be broadly divided into epistemic, modal, and ontic to the context of how-possibly explanations. Moreover, it is argued that each of the three above-mentioned varieties of how-possibly explanation occurs in science. To recognize this may be especially relevant for philosophers. We are often misled by the promises of various why-explanation accounts, and seem to have forgotten nearly everything about the diversity of how-possibly explanations. (shrink)

We discuss the case against Factorism, which is the standard assumption in quantum mechanics that the labels of the $$\otimes$$ ⊗ -factor Hilbert-spaces in direct-product Hilbert-spaces of composite physical systems of similar particles refer to particles, either directly or descriptively. We distinguish different versions of Factorism and argue for their truth or falsehood. In particular, by introducing the concepts of snapshot Hilbert-space and Schrödinger-movie, we demonstrate that there are Hilbert-spaces and $$\otimes$$ ⊗ -factorisations where the labels do refer, even descriptively, (...) to similar particles, which renders them probabilistically absolutely discernible. (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)

We discuss the case against Factorism, which is the standard assumption in quantum mechanics that the labels of the ⊗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\otimes$$\end{document}-factor Hilbert-spaces in direct-product Hilbert-spaces of composite physical systems of similar particles refer to particles, either directly or descriptively. We distinguish different versions of Factorism and argue for their truth or falsehood. In particular, by introducing the concepts of snapshot Hilbert-space and Schrödinger-movie, we demonstrate that there are Hilbert-spaces and ⊗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\otimes$$\end{document}-factorisations where the labels do refer, even descriptively, to similar particles, which renders them probabilistically absolutely discernible. (shrink)

Physical theories continue to be interpreted in terms of particles. The idea of a particle required modification with the advent of quantum theory, but remains central to scientific explanation. Particle ontologies also have the virtue of explaining basic epistemic features of the world, and so remain appealing for the scientific realist. However, particle ontologies are untenable when coupled with the empirically necessary postulate of permutation invariance—the claim that permuting the roles of particles in a representation of a physical state results (...) in a representation of the same physical state. I demonstrate that any theory which is permutation invariant in this sense is incompatible with a particle ontology. (shrink)

Simon Saunders argues that, although distinct objects must be discernible, they need only be weakly discernible (Saunders 2003, 2006a). I will argue that this combination of views is unmotivated: if there can be objects which differ only weakly, there can be objects which don’t differ at all.

Ontic structural realism (OSR) claims that all there is to the world is structure. But how can this slogan be turned into a worked-out metaphysics? Here I consider one potential answer: a metaphysical framework known as generalism (Dasgupta, 2009, 2016). According to the generalist, the most fundamental description of the world is not given in terms of individuals bearing properties, but rather, general facts about which states of affairs obtain. However, I contend that despite several apparent similarities between the positions, (...) generalism is unable to capture the two main motivations for OSR. I suggest instead that OSR should be construed as a meta-metaphysical position. (shrink)

Ontic structural realism claims that all there is to the world is structure. But how can this slogan be turned into a worked-out metaphysics? Here I consider one potential answer: a metaphysical framework known as ‘generalism’. According to the generalist, the most fundamental description of the world is not given in terms of individuals bearing properties, but rather, general facts about which states of affairs obtain. However, I contend that despite several apparent similarities between the positions, generalism is unable to (...) capture the two main motivations for OSR. I suggest instead that OSR should be construed as a meta-metaphysical position. 1Introduction 2Motivations 2.1Theory change 2.2Permutation invariance 3Metaphysics 4Generalism 4.1Quantifier generalism 4.2Algebraic generalism 5Why Generalism Is Not Ontic Structural Realism 6Ontic Structural Realism as Meta-metaphysics 7Conclusion. (shrink)

According to the substantialist, substances should be regarded as the fundamental ontological category. It is substances that are the bearer of properties, that are causally efficacious and that compose the things we see and touch around us. Cumpa has argued that this metaphysics fits poorly with classical physics and Buonomo has extended this argument into the quantum realm. After reviewing their claims, I shall argue that simple reflection on the form of the Standard Model also undermines substantialism. I will then (...) explore Dasgupta’s qualitative factualism in this context before suggesting that modern physics does not compel us to adopt such a stance. The alternative is to adopt a form of structuralism which, although it may be rendered compatible with factualism, can also stand as a ‘third way’ between these stances. (shrink)

Fermi-Dirac statistics are one of two kinds of statistics exhibited by !identical quantum particles, the other being !Bose-Einstein statistics. Such particles are called fermions and bosons respectively (the terminology is due to Dirac [1902-1984] [1]). In the light of the !spin-statistics theorem, and consistent with observation, fermions are invariably spinors (of half-integral spin), whilst bosons are invariably scalar or vector particles (of integral spin). See !spin.

Identity. From very early days of quantum theory it was recognized that quanta were statistically strange (see !Bose-Einstein statistics). Suspicion fell on the identity of quanta, of how they are to be counted [1], [2]. It was not until Dirac’s [1902-1984] work of 1926 (and his discovery of !Fermi-Dirac statistics [3]) that the nature of the novelty was clear: the quantum state of exactly similar particles of the same mass, charge, and spin must be symmetrized, yielding states either symmetric or (...) antisymmetric under permutations. This is the symmetry postulate (SP). (shrink)

The view that quantum particles cannot be regarded as individuals was articulated in the early days of the 'quantum revolution' and became so well-entrenched that French and Krause called it 'the Received View'. However it was subsequently shown that quantum statistics is in fact compatible with a metaphysics of particle individuality, subject to certain caveats. As a consequent it has been claim that there exists a kind of underdetermination of the metaphysics by the physics which in turn has been used (...) to motivate a form of 'notice' structural realism. In this essay I will review this purported underdetermination and the motivation for structural realism that it purportedly provides in the context of recent developments in both the philosophy of physics and metaphysics. I aim to conclude that such developments reinforce the underdetermination and allow one to respond to certain critical concerns regarding its motivational power. (shrink)

This is an extensive review of recent work on the foundations of statistical mechanics.

Starting from the sixties of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, (...) i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories - the so called "conjunctive propositions" - will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth. (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)

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...) The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

'Structural realism' is a buzzword in the scientific realism debate. Various positions with diverse motivations fall under this label. A much advertised distinction is between epistemic and ontological forms of structuralism. This paper scrutinizes the alleged dichotomy between these two 'alternatives', and criticises the considerations that have been taken to motivate the ontic variety over the epistemic. I will argue that ontological structural realism is not called for within the traditional realism debate.

an article written with Tom Imbo for the forthcoming Compendium of Quantum Mechanics.

Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical mechanics should be revised, either on the basis of quantum mechanics or on the basis of general and fundamental considerations about the distinguishability of particles. In this article we argue against this response. We show that both the extensive thermodynamic and the non-extensive statistical entropy are (...) perfectly alright within their own fields of application. Changes in the statistical formulas that remove the discrepancy must be seen as motivated by pragmatic reasons rather than as justified by basic arguments about particle statistics. (shrink)

Classical particles of the same kind are distinguishable: they can be labeled by their positions and follow different trajectories. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and via S=k ln W this leads to a non-extensive expression for the entropy. This result is generally considered wrong because of its inconsistency with thermodynamics. It is sometimes concluded from this inconsistency, notoriously illustrated by the Gibbs paradox, that identical particles must be treated as (...) indistinguishable after all; and even that quantum mechanics is indispensable for making sense of this. In this article we argue, by contrast, that the classical statistics of distinguishable particles and the resulting non-extensive entropy function are perfectly all-right both from a theoretical and an experimental perspective. We remove the inconsistency with thermodynamics by pointing out that the entropy concept in statistical mechanics is not completely identical to the thermodynamical one. Finally, we observe that even identical quantum particles are in some cases distinguishable; and conclude that quantum mechanics is irrelevant to the Gibbs paradox. (shrink)

This paper discusses the issue of the identity and individuality (or lack thereof) of quantum mechanical particles. It first reconstructs, on the basis of the extant literature, a general argument in favour of the conclusion that such particles are not individual objects. Then, it critically assesses each one of the argument’s premises. The upshot is that, in fact, there is no compelling reason for believing that quantum particles are not individual objects.

The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory, some to classical theory. The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability. Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of (...) the tensor product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. ‘Distinguishability’, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction. (shrink)