When dealing with a certain class of physical systems, the mathematical characterization of a generic system aims to describe the phase portrait of all its possible states. Because they are defined only up to isomorphism, the mathematical objects involved are “schematic structures”. If one imposes the condition that these mathematical definitions completely capture the physical information of a given system, one is led to a strong requirement of individuation for physical states. However, we show there are not enough qualitatively distinct (...) properties in an abstract Hilbert space to fulfill such a requirement. It thus appears there is a fundamental tension between the physicist’s purpose in providing a mathematical definition of a mechanical system and a feature of the basic formalism used in the theory. We will show how group theory provides tools to overcome this tension and to define physical properties. (shrink)

This article presents and argues for modal structuralism, which is loosely derived from a position described by Wilfrid Sellars. Modal structuralism holds that a fundamental property is identified by the role it plays in the structure of possibilities. It implies necessitarianism about laws, which holds that at least some laws of nature are metaphysically necessary. The argument for these positions derives from the following assumptions: the principle of the identity of indiscernible properties and a modest antiquidditism. These assumptions are weaker (...) than those of causal structuralism, which is a closely related view. (shrink)

The identity of indiscernibles states that indiscernible objects must be identical. Many philosophers have held that the PII turns out to be either true but trivial, or non-trivial but false, depending on how the notion of discernibility is spelled out. In this paper, I propose and defend an account of this notion which aims to yield a minimally non-trivial and yet plausible version of the PII. I argue moreover that this version of the principle is immune to a number of (...) well-known and recent objections to the PII. (shrink)

Esfeld has proposed a minimalist ontology of nature called ‘super-Humeanism’ that purports to accommodate quantum phenomena and avoid standard objections to neo-Humean metaphysics. I argue that Esfeld’s sparse ontology has counterintuitive consequences and generates two self-undermining dilemmas concerning the nature of time and space. Contrary to Esfeld, I deny that super-Humeanism supports an ontology of microscopic particles that follow continuous trajectories through space.

Identity and distinctness facts are ones like “The Eiffel Tower is identical to the Eiffel Tower,” and “The Eiffel Tower is distinct from the Louvre.” This paper concerns one question in the metaphysics of identity: Are identity and distinctness facts metaphysically fundamental or are they nonfundamental? I provide an overview of answers to this question.

This paper offers a metaphysical explanation of the identity and distinctness of concrete objects. It is tempting to try to distinguish concrete objects on the basis of their possessing different qualitative features, where qualitative features are ones that do not involve identity. Yet, this criterion for object identity faces counterexamples: distinct objects can share all of their qualitative features. This paper suggests that in order to distinguish concrete objects we need to look not only at which properties and relations objects (...) instantiate but also how they instantiate these properties and relations. I propose that objects are identical when they stand in certain qualitative relations in virtue of their existence. And concrete objects are distinct when they do not stand in the same kinds of relations to one another in virtue of their existence. (shrink)

Paul (Noûs 36:578–596, 2002; Noûs 40:623–659, 2006, The Handbook of Mereology, forthcoming) has argued for a bundle theory of objects that analyzes the bundling relation between properties and objects in terms of parthood relations. In this paper I argue that any mereological bundle theory with the explanatory power of Paul’s theory will entail the principle of the identity of indiscernibles (PII). This is problematic, since similar bundle theories seem to fall to Max Black’s two sphere counterexample to (PII). I argue, (...) however, that a fully developed mereological bundle theory provides a new way of interpreting Black’s two sphere universe that dispels the counterexample. I argue that this solution to Black’s puzzle is superior to other solutions on offer, and consequently that mereological bundle theory is an attractive ontological strategy for friends of (PII). (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).

This paper is concerned with two concepts of qualitativeness that apply to intensional entities. I propose an account of pure qualitativeness that largely follows the traditional understanding established by Carnap, and try to shed light on its ontological presuppositions. On this account, an intensional entity is purely qualitative iff it does not ‘involve’ any particular. An alternative notion of qualitativeness—which I propose to refer to as a concept of strict qualitativeness—has recently been introduced by Chad Carmichael. However, Carmichael’s definition presupposes (...) a highly fine-grained conception of properties and relations. To eliminate this presupposition, I tentatively suggest a different definition that rests on a concept of perspicuous denotation. In the penultimate section, both concepts of qualitativeness are put to work in distinguishing between different ‘grades’ of qualitative discriminability. (shrink)

Some authors have attempted to defend Leibniz’s Identity of Indiscernibles through weak discernibility. The idea is that if there is a symmetric, nonreflexive physical relation that holds between two particles, then those particles cannot be identical. In this article I focus only on Muller and Saunders’s account and argue that the means by which they achieve weak discernibility is not through a quantum mechanical observable but an alternate mathematical construction that is both unorthodox and incomplete.

One of the reasons provided for the shift away from an ontology for physical reality of material objects & properties towards one of physical structures & relations (Ontological Structural Realism: OntSR) is that the quantum-mechanical description of composite physical systems of similar elementary particles entails they are indiscernible. As material objects, they 'whither away', and when they wither away, structures emerge in their stead. We inquire into the question whether recent results establishing the weak discernibility of elementary particles pose a (...) threat for this quantum-mechanical reason for OntSR, because precisely their newly discovered discernibility prevents them from 'whithering away'. We argue there is a straightforward manner to consider the recent results as a reason in favour of OntSR rather than against it. (shrink)

I begin by criticizing an elaboration of an argument in this journal due to Hawley , who argued that, where Leibniz’s Principle of the Identity of Indiscernibles faces counterexamples, invoking relations to save PII fails. I argue that insufficient attention has been paid to a particular distinction. I proceed by demonstrating that in most putative counterexamples to PII , the so-called Discerning Defence trumps the Summing Defence of PII. The general kind of objects that do the discerning in all cases (...) form a category that has received little if any attention in metaphysics. This category of objects lies between indiscernibles and individuals and is called relationals: objects that can be discerned by means of relations only and not by properties. Remarkably, relationals turn out to populate the universe. (shrink)

In this journal (Studia Logica), D. Rizza [2010: 176] expounded a solution of what he called “the indiscernibility problem for ante rem structuralism”, which is the problem to make sense of the presence, in structures, of objects that are indiscernible yet distinct, by only appealing to what that structure provides. We argue that Rizza’s solution is circular and expound a different solution that not only solves the problem for completely extensive structures, treated by Rizza, but for nearly (but not) all (...) mathematical structures. (shrink)

Nous proposons une traduction inédite du fameux dialogue de Max Black intitulé « L’identité des indiscernables », paru en 1952 (Mind, vol. 61, no 242, avril 1952, 153-164) et aujourd’hui considéré comme un classique de la philosophie contemporaine. Cette traduction est précédée d’une présentation rapide du texte et du problème philosophique qu’il soulève.

Nous proposons une traduction inédite du fameux dialogue de Max Black intitulé « L’identité des indiscernables », paru en 1952 (Mind, vol. 61, no 242, avril 1952, 153-164) et aujourd’hui considéré comme un classique de la philosophie contemporaine. Cette traduction est précédée d’une présentation rapide du texte et du problème philosophique qu’il soulève.

Nous proposons une traduction inédite du fameux dialogue de Max Black intitulé « L’identité des indiscernables », paru en 1952 (Mind, vol. 61, no 242, avril 1952, 153-164) et aujourd’hui considéré comme un classique de la philosophie contemporaine. Cette traduction est précédée d’une présentation rapide du texte et du problème philosophique qu’il soulève.

Saunders' recent arguments in favour of the weak discernibility of (certain) quantum particles seem to be grounded in the 'generalist' view that science only provides general descriptions of the worlIn this paper, I introduce the ‘generalist’ perspective and consider its possible justification and philosophical basis; and then look at the notion of weak discernibility. I expand on the criticisms formulated by Hawley (2006) and Dieks and Veerstegh (2008) and explain what I take to be the basic problem: that the properties (...) invoked by Saunders cannot be pointed to as ‘individuators’ of otherwise indiscernible (and thus numerically identical) entities because their ontological status remains underdetermined by the evidence and the established interpretation of the theory. In addition to to this, I suggest that Saunders does not deal adequately with bosons, and cannot do so exactly because he subscribes to PII and the generalist picture. The last part of the paper contains a critical examination of the claim (or at least implicit assumption) that the generalist picture should be regarded as obviously compelling by the modern-day empiricist. (shrink)

In a recent paper, Jiri Benovsky argues that the bundle theory and the substratum theory, traditionally regarded as ‘deadly enemies’ in the metaphysics literature, are in fact ‘twin brothers’. That is, they turn out to be ‘equivalent for all theoretical purposes’ upon analysis. The only exception, according to Benovsky, is a particular version of the bundle theory whose distinguishing features render unappealing. In the present reply article, I critically analyse these undoubtedly relevant claims, and reject them.

In the context of discussions about the nature of ‘identical particles’ and the status of Leibniz’s Principle of the Identity of Indiscernibles in Quantum Mechanics, a novel kind of physical discernibility has recently been proposed, which we call witness-discernibility. We inquire into how witness-discernibility relates to known kinds of discernibility. Our conclusion will be that for a wide variety of cases, including the intended quantum-mechanical ones, witness-discernibility collapses extensionally to absolute discernibility, that is, to discernibility by properties.

The apparent chasm between two camps in metaphysics, analytic metaphysics and scientific metaphysics, is well recognized. I argue that the relationship between them is not necessarily a rivalry; a division of labour that resembles the relationship between pure mathematics and science is possible. As a case study, I look into the metaphysical underdetermination argument for ontic structural realism, a well‐known position in scientific metaphysics, together with an argument for the position in analytic metaphysics known as ontological nihilism. I argue that (...) we can ascribe the same schema to both arguments, which indicates that analytic metaphysics can offer an abstract model that scientific metaphysics may find useful. (shrink)

Bundle Theory is the view that every concrete particular object is solely constituted by its universals. This theory is often criticized for not accommodating the possibility of symmetrical universes, such as one that contains two indiscernible spheres two meters from each other in otherwise empty space. One bundle theoretic solution to this criticism holds that the fact that the spheres stand in a weakly discerning—i.e., irreflexive and symmetric—relation, such as being two meters from, is sufficient for the numerical diversity of (...) the spheres. For this solution to be effective, however, it should be established that weak discernibility not only necessitates but also explains numerical diversity. In this paper, I argue that the fact that two objects have a certain distance between them does explain why they are non-identical. I also argue that the worry that the weak discernibility approach has some circularity problems is not well-founded. (shrink)

Bundle Theory is the view that every concrete particular object is solely constituted by its universals. This theory is often criticized for not accommodating the possibility of symmetrical universes, such as one that contains two indiscernible spheres two meters from each other in otherwise empty space. One bundle theoretic solution to this criticism holds that the fact that the spheres stand in a weakly discerning—i.e., irreflexive and symmetric—relation, such as being two meters from, is sufficient for the numerical diversity of (...) the spheres. For this solution to be effective, however, it should be established that weak discernibility not only necessitates but also explains numerical diversity. In this paper, I argue that the fact that two objects have a certain distance between them does explain why they are non-identical. I also argue that the worry that the weak discernibility approach has some circularity problems is not well-founded. (shrink)

Questions about the relation between identity and discernibility are important both in philosophy and in model theory. We show how a philosophical question about identity and dis- cernibility can be ‘factorized’ into a philosophical question about the adequacy of a formal language to the description of the world, and a mathematical question about discernibility in this language. We provide formal definitions of various notions of discernibility and offer a complete classification of their logical relations. Some new and surprising facts are (...) proved; for instance, that weak dis- cernibility corresponds to discernibility in a language with constants for every object, and that weak discernibility is the most discerning nontrivial discernibility relation. (shrink)

Among the most interesting features of Homotopy Type Theory is the way it treats identity, which has various unusual characteristics. We examine the formal features of “identity types” in HoTT, and how they relate to its other features including intensionality, constructive logic, the interpretation of types as concepts, and the Univalence Axiom. The unusual behaviour of identity types might suggest that they be reinterpreted as representing indiscernibility. We explore this by defining indiscernibility in HoTT and examine its relationship with identity. (...) We argue that identity types are a primitive component of HoTT and cannot be reduced to indiscernibility. (shrink)

The identity and diversity of individual objects may be grounded or ungrounded, and intrinsic or contextual. Intrinsic individuation can be grounded in haecceities, or absolute discernibility. Contextual individuation can be grounded in relations, but this is compatible with absolute, relative or weak discernibility. Contextual individuation is compatible with the denial of haecceitism, and this is more harmonious with science. Structuralism implies contextual individuation. In mathematics contextual individuation is in general primitive. In physics contextual individuation may be grounded in relations via (...) weak discernibility. (shrink)

The notion of strict identity is sometimes given an explicit second-order definition: objects with all the same properties are identical. Here, a somewhat different problem is raised: Under what conditions is the identity relation on the domain of a structure first-order definable? A structure may have objects that are distinct, but indiscernible by the strongest means of discerning them given the language (the indiscernibility formula). Here a number of results concerning the indiscernibility formula, and the definability of identity, are collected (...) and a number of applications discussed. (shrink)

Muller and Saunders ([2008]) purport to demonstrate that, surprisingly, bosons and fermions are discernible; this article disputes their arguments, then derives a similar conclusion in a more satisfactory fashion. After briefly explicating their proof and indicating how it escapes earlier indiscernibility results, we note that the observables which Muller and Saunders argue discern particles are (i) non-symmetric in the case of bosons and (ii) trivial multiples of the identity in the case of fermions. Both problems undermine the claim that they (...) have shown particles to be physically discernible. We then prove two results concerning observables that are truly physical: one showing when particles are discernible and one showing when they are not (categorically) discernible. Along the way we clarify some frequently misunderstood issues concerning the interpretation of quantum observables. 1 Background2 Criticisms2.1 Bosons2.2 Fermions3 Reformulating the Insight3.1 What weakly discerns?3.2 General results4 Conclusion. (shrink)

Newton's arguments for the immobility of the parts of absolute space have been claimed to licence several proposals concerning his metaphysics. This paper clarifies Newton, first distinguishing two distinct arguments. Then, it demonstrates, contrary to Nerlich ([2005]), that Newton does not appeal to the identity of indiscernibles, but rather to a view about de re representation. Additionally, DiSalle ([1994]) claims that one argument shows Newton to be an anti-substantivalist. I agree that its premises imply a denial of a kind of (...) substantivalism, but I show that they are inconsistent with Newton's core doctrine that not all motion is the relative motions of bodies, and so conclude that they are not part of his considered views on space. The Arguments The Identity Argument 2.1 Identity of indiscernibles for individuals 2.2 Identity of indiscernibles for worlds and states 2.3 Representation de re Kinematic Relationism Conclusion CiteULike Connotea Del.icio.us What's this? (shrink)

The significance of Max Black’s indistinguishable spheres for the nature of particles in quantum mechanics is discussed, focusing in particular on the use of the idea of weak indiscernibility. It is argued that there can be four such Black spheres but that five are impossible. It follows from this that Black’s example cannot serve as a model for indistinguishability in physics. But Black’s discussion of his spheres gave rise to the idea of weak discernibility and it is argued that such (...) predicates are unsatisfiable in the way intended. The underlying problem with weak discernibility spreads out to also undermine the whole notion that indistinguishability rests on a notion of the permutation invariance of particles. A better foundation is indicated. (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.

Roughly speaking, perdurantism is the view that ordinary objects persist through time by having temporal parts, whilst endurantism is the view that they persist by being wholly present at different times. (Speaking less roughly will be important later.) It is often thought that perdurantists have an advantage over endurantists when dealing with objects which appear to coincide temporarily: lumps, statues, cats, tail-complements, bisected brains, repaired ships, and the like. Some cases – personal fission, for example – seem to involve temporary (...) coincidence between objects of the same kind. Other cases – a cat and its flesh, a statue and its lump – seem to involve objects of different kinds. (shrink)

Putative counterexamples to the Principle of Identity of Indiscernibles (PII) are notoriously inconclusive. I establish ground rules for debate in this area, offer a new response to such counterexamples for friends of the PII, but then argue that no response is entirely satisfactory. Finally, I undermine some positive arguments for PII.

Current analytic metaphysics has been claimed to be, at best, out of touch with modern physics, at worst, actually in conflict with the latter The continuum companion to the philosophy of science, Continuum, London, 2011; Ladyman and Ross Every thing must go: metaphysics naturalized, Oxford University Press, Oxford, 2007). While agreeing with some of these claims, it has been suggested that metaphysics may still be of service by providing a kind of ‘toolbox’ of devices that philosophers of science can access (...) in order to help provide an interpretation of theories in fundamental physics Metaphysics in contemporary physics, Rodopi, Amsterdam, 2015). In this context it has been argued that ‘standard’ forms of dispositionalism simply cannot be sustained in the context of modern physics but that certain ‘non-standard’ views may provide the resources to help explicate the sense in which physics may be regarded as ‘modally informed’. Here that suggestion will be further extended in order to consider the implications both with regard to the overall relevance of metaphysics given advances in science and for the prospects of a naturalised metaphysics more generally. In particular, this paper will focus on three concerns: that the particular tools identified are not, in fact, ‘scientifically disinterested’ and thus that the distinction between ‘naturalised’ and ‘non-naturalised’ metaphysics is at best vague or poorly drawn; that the usefulness of such tools depends on their being shaped to fit the relevant physics and thus the latter ‘guts’ metaphysics; that if metaphysics does prove to be useful in this sense then we have no reason to scorn non-naturalised metaphysics to begin with. (shrink)

Cet article se propose de reprendre les discussions autour du principe d’identité des indiscernables (PIdI) en précisant le type d’entités qui pourraient y déroger. J’y défends l’idée que le rejet du PIdI ressortit à la possibilité de trois types de doubles : les répliques pures, ou reproductions parfaites, les doubles purs, doubles qui ne peuvent pas même être distingués par des relations spatio-temporelles, et enfin les coïncidents purs qui sont des doubles « superposés ». La thèse que je défends consiste (...) à montrer que l’existence de telles entités est non seulement concevable, mais même, pour les deux premières sortes, physiquement possible. Pour ce qui concerne la possibilité des coïncidents purs, le rejet de telles entités peut être appuyé indépendamment du PIdI sur un principe de parcimonie ontologique basé sur une indifférence causale. (shrink)

The mathematical field of graph theory has recently been used to provide counterexamples to the Principle of the Identity of Indiscernibles. In response to this, it has been argued that appeal to relations between graphs allows the Principle to survive the counterexamples. In this paper, I aim to show why that proposal does not succeed.

This paper offers a critical assessment of the current state of the debate about the identity and individuality of material objects. Its main aim, in particular, is to show that, in a sense to be carefully specified, the opposition between the Leibnizian ‘reductionist’ tradition, based on discernibility, and the sort of ‘primitivism’ that denies that facts of identity and individuality must be analysable has become outdated. In particular, it is argued that—contrary to a widespread consensus—‘naturalised’ metaphysics supports both the acceptability (...) of non-qualitatively grounded (both ‘contextual’ and intrinsic) identity and a pluralistic approach to individuality and individuation. A case study is offered that focuses on non-relativistic quantum mechanics, in the context of which primitivism about identity and individuality, rather than being regarded as unscientific, is on the contrary suggested to be preferable to the complicated forms of reductionism that have recently been proposed. More generally, by assuming a plausible form of anti-reductionism about scientific theories and domains, it is claimed that science can be regarded as compatible with, or even as suggesting, the existence of a series of equally plausible grades of individuality. The kind of individuality that prevails in a certain context and at a given level can be ascertained only on the basis of the specific scientific theory at hand. (shrink)

ABSTRACT This paper reveals David Hilbert’s position in the philosophy of mathematics, circa 1900, to be a form of non-eliminative structuralism, predating his formalism. I argue that Hilbert withstands the pressing objections put to him by Frege in the course of the Frege-Hilbert controversy in virtue of this early structuralist approach. To demonstrate that this historical position deserves contemporary attention I show that Hilbertian structuralism avoids a recent wave of objections against non-eliminative structuralists to the effect that they cannot distinguish (...) between structurally identical but importantly distinct mathematical objects, such as the complex roots of $-1$. (shrink)

In this article we investigate putative counterexamples to Leibniz’s principle of the Identity of Indiscernibles. In particular, we look at the status of spacetime points: although these all possess exactly the same properties in symmetrical spacetimes and thus seem indiscernible, there are certainly more than one of them. However, we shall defend Leibniz’s principle, even for such highly symmetrical cases. Part of our strategy will be to invoke the notion of “weak discernibility”, as proposed in the recent literature. Weakly discernible (...) objects share all their properties but stand in irreflexive relations to one another—this irreflexivity makes it possible to show that Leibniz's principle implies their numerical diversity. However, we shall argue that this notion of weak discernibility only serves its purpose if it is supplemented by a criterion of physical meaningfulness of the relations and relata in question; and that in the final analysis weak discernibility only helps out when it can be seen as a degenerate case of strong, absolute discernibility. The case of spacetime points is an example of such a situation. (shrink)

Saunders has recently claimed that “identical quantum particles” with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black’s spheres, for example). Weakly discernible objects have all their qualitative properties in common but nevertheless differ from each other by virtue of (a generalized version of) Leibniz’s principle, since they stand in relations an entity cannot have to itself. This notion of weak discernibility has been criticized as question begging, but we (...) defend and accept it for classical cases likes Black’s spheres. We argue, however, that the quantum mechanical case is different. Here the application of the notion of weak discernibility indeed is question begging and in conflict with standard interpretational ideas. We conclude that the introduction of the conceptual resource of weak discernibility does not change the interpretational status quo in quantum mechanics. (shrink)

According to classical physics particles are basic building blocks of the world. These classical particles are distinguishable objects, individuated by unique combinations of physical properties. By contrast, in quantum mechanics the received view is that particles of the same kind are physically indistinguishable from each other and lack identity. This doctrine rests on the quantum mechanical symmetrization postulates together with the “factorist” assumption that each single particle is represented in exactly one factor space of the tensor product Hilbert space of (...) a many-particle system. Even though standard in theoretical physics and the philosophy of physics, the assumption of factorism and the ensuing indistinguishability of particles are problematic. Particle indistinguishability is irreconcilable with the everyday meaning of “particle”, and also with how this term is used in the practice of physics. Moreover, it is a consequence of the standard view that identical quantum particles remain indistinguishable even in the classical limit, which makes a smooth transition to the classical particle concept impossible. Lubberdink and Dieks and Lubberdink have proposed an alternative conception of quantum particles that does not rely on factorism and avoids these difficulties. We further explain and discuss this alternative framework here. One of its key consequences is that particles in quantum theory are not fundamental but emergent; another that once they have emerged, quantum particles are always physically distinguishable and thus possess a physically grounded identity. (shrink)

According to classical physics _particles_ are basic building blocks of the world. These classical particles are distinguishable objects, individuated by unique combinations of physical properties. By contrast, in quantum mechanics the received view is that particles of the same kind (“identical particles”) are physically indistinguishable from each other and lack identity. This doctrine rests on the quantum mechanical (anti)symmetrization postulates together with the “factorist” assumption that each single particle is represented in exactly one factor space of the tensor product Hilbert (...) space of a many-particle system. Even though standard in theoretical physics and the philosophy of physics, the assumption of factorism and the ensuing indistinguishability of particles are problematic. Particle indistinguishability is irreconcilable with the everyday meaning of “particle”, and also with how this term is used in the practice of physics. Moreover, it is a consequence of the standard view that identical quantum particles remain indistinguishable even in the classical limit, which makes a smooth transition to the classical particle concept impossible. Lubberdink (1998; 2009) and Dieks and Lubberdink (2011) have proposed an alternative conception of quantum particles that does not rely on factorism and avoids these difficulties. We further explain and discuss this alternative framework here. One of its key consequences is that particles in quantum theory are not fundamental but _emergent_; another that once they have emerged, quantum particles are always physically distinguishable and thus possess a physically grounded identity. (shrink)

The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that quantum particles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state—in clear conflict with what we know about (...) classical particles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles emerge, as new entities that do not correspond to the “particle indices” defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises the question of whether many discussions in the literature about the status of identical quantum particles have not been misguided. (shrink)