Pluralists argue for the distinctness of coinciding objects on the grounds that they have different properties. The grounding problem is the problem of explaining how the supposed difference in properties can arise in the first place. This paper considers this problem as an instance of a more general phenomenon, namely, the problem of dealing with underdetermination in asymmetrical systems admitting of non-trivial automorphisms. It argues in favour of primitivism by developing an account of stochastic grounding that makes room for non-fundamental (...) bruteness and substantially mitigates the costs of primitivism. (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)

'Chains of Being' argues that there can be infinite chains of dependence or grounding. Cameron also defends the view that there can be circular relations of ontological dependence or grounding, and uses these claims to explore issues in logic and ontology.

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)

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)

I explore proposals for stating identity criteria in terms of ground. I also address considerations for and against taking identity and distinctness facts to be ungrounded.

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)

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.

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)

Physicalistic theories of psychology are a classic case of scientific imperialism: the explanatory capacity of physics, both with respect to its methods and to its domain, is taken to extend beyond the traditional realm of physics, and into that of psychology. I argue in this paper that this particular imperialistic venture has failed. Contemporary psychology uses methods not modelled on those of physics, embracing first-personal methodology where physics is strictly impersonal. I make the case that whether or not scientific imperialism (...) is in general harmful, in this instance naturalists who reject first philosophy should give up physicalist imperialism. Using only general principles from the philosophy of logic plus accepted physicalist criteria of identity, I show that first-personal psychology embodies a minor but fruitful increase in expressive strength compared to impersonal psychology: the ability to distinguish descriptively indiscriminable posits. (shrink)

There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in some detail. (...) However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas and draws connections with definability theory. (shrink)

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.

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)

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).

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.

In der modernen Physik spielen Symmetrien eine herausragende Rolle zur Identifikation und Klassifizierung der fundamentalen Theorien und Entitäten. Symmetrien dienen der Darstellung invarianter Strukturen, das geeignete mathematische Werkzeug hierfür ist die Gruppentheorie. Eine Struktur lässt sich als eine Menge von Relationen verstehen, die einer Menge von Objekten aufgeprägt sind. Strukturell charakterisierte Objekte sind daher wesentlich über ihre relationalen Eigenschaften charakterisiert. Sieht man die theoretischen Entitäten wissenschaftlicher Theorien vornehmlich in dieser strukturellen Weise an, vertritt man eine moderate Variante eines wissenschaftlichen Realismus, (...) die als Strukturenrealismus bekannt ist. Im Umfeld dieser drei Konzepte – Symmetrien, Strukturen, Realismus – bewegt sich der folgende Aufsatz. (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)

This paper addresses the issue of the multiplicity of various grades of discernibility that can be defined in model theory. Building upon earlier works on the subject, I first expand the known logical categorizations of discernibility by introducing several symmetry-based concepts of discernibility, including one I call “witness symmetry-discernibility”. Then I argue that only grades of discernibility stronger than this one possess certain intuitive features necessary to individuate objects. Further downsizing of the set of non-equivalent grades of discernibility can be (...) achieved by stipulating that any relation of discernibility should be applied only to those pairs of objects which have been previously distinguished from the rest of the universe. Restricting discernibility to pairs of objects satisfying this condition gives an additional bonus in the form of restoring the transitivity of some types of indiscernibility which have been known to be non-transitive. (shrink)

Defines and examines a notion of logical friendliness, a broadening of the familiar notion of classical consequence. Also reviews familiar notions and operations with which friendliness makes contact, providing a new light in which they may be seen.

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)

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)

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.

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)

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.

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)

In a recent paper, Sun Demirli (2010) proposes an allegedly new way of conceiving of individuation in the context of the bundle theory of object constitution. He suggests that allowing for distance relations to individuate objects solves the problems with worlds containing indiscernible objects that would otherwise affect the theory. The aim of the present paper is i) To show that Demirli’s proposal falls short of achieving this goal and ii) To carry out a more general critical assessment of the (...) issue by appraising the costs and benefits of Demirli’s view as well as of existing alternatives. (shrink)

After sketching some aspects of truthmaker doctrines and "truthmaker projects", and canvassing some prima facie objections to the latter, I turn to an issue which might seem to involve confusion about the nature of character of truthmakers if such there be, viz for statements of identity and (specially) distinctness. The real issue here is versions of the Identity of Indiscernibles. I discuss ways of discriminating versions, which are almost certainly true but trivial, which almost certainly substantive but false, and explore (...) an interesting intermediate possibility which might if developed yield a plausibly true yet not-entirely-trivial version of the doctrine: it is equivalent to what I call "the Denial of Bare Distinctness". (shrink)

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)

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)

This article develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR, the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature—a theory's ‘not caring which point, or particle, is which’—supported a structuralist ontology. Pooley criticizes this analogy: (...) in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived. (shrink)

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)

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.

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)

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)

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)

I investigate substitutional interpretations of quantifiers that count existential sentences true just in case they have true instances in a parametric extension of the language. I devise a semantics meeting four criteria: (1) it accounts adequately for natural language quantification; (2) it provides an account of justification in abstract sciences; (3) it constitutes a continuous semantics for natural and formal languages; and (4) it is purely substitutional, containing no appeal to referential interpretations. The prospects for a purely substitutional theory of (...) quantification are thus no worse than for a referential account. (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)

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)

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)

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.

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)

Recently, there has been a debate as to whether or not the principle of the identity of indiscernibles (the PII) is compatible with quantum physics. It is also sometimes argued that the answer to this question has implications for the debate over the tenability of ontic structural realism (OSR). The central aim of this paper is to establish what relationship there is (if any) between the PII and OSR. It is argued that one common interpretation of OSR is undermined if (...) the PII turns out to be false, since it is committed to a version of the bundle theory of objects, which implies the PII. However, if OSR is understood as the physical analogue of (sophisticated) mathematical structuralism then OSR does not imply the PII. It is further noted that it is (arguably) a virtue of OSR that it is compatible with a version of the PII for possible worlds. (shrink)

Recently, several authors have claimed to have found graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles. In this paper, I argue that their counterexamples presuppose a certain view of what unlabeled graphs are, and that this view is optional at best.

The paper is a kind of opinionated review paper on current issues in the debate about Structural Realism, roughly the view that we should be committed in the structural rather than object-like content of our best current scientific theories. The major thesis in the first part of the paper is that Structural Realism has to take structurally derived intrinsic properties into account, while in the second part key elements of aligning Structural Realism with a Humean framework are outlined.