Can there be two things that are completely indistinguishable? This simple question has raised numerous debates throughout the history of philosophy and science. The principle of the identity of indiscernibles claims that no two things can be completely indiscernible. But this thesis has been challenged in quantum physics and continues to be a hot topic in cutting edge areas of mathematics. The question has gained a renewed interest with the possibility of harnessing indistinguishability as a resource in quantum (...) information tasks. This theme issue is devoted to understanding identity and indistinguishability in philosophy and science, gathering an interdisciplinary group of experts in the field. It will allow readers of diverse disciplines to have an updated introduction to the topic. (shrink)

Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly (...) the same relations to all objects (including themselves). I conclude that realistic structuralists must compromise and treat some structures eliminativistically. (shrink)

In a series of recent papers, Simon Saunders, Fred Muller, and Michael Seevinck have collectively argued, against the folklore, that some nontrivial version of Leibniz’s principle of the identity of indiscernibles is upheld in quantum mechanics. They argue that all particles—fermions, paraparticles, anyons, even bosons—may be weakly discerned by some physical relation. Here I show that their arguments make illegitimate appeal to nonsymmetric, that is, permutation-noninvariant, quantities and that therefore their conclusions do not go through. However, I show that (...) alternative, symmetric quantities may be found to do the required work. I conclude that the Saunders-Muller-Seevinck heterodoxy can be saved. (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)

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)

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)

In this research work I take into account the relation of indistinguishability. This relation seems to be prima facie reflexive, symmetric and transitive; in short, an equivalence relation. However, there are some cases where the relation under consideration fails to be transitive. In this thesis I will discuss two of those cases: vagueness of gradabale adjectives and count nouns, and identity criteria involving perceptual phenomena. My research attempts to answer the following question: how is it possible to communicate and (...) to make meaningful judgments using vague terms and non-transitive identity criteria? This thesis presents an analysis of vagueness and identity criteria that shows that speakers always consider the elements which vague expressions refer to or whose names compose identity statements within a context and from a certain level of precision. I also attempt to provide a formal treatment of vague adjectives and count nouns on the one hand, and of identity criteria on the other. I employ two key concepts in both the treatments: context dependence and granularity. (shrink)

David Hilbert’s distinction between mathematics and metamathematics assumes mathematics is not metamathematics, cardinality of mathematics is less than cardinality of metamathematics, and metamathematics contains mathematics. Only by abandoning the last renders these characteristics consistent. Every set identifiable only in a metaset, following Kurt Gödel, the metaset is convertible into the set by translation of its constituents into constituents of the set, rendering the set indistinguishable from the metaset. Reversing Kurt Gödel, the set is convertible into the metaset by translation (...) of its constituents into constituents of themetaset, rendering the set indistinguishable from the metaset. Set being indistinguishable from metaset, the set of mathematics is unidentifiable as constituent of the set of metamathematics. Only inductively by exclusive resolution of all constituents of the set of all disjunctives of the sets of mathematics and metamathematics is the set of mathematics identifiable. Generated is endless arbitrary qualification of mathematical identity exhibited in continual proofsof its axioms. Understood as clarification, when everything is unique, no concealed contradiction is contained. Constituted is the endless non-repeating digit to the left of the decimal of an algebraic unknown number. Manifest is casuistry, now neither objective nor specious identity, but instead necessary subjective identity distinguishing sets. (shrink)

In a naïve realist approach to reading an ontology off the models of a physical theory, the invariance of a given theory under permutations of its property-bearing objects entails the existence of distinct possible worlds from amongst which the theory cannot choose. A brand of Ontic Structural Realism attempts to avoid this consequence by denying that objects possess primitive identity, and thus worlds with property values permuted amongst those objects are really one and the same world. Assuming that any (...) successful ontology of objects is able to describe a universe containing a determinate number of them, I argue that no version of OSR which both retains objects and understands ‘structure’ in terms of relations can be successful. This follows from the fact that no set of relational facts is sufficient to fix the cardinality of the collection of objects implied by those facts. More broadly, I offer reasons to believe that no version of OSR is compatible with the existence of objects, no matter how ontologically derivative they are taken to be. Any such account would have to attribute a definite cardinality to a collection of objects while denying that those objects are possessed of a primitive identity. With no compelling reason to abandon the classical conception of cardinality, such an attribution is incoherent. (shrink)

In the philosophy of science, identity over time emerges as a central concern both as an ontological category in the interpretation of physical theories, and as an epistemological problem concerning the conditions of possibility of knowledge. In Reichenbach and subsequent writers on the problem of indistinguishable quantum particles we see the return of a contrast between Leibniz and Aquinas on the subject of individuation. The possibility of rejecting the principle of the identity of indiscernibles has certain logical (...) difficulties, leading us inexorably from ontology into epistemology. For the epistemological problem we attend to the differences that emerged between the (neo-)Kantian and logical empiricist traditions, also saliently displayed in Reichenbach's writings. After examining the contrast between Kant's and Leibniz's conceptions of empirical knowledge, specifically with respect to the irreducibility of spatiotemporal determinations, we explore an application of a neo-Kantian view to the same problem of indistinguishable quantum particles. (shrink)

Standard sorites paradoxes can always be put into a simple canonical form, employing the sole inference modus ponens. For example, consider the following paradox. Take a continuum of colours going from red to blue, and let a1,..., am be a sequence of segments of this continuum such that each segment is phenomenologically indistinguishable in colour from its immediate neighbours. Let Fx be the predicate ‘x is red’. Then the untrue conclusion Fam can be inferred from the premises Fa0 and (...) Fan → Fan + 1. (shrink)

It is argued that the symmetry and anti-symmetry of the wave functions of systems consisting of identical particles have nothing to do with the observational indistinguishability of these particles. Rather, a much stronger conceptual indistinguishability is at the bottom of the symmetry requirements. This can be used to argue further, in analogy to old arguments of De Broglie and Schrödinger, that the reality described by quantum mechanics has a wave-like rather than particle-like structure. The question of whether quantum statistics alone (...) can give rise to empirically observable correlations between results of distant measurements is also discussed. (shrink)

‘Semantic externalism’ is the view that the thought and speech of internally identical subjects can have different contents, depending on facts about their environments. ‘Semantic internalism’ is the negation of this view. The details of these two views depend on the definition of ‘internal identity’. Katalin Farkas has shown that the traditional definition of internal identity as physical identity is too permissive: it misclassifies certain bodily states as internal. She has proposed defining internal identity as phenomenal (...) identity instead. In the critical part of my paper, I argue that Farkas’s proposal fails for being too restrictive: it misclassifies non-conscious mental states, most notably dispositional belief, as external. I consider two interpretations of Farkas’s proposal but conclude that neither succeeds, because each requires internal features to influence the subject’s phenomenal life in a way in which dispositional belief does not. In the constructive part of my paper, I consider dispositional identity as an alternative definition of internal identity. I argue that the dispositional-identity definition avoids the phenomenal-identity definition’s shortcoming and retains its main attraction, viz., that of securing the subjective indistinguishability that obtains between Twin Earth duplicates. My argument that it does the latter, however, faces potentially decisive obstacles. Thus, I retreat to a disjunctive proposal: internal identity should be defined either as dispositional identity or as dispositional-plus-phenomenal identity. I conclude by defending my proposal against a different charge that may be levelled against it, viz., that of misclassifying Cartesian dualism as an externalist theory of the mind. (shrink)

Physics is not just mathematics. This seems trivial, but poses difficult and interesting questions. In this paper we analyse a particular discrepancy between non-relativistic quantum mechanics and ‘classical’ space and time. We also suggest, but not discuss, the case of the relativistic QM. In this work, we are more concerned with the notion of space and its mathematical representation. The mathematics entails that any two spatially separated objects are necessarily different, which implies that they are discernible —we say that the (...) space is T2, or “Hausdorff”, or yet “separable”. But when enters QM, sometimes the systems need to be taken as completely indistinguishable, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in the NST setting, it seems that we can always give an identity to them by means of their individuation, which seems to be contra the quantum physical situation, where individuation does not entail identity. Here we discuss this topic by considering a case study and conclude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. This case study seems to be relevant for a more detailed discussion on the interplay between physical theories and their underlying mathematics, in a simple way apparently never realized before. (shrink)

Kant, in the third paralogism, needs to be rescued from his commentators. His argument that the identity of one's consciousness of oneself is no proof of the numerical identity of a soul-substance, since an indistinguishable identity of consciousness could result from one subject's handing over of memories to another, is sound and complete, and does not need the supplementations offered by Strawson, Bennett and James Anderson. But a possible supplementation is that this identity of consciousness (...) calls for explanation and is partly explained by the continuity of the central nervous system, though this continuity is not guaranteed or conceptually required by that identity. (shrink)

Kant, in the third paralogism, needs to be rescued from his commentators. His argument that the identity of one's consciousness of oneself is no proof of the numerical identity of a soul-substance, since an indistinguishable identity of consciousness could result from one subject's handing over of memories to another, is sound and complete, and does not need the supplementations offered by Strawson, Bennett and James Anderson. But a possible supplementation is that this identity of consciousness (...) calls for explanation and is partly explained by the continuity of the central nervous system, though this continuity is not guaranteed or conceptually required by that identity. (shrink)

We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same particle, just as spin-up and spin-down do. The implications of this viewpoint can be best appreciated within Bohmian mechanics, a precise formulation of quantum mechanics with particle trajectories. The implementation of this viewpoint in such a theory leads to trajectories different from those of the (...) usual formulation, and thus to a version of Bohmian mechanics that is inequivalent to, though arguably empirically indistinguishable from, the usual one. The mathematical core of this viewpoint is however rather independent of the detailed dynamical scheme Bohmian mechanics provides, and it amounts to the assertion that the configuration space for N particles, even N “distinguishable particles,” is the set of all N -point subsets of physical 3-space. (shrink)

Tolerance spaces are sets equipped with a reflexive, symmetric, but not necessarily transitive, relation of indistinguishability, and are useful for describing vagueness based on error-prone measurements. We show that any tolerance space can be embedded in one generated by comparisons using prototypical objects. As a result propositions, definable on a tolerance space can be translated into propositions behaving classically.

Fregeanism and Relationism are competing families of solutions to Frege’s Puzzle, and by extension, competing theories of propositional representation. My aim is to clarify what is at stake between them by characterizing and evaluating a Relationist argument. Relationists claim that it is cognitively possible for distinct token propositional attitudes to be, in a sense, qualitatively indistinguishable: to differ in no intrinsic representational features. The idea of an ‘intrinsic representational feature’ is not, however, made especially clear in the argument. I (...) clarify it here and, having done so, offer reason to doubt the argument. This will put us in a position to draw some lessons about the relation between object-directed and representation-internal aspects of cognitive significance. (shrink)

Nadia Anghelescu, Identitatea arabă: istorie, limbă, cultură. (Arab Identity: History, Language, Culture) Iaşi: Polirom, 2009, 442 p.

Ordinary measurement using a standard scale, such as a ruler or a standard set of weights, has two fundamental properties. First, the results are approximate, for example, within 0.1 g. Second, the resulting indistinguishability is transitive, rather than nontransitive, as in the standard psychological comparative judgments without a scale. Qualitative axioms are given for structures having the two properties mentioned. A representation theorem is then proved in terms of upper and lower measures.

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.

What Are Zombies? Zombies are stipulated to be creatures that are in some way identical to human beings-and thus, in some sense, indistinguishable from human beings-but which lack consciousness. Zombies are at least behaviorally identical to human beings or other conscious creatures, and they may also be like us in other ways.

A popular view is that we create our own identities and values. An attractive version of this is the thesis that the creation of values follows from the creation of identities. The thesis is best supported by a conception of identity in terms of projects and a conception of values that are internal to projects: in creating my projects, I create values internal to them; so I create those values. This paper argues that the thesis faces a dilemma: it (...) is either true but uninteresting or interesting by false. The dilemma persists whether the values in question are conceived as purpose-relative, as moral, or as both purpose-relative and moral. (shrink)

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