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  1. Identity in Homotopy Type Theory: Part II, The Conceptual and Philosophical Status of Identity in HoTT.James Ladyman & Stuart Presnell - 2017 - Philosophia Mathematica 25 (2):210-245.
    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. (...)
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  • The Parthood of Indiscernibles.Lidia Obojska - forthcoming - Axiomathes:1-13.
    In the following work we propose to incorporate the main feature of quantum mechanics, i.e., the concept of indiscernibility. To achieve this goal, first we present two models of set theories: a quasi-set theory and a non-antisymmetric mereology. Next, we show how specific objects of QST—m-atoms—can be defined within NAM. Finally, we introduce a concept of a parthood of indiscernibles and discuss its features in respect to standard notions of indiscernibles and within NAM.
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  • The Rise of Relationals.F. A. Muller - 2015 - Mind 124 (493):201-237.
    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 (...)
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  • Entities Without Identity: A Semantical Dilemma.Benjamin C. Jantzen - 2019 - Erkenntnis 84 (2):283-308.
    It has been suggested that puzzles in the interpretation of quantum mechanics motivate consideration of entities that are numerically distinct but do not stand in a relation of identity with themselves or non-identity with others. Quite apart from metaphysical concerns, I argue that talk about such entities is either meaningless or not about such entities. It is meaningless insofar as we attempt to take the foregoing characterization literally. It is meaningful, however, if talk about entities without identity is taken as (...)
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  • Symmetries and Paraparticles as a Motivation for Structuralism.Adam Caulton & Jeremy Butterfield - 2012 - British Journal for the Philosophy of Science 63 (2):233-285.
    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: (...)
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  • Is Identity Really so Fundamental?Décio Krause & Jonas R. Becker Arenhart - 2019 - Foundations of Science 24 (1):51-71.
    We critically examine the claim that identity is a fundamental concept. According to those putting forward this thesis, there are four related reasons that can be called upon to ground the fundamental character of identity: identity is presupposed in every conceptual system; identity is required to characterize individuality; identity cannot be defined; the intelligibility of quantification requires identity. We address each of these points and argue that none of them advances compelling reasons to hold that identity is fundamental; in fact, (...)
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  • Dissecting Weak Discernibility of Quanta.Tomasz Bigaj - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 50:43-53.
  • In Defence of Utterly Indiscernible Entities.Bahram Assadian - forthcoming - Philosophical Studies:1-11.
    Are there entities which are just distinct, with no discerning property or relation? Although the existence of such utterly indiscernible entities is ensured by mathematical and scientific practice, their legitimacy faces important philosophical challenges. I will discuss the most fundamental objections that have been levelled against utter indiscernibles, argue for the inadequacy of the extant arguments to allay perplexity about them, and put forward a novel defence of these entities against those objections.
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  • Entities Without Intrinsic Physical Identity.Vincent Lam - 2014 - Erkenntnis 79 (5):1157-1171.
    This paper critically discusses recent objections that have been raised against the contextual understanding of fundamental physical objects advocated by non-eliminative ontic structural realism. One of these recent objections claims that such a purely relational understanding of objects cannot account for there being a determinate number of them. A more general objection concerns a well-known circularity threat: relations presuppose the objects they relate and so cannot account for them. A similar circularity objection has also been raised within the framework of (...)
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  • The Received View on Quantum Non-Individuality: Formal and Metaphysical Analysis.Jonas Arenhart - 2017 - Synthese 194 (4).
    The Received View on quantum non-individuality is, roughly speaking, the view according to which quantum objects are not individuals. It seems clear that the RV finds its standard expression nowadays through the use of the formal apparatuses of non-reflexive logics, mainly quasi-set theory. In such logics, the relation of identity is restricted, so that it does not apply for terms denoting quantum particles; this “lack of identity” formally characterizes their non-individuality. We face then a dilemma: on the one hand, identity (...)
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  • On Discernibility and Symmetries.Tomasz Bigaj - 2015 - Erkenntnis 80 (1):117-135.
    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 (...)
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  • Discerning "Indistinguishable" Quantum Systems.Adam Caulton - unknown
    In a series of recent papers, Simon Saunders, Fred Muller and Michael Seevinck have collectively argued, against the folklore, that some non-trivial 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 non-symmetric, i.e.~permutation-non-invariant, quantities, and that therefore their conclusions do not go through. However, I show that alternative, symmetric quantities (...)
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  • New Logics for Quantum Non-Individuals?Jonas R. Becker Arenhart - 2018 - Logica Universalis 12 (3-4):375-395.
    According to a very widespread interpretation of the metaphysical nature of quantum entities—the so-called Received View on quantum non-individuality—, quantum entities are non-individuals. Still according to this understanding, non-individuals are entities for which identity is restricted or else does not apply at all. As a consequence, it is said, such approach to quantum mechanics would require that classical logic be revised, given that it is somehow committed with the unrestricted validity of identity. In this paper we examine the arguments to (...)
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  • On Witness-Discernibility of Elementary Particles.Oystein Linnebo & F. A. Muller - 2013 - Erkenntnis 78 (5):1133-1142.
    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.
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  • The Entanglement Structure of Quantum Field Systems.Vincent Lam - 2013 - International Studies in the Philosophy of Science 27 (1):59 - 72.
    This article discusses the peculiar features of quantum entanglement and quantum non-locality within the algebraic approach to relativistic quantum field theory (RQFT). The debate on the ontology of RQFT is considered in the light of these well-known but little discussed features. In particular, this article examines the ontic structural realist understanding of quantum entanglement and quantum non-locality and its contribution to this debate.
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  • Defining Qualitative Properties.Vera Hoffmann-Kolss - forthcoming - Erkenntnis:1-16.
    The aim of this paper is to provide a systematic account of the metaphysically important distinction between haecceitistic properties, such as being David Lewis or being acquainted with David Lewis, and qualitative properties, such as being red or being acquainted with a famous philosopher. I first argue that this distinction is hyperintensional, that is, that cointensional properties can differ in whether they are qualitative. Then I develop an analysis of the qualitative/haecceitistic distinction according to which haecceitistic properties are relational in (...)
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  • Graph Theory and The Identity of Indiscernibles.Callum Duguid - 2016 - Dialectica 70 (3):463-474.
    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.
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  • Haecceities and Mathematical Structuralism.Christopher Menzel - 2018 - Philosophia Mathematica:84-111.
    Recent work in the philosophy of mathematics has suggested that mathematical structuralism is not committed to a strong form of the Identity of Indiscernibles (II). José Bermúdez demurs, and argues that a strong form of II can be warranted on structuralist grounds by countenancing identity properties, or haecceities, as legitimately structural. Typically, structuralists dismiss such properties as obviously non-structural. I will argue to the contrary that haecceities can be viewed as structural but that this concession does not warrant Bermdez’s version (...)
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  • A Formal Framework for the Study of the Notion of Undefined Particle Number in Quantum Mechanics.Newton C. A. Da Costa & Federico Holik - 2015 - Synthese 192 (2):505-523.
    It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...)
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  • Identity and Discernibility in Philosophy and Logic.James Ladyman, Øystein Linnebo & Richard Pettigrew - 2012 - Review of Symbolic Logic 5 (1):162-186.
    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 (...)
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