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Identity and Indiscernibility

Mind 118 (469):101-119 (2009)

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  1. A One Category Ontology.L. A. Paul - 2017 - In John A. Keller (ed.), Being, Freedom, and Method: Themes From the Philosophy of Peter van Inwagen. New York: Oxford University Press UK. pp. 32-62.
    I defend a one category ontology: an ontology that denies that we need more than one fundamental category to support the ontological structure of the world. Categorical fundamentality is understood in terms of the metaphysically prior, as that in which everything else in the world consists. One category ontologies are deeply appealing, because their ontological simplicity gives them an unmatched elegance and spareness. I’m a fan of a one category ontology that collapses the distinction between particular and property, replacing it (...)
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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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  • The Multi-location Trilemma.Damiano Costa & Claudio Calosi - 2020 - Erkenntnis 87 (3):1063-1079.
    The possibility of multi-location—of one entity having more than one exact location—is required by several metaphysical theories such as the immanentist theory of universals and three-dimensionalism about persistence. One of the most pressing challenges for multi-location theorists is that of making sense of exact location—in that extant definitions of exact location entail a principle called ‘functionality’, according to which nothing can have more than one exact location. Recently in a number of promising papers, Antony Eagle has proposed and defended a (...)
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  • The Great Loop: From Conformal Cyclic Cosmology to Aeon Monism.Baptiste Le Bihan - 2024 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 1:1-16.
    Penrose's conformal cyclic cosmology describes the cosmos as a collection of successive universes, the so-called aeons. The beginning and ending of our universe are directly connected to two other, anterior and posterior, universes. Penrose considers but rules out a different interpretation of conformal cyclic cosmology: that the beginning of our universe is connected to its own end in a cosmic loop. The paper argues that the view, aeon monism, should be regarded as a natural interpretation of conformal cyclic cosmology and (...)
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  • Priority and Particle Physics: Ontic Structural Realism as a Fundamentality Thesis.Kerry McKenzie - 2014 - British Journal for the Philosophy of Science 65 (2):353-380.
    In this article, I address concerns that the ontological priority claims definitive of ontic structural realism are as they stand unclear, and I do so by placing these claims on a more rigorous formal footing than they typically have been hitherto. I first of all argue that Kit Fine’s analysis of ontological dependence furnishes us with an ontological priority relation that is particularly apt for structuralism. With that in place, and with reference to two case studies prominent within the structuralist (...)
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  • Broadening the problem agenda of biological individuality: individual differences, uniqueness and temporality.Rose Trappes & Marie I. Kaiser - 2021 - Biology and Philosophy 36 (2):1-28.
    Biological individuality is a notoriously thorny topic for biologists and philosophers of biology. In this paper we argue that biological individuality presents multiple, interconnected questions for biologists and philosophers that together form a problem agenda. Using a case study of an interdisciplinary research group in ecology, behavioral and evolutionary biology, we claim that a debate on biological individuality that seeks to account for diverse practices in the biological sciences should be broadened to include and give prominence to questions about uniqueness (...)
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  • The Metaphysics of Identity: Is Identity Fundamental?Erica Shumener - 2017 - Philosophy Compass 12 (1):1-13.
    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.
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  • Grades of individuality. A pluralistic view of identity in quantum mechanics and in the sciences.Mauro Dorato & Matteo Morganti - 2013 - Philosophical Studies 163 (3):591-610.
    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 (...)
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  • Explaining identity and distinctness.Erica Shumener - 2020 - Philosophical Studies 177 (7):2073-2096.
    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 (...)
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  • Identity and individuality in quantum theory.Steven French - 2008 - Stanford Encyclopedia of Philosophy.
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  • Strange Parts: The Metaphysics of Non‐classical Mereologies.Aaron Cotnoir - 2013 - Philosophy Compass 8 (9):834-845.
    The dominant theory of parts and wholes – classical extensional mereology – has faced a number of challenges in the recent literature. This article gives a sampling of some of the alleged counterexamples to some of the more controversial principles involving the connections between parthood and identity. Along the way, some of the main revisionary approaches are reviewed. First, counterexamples to extensionality are reviewed. The ‘supplementation’ axioms that generate extensionality are examined more carefully, and a suggested revision is considered. Second, (...)
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  • On Kinds of Indiscernibility in Logic and Metaphysics.Adam Caulton & Jeremy Butterfield - 2012 - British Journal for the Philosophy of Science 63 (1):27-84.
    Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle---some natural conjectures about them are (...)
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  • Non-qualitative Properties.Sam Cowling - 2015 - Erkenntnis 80 (2):275-301.
    The distinction between qualitative properties like mass and shape and non-qualitative properties like being Napoleon and being next to Obama is important, but remains largely unexamined. After discussing its theoretical significance and cataloguing various kinds of non-qualitative properties, I survey several views about the nature of this distinction and argue that all proposed reductive analyses of this distinction are unsatisfactory. I then defend primitivism, according to which the distinction resists reductive analysis.
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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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  • Endurantism vs. Perdurantism?: A Debate Reconsidered.Ofra Magidor - 2015 - Noûs 50 (3):509-532.
    One of the central debates in contemporary metaphysics has been the debate between endurantism and perdurantism about persistence. In this paper I argue that much of this debate has been misconstrued: most of the arguments in the debate crucially rely on theses which are strictly orthogonal to the endurantism/perdurantism debate. To show this, I note that the arguments in the endurantism/perdurantism debate typically take the following form: one presents a challenge that endurantists allegedly have some trouble addressing, and to which (...)
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  • No Simples, No Gunk, No Nothing.Sam Cowling - 2014 - Pacific Philosophical Quarterly 95 (1):246-260.
    Mereological realism holds that the world has a mereological structure – i.e. a distribution of mereological properties and relations. In this article, I defend Eleaticism about properties, according to which there are no causally inert non-logical properties. I then present an Eleatic argument for mereological anti-realism, which denies the existence of both mereological composites and mereological simples. After defending Eleaticism and mereological anti-realism, I argue that mereological anti-realism is preferable to mereological nihilism. I then conclude by examining the thesis that (...)
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  • Toying with the Toolbox: How Metaphysics Can Still Make a Contribution.Steven French - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (2):211-230.
    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 (...)
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  • The Case Against Factorism: On the Labels of $$\otimes$$-Factor Hilbert-Spaces of Similar Particles in Quantum Mechanics.F. A. Muller & Gijs Leegwater - 2022 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (3):291-306.
    We discuss the case against Factorism, which is the standard assumption in quantum mechanics that the labels of the $$\otimes$$ ⊗ -factor Hilbert-spaces in direct-product Hilbert-spaces of composite physical systems of similar particles refer to particles, either directly or descriptively. We distinguish different versions of Factorism and argue for their truth or falsehood. In particular, by introducing the concepts of snapshot Hilbert-space and Schrödinger-movie, we demonstrate that there are Hilbert-spaces and $$\otimes$$ ⊗ -factorisations where the labels do refer, even descriptively, (...)
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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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  • Identity.Erica Shumener - 2020 - In Michael J. Raven (ed.), The Routledge Handbook of Metaphysical Grounding. New York: Routledge. pp. 413-424.
    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.
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  • Grounding, Essence, and Contingentism.Karol Lenart - 2021 - Philosophia 49 (5):2157-2172.
    According to grounding necessitarianism if some facts ground another fact, then the obtaining of the former necessitates the latter. Proponents of grounding contingentism argue against this claim, stating that it is possible for the former facts to obtain without necessitating the latter. In this article I discuss a recent argument from restricted accidental generalisations provided by contingentists that advances such possibility. I argue that grounding necessitarianism can be defended against it. To achieve this aim, I postulate a relationship between grounding (...)
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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.
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  • On making a difference: towards a minimally non-trivial version of the identity of indiscernibles.David Https://Orcidorg Wörner - 2021 - Philosophical Studies 178 (12):4261-4278.
    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 (...)
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  • Haecceitism.Sam Cowling - 2015 - Stanford Encyclopedia of Philosophy.
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  • Bundle theory and weak discernibility.Seungil Lee - 2023 - Analytic Philosophy 64 (3):197-210.
    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 (...)
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  • The identity of indiscernibles.Peter Forrest - 2008 - Stanford Encyclopedia of Philosophy.
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  • Individuality, distinguishability, and entanglement: A defense of Leibniz׳s principle.Cord Friebe - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48 (1):89-98.
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  • Ontological Frameworks for Scientific Theories.Jonas R. Becker Arenhart - 2012 - Foundations of Science 17 (4):339-356.
    A close examination of the literature on ontology may strike one with roughly two distinct senses of this word. According to the first of them, which we shall call traditional ontology , ontology is characterized as the a priori study of various “ontological categories”. In a second sense, which may be called naturalized ontology , ontology relies on our best scientific theories and from them it tries to derive the ultimate furniture of the world. From a methodological point of view (...)
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  • Do identity and distinctness facts threaten the PSR?Erica Shumener - 2020 - Philosophical Studies 178 (4):1023-1041.
    One conception of the Principle of Sufficient Reason maintains that every fact is metaphysically explained. There are different ways to challenge this version of the PSR; one type of challenge involves pinpointing a specific set of facts that resist metaphysical explanation. Certain identity and distinctness facts seem to constitute such a set. For example, we can imagine a scenario in which we have two qualitatively identical spheres, Castor and Pollux. Castor is distinct from Pollux but it is unclear what could (...)
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  • The Partial Identity Account of Partial Similarity Revisited.Matteo Morganti - 2011 - Philosophia 39 (3):527-546.
    This paper provides a defence of the account of partial resemblances between properties according to which such resemblances are due to partial identities of constituent properties. It is argued, first of all, that the account is not only required by realists about universals à la Armstrong, but also useful (of course, in an appropriately re-formulated form) for those who prefer a nominalistic ontology for material objects. For this reason, the paper only briefly considers the problem of how to conceive of (...)
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  • The Identity of Necessary Indiscernibles.Zach Thornton - forthcoming - Philosophers' Imprint.
    I propose a novel metaphysical explanation of identity and distinctness facts called the Modal Proposal. According to the Modal Proposal, for each identity fact – that is, each fact of the form a=b – that fact is metaphysically explained by the fact that it is necessary that the entities involved are indiscernible, and for each distinctness fact –that is, each fact of the form a≠b – that fact is metaphysically explained by the fact that it is possible for the entities (...)
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  • Fundamental non-qualitative properties.Byron Simmons - 2021 - Synthese 198 (7):6183-6206.
    The distinction between qualitative and non-qualitative properties should be familiar from discussions of the principle of the identity of indiscernibles: two otherwise exactly similar individuals, Castor and Pollux, might share all their qualitative properties yet differ with respect to their non-qualitative properties—for while Castor has the property being identical to Castor, Pollux does not. But while this distinction is familiar, there has not been much critical attention devoted to spelling out its precise nature. I argue that the class of non-qualitative (...)
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  • Heterodox underdetermination: Metaphysical options for discernibility and (non-)entanglement.Maren Bräutigam - 2024 - Studies in History and Philosophy of Science Part A 103 (C):77-84.
    Broadly speaking, there are three views on whether Leibniz’s Principle of the Identity of Indiscernibles (PII) is violated in the case of similar particles. According to the earliest view, PII is always violated (call this the no discernibility view); according to the more recent weak discernibility view, PII is at least valid in a weak sense. No and weak discernibility have been referred to as orthodoxy. Steven French has argued that although PII is violated, similar particles can still be regarded (...)
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  • Structuralism in the philosophy of physics.Vincent Lam - 2017 - Philosophy Compass 12 (6):e12421.
    Ontic structuralism or ontic structural realism in the philosophy of physics can be broadly considered as an interpretative strategy providing a set of conceptual and metaphysical tools—or, more ambitiously, an ontological framework—in order to account for central features of current fundamental physics. This article aims to review the main structuralist interpretative moves in the context of our two best fundamental physical theories of matter and spacetime, namely, quantum theory and general relativity. We highlight in particular the structuralist understanding of permutation (...)
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  • Mereological bundle theory and the identity of indiscernibles.Anthony Shiver - 2014 - Synthese 191 (5):1-13.
    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, (...)
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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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  • 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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  • Haecceities and Mathematical Structuralism.Christopher Menzel - 2018 - Philosophia Mathematica 26 (1):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 Bermúdez’s version (...)
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  • Unsharp Humean Chances in Statistical Physics: A Reply to Beisbart.Luke Glynn, Radin Dardashti, Karim P. Y. Thebault & Mathias Frisch - 2014 - In M. C. Galavotti (ed.), New Directions in the Philosophy of Science. Cham: Springer. pp. 531-542.
    In an illuminating article, Claus Beisbart argues that the recently-popular thesis that the probabilities of statistical mechanics (SM) are Best System chances runs into a serious obstacle: there is no one axiomatization of SM that is robustly best, as judged by the theoretical virtues of simplicity, strength, and fit. Beisbart takes this 'no clear winner' result to imply that the probabilities yielded by the competing axiomatizations simply fail to count as Best System chances. In this reply, we express sympathy for (...)
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  • From primitive identity to the non-individuality of quantum objects.Jonas Becker Arenhart & Décio Krause - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46 (2):273-282.
    We consider the claim by Dorato and Morganti 591–610) that primitive individuality should be attributed to the entities dealt with by non-relativistic quantum mechanics. There are two central ingredients in the proposal: in the case of non-relativistic quantum mechanics, individuality should be taken as a primitive notion and primitive individuality is naturalistically acceptable. We argue that, strictly understood, naturalism faces difficulties in helping to provide a theory with a unique principle of individuation. We also hold that even when taken in (...)
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  • A Defense of Hume's Dictum.Cameron Gibbs - 2019 - Dissertation, University of Massachusetts Amherst
    Is the world internally connected by a web of necessary connections or is everything loose and independent? Followers of David Hume accept the latter by upholding Hume’s Dictum, according to which there are no necessary connections between distinct existences. Roughly put, anything can coexist with anything else, and anything can fail to coexist with anything else. Hume put it like this: “There is no object which implies the existence of any other if we consider these objects in themselves.” Since Hume’s (...)
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  • Weak Discernibility in Quantum Mechanics: Does It Save PII?Jonas Rafael Becker Arenhart - 2013 - Axiomathes 23 (3):461-484.
    The Weak Principle of the Identity of Indiscernibles (weak PII), states that numerically distinct items must be discernible by a symmetrical and irreflexive relation. Recently, some authors have proposed that weak PII holds in non relativistic quantum mechanics, contradicting a long tradition claiming PII to be simply false in that theory. The question that arises then is: are relations allowed in the scope of PII? In this paper, we propose that quantum mechanics does not help us in deciding matters concerning (...)
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  • On the Logical Positivists' Philosophy of Psychology: Laying a Legend to Rest.Sean Crawford - 2014 - In Thomas Uebel (ed.), New Directions in the Philosophy of Science. Cham: Springer. pp. 711-726.
    The received view in the history of the philosophy of psychology is that the logical positivists—Carnap and Hempel in particular—endorsed the position commonly known as “logical” or “analytical” behaviourism, according to which the relations between psychological statements and the physical-behavioural statements intended to give their meaning are analytic and knowable a priori. This chapter argues that this is sheer legend: most, if not all, such relations were viewed by the logical positivists as synthetic and knowable only a posteriori. It then (...)
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  • Pluralists about Pluralism? Versions of Explanatory Pluralism in Psychiatry.Jeroen Van Bouwel - 2014 - In Thomas Uebel (ed.), New Directions in the Philosophy of Science. Cham: Springer. pp. 105-119.
    In this contribution, I comment on Raffaella Campaner’s defense of explanatory pluralism in psychiatry (in this volume). In her paper, Campaner focuses primarily on explanatory pluralism in contrast to explanatory reductionism. Furthermore, she distinguishes between pluralists who consider pluralism to be a temporary state on the one hand and pluralists who consider it to be a persisting state on the other hand. I suggest that it would be helpful to distinguish more than those two versions of pluralism – different understandings (...)
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  • Wither away individuals.Jonas Rafael Becker Arenhart - 2013 - Synthese 190 (16):3475-3494.
    In this paper we deal with the problem of identity and individuality in quantum mechanics. We analyze three definitions of the concept of an individual and propose to check their merits in relation to the theory. In order to achieve our goals our approach also ties those definitions of individuality to two distinct kinds of naturalism in ontology: a strong version, according to which quantum mechanics must somehow authorize in a positive fashion the ontological concepts being dealt with, and a (...)
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  • Causal essentialism and the identity of indiscernibles.Cameron Gibbs - 2018 - Philosophical Studies 175 (9):2331-2351.
    Causal essentialists hold that a property essentially bears its causal and nomic relations. Further, as many causal essentialists have noted, the main motivations for causal essentialism also motivate holding that properties are individuated in terms of their causal and nomic relations. This amounts to a kind of identity of indiscernibles thesis; properties that are indiscernible with respect to their causal and nomic relations are identical. This can be compared with the more well-known identity of indiscernibles thesis, according to which particulars (...)
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  • Bundles, Individuation and Indiscernibility.Matteo Morganti - 2011 - European Journal of Analytic Philosophy 7 (1):36-48.
    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 (...)
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  • Interactionism, haecceities, and the pairing argument.Bradford Saad - 2017 - Inquiry: An Interdisciplinary Journal of Philosophy 60 (7):724-741.
    Interactionists hold that non-spatial objects causally interact with physical objects. Interactionists have traditionally grappled with the puzzle of how such interaction is possible. More recently, Jaegwon Kim has presented interactionists with a more daunting threat: the pairing argument, which purports to refute interactionism by showing that non-spatial objects cannot stand in causal relations. After reviewing that argument, I develop a challenge to it on behalf of the interactionist. The challenge poses a dilemma: roughly, either haecceities exist or they do not. (...)
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  • Grades of Discrimination: Indiscernibility, Symmetry, and Relativity.Tim Button - 2017 - Notre Dame Journal of Formal Logic 58 (4):527-553.
    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. (...)
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  • Five Indistinguishable Spheres.Adrian Heathcote - 2022 - Axiomathes 32 (2):367-383.
    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 (...)
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