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  1. Identity and Indiscernibility.K. Hawley - 2009 - Mind 118 (469):101-119.
    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.
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  • A taxonomy for the mereology of entangled quantum systems.Paul M. Näger & Niko Strobach - manuscript
    The emerging field of quantum mereology considers part-whole relations in quantum systems. Entangled quantum systems pose a peculiar problem in the field, since their total states are not reducible to that of their parts. While there exist several established proposals for modelling entangled systems, like monistic holism or relational holism, there is considerable unclarity, which further positions are available. Using the lambda operator and plural logic as formal tools, we review and develop conceivable models and evaluate their consistency and distinctness. (...)
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  • James Ladyman und Don Ross. Every Thing Must Go - Metaphysics Naturalized (2007) [Rezension].Johannes Heinle - manuscript
    Eine Rezension des Buches "Every Thing Must Go - Metaphysics Naturalized" von James Ladyman und Don Ross.
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  • A Trope Theoretical Analysis of Relational Inherence.Markku Keinänen - 2018 - In Jaakko Kuorikoski & Teemu Toppinen (eds.), Action, Value and Metaphysics - Proceedings of the Philosophical Society of Finland Colloquium 2018, Acta Philosophica Fennica 94. Helsinki: Societas Philosophica Fennica. pp. 161-189.
    The trope bundle theories of objects are capable of analyzing monadic inherence (objects having tropes), which is one of their main advantage. However, the best current trope theoretical account of relational tropes, namely, the relata specific view leaves relational inherence (a relational trope relating two or more entities) primitive. This article presents the first trope theoretical analysis of relational inherence by generalizing the trope theoretical analysis of inherence to relational tropes. The analysis reduces the holding of relational inherence to the (...)
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  • Identity in physics: Statistics and the (non-)individuality of quantum particles.Matteo Morganti - 2010 - In H. De Regt, S. Hartmann & S.: Okasha (eds.), EPSA Philosophy of Science: Amsterdam 2009. Springer.
    This paper discusses the issue of the identity and individuality (or lack thereof) of quantum mechanical particles. It first reconstructs, on the basis of the extant literature, a general argument in favour of the conclusion that such particles are not individual objects. Then, it critically assesses each one of the argument’s premises. The upshot is that, in fact, there is no compelling reason for believing that quantum particles are not individual objects.
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  • Gauge symmetry and the Theta vacuum.Richard Healey - 2009 - In Mauricio Suárez, Mauro Dorato & Miklós Rédei (eds.), EPSA Philosophical Issues in the Sciences · Launch of the European Philosophy of Science Association. Dordrecht, Netherland: Springer. pp. 105--116.
    According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, which degeneracy (...)
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  • Relational Holism and Humean Supervenience.George Darby - 2012 - British Journal for the Philosophy of Science 63 (4):773-788.
    It has been widely noted that Humean supervenience , according to which everything supervenes on intrinsic properties of point-sized things and the spatiotemporal relations between them, is at odds with the nonlocal character of quantum mechanics, according to which not everything supervenes on intrinsic properties of point-sized things and the spatiotemporal relations between them. In particular, a standard view is that the parts of a composite quantum system instantiate further relations which are not accounted for in Lewis's Humean mosaic. But (...)
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  • Lewis's worldmate relation and the apparent failure of Humean supervenience.George Darby - 2009 - Dialectica 63 (2):195-204.
    This paper considers two aspects of Lewis 's metaphysics to which spatiotemporal relations appear central, with the aim of showing them to be less so. First, Lewis reluctantly characterises what it is for two things to be part of the same possible world in terms of an analogically spatiotemporal category of relations, rather than a wider natural external category. But Lewis 's reason for restricting himself to the narrower category is unpersuasive. Second, Humean supervenience is formulated with spatiotemporal relations at (...)
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  • Lewis’s worldmate relation and the apparent failure of Humean supervenience.George Darby - 2009 - Dialectica 63 (2):195-204.
    This paper considers two aspects of Lewis's metaphysics to which spatiotemporal relations appear central, with the aim of showing them to be less so. First, Lewis reluctantly characterises what it is for two things to be part of the same possible world in terms of an analogically spatiotemporal category of relations, rather than a wider natural external category. But Lewis's reason for restricting himself to the narrower category is unpersuasive. Second, Humean supervenience is formulated with spatiotemporal relations at its core. (...)
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  • Entanglement and the Metaphysician on the Clapham Omnibus.George Darby - 2015 - Topoi 34 (2):387-396.
    This paper explores some of the consequences of quantum entanglement for the mainstream metaphysician. The basic idea that entanglement has metaphysical consequences in the form of some kind of “holism” is familiar in the philosophy of physics literature, and finds its way into recent metaphysics, in discussions of failure of Humean supervenience, monism and emergence, for example. The principle aim here is to highlight some questions of detail that occur when attempting to make contact with those metaphysical debates as they (...)
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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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  • A formal framework for the study of the notion of undefined particle number in quantum mechanics.Federico Holik & Newton C. A. da Costa - 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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  • Quantum theory and explanatory discourse: Endgame for understanding?James T. Cushing - 1991 - Philosophy of Science 58 (3):337-358.
    Empirical adequacy, formal explanation and understanding are distinct goals of science. While no a priori criterion for understanding should be laid down, there may be inherent limitations on the way we are able to understand explanations of physical phenomena. I examine several recent contributions to the exercise of fashioning an explanatory discourse to mold the formal explanation provided by quantum mechanics to our modes of understanding. The question is whether we are capable of truly understanding (or comprehending) quantum phenomena, as (...)
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  • Exploring Philosophical Implications of Quantum Decoherence.Elise M. Crull - 2013 - Philosophy Compass 8 (9):875-885.
    Quantum decoherence is receiving a great deal of attention today not only in theoretical and experimental physics but also in branches of science as diverse as molecular biology, biochemistry, and even neuropsychology. It is no surprise that it is also beginning to appear in various philosophical debates concerning the fundamental structure of the world. The purpose of this article is primarily to acquaint non-specialists with quantum decoherence and clarify related concepts, and secondly to sketch its possible implications – independent of (...)
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  • On entanglement as a relation.Enrico Cinti, Alberto Corti & Marco Sanchioni - 2022 - European Journal for Philosophy of Science 12 (1):1-29.
    This paper aims to characterise properly entanglement as an external relation obtaining between multiple quantum degrees of freedom. In particular, we argue that the entanglement relation is a unique relation fully characterised by mutual information, i.e. a quantity standardly used as a measure of entanglement. This analysis leads us to propose a new metaphysical account of entanglement, which we call Relational Entanglement Tesseract. Such an account characterises entanglement for both bipartite and multipartite cases, and, at the same time, it satisfies (...)
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  • From Time Asymmetry to Quantum Entanglement: The Humean Unification.Eddy Keming Chen - 2022 - Noûs 56 (1):227-255.
    Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. I propose a unified 'Humean' solution to the two problems. Humeanism allows us to incorporate the Past Hypothesis and the Statistical Postulate into the best system, which we then use to simplify the quantum state of the universe. This enables us to confer the nomological status to the quantum state in (...)
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  • Emergentism and the Contingent Solubility of Salt.Lok-Chi Chan - 2018 - Theoria 84 (4):309-324.
    Alexander Bird (2001; 2002; 2007) offers a powerful argument showing that, regardless of whether necessitarianism or contingentism about laws is true, salt necessarily dissolves in water. The argument is that the same laws of nature that are necessary for the constitution of salt necessitate the solubility of salt. This paper shows that Bird’s argument faces a serious objection if the possibility of emergentism – in particular, C. D. Broad’s account – is taken into account. The idea is (roughly) that some (...)
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  • Integrated information theory of consciousness is a functionalist emergentism.Ignacio Cea - 2020 - Synthese 8 (1-2):2199-2224.
    In this paper I argue that the Integrated Information Theory of Consciousness has an underlying emergentist metaphysics, specifically of a kind that has received minimal attention and we may call functionalist emergentism. I will try to show that in this scientific theory conscious experience is a functional-role property possessed by the whole system, not by their parts, which is dependent on, but also (purportedly) causally powerful over and above, the properties of the parts. However, I will argue that depicting conscious (...)
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  • Discerning “Indistinguishable” Quantum Systems.Adam Caulton - 2013 - Philosophy of Science 80 (1):49-72.
    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, (...)
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  • Quantum mechanics and Priority Monism.Claudio Calosi - 2014 - Synthese 191 (5):915-928.
    The paper address the question of whether quantum mechanics (QM) favors Priority Monism, the view according to which the Universe is the only fundamental object. It develops formal frameworks to frame rigorously the question of fundamental mereology and its answers, namely (Priority) Pluralism and Monism. It then reconstructs the quantum mechanical argument in favor of the latter and provides a detailed and thorough criticism of it that sheds furthermore new light on the relation between parthood, composition and fundamentality in QM.
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  • Interpreting Quantum Entanglement: Steps towards Coherentist Quantum Mechanics.Claudio Calosi & Matteo Morganti - 2018 - British Journal for the Philosophy of Science:axy064.
    We put forward a new, ‘coherentist’ account of quantum entanglement, according to which entangled systems are characterized by symmetric relations of ontological dependence among the component particles. We compare this coherentist viewpoint with the two most popular alternatives currently on offer—structuralism and holism—and argue that it is essentially different from, and preferable to, both. In the course of this article, we point out how coherentism might be extended beyond the case of entanglement and further articulated.
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  • Humean Supervenience, Composition as Identity and Quantum Wholes.Claudio Calosi & Matteo Morganti - 2016 - Erkenntnis 81 (6):1173-1194.
    In this paper, we focus on two related reductive theses in metaphysics—Humean Supervenience and Composition as Identity—and on their status in light of the indications coming from science, in particular quantum mechanics. While defenders of these reductive theses claim that they can be updated so as to resist the quantum evidence, we provide arguments against this contention. We claim that physics gives us reason for thinking that both Humean Supervenience and Composition as Identity are at least contingently false, as the (...)
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  • Interpretation and identity in quantum theory.Jeremy Butterfield - 1993 - Studies in History and Philosophy of Science Part A 24 (3):443--76.
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  • 量子的対象とは何か.大畑 浩志 - 2024 - Journal of the Japan Association for Philosophy of Science 51 (1-2):93-113.
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  • The scientific turn in metaphysics: a factualist approach.Valerio Buonomo - 2017 - Synthese 198 (Suppl 3):793-807.
    In a recent paper, Cumpa : 319–324, 2014) argues that a scientific turn in metaphysics requires the acceptance of a materialist criterion of fundamentality, according to which the most fundamental metaphysical category is the one that provides us with a reconciliation of the ordinary world and the physical universe. He concludes that the dominant category of substance cannot be the most fundamental category, for it does not satisfy this criterion of fundamentality. The most fundamental category is instead the category of (...)
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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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  • Downward causation in fluid convection.Robert C. Bishop - 2008 - Synthese 160 (2):229 - 248.
    Recent developments in nonlinear dynamics have found wide application in many areas of science from physics to neuroscience. Nonlinear phenomena such as feedback loops, inter-level relations, wholes constraining and modifying the behavior of their parts, and memory effects are interesting candidates for emergence and downward causation. Rayleigh–Bénard convection is an example of a nonlinear system that, I suggest, yields important insights for metaphysics and philosophy of science. In this paper I propose convection as a model for downward causation in classical (...)
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  • Some Consequences (and Enablings) of Process Metaphysics.Mark H. Bickhard - 2011 - Axiomathes 21 (1):3-32.
    The interactivist model has explored a number of consequences of process metaphysics. These include reversals of some fundamental metaphysical assumptions dominant since the ancient Greeks, and multiple further consequences throughout the metaphysics of the world, minds, and persons. This article surveys some of these consequences, ranging from issues regarding entities and supervenience to the emergence of normative phenomena such as representation, rationality, persons, and ethics.
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  • Holism in the philosophy of physics: an introduction.Andreas Bartels, Holger Lyre & Michael Esfeld - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (4):597-599.
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  • 12 God and/as the Universe.István Aranyosi - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. De Gruyter. pp. 269-290.
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  • Quantum entanglement: a hylomorphic account.Matteo Morganti - 2019 - Synthese 198 (Suppl 11):2773-2793.
    In this paper, it is argued that Aristotelian hylomorphism can supply a useful and informative account of composite entities as these are described by physical theory. In particular, a hylomorphic account of quantum entangled systems is defined in detail, and compared to other alternatives currently on offer—in particular, ontic structural realism. In closing, it is suggested that the view of entanglement outlined here meshes well with a recently proposed ‘coherentist’ conception.
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  • Interpreting Quantum Entanglement: Steps towards Coherentist Quantum Mechanics.Matteo Morganti & Claudio Calosi - 2021 - British Journal for the Philosophy of Science 72 (3):865-891.
    We put forward a new, ‘coherentist’ account of quantum entanglement, according to which entangled systems are characterized by symmetric relations of ontological dependence among the component particles. We compare this coherentist viewpoint with the two most popular alternatives currently on offer—structuralism and holism—and argue that it is essentially different from, and preferable to, both. In the course of this article, we point out how coherentism might be extended beyond the case of entanglement and further articulated.
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  • Tropes – The Basic Constituents of Powerful Particulars.Markku Keinänen - 2011 - Dialectica 65 (3):419-450.
    This article presents a trope bundle theory of simple substances, the Strong Nuclear Theory[SNT] building on the schematic basis offered by Simons's (1994) Nuclear Theory[NT]. The SNT adopts Ellis's (2001) dispositional essentialist conception of simple substances as powerful particulars: all of their monadic properties are dispositional. Moreover, simple substances necessarily belong to some natural kind with a real essence formed by monadic properties. The SNT develops further the construction of substances the NT proposes to obtain an adequate trope bundle theory (...)
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  • Ontology of Divinity.Mirosław Szatkowski (ed.) - 2024 - De Gruyter.
    This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...)
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  • Hypothetical Metaphysics of Nature.Michael Esfeld - 2009 - In Michael Heidelberger & Gregor Schiemann (eds.), The Significance of the Hypothetical in Natural Science. De Gruyter. pp. 341-364.
    The paper first sketches out a reply to the underdetermination challenge and the incommensurability challenge that rebuts the sceptical conclusions of these challenges and that is sufficient to lay the ground for the project of a metaphysics of nature. That metaphysics is as hypothetical as are our scientific theories. The paper then explains how can one can argue for certain views in the metaphysics of nature based on our current fundamental physical theories, namely the commitments to a tenseless theory of (...)
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  • Three arguments for wave function realism.Alyssa Ney - 2023 - European Journal for Philosophy of Science 13 (4):1-18.
    Wave function realism is an interpretative framework for quantum theories which recommends taking the central ontology of these theories to consist of the quantum wave function, understood as a field on a high-dimensional space. This paper presents and evaluates three standard arguments for wave function realism, and clarifies the sort of ontological framework these arguments support.
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  • Lowe’s Eliminativism about Relations and the Analysis of Relational Inherence.Markku Keinänen - 2022 - In Mirosław Szatkowski (ed.), E. J. Lowe and Ontology. New York, NY: Routledge. pp. 105-122.
    Contrary to widely shared opinion in analytic metaphysics, E.J. Lowe argues against the existence of relations in his posthumously published paper There are probably no relations (2016). In this article, I assess Lowe’s eliminativist strategy, which aims to show that all contingent “relational facts” have a monadic foundation in modes characterizing objects. Second, I present two difficult ontological problems supporting eliminativism about relations. Against eliminativism, metaphysicians of science have argued that relations might well be needed in the best a posteriori (...)
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  • The Naturalness of the Naturalistic Fallacy and the Ethics of Nanotechnology.Mauro Dorato - 2015 - In Sven Ove Hansson (ed.), The Role of Technology in Science: Philosophical Perspectives. Dordrecht: Springer Verlag.
    In the first part of this paper, I try to clear the ground from frequent misconceptions about the relationship between fact and value by examining some uses of the adjective “natural” in ethical controversies. Such uses bear evidence to our “natural” tendency to regard nature (considered in a descriptive sense, as the complex of physical and biological regularities) as the source of ethical norms. I then try to account for the origin of this tendency by offering three related explanations, the (...)
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  • 8 Delayed-Choice Experiments and the Metaphysics of Entanglement.Matthias Egg - 2014 - In Scientific Realism in Particle Physics: A Causal Approach. De Gruyter. pp. 137-148.
    Delayed-choice experiments in quantum mechanics are often taken to undermine a realistic interpretation of the quantum state. More specifically, Healey has recently argued that the phenomenon of delayed-choice entanglement swapping is incompatible with the view that entanglement is a physical relation between quantum systems. This paper argues against these claims. It first reviews two paradigmatic delayed-choice experiments and analyzes their metaphysical implications. It then applies the results of this analysis to the case of entanglement swapping, showing that such experiments pose (...)
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  • Wave Function Realism.Alyssa Ney - manuscript
    This is an introduction to wave function realism for a compendium on the philosophy of quantum mechanics that will be edited and translated into Portuguese by Raoni Arroyo, entitled Compêndio de Filosofia da Física Quântica. This essay presents the history of wave function realism, its various interpretations, the main arguments that are given for the position, and the main objections that have been raised to it.
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  • The meaning of the wave function: in search of the ontology of quantum mechanics.Shan Gao - 2017 - New York, NY, USA: Cambridge University Press.
    The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical (...)
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  • Dispositions and the Argument from Science.Neil E. Williams - 2011 - Australasian Journal of Philosophy 89 (1):71 - 90.
    Central to the debate between Humean and anti-Humean metaphysics is the question of whether dispositions can exist in the absence of categorical properties that ground them (that is, where the causal burden is shifted on to categorical properties on which the dispositions would therefore supervene). Dispositional essentialists claim that they can; categoricalists reject the possibility of such ?baseless? dispositions, requiring that all dispositions must ultimately have categorical bases. One popular argument, recently dubbed the ?Argument from Science?, has appeared in one (...)
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  • Laws of Nature and Theory Choice.Alessandro Torza - 2022 - Synthese 200 (6):1-28.
    I articulate a Global Best-System Account (GBSA) of laws of nature along broadly Mill–Ramsey–Lewis lines. The guiding idea is that the job of laws is to capture real patterns across time—where a pattern is real if it allows to compress information about matters of particular fact. The GBSA’s key ingredient is a definition of ‘best system’ in terms of a ranking method that meets a number of desiderata: it is rigorously defined; it outputs the ranking based on the candidate systems’ (...)
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  • An explication of emergence.Elanor Taylor - 2015 - Philosophical Studies 172 (3):653-669.
    Philosophical debates about emergence are often marred by equivocation and lack of common ground, and dialogue about emergence between scientists and philosophers can be equally difficult. In this paper I offer a unified explication of emergence and argue that this explication can cut through much of the confusion evident in discussions of emergence. I defend an explication of the concept of emergence as the unavailability of a certain kind of scientific explanation for an observer or observers.
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  • Philosophy of Science A Personal Peek into the Future.Michela Massimi Steven French - 2013 - Metaphilosophy 44 (3):230-240.
    In this opinion piece, the authors offer their personal and idiosyncratic views of the future of the philosophy of science, focusing on its relationship with the history of science and metaphysics, respectively. With regard to the former, they suggest that the Kantian tradition might be drawn upon both to render the history and philosophy of science more relevant to philosophy as a whole and to overcome the challenges posed by naturalism. When it comes to the latter, they suggest both that (...)
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  • Counterfactual Skepticism and Multidimensional Semantics.H. Orri Stefánsson - 2018 - Erkenntnis 83 (5):875-898.
    It has recently been argued that indeterminacy and indeterminism make most ordinary counterfactuals false. I argue that a plausible way to avoid such counterfactual skepticism is to postulate the existence of primitive modal facts that serve as truth-makers for counterfactual claims. Moreover, I defend a new theory of ‘might’ counterfactuals, and develop assertability and knowledge criteria to suit such unobservable ‘counterfacts’.
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  • The Search for Ontological Emergence.Michael Silberstein & John McGeever - 1999 - Philosophical Quarterly 49 (195):201-214.
    We survey and clarify some recent appearances of the term ‘emergence’. We distinguish epistemological emergence, which is merely a limitation of descriptive apparatus, from ontological emergence, which should involve causal features of a whole system not reducible to the properties of its parts, thus implying the failure of part/whole reductionism and of mereological supervenience for that system. Are there actually any plausible cases of the latter among the numerous and various mentions of ‘emergence’ in the recent literature? Quantum mechanics seems (...)
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  • Hegel, Humility, and the Possibility of Intrinsic Properties.Jonathan L. Shaheen - 2011 - Hegel Bulletin 32 (1-2):100-117.
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  • Holism, physical theories and quantum mechanics.Michael Patrick Seevinck - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (4):693-712.
    Motivated by the question what it is that makes quantum mechanics a holistic theory, I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these (...)
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  • Monism: The Priority of the Whole.Jonathan Schaffer - 2010 - Philosophical Review 119 (1):31-76.
    Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?
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