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  1. Trope Ontology and Algebraic Quantum Field Theory: An Evaluation of Kuhlmann's Proposal.Emanuele Rossanese - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):417-423.
    Meinard Kuhlmann has recently provided an interpretation of quantum field theory that seems to offer an alternative to the particle and field interpretations. The main idea is to adopt a trope ontology and, then, consider particles and fields as derivative entities. The aim of this paper is to discuss Kuhlmann's proposal. In the first part of the paper I will offer a reconstruction of his position. I will then show that this interpretation faces some problems about the distinction between essential (...)
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  • A Topological Theory of Fundamental Concrete Particulars.Daniel Giberman - 2015 - Philosophical Studies 172 (10):2679-2704.
    Fundamental concrete particulars are needed to explain facts about non-fundamental concrete particulars. However, the former can only play this explanatory role if they are properly discernible from the latter. Extant theories of how to discern fundamental concreta primarily concern mereological structure. Those according to which fundamental concreta can bear, but not be, proper parts are motivated by the possibilities that all concreta bear proper parts and that some properties of wholes are not fixed by the properties of their proper parts. (...)
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  • Clases de Tropos Como Universales Ersatz.José Tomás Alvarado Marambio - 2011 - Trans/Form/Ação 34 (1):87-114.
    Este trabajo considera el programa de reducción de universales por clases de tropos semejantes. Diversas cuestiones surgen acerca de la relación de semejanza: ¿Presuponen los "respectos" de semejanza un universal? ¿Induce un regres vicioso el hecho de que la relación de semejanza sea una relación? Si hay diferentes respectos de comparación entre tropos, entonces hay espacio para las dificultades tradicionales contra el nominalismo de semejanza: la "comunidad imperfecta" y la "compañía". ¿Pueden ser manejados estos problemas con clases de tropos semejantes? (...)
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  • Bundle Theory with Kinds.Markku Keinänen & Tuomas E. Tahko - 2019 - Philosophical Quarterly 69 (277):838-857.
    Is it possible to get by with just one ontological category? We evaluate L.A. Paul's attempt to do so: the mereological bundle theory. The upshot is that Paul's attempt to construct a one category ontology may be challenged with some of her own arguments. In the positive part of the paper we outline a two category ontology with property universals and kind universals. We will also examine Paul's arguments against a version of universal bundle theory that takes spatiotemporal co-location instead (...)
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  • Two Kinds of Universals and Two Kinds of Collections.Friederike Moltmann - 2004 - Linguistics and Philosophy 27 (6):739 - 776.
    This paper argues for an ontological distinction between two kinds of universals, 'kinds of tropes' such as 'wisdom' and properties such as 'the property of being wise'. It argues that the distinction is parallel to that between two kinds of collections, pluralities such as 'the students' and collective objects such as 'the class'. The paper argues for the priortity of distributive readings with pluralities on the basis of predicates of extent or shape, such 'large' or 'long'.
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  • Nominalizing Quantifiers.Friederike Moltmann - 2003 - Journal of Philosophical Logic 32 (5):445-481.
    Quantified expressions in natural language generally are taken to act like quantifiers in logic, which either range over entities that need to satisfy or not satisfy the predicate in order for the sentence to be true or otherwise are substitutional quantifiers. I will argue that there is a philosophically rather important class of quantified expressions in English that act quite differently, a class that includes something, nothing, and several things. In addition to expressing quantification, such expressions act like nominalizations, introducing (...)
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  • Events, Tropes, and Truthmaking.Friederike Moltmann - 2007 - Philosophical Studies 134 (3):363-403.
    Nominalizations are expressions that are particularly challenging philosophically in that they help form singular terms that seem to refer to abstract or derived objects often considered controversial. The three standard views about the semantics of nominalizations are [1] that they map mere meanings onto objects, [2] that they refer to implicit arguments, and [3] that they introduce new objects, in virtue of their compositional semantics. In the second case, nominalizations do not add anything new but pick up objects that would (...)
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  • Aristotelian Endurantism: A New Solution to the Problem of Temporary Intrinsics.J. E. Brower - 2010 - Mind 119 (476):883-905.
    It is standardly assumed that there are three — and only three — ways to solve problem of temporary intrinsics: (a) embrace presentism, (b) relativize property possession to times, or (c) accept the doctrine of temporal parts. The first two solutions are favoured by endurantists, whereas the third is the perdurantist solution of choice. In this paper, I argue that there is a further type of solution available to endurantists, one that not only avoids the usual costs, but is structurally (...)
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  • Laws of Nature, Exceptions and Tropes.Max Kistler - 2003 - Philosophia Scientiae 7 (2):189-219.
    I propose a realist theory of laws formulated in terms of tropes that avoids both the problems of the "best-systems-analysis" and the "inference problem" of realism of universals. I analyze the concept of an exceptional situation, characterized as a situation in which a particular object satisfies the antecedent but not the consequent of the regularity associated with a law, without thereby falsifying that law. To take this possibility into account, the properties linked by a law must be conceived as dispositional (...)
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  • In Defense of Substance.Kathrin Koslicki - 2015 - Grazer Philosophische Studien 91 (1):59-80.
    In his “Farewell to Substance: A Differentiated Leave-Taking”, Peter Simons reaches the provocative conclusion that the concept of substance, as it is employed by metaphysicians, has become obsolete, since in the end there may be nothing at all which answers to it. No harm is done, Simons allows, if we continue to retain an everyday notion of substance, as long as we are aware of the limitations of this practice: there is no reason in general to expect that what is (...)
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  • Ontological Scope and Linguistic Diversity: Are There Universal Categories?Johanna Seibt - 2015 - The Monist 98 (3):318-343.
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  • ‘An Argument for the Existence of Tropes.Anna-Sofia Maurin - 2011 - Erkenntnis 74 (1):69-79.
    That there could be ontologically complex concrete particulars is self-evidently true. A reductio may however be formulated which contradicts this truth. In this paper I argue that all of the reasonable ways in which we might refute this reductio will require the existence of at least some tropes.
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  • Quantity Tropes and Internal Relations.Markku Keinänen, Antti Keskinen & Jani Hakkarainen - 2019 - Erkenntnis 84 (3):519-534.
    In this article, we present a new conception of internal relations between quantity tropes falling under determinates and determinables. We begin by providing a novel characterization of the necessary relations between these tropes as basic internal relations. The core ideas here are that the existence of the relata is sufficient for their being internally related, and that their being related does not require the existence of any specific entities distinct from the relata. We argue that quantity tropes are, as determinate (...)
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  • The Problem of Trope Individuation: A Reply to Lowe.Markku Keinänen & Jani Hakkarainen - 2013 - Erkenntnis 79 (1):65-79.
    This paper is the first trope-theoretical reply to E. J. Lowe’s serious dilemma against trope nominalism in print. The first horn of this dilemma is that if tropes are identity dependent on substances, a vicious circularity threatens trope theories because they must admit that substances are identity dependent on their constituent tropes. According to the second horn, if the trope theorist claims that tropes are identity independent, she faces two insurmountable difficulties. (1) It is hard to understand the ontological dependence (...)
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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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  • Estados de cosas en el tiempo.José Tomás Alvarado Marambio - 2013 - Revista de Humanidades de Valparaíso 2:83-104.
    Un ‘estado de cosas’ es comprendido aquí como cualquier tipo de entidad que pueda jugar el rol de verificador. Diferentes ontologías proponen diferentes estructuras de entidades para funcionar como ‘estados de cosas’ en este sentido. Los defensores de universales van a proponer para este rol estructuras no-mereológicas de universales, objetos y tiempos. Los defensores de tropos van a proponer tropos, ya sea con o sin universales y objetos. Los nominalistas de semejanza van a proponer hechos ontológicos primitivos de semejanza entre (...)
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  • SNAP and SPAN: Towards Dynamic Spatial Ontology.Pierre Grenon & Barry Smith - 2004 - Spatial Cognition and Computation 4 (1):69–103.
    We propose a modular ontology of the dynamic features of reality. This amounts, on the one hand, to a purely spatial ontology supporting snapshot views of the world at successive instants of time and, on the other hand, to a purely spatiotemporal ontology of change and process. We argue that dynamic spatial ontology must combine these two distinct types of inventory of the entities and relationships in reality, and we provide characterizations of spatiotemporal reasoning in the light of the interconnections (...)
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  • A Trope Nominalist Theory of Natural Kinds.Markku Keinänen - 2015 - In Ghislain Guigon & Gonzalo Rodriguez-Pereyra (eds.), Nominalism about Properties. Routledge. pp. 156-174.
    In this chapter, I present the first systematic trope nominalist approach to natural kinds of objects. It does not identify natural kinds with the structures of mind-independent entities (objects, universals or tropes). Rather, natural kinds are abstractions from natural kind terms and objects belong to a natural kind if they satisfy their mind-independent application conditions. By relying on the trope theory SNT (Keinänen 2011), I show that the trope parts of a simple object determine the kind to which it belongs. (...)
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  • Persistence of Simple Substances.Markku Keinänen & Jani Hakkarainen - 2010 - Metaphysica 11 (2):119-135.
    In this paper, we argue for a novel three-dimensionalist solution to the problem of persistence, i.e. cross-temporal identity. We restrict the discussion of persistence to simple substances, which do not have other substances as their parts. The account of simple substances employed in the paper is a trope-nominalist strong nuclear theory, which develops Peter Simons' trope nominalism. Regarding the distinction between three dimensionalism and four dimensionalism, we follow Michael Della Rocca's formulation, in which 3D explains persistence in virtue of same (...)
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  • Theories of Properties and Ontological Theory-Choice: An Essay in Metaontology.Christopher Gibilisco - 2016 - Dissertation, University of Nebraska-Lincoln
    This dissertation argues that we have no good reason to accept any one theory of properties as correct. To show this, I present three possible bases for theory-choice in the properties debate: coherence, explanatory adequacy, and explanatory value. Then I argue that none of these bases resolve the underdetermination of our choice between theories of properties. First, I argue considerations about coherence cannot resolve the underdetermination, because no traditional theory of properties is obviously incoherent. Second, I argue considerations of explanatory (...)
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  • Individuação.Rodrigo Guerizoli - 2014 - Compêndio Em Linha de Problemas de Filosofia Analítica.
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  • From Ontology of Interaction to Semiotics of Education.Eetu Pikkarainen - 2013 - In K. Tirri, E. Hanhimäki & E. Kuusisto (eds.), Interaction in Educational Domains. Sense Publishers. pp. 51-62.
    In this article I try to show that the most deep level ontology can have rich meaning for our understanding of such practical and everyday phenomena as education and interaction. With this deep level ontology I mean the problem of universals. Starting from famous traditional stances of realism and nominalism, which both are for the modern theories of growth and Bildung, I continue to the third and more recently developed ontological theory, trope theory according to which the properties (qualities, relations (...)
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  • Nominalist Constituent Ontologies: A Development and Critique.Robert K. Garcia - 2009 - Dissertation, University of Notre Dame
    In this dissertation I consider the merits of certain nominalist accounts of phenomena related to the character of ordinary objects. What these accounts have in common is the fact that none of them is an error theory about standard cases of predication and none of them deploys God or uniquely theistic resources in its explanatory framework. -/- The aim of the dissertation is to answer the following questions: -/- • What is the best nominalist account on offer? • How might (...)
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  • Tropes: For and Against.Anna-Sofia Maurin - 2016 - In Francesco Federico Calemi (ed.), Metaphysics and Scientific Realism: Essays in Honour of David Malet Armstrong. De Gruyter. pp. 85-104.
    Trope theory is the view that the world consists (wholly or partly) of particular qualities, or tropes. This admittedly thin core assumption leaves plenty of room for variation. Still, most trope theorists agree that their theory is best developed as a one-category theory according to which there is nothing but tropes. Most hold that ‘sameness of property’ should be explained in terms of resembling tropes. And most hold that concrete particulars are made up from tropes in compresence (for an overview, (...)
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  • Tropes and Mental Causation.Simone Gozzano - 2007 - Documenti E Studi Sulla Tradizione Filosofica Medievale 18:587-600.
    The paper argues that tropes cannot be used to solve the mind-body problem, as advocated by David Robb in some paper.
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  • Trooppinominalismi Ja Kvantiteettitrooppien "Samanlaisuus".Markku Keinänen - 2014 - Ajatus 71:121-141.
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  • The Ontological Form of Tropes - Refuting Douglas Ehring’s Main Argument Against Standard Trope Nominalism.Jani Hakkarainen & Markku Keinänen - 2017 - Philosophia 45 (2):647-658.
    According to standard trope nominalism, there are simple tropes that do not have parts or multiply distinct aspects. Douglas Ehring’s reductio ad absurdum against this standard view concludes that there are no simple tropes. In this paper, we provide a response to Ehring defending the standard view. Ehring’s argument may be refuted by (1) distinguishing the ontological form of tropes from their contribution to the ontological content of the world, and (2) construing tropes as having primitive identity. At the same (...)
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  • Natural Language and its Ontology.Friederike Moltmann - 2019 - In Alvin Goldman & Brian Mclaughlin (eds.), Metaphysics and Cognitive Science. Oxford: Oxford University Press. pp. 206-232.
    This paper gives a characterization of the ontology implicit in natural language and the entities it involves, situates natural language ontology within metaphysics, and responds to Chomskys' dismissal of externalist semantics.
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  • Bare Particulars and Exemplifcation.Timothy Pickavance - 2014 - American Philosophical Quarterly 51 (2):95-108.
    Bare particulars tend to get a bad rap. But often, the arguments lodged against bare particulars seem to miss important aspects of the theoretical context of bare particulars. In particular, these arguments fail to situate bare particulars within a constituent ontology with substrates, and thus fail to appreciate an important consequence of that context: the need for two types of exemplification. In this paper, I do three things. First, I motivate and describe the need, given bare particulars, for two types (...)
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  • Three Concepts of Chemical Closure and Their Epistemological Significance.Joseph E. Earley - 2013 - In Jean-Pierre Llored (ed.), The Philosophy of Chemistry: Practices, Methodology, and Concepts. Newcastle upon Tyne: Cambridge Scholars Press. pp. 506-616.
    Philosophers have long debated ‘substrate’ and ‘bundle’ theories as to how properties hold together in objects ― but have neglected to consider that every chemical entity is defined by closure of relationships among components ― here designated ‘Closure Louis de Broglie.’ That type of closure underlies the coherence of spectroscopic and chemical properties of chemical substances, and is importantly implicated in the stability and definition of entities of many other types, including those usually involved in philosophic discourse ― such as (...)
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  • Instantiation in Trope Theory.A. R. J. Fisher - 2018 - American Philosophical Quarterly 55 (2):153-164.
    The concept of instantiation is realized differently across a variety of metaphysical theories. A certain realization of the concept in a given theory depends on what roles are specified and associated with the concept and its corresponding term as well as what entities are suited to fill those roles. In this paper, the classic realization of the concept of instantiation in a one-category ontology of abstract particulars or tropes is articulated in a novel way and defended against unaddressed objections.
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  • Regressões ao Infinito em Metafísica.João Branquinho & Guido Imaguire - 2014 - Compêndio Em Linha de Problemas de Filosofia Analítica.
    Este ensaio consiste num exame crítico da estrutura e do valor de um conjunto diverso de argumentos por regressão ao infinito que têm sido objecto de discussão recorrente na metafísica contemporânea. O seminal livro de David Armstrong Nominalism and Realism (Armstrong 1978) contém uma das mais compreensivas discussões de argumentos regressivos em metafísica, os quais variam entre argumentos que foram de facto avançados ao longo da história da disciplina (como o Argumento do Terceiro Homem, de Platão) e argumentos construídos de (...)
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  • Material Objects and Essential Bundle Theory.Stephen Barker & Mark Jago - 2018 - Philosophical Studies 175 (12):2969-2986.
    In this paper we present a new metaphysical theory of material objects. On our theory, objects are bundles of property instances, where those properties give the nature or essence of that object. We call the theory essential bundle theory. Property possession is not analysed as bundle-membership, as in traditional bundle theories, since accidental properties are not included in the object’s bundle. We have a different story to tell about accidental property possession. This move reaps many benefits. Essential bundle theory delivers (...)
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  • Where Are You Going, Metaphysics, and How Are You Getting There? - Grounding Theory as a Case Study.Gila Sher - forthcoming - In Quo Vadis, Metaphysics? Berlin, Germany: de Gruyter Studium.
    The viability of metaphysics as a field of knowledge has been challenged time and again. But in spite of the continuing tendency to dismiss metaphysics, there has been considerable progress in this field in the 20th- and 21st- centuries. One of the newest − though, in a sense, also oldest − frontiers of metaphysics is the grounding project. In this paper I raise a methodological challenge to the new grounding project and propose a constructive solution. Both the challenge and its (...)
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  • A Neo-Armstrongian Defense of States of Affairs: A Reply to Vallicella.Katarina Perovic - 2016 - Metaphysica 17 (2):143-161.
    Vallicella’s influential work makes a case that, when formulated broadly, as a problem about unity, Bradley’s challenge to Armstrongian states of affairs is practically insurmountable. He argues that traditional relational and non-relational responses to Bradley are inadequate, and many in the current metaphysical debate on this issue have come to agree. In this paper, I argue that such a conclusion is too hasty. Firstly, the problem of unity as applied to Armstrongian states of affairs is not clearly defined; in fact, (...)
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  • Abstracta and Abstraction in Trope Theory.A. R. J. Fisher - forthcoming - Philosophical Papers:1-27.
    Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars...
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  • Emergent Individuals.Timothy O'Connor & Jonathan D. Jacobs - 2003 - Philosophical Quarterly 53 (213):540-555.
    We explain the thesis that human mental states are ontologically emergent aspects of a fundamentally biological organism. We then explore the consequences of this thesis for the identity of a human person over time. As these consequences are not obviously independent of one's general ontology of objects and their properties, we consider four such accounts: transcendent universals, kind-Aristotelianism, immanent universals, and tropes. We suggest there are reasons for emergentists to favor the latter two accounts. We then argue that within such (...)
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  • Entiteettien kategorioiden onttisesta statuksesta.Markku Keinänen - 2012 - Maailma.
    This paper (in Finnish) concerns the ontological status of categories of entities. I argue that categories are not be considered as further entities. Rather, it is suffcient for entities belonging to the same category that they are in exactly the same formal ontological relations and have the same general category features.
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  • Hume as a Trope Nominalist.Jani Hakkarainen - 2012 - Canadian Journal of Philosophy 42 (S1):55-66.
    In this paper, I argue that Hume's solution to a problem that contemporary metaphysicians call “the problem of universals” would be rather trope-theoretical than some other type of nominalism. The basic idea in different trope theories is that particular properties, i.e., tropes are postulated to account for the fact that there are particular beings resembling each other. I show that Hume's simple sensible perceptions are tropes: simple qualities. Accordingly, their similarities are explained by these tropes themselves and their resemblance. Reading (...)
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  • La natura e l'identità degli oggetti materiali.Achille C. Varzi - 2007 - In Annalisa Coliva (ed.), Filosofia analitica. Temi e problemi. Carocci Editore. pp. 17–56.
    A critical survey of the main metaphysical theories concerning the nature of material objects (substratum theories, bundle theories, substance theories, stuff theories) and their identity conditions, both synchronic (monist vs. pluralist theories) and diachronic (three-dimensionalism, four-dimensionalism, sequentialism).
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  • The Problem of Free Mass: Must Properties Cluster?Jonathan Schaffer - 2003 - Philosophy and Phenomenological Research 66 (1):125–138.
    Properties come in clusters. It seems impossible, for instance, that a mass could float free, unattached to any other property. David Armstrong takes this as a reductio of the bundle theory and an argument for substrata, while Peter Simons and Arda Denkel reply by supplementing the bundle theory with accounts of property interdependencies. I argue against both views. Virtually all plausible ontologies turn out to be committed to the existence of free masses.
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  • The Metaphysics of Similarity and Analogical Reasoning.Jarrod W. Brown - 2018 - Dissertation, University of Hawaiʻi at Mānoa
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  • The Dual Nature of Properties: The Powerful Qualities View Reconsidered.Joaquim Giannotti - 2019 - Dissertation, University of Glasgow
    Metaphysical orthodoxy holds that a privileged minority of properties carve reality at its joints. These are the so-called fundamental properties. This thesis concerns the contemporary philosophical debate about the nature of fundamental properties. In particular, it aims to answer two questions: What is the most adequate conception of fundamental properties? What is the “big picture” world-view that emerges by adopting such a conception? I argue that a satisfactory answer to both questions requires us to embrace a novel conception of powerful (...)
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  • The Identity Theory of Powers Revised.Joaquim Giannotti - forthcoming - Erkenntnis:1-19.
    Dispositionality and qualitativity are key notions to describe the world that we inhabit. Dispositionality is a matter of what a thing is disposed to do in certain circumstances. Qualitativity is a matter of how a thing is like. According to the Identity Theory of powers, every fundamental property is at once dispositional and qualitative, or a powerful quality. Canonically, the Identity Theory holds a contentious identity claim between a property’s dispositionality and its qualitativity. In the literature, this view faces a (...)
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  • Against Zero-Dimensional Material Objects (and Other Bare Particulars).Daniel Giberman - 2012 - Philosophical Studies 160 (2):305-321.
    A modus tollens against zero-dimensional material objects is presented from the premises (i) that if there are zero-dimensional material objects then there are bare particulars, and (ii) that there are no bare particulars. The argument for the first premise proceeds by elimination. First, bare particular theory and bundle theory are motivated as the most appealing theories of property exemplification. It is then argued that the bundle theorist’s Ockhamism ought to lead her to reject spatiotemporally located zero-dimensional property instances. Finally, it (...)
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  • “Tropes in Space.Daniel Giberman - 2014 - Philosophical Studies 167 (2):453-472.
    Tropes are particular features of concrete objects. Properties—the extensions of predicates—are primitive resemblance classes of tropes. Friends of tropes have been criticized for failing to answer three questions. First, are there fundamental items other than tropes? Second, what criteria determine whether some tropes are all and only the features of some one object? Third, can trope classes be formed adequately using only primitive resemblance? Trading on the spatiotemporal status of tropes, this essay offers new responses to each of these questions. (...)
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  • Bundle Theory’s Black Box: Gap Challenges for the Bundle Theory of Substance.Robert Garcia - 2014 - Philosophia 42 (1):115-126.
    My aim in this article is to contribute to the larger project of assessing the relative merits of different theories of substance. An important preliminary step in this project is assessing the explanatory resources of one main theory of substance, the so-called bundle theory. This article works towards such an assessment. I identify and explain three distinct explanatory challenges an adequate bundle theory must meet. Each points to a putative explanatory gap, so I call them the Gap Challenges. I consider (...)
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  • The Impossibility of Relations Between Non-Collocated Spatial Objects and Non-Identical Topological Spaces.Jeffrey Grupp - 2005 - Axiomathes 15 (1):85-141.
    I argue that relations between non-collocated spatial entities, between non-identical topological spaces, and between non-identical basic building blocks of space, do not exist. If any spatially located entities are not at the same spatial location, or if any topological spaces or basic building blocks of space are non-identical, I will argue that there are no relations between or among them. The arguments I present are arguments that I have not seen in the literature.
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  • Bradley’s Regress and Visual Content.Błażej Skrzypulec - 2019 - Axiomathes 29 (2):155-172.
    According to the well-known Bradley’s Regress argument, one cannot explain the unity of states of affairs by referring to relations combining objects with properties. This argument has been widely discussed within analytic metaphysics, but has not been recognized as relevant for the philosophy of perception. I argue that the mainstream characterization of visual content is threatened by the Bradley’s Regress, and the most influential metaphysical solutions to the regress argument cannot be applied in the context of visual content. However, I (...)
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  • Tropes, Causal Processes, and Functional Laws.Markku Keinänen - 2014 - In Miroslaw Szatkowski & Marek Rosiak (eds.), Substantiality and Causality. De Gruyter. pp. 35-50.
    My earlier attempt to develop a trope nominalist account of the relation between tropes and causal processes. In accordance with weak dispositional essentialism (Hendry & Rowbottom 2009), I remain uncommitted to full-blown necessity of causal functional laws. Instead, the existence of tropes falling under a determinable and certain kind of causal processes guarantee that corresponding functional laws do not have falsifying instances.
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