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Ontological Pluralism

Journal of Philosophy 107 (1):5-34 (2010)

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  1. Functional Monotheism and the Tri-Theism Objection.Joshua R. Sijuwade - 2020 - Dissertation, University of York
    In this thesis, I argue that the Functional Monotheism model is not tri-theistic, but is a model of pro-Nicene Trinitarianism. In establishing this thesis, I focus on countering a specific objection prevalent in the Analytic Theology literature; the Tri-Theism Objection, which has charged the Functional Monotheism model with “tri-theism”. This objection, formulated by Kelly James Clark and Edward Feser, asserts that the Functional Monotheism model is tritheistic and thus should be rejected as a possible model of scriptural monotheism and “orthodox” (...)
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  • The Metaphysical Commitments of Logic.Thomas Brouwer - 2013 - Dissertation, University of Leeds
    This thesis is about the metaphysics of logic. I argue against a view I refer to as ‘logical realism’. This is the view that the logical constants represent a particular kind of metaphysical structure, which I dub ‘logico-metaphysical structure’. I argue instead for a more metaphysically lightweight view of logic which I dub ‘logical expressivism’. -/- In the first part of this thesis (Chapters I and II) I argue against a number of arguments that Theodore Sider has given for logical (...)
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  • Against philosophical proofs against common sense.Louis Doulas & Evan Welchance - 2021 - Analysis 81 (2):207–215.
    Many philosophers think that common sense knowledge survives sophisticated philosophical proofs against it. Recently, however, Bryan Frances (forthcoming) has advanced a philosophical proof that he thinks common sense can’t survive. Exploiting philosophical paradoxes like the Sorites, Frances attempts to show how common sense leads to paradox and therefore that common sense methodology is unstable. In this paper, we show how Frances’s proof fails and then present Frances with a dilemma.
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  • Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.Jared Warren - 2020 - New York, USA: Oxford University Press.
    What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...)
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  • Ontological Pluralism about Non-Being.Sarah Bernstein - 2021 - In Sara Bernstein & Tyron Goldschmidt (eds.), Non-Being: New Essays on the Metaphysics of Nonexistence. Oxford: Oxford University Press. pp. 1-16.
    I develop ontological pluralism about non-being, the view that there are multiple ways, kinds, or modes of non-being. I suggest that the view is both more plausible and defensible than it first seems, and that it has many useful applications across a wide variety of metaphysical and explanatory problems. After drawing out the relationship between pluralism about being and pluralism about non-being, I discuss quantificational strategies for the pluralist about non-being. I examine historical precedent for the view. Finally, I suggest (...)
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  • Variance Theses in Ontology and Metaethics.Matti Eklund - 2019 - In Alexis Burgess, Herman Cappelen & David Plunkett (eds.), Conceptual Engineering and Conceptual Ethics. New York, USA: Oxford University Press.
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  • Ontological Pluralism and the Generic Conception of Being.Byron Simmons - 2022 - Erkenntnis 87 (3):1275-1293.
    Ontological pluralism is the view that there are different fundamental ways of being. Trenton Merricks has recently raised three objections to combining pluralism with a generic way of being enjoyed by absolutely everything there is: first, that the resulting view contradicts the pluralist’s core intuition; second, that it is especially vulnerable to the charge—due to Peter van Inwagen—that it posits a difference in being where there is simply a difference in kind; and, third, that it is in tension with various (...)
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  • Introducción a la Ontología.Axel Barceló - manuscript
    Intuitivamente, la realidad está formada por entidades y hechos existentes y concretos. Sin embargo, nuestro lenguaje y pensamiento versa también sobre hechos meramente posibles, sobre cosas inexistentes y entidades abstractas. ¿Cómo es esto posible? ¿Significa ello que cuando hablamos y pensamos de estas otras cosas no hablamos de nada real? ¿o mas bien la realidad está mas poblada de lo que pensábamos y hay diferentes maneras de formar parte de la realidad además de la de existir de manera positiva y (...)
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  • A puzzle about Moorean metaphysics.Louis Doulas - 2020 - Philosophical Studies 178 (2):493-513.
    Some metaphysicians believe that existence debates are easily resolved by trivial inferences from Moorean premises. This paper considers how the introduction of negative Moorean facts—negative existentials that command Moorean certainty—complicates this picture. In particular, it shows how such facts, when combined with certain plausible metaontological principles, generate a puzzle that commits the proponents of this method to a contradiction.
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  • Ways of thinking about ways of being.Bradley Rettler - 2020 - Analysis 80 (4):712-722.
    Monism about being says that there is one way to be. Pluralism about being says that there are many ways to be. Recently, Trenton Merricks and David Builes have offered arguments against Pluralism. In this paper, I show how Pluralists who appeal to the relative naturalness of quantifiers can respond to these arguments.
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  • Quantification in the Ontology Room.Bradley Rettler - 2019 - Dialectica 73 (4):563-585.
    There is a growing movement towards construing some classic debates in ontology as meaningless, either because the answers seem obvious or the debates seem intractable. In this paper, I respond to this movement. The response has three components: First, the members of the two sides of the ontological debates that dismissivists have targeted are using different quantifiers. Second, the austere ontologist is using a more fundamental quantifier than her opponent. Third, the austere ontologist’s more fundamental quantifier is a restriction of (...)
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  • Grief and Composition as Identity.C. E. Garland - 2020 - Philosophical Quarterly 70 (280):464-479.
    ‘It feels like I have lost a part of myself’ is frequently uttered by those grieving the death of a loved one. Despite the ubiquity of such utterances, and the palpable sense that they express something true, few philosophers have considered what, if anything, accounts for their truth. Here, I develop a suggestion from Donald Baxter according to which Composition as Identity provides us a means to understand the grief utterances literally. In doing so, I identify and develop a version (...)
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  • De Dicto and De Re: A Brandomian experiment on Kierkegaard.Gabriel Ferreira - 2019 - Revista de Filosofia Moderna E Contemporânea 2 (7):221-238.
    During the last few decades, the historical turn within the tradition of the analytic tradition has experienced growing enthusiasm concerning the procedure of rational reconstruction, whose validity or importance, despite its paradigmatic examples in Frege and Russell, has not always enjoyed a consensus. Among the analytic philosophers who are the frontrunners of this movement, Robert Brandom is one of a kind: his work on Hegel as well as on German Idealism has been increasing interest in, as well as awareness of, (...)
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  • Existential Quantifier and Ontological Pluralism.Pawel Garbacz - 2019 - Axiomathes 29 (5):531-540.
    Within the context of the debate between ontological monists and pluralists the paper discusses a number of argumentative strategies that the latter can apply to answer the “there can be only one” argument. I show here that the reply to this argument suggested by J. Turner has its disadvantages and suggest a number of adjustments thereof. In particular, I develop a concept of domain-specific quantifiers that allow the pluralist to elaborate his or her ontological position.
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  • Rayo’s Metametaphysics.Matti Eklund - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (4):483-497.
    In his important book The Construction of Logical Space, Agustín Rayo lays out a distinctive metametaphysical view and applies it fruitfully to disputes concerning ontology and concerning modality. In this article, I present a number of criticisms of the view developed, mostly focusing on the underlying metametaphysics and Rayo’s claims on its behalf.
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  • Ontological Pluralism and Notational Variance.Bruno Whittle - 2021 - Oxford Studies in Metaphysics 12:58-72.
    Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist (...)
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  • A Language for Ontological Nihilism.Catharine Diehl - 2018 - Ergo: An Open Access Journal of Philosophy 5:971-996.
    According to ontological nihilism there are, fundamentally, no individuals. Both natural languages and standard predicate logic, however, appear to be committed to a picture of the world as containing individual objects. This leads to what I call the \emph{expressibility challenge} for ontological nihilism: what language can the ontological nihilist use to express her account of how matters fundamentally stand? One promising suggestion is for the nihilist to use a form of \emph{predicate functorese}, a language developed by Quine. This proposal faces (...)
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  • Are All Primitives Created Equal?J. T. M. Miller - 2018 - Southern Journal of Philosophy 56 (2):273-292.
    Primitives are both important and unavoidable, and which set of primitives we endorse will greatly shape our theories and how those theories provide solutions to the problems that we take to be important. After introducing the notion of a primitive posit, I discuss the different kinds of primitives that we might posit. Following Cowling (2013), I distinguish between ontological and ideological primitives, and, following Benovsky (2013) between functional and content views of primitives. I then propose that these two distinctions cut (...)
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  • Counting Incompossibles.Peter Fritz & Jeremy Goodman - 2017 - Mind 126 (504):1063–1108.
    We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases (...)
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  • The Only Way To Be.Trenton Merricks - 2017 - Noûs 53 (3):593-612.
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  • Intensional type theory for higher-order contingentism.Peter Fritz - 2015 - Dissertation, University of Oxford
    Things could have been different, but could it also have been different what things there are? It is natural to think so, since I could have failed to be born, and it is natural to think that I would then not have been anything. But what about entities like propositions, properties and relations? Had I not been anything, would there have been the property of being me? In this thesis, I formally develop and assess views according to which it is (...)
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  • Nominalist Realism.Nicholas K. Jones - 2017 - Noûs 52 (4):808-835.
    This paper explores the impact of quantification into predicate position on the metaphysics of properties, arguing that two familiar debates about properties are fundamentally altered by recasting them in a second-order setting. Two theories of properties are outlined, differing over whether the existence of properties is expressed using first-order or second-order quantifiers. It is argued that the second-order theory: provides good reason to regard debate about the locations of properties as contentless; resolves debate about whether properties are particulars or universals (...)
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  • An Epistemic Account Of Metaphysical Equivalence1.Michaela Markham McSweeney - 2016 - Philosophical Perspectives 30 (1):270-293.
    I argue that, in order for us to be justified in believing that two theories are metaphysically equivalent, we must be able to conceive of them as unified into a single theory, which says nothing over and above either of them. I propose one natural way of precisifying this condition, and show that the quantifier variantist cannot meet it. I suggest that the quantifier variantist cannot meet the more general condition either, and argue that this gives the metaphysical realist a (...)
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  • 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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  • Counting on Strong Composition as Identity to Settle the Special Composition Question.Joshua Spencer - 2017 - Erkenntnis 82 (4):857-872.
    Strong Composition as Identity is the thesis that necessarily, for any xs and any y, those xs compose y iff those xs are non-distributively identical to y. Some have argued against this view as follows: if some many things are non-distributively identical to one thing, then what’s true of the many must be true of the one. But since the many are many in number whereas the one is not, the many cannot be identical to the one. Hence is mistaken. (...)
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  • Emergence for Nihilists.Richard L. J. Caves - 2018 - Pacific Philosophical Quarterly 99 (1):2-28.
    I defend mereological nihilism, the view that there are no composite objects, against a challenge from ontological emergence, the view that some things have properties that are ‘something over and above’ the properties of their parts. As the nihilist does not believe in composite wholes, there is nothing in the nihilist's ontology to instantiate emergent properties – or so the challenge goes. However, I argue that some simples can collectively instantiate an emergent property, so the nihilist's ontology can in fact (...)
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  • Abstract entities in a presentist world.Aldo Filomeno - 2016 - Metaphysica 17 (2):177-193.
    How can a metaphysics of abstract entities be built upon a metaphysics of time? In this paper, I address the question of how to accommodate abstract entities in a presentist world. I consider both the traditional metaontological approach of unrestricted fundamental quantification and then ontological pluralism. I argue that under the former we need to impose two constraints in the characterization of presentism in order to avoid undesired commitments to abstract entities: we have to characterize presentism as a thesis only (...)
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  • What Do We Mean When We Ask “Why is There Something Rather Than Nothing?".Andrew Brenner - 2016 - Erkenntnis 81 (6):1305-1322.
    Let’s call the sentence “why is there something rather than nothing?” the Question. There’s no consensus, of course, regarding which proposed answer to the Question, if any, is correct, but occasionally there’s also controversy regarding the meaning of the Question itself. In this paper I argue that such controversy persists because there just isn’t one unique interpretation of the Question. Rather, the puzzlement expressed by the sentence “why is there something rather than nothing?” varies depending on the ontology implicitly or (...)
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  • Composition.Daniel Z. Korman & Chad Carmichael - 2016 - Oxford Handbooks Online.
    When some objects are the parts of another object, they compose that object and that object is composite. This article is intended as an introduction to the central questions about composition and a highly selective overview of various answers to those questions. In §1, we review some formal features of parthood that are important for understanding the nature of composition. In §2, we consider some answers to the question: which pluralities of objects together compose something? As we will see, the (...)
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  • I—The Presidential Address: Being, Univocity, and Logical Syntax.A. W. Moore - 2015 - Proceedings of the Aristotelian Society 115 (1pt1):1-23.
    In this essay I focus on the idea of the univocity of being, championed by Duns Scotus and given prominence more recently by Deleuze. Although I am interested in how this idea can be established, my primary concern is with something more basic: how the idea can even be properly thought. In the course of exploring this issue, which I do partly by borrowing some ideas about logical syntax from Wittgenstein's Tractatus, I try to show how there can be dialogue (...)
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  • Quantifier Variance and the Collapse Argument.Jared Warren - 2015 - Philosophical Quarterly 65 (259):241-253.
    Recently a number of works in meta-ontology have used a variant of J.H. Harris's collapse argument in the philosophy of logic as an argument against Eli Hirsch's quantifier variance. There have been several responses to the argument in the literature, but none of them have identified the central failing of the argument, viz., the argument has two readings: one on which it is sound but doesn't refute quantifier variance and another on which it is unsound. The central lesson I draw (...)
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  • Tensed Truthmaker Theory.Sam Baron - 2015 - Erkenntnis 80 (5):923-944.
    Presentism faces a serious challenge from truthmaker theory. Standard solutions to the truthmaker objection against presentism proceed in one of two ways. Easy road presentists invoke new entities to satisfy the requirements of truthmaker theory. Hard road presentists, by contrast, flatly refuse to give in to truthmaker demands. Recently, a third way has been proposed. This response seeks to address the truthmaking problem by tensing our truthmaker principles. These views, though intuitive, are under-developed. In this paper, I get serious about (...)
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  • Time, Modality, and the Unbearable Lightness of Being.Akiko M. Frischhut & Alexander Skiles - 2013 - Thought: A Journal of Philosophy 2 (1):264-273.
    We develop a theory about the metaphysics of time and modality that combines the conceptual resources devised in recent sympathetic work on ontological pluralism (the thesis that there are fundamentally distinct kinds of being) with the thought that what is past, future, and merely possible is less real than what is present and actual (albeit real enough to serve as truthmakers for statements about the past, future, and merely possible). However, we also show that despite being a coherent, distinctive, and (...)
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  • The Way of Actuality.Sam Cowling - 2014 - Australasian Journal of Philosophy 92 (2):231-247.
    In this paper, I defend an indexical analysis of the abstract-concrete distinction within the framework of modal realism. This analysis holds the abstract-concrete distinction to be conceptually inseparable from the distinction between the actual and the merely possible, which is assumed to be indexical in nature. The resulting view contributes to the case for modal realism by demonstrating how its distinctive resources provide a reductive analysis of the abstract-concrete distinction. This indexical analysis also provides a solution to a sceptical problem (...)
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  • Fundamental Quantification and the Language of the Ontology Room.Daniel Z. Korman - 2013 - Noûs 49 (2):298-321.
    Nihilism is the thesis that no composite objects exist. Some ontologists have advocated abandoning nihilism in favor of deep nihilism, the thesis that composites do not existO, where to existO is to be in the domain of the most fundamental quantifier. By shifting from an existential to an existentialO thesis, the deep nihilist seems to secure all the benefits of a composite-free ontology without running afoul of ordinary belief in the existence of composites. I argue that, while there are well-known (...)
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  • Recent work on alethic pluralism.Nikolaj Jang Lee Linding Pedersen - 2012 - Analysis 72 (3):588-607.
    While historically prominent theories of truth such as the correspondence theory, coherentism, pragmatism, verificationism, and instrumentalism diverge in many ways, they converge in at least one fundamental respect. They are all monist theories of truth. They incorporate the thesis that there is one property—and one property only—in virtue of which propositions can be true. The truth pluralist, on the other hand, rejects this idea. There are several properties in virtue of which propositions can be true. This article offers a survey (...)
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  • Looking for the Nature of Law: On Shapiro’s Challenge. [REVIEW]Damiano Canale - 2012 - Law and Philosophy 31 (4):409-441.
    This article critically focuses on the methodological aspects of Scott Shapiro’s book Legality . Indeed Shapiro’s book sets out several original theses about not only the nature of law and the main problems of jurisprudence, but also about how the nature of law can be discovered by jurisprudence. In this sense, the method of inquiry adopted by Shapiro can be considered as one of the most challenging outcomes of his research. The article is divided into two parts. In the first (...)
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  • Existence Predicates.Friederike Moltmann - 2020 - Synthese 197 (1):311-335.
    Natural languages generally distinguishes among different existence predicates for different types of entities, such as English 'exist', 'occur', and 'obtain'. The paper gives an in-depth discussion and analysis of a range of existence predicates in natural language within the general project of descriptive metaphysics, or more specifically ‘natural language ontology’.
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  • Elucidating Divine Atemporality.Joshua R. Sijuwade - 2024 - Metaphysica 25 (2):1-60.
    This article aims to provide a philosophical elucidation of the concept of divine atemporality (i.e. divine timelessness and immutability), found within the theological trajectory of Classical Theism, and a philosophical model – termed Aspectival Pluralism – that demonstrates its compatibility with the further notion of Divine Preservation. To achieve this end, an original interpretation of the concept is formulated within the Aspectival Account and the thesis of Theistic Ontological Pluralism, as extended by the temporal ontology of Priority Presentism, introduced by (...)
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  • On the metaphysics of the incarnation.Joshua R. Sijuwade - 2024 - International Journal for Philosophy of Religion 95 (2):153-185.
    This article aims to provide an elucidation of the doctrine of the Incarnation. A new ‘reduplication strategy’ and ‘compositional model’ is formulated through the utilisation of certain concepts and theses from contemporary metaphysics, which will enable the doctrine of the Incarnation to be explicated in a clear and consistent manner, and the oft-raised objections against it being fully dealt with.
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  • Against Instantiation.Christopher Frugé - forthcoming - Australasian Journal of Philosophy.
    According to traditional universalism, properties are instantiated by objects, where instantiation is a ‘tie’ that binds objects and properties into facts. I offer two arguments against this view. I then develop an alternative higher-order account which holds that properties are primitively predicated of objects yet, unlike traditional nominalism, are nevertheless genuinely real. When it’s a fact that Fo, it’s not because object o instantiates F-ness, but just that Fo – where F still exists. Against orthodox higher-order approaches, however, my arguments (...)
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  • Perspectivalism about temporal reality.Bahadir Eker - 2023 - Synthese 202 (2):1-29.
    It is usually agreed that reality is temporal in the sense of containing entities that exist in time, but some philosophers, roughly those who have been traditionally called A-theorists, hold that reality is temporal in a far more profound sense than what is implied by the mere existence of such entities. This hypothesis of deep temporality typically involves two ideas: that reality is temporally compartmentalised into distinct present, past, and future ‘realms’, and that this compartmentalisation is temporally dynamic in the (...)
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  • Much ado about ontological nihilism.Alice van'T. Hoff - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    According to ontological nihilism nothing exists. A recent argument purports to show that this view is indefensible, since its most plausible formulations are tacitly committed to quantificational claims that are inconsistent with the nihilist's view that there aren't any existents. I show that this objection begs the question against the nihilist. The objector's argument relies on an equivalence principle implying that claims which nihilists regard as non-quantificational should nonetheless be interpreted as equivalent to quantified claims, given that both kinds of (...)
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  • La diferencia ontológica según las maneras del ser en la ontología-fundamental.Christian Ivanoff-Sabogal - 2023 - Contrastes: Revista Internacional de Filosofía 28 (1):41-60.
    Esta investigación aborda el tema de la diferencia ontológica desde la perspectiva de las maneras del ser (ser-cómo), uno de los momentos constitutivos de la idea complejo-unitaria del ser. Tema y perspectiva se complementan recíprocamente. Primero, la diferencia ontológica posibilita evidenciar el fenómeno óntico de las maneras de ser del ente y el ontológico de las maneras del ser. Segundo, ambas maneras proveen una palpable visualización sobre los términos de la diferencia ontológica, desbrozando el terreno para distinguir al ser, no (...)
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  • Temporal quantifier relativism.Peter Finocchiaro - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    In this paper, I introduce a quantifier-pluralist theory of time, temporal quantifier relativism. Temporal quantifier relativism includes a restricted quantifier for every instantaneous moment of time. Though it flies in the face of orthodoxy, it compares favorably to rival theories of time. To demonstrate this, I first develop the basic syntax and semantics of temporal quantifier relativism. I then compare the theory to its rivals on three issues: the passage of time, the analysis of change, and temporal ontology.
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  • Formal Ontology.Jani Hakkarainen & Markku Keinänen - 2023 - Cambridge: Cambridge University Press.
    Formal ontology as a main branch of metaphysics investigates categories of being. In the formal ontological approach to metaphysics, these ontological categories are analysed by ontological forms. This analysis, which we illustrate by some category systems, provides a tool to assess the clarity, exactness and intelligibility of different category systems or formal ontologies. We discuss critically different accounts of ontological form in the literature. Of ontological form, we propose a character- neutral relational account. In this metatheory, ontological forms of entities (...)
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  • Ontological Pluralism and Ontological Category.Ataollah Hashemi & Davood Hosseini - 2023 - European Journal of Analytic Philosophy 19 (1):page A1-16.
    Ontological pluralism is the view that there are different ways of being. Historically, ways of being are aligned with the ontological categories. This paper is about to investigate why there is such a connection, and how it should be understood. Ontological pluralism suffers from an objection, according to which ontological pluralism collapses into ontological monism, i.e., there is only one way to be. Admitting to ontological categories can save ontological pluralism from this objection if ways of being ground ontological categories. (...)
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  • Quantifier Variance.Rohan Sud & David Manley - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York, NY: Routledge. pp. 100-17.
    We provide an overview of the meta-ontological position known as "Quantifier Variance".
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  • The logical problem of the incarnation: a new solution.Joshua R. Sijuwade - 2022 - Religious Studies:1-21.
    This article aims to provide a new solution to the Logical Problem of the Incarnation by proposing a novel metaphysical reconstrual of the method of reduplicative predication. This reconstrual will be grounded upon the metaphysical thesis of ‘Ontological Pluralism, proposed by Kris McDaniel and Jason Turner, and the notion of an ‘aspect’ proposed by Donald L. M. Baxter. Utilising this thesis and notion will enable the method of reduplicative predication to be further clarified, and the central objection that is often (...)
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  • One-step Modal Logics, Intuitionistic and Classical, Part 1.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):837-872.
    This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...)
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