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  1. Symmetric relations.Scott Dixon - 2023 - Philosophical Studies 180 (12):3615-3639.
    There are two ways to characterize symmetric relations. One is intensional: necessarily, _Rxy_ iff _Ryx_. In some discussions of relations, however, what is important is whether or not a relation gives rise to the same completion of a given type (fact, state of affairs, or proposition) for each of its possible applications to some fixed relata. Kit Fine calls relations that do ‘strictly symmetric’. Is there is a difference between the notions of necessary and strict symmetry that would prevent them (...)
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  • Abstraction and grounding.Louis deRosset & Øystein Linnebo - 2023 - Philosophy and Phenomenological Research 109 (1):357-390.
    The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one:. The principal aim of this article is to use the notion of grounding to develop this (...)
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  • Indiscernibility and the Grounds of Identity.Samuel Z. Elgin - forthcoming - Philosophical Studies:1-23.
    I provide a theory of the metaphysical foundations of identity: an account what grounds facts of the form a=b. In particular, I defend the claim that indiscernibility grounds identity. This is typically rejected because it is viciously circular; plausible assumptions about the logic of ground entail that the fact that a=b partially grounds itself. The theory I defend is immune to this circularity.
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  • Thin objects: An overview.Massimiliano Carrara & Luca Zanetti - 2023 - Theoria 89 (3):239-246.
    In Thin objects: an abstractionist account (Oxford University Press, 2018), Øystein Linnebo claims that ‘mathematical objects are thin in the sense that very little is required for their existence’. Linnebo articulates his view in an abstractionist manner: according to Linnebo, the truth of the right‐hand side of a Fregean abstraction principle, which states that two items stand in a given equivalence relation, is sufficient for the truth of its left‐hand side, which states that the same abstract object is associated to (...)
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  • Grounding and defining identity.Jon Erling Litland - 2022 - Noûs 57 (4):850-876.
    I systematically defend a novel account of the grounds for identity and distinctness facts: they are all uniquely zero‐grounded. First, this Null Account is shown to avoid a range of problems facing other accounts: a relation satisfying the Null Account would be an excellent candidate for being the identity relation. Second, a plenitudinist view of relations suggests that there is such a relation. To flesh out this plenitudinist view I sketch a novel framework for expressing real definitions, use this framework (...)
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  • A Metaphysical Puzzle for Neo‐Fregean Abstractionists.Thomas Donaldson - 2023 - Theoria 89 (3):266-279.
    We discuss abstraction principles in the context of modal and temporal logic. It is argued that abstractionism conflicts with both serious presentism and serious actualism.
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  • (1 other version)Review of Øystein Linnebo, Thin Objects. [REVIEW]Thomas Donaldson - forthcoming - Philosophia Mathematica:6.
    A brief review of Øystein Linnebo's Thin Objects. The review ends with a brief discussion of cardinal number and metaphysical ground.
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  • (1 other version)Conceivability, Essence, and Haecceities.David Elohim - manuscript
    This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I introduce a novel epistemic two-dimensional truthmaker semantics. I argue that the interaction between the two-dimensional framework and the mereological parthood relation, which is super-rigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a two-dimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining (...)
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  • The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York, NY: Routledge.
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  • Reasons and Causes in Psychiatry: Ideas from Donald Davidson’s Work.Elisabetta Lalumera - 2018 - In Annalisa Coliva, Paolo Leonardi & Sebastiano Moruzzi (eds.), Eva Picardi on Language, Analysis and History. Londra, Regno Unito: Palgrave. pp. 281-296.
    Though the divide between reason-based and causal-explanatory approaches in psychiatry and psychopathology is old and deeply rooted, current trends involving multi-factorial explanatory models and evidence-based approaches to interpersonal psychotherapy, show that it has already been implicitly bridged. These trends require a philosophical reconsideration of how reasons can be causes. This paper contributes to that trajectory by arguing that Donald Davidson’s classic paradigm of 1963 is still a valid option.
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  • Do identity and distinctness facts threaten the PSR?Erica Shumener - 2020 - Philosophical Studies 178 (4):1023-1041.
    One conception of the Principle of Sufficient Reason maintains that every fact is metaphysically explained. There are different ways to challenge this version of the PSR; one type of challenge involves pinpointing a specific set of facts that resist metaphysical explanation. Certain identity and distinctness facts seem to constitute such a set. For example, we can imagine a scenario in which we have two qualitatively identical spheres, Castor and Pollux. Castor is distinct from Pollux but it is unclear what could (...)
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  • Grounding and auto-abstraction.Luca Zanetti - 2020 - Synthese 198 (11):10187-10205.
    Abstraction principles and grounding can be combined in a natural way Modality: metaphysics, logic, and epistemology, Oxford University Press, Oxford, pp 109–136, 2010; Schwartzkopff in Grazer philosophische studien 82:353–373, 2011). However, some ground-theoretic abstraction principles entail that there are circles of partial ground :775–801, 2017). I call this problem auto-abstraction. In this paper I sketch a solution. Sections 1 and 2 are introductory. In Sect. 3 I start comparing different solutions to the problem. In Sect. 4 I contend that the (...)
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  • The Essences of Fundamental Properties.Jennifer Wang - 2019 - Metaphysics 2 (1):40-54.
    There is a puzzle concerning the essences of fundamental entities that arises from considerations about essence, on one hand, and fundamentality, on the other. The Essence-Dependence Link (EDL) says that if x figures in the essence of y, then y is dependent upon x. EDL is prima facie plausible in many cases, especially those involving derivative entities. But consider the property negative charge. A negatively charged object exhibits certain behaviors that a positively charged object does not: it moves away from (...)
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  • Grounding as Minimal Necessitation.Brannon McDaniel - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy:1-22.
    Let NNG be the claim that necessitation is necessary for grounding, and let NSG be the claim that necessitation is sufficient for grounding. The consensus view is that grounding cannot be reduced to necessitation, and this is due to the (approximately) universally-accepted claim that NSG is false. Among deniers of NSG: grounding contingentists think NNG is also false, but they are in the minority compared to grounding necessitarians who uphold NNG. For one who would defend the claim that grounding is (...)
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  • Grounding nonexistence.Daniel Muñoz - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (2):209-229.
    Contingent negative existentials give rise to a notorious paradox. I formulate a version in terms of metaphysical grounding: nonexistence can't be fundamental, but nothing can ground it. I then argue for a new kind of solution, expanding on work by Kit Fine. The key idea is that negative existentials are contingently zero-grounded – that is to say, they are grounded, but not by anything, and only in the right conditions. If this is correct, it follows that grounding cannot be an (...)
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  • Explaining identity and distinctness.Erica Shumener - 2020 - Philosophical Studies 177 (7):2073-2096.
    This paper offers a metaphysical explanation of the identity and distinctness of concrete objects. It is tempting to try to distinguish concrete objects on the basis of their possessing different qualitative features, where qualitative features are ones that do not involve identity. Yet, this criterion for object identity faces counterexamples: distinct objects can share all of their qualitative features. This paper suggests that in order to distinguish concrete objects we need to look not only at which properties and relations objects (...)
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  • On the Schwartzkopff-Rosen Principle.Ciro De Florio & Luca Zanetti - 2020 - Philosophia 48 (1):405-419.
    Hume’s Principle states that the cardinal number of the concept F is identical with the cardinal number of G if and only if F and G can be put into one-to-one correspondence. The Schwartzkopff-Rosen Principle is a modification of HP in terms of metaphysical grounding: it states that if the number of F is identical with the number of G, then this identity is grounded by the fact that F and G can be paired one-to-one, 353–373, 2011, 362). HP is (...)
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  • Composition as Abstraction.Jeffrey Sanford Russell - 2017 - Journal of Philosophy 114 (9):453-470.
    The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.
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  • Emptying a Paradox of Ground.Jack Woods - 2018 - Journal of Philosophical Logic 47 (4):631-648.
    Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation—any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, (...)
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  • (1 other version)Forms of Luminosity: Epistemic Modality and Hyperintensionality in Mathematics.David Elohim - 2017 - Dissertation, Arché, University of St Andrews
    This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...)
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  • (1 other version)Forms of Luminosity: Epistemic Modality and Hyperintensionality in Mathematics.David Elohim - 2017
    This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...)
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  • Fundamentality And Modal Freedom.Jennifer Wang - 2016 - Philosophical Perspectives 30 (1):397-418.
    A fundamental entity is an entity that is ‘ontologically independent’; it does not depend on anything else for its existence or essence. It seems to follow that a fundamental entity is ‘modally free’ in some sense. This assumption, that fundamentality entails modal freedom (or ‘FEMF’ as I shall label the thesis), is used in the service of other arguments in metaphysics. But as I will argue, the road from fundamentality to modal freedom is not so straightforward. The defender of FEMF (...)
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  • Abstract mathematical tools and machines for mathematics.Jean-Pierre Marquis - 1997 - Philosophia Mathematica 5 (3):250-272.
    In this paper, we try to establish that some mathematical theories, like K-theory, homology, cohomology, homotopy theories, spectral sequences, modern Galois theory (in its various applications), representation theory and character theory, etc., should be thought of as (abstract) machines in the same way that there are (concrete) machines in the natural sciences. If this is correct, then many epistemological and ontological issues in the philosophy of mathematics are seen in a different light. We concentrate on one problem which immediately follows (...)
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  • Minimalism, Trivialism, Aristotelianism.Andrea Sereni & Luca Zanetti - 2023 - Theoria 89 (3):280-297.
    Minimalism and Trivialism are two recent forms of lightweight Platonism in the philosophy of mathematics: Minimalism is the view that mathematical objects arethinin the sense that “very little is required for their existence”, whereas Trivialism is the view that mathematical statements have trivial truth‐conditions, that is, that “nothing is required of the world in order for those conditions to be satisfied”. In order to clarify the relation between the mathematical and the non‐mathematical domain that these views envisage, it has recently (...)
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  • Prospects for a Theory of Decycling.Jon Erling Litland - 2020 - Notre Dame Journal of Formal Logic 61 (3):467-499.
    Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of ground. In this paper—drawing on graph-theoretic and topological ideas—I develop a general framework in which various theories of decycling can be compared. This allows us to improve on proposals made earlier by Fine and Litland. However, it turns out that (...)
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  • Axiomatic Theories of Partial Ground II: Partial Ground and Hierarchies of Typed Truth.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):193-226.
    This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is (...)
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  • (1 other version)Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
    Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.
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  • Replies.Øystein Linnebo - 2023 - Theoria 89 (3):393-406.
    Thin Objects has two overarching ambitions. The first is to clarify and defend the idea that some objects are ‘thin’, in the sense that their existence does not make a substantive demand on reality. The second is to develop a systematic and well-motivated account of permissible abstraction, thereby solving the so-called ‘bad company problem’. Here I synthesise the book by briefly commenting on what I regard as its central themes.
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  • Collective Abstraction.Jon Erling Litland - 2022 - Philosophical Review 131 (4):453-497.
    This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead (...)
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  • Identity.Erica Shumener - 2020 - In Michael J. Raven (ed.), The Routledge Handbook of Metaphysical Grounding. New York: Routledge. pp. 413-424.
    I explore proposals for stating identity criteria in terms of ground. I also address considerations for and against taking identity and distinctness facts to be ungrounded.
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  • Prioritizing platonism.Kelly Trogdon & Sam Cowling - 2019 - Philosophical Studies 176 (8):2029-2042.
    Discussion of atomistic and monistic theses about abstract reality.
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  • A new perspective on the problem of applying mathematics.Christopher Pincock - 2004 - Philosophia Mathematica 12 (2):135-161.
    This paper sets out a new framework for discussing a long-standing problem in the philosophy of mathematics, namely the connection between the physical world and a mathematical domain when the mathematics is applied in science. I argue that considering counterfactual situations raises some interesting challenges for some approaches to applications, and consider an approach that avoids these challenges.
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  • The Metaphysics of Identity: Is Identity Fundamental?Erica Shumener - 2017 - Philosophy Compass 12 (1):1-13.
    Identity and distinctness facts are ones like “The Eiffel Tower is identical to the Eiffel Tower,” and “The Eiffel Tower is distinct from the Louvre.” This paper concerns one question in the metaphysics of identity: Are identity and distinctness facts metaphysically fundamental or are they nonfundamental? I provide an overview of answers to this question.
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  • Structure by proxy, with an application to grounding.Peter Fritz - 2019 - Synthese 198 (7):6045-6063.
    An argument going back to Russell shows that the view that propositions are structured is inconsistent in standard type theories. Here, it is shown that such type theories may nevertheless provide entities which can serve as proxies for structured propositions. As an illustration, such proxies are applied to the case of grounding, as standard views of grounding require a degree of propositional structure which suffices for a version of Russell’s argument. While this application solves some of the problems grounding faces, (...)
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