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Plural Slot Theory

In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics Volume 11. Oxford University Press. pp. 193-223 (2018)

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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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  • Introduction to the Routledge Handbook of Propositions.Adam Russell Murray & Chris Tillman - 2019 - In Chris Tillman & Adam Murray (eds.), The Routledge Handbook of Propositions. Routledge.
    Provides a comprehensive overview and introduction to the Routledge Handbook of Propositions.
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  • Symmetric relations, symmetric theories, and Pythagrapheanism.Tim Button - 2022 - Philosophy and Phenomenological Research (3):583-612.
    It is a metaphysical orthodoxy that interesting non-symmetric relations cannot be reduced to symmetric ones. This orthodoxy is wrong. I show this by exploring the expressive power of symmetric theories, i.e. theories which use only symmetric predicates. Such theories are powerful enough to raise the possibility of Pythagrapheanism, i.e. the possibility that the world is just a vast, unlabelled, undirected graph.
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  • Directionalism and Relations of Arbitrary Symmetry.Scott Dixon - forthcoming - Dialectica.
    Maureen Donnelly has recently argued that directionalism, the view that relations have a direction, applying to their relata in an order, is unable to properly treat certain symmetric relations. She alleges that it must count the application of such a relation to an appropriate number of objects in a given order as distinct from its application to those objects in any other ordering of them. I reply by showing how the directionalist can link the application conditions of any fixed arity (...)
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  • Relationism and the Problem of Order.Michele Paolini Paoletti - 2023 - Acta Analytica 38 (2):245-273.
    Relationism holds that objects entirely depend on relations or that they must be eliminated in favour of the latter. In this article, I raise a problem for relationism. I argue that relationism cannot account for the order in which non-symmetrical relations apply to their relata. In Section 1, I introduce some concepts in the ontology of relations and define relationism. In Section 2, I present the Problem of Order for non-symmetrical relations, after distinguishing it from the Problem of Differential Application. (...)
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  • Properties.Francesco Orilia & Michele Paolini Paoletti - 2020 - Stanford Encyclopedia of Philosophy.
    2020 update of the entry "Properties".
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  • A Theory of Structured Propositions.Andrew Bacon - 2023 - Philosophical Review 132 (2):173-238.
    This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a (...)
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  • Relative Positionalism and Variable Arity Relations.T. Scott Dixon - 2019 - Metaphysics 2 (1):55-72.
    Maureen Donnelly’s (2016) relative positionalism correctly handles any fixed arity relation with any symmetry such a relation can have, yielding the intuitively correct way(s) in which that relation can apply. And it supplies an explanation of what is going on in the world that makes this the case. But it has at least one potential shortcoming — one that its opponents are likely to seize upon: it can only handle relations with fixed arities. It is unable to handle relations with (...)
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  • Against relationalism about modality.Carlos Romero - 2023 - Philosophical Studies 180 (8):2245-2274.
    On a highly influential way to think of modality, that I call ‘relationalism’, the modality of a state is explained by its being composed of properties, and these properties being related by a higher-order and primitively modal relation. Examples of relationalism are the Dretske-Tooley-Armstrong account of natural necessity, many dispositional essentialist views, and Wang’s incompatibility primitivism. I argue that relationalism faces four difficulties: that the selection between modal relations is arbitrary, that the modal relation cannot belong to any logical order, (...)
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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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  • Slot Theory and Slotite Theory.Nikk Effingham - 2020 - Philosophia 49 (1):17-35.
    ‘Instantiation-directed slot theorists’ believe that properties/relations have slots which are filled by their instances/relata e.g., where Abigail is taller than Bronia, there are two slots in the relation Taller Than such that Abigail fills the first slot and Bronia fills the second. This crude statement of the theory runs into ‘The Problem of Filling’, whereby a natural understanding of the relation between slots, filling, and instantiation leads to absurd results. This paper examines a variety of solutions to that problem, one (...)
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