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Switch to: Citations
References in:
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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Slot theory is the view that (i) there exist such entities as argument places, or ‘slots’, in universals, and that (ii) a universal u is n-adic if and only if there are n slots in u. I argue that those who take properties and relations to be abundant, fine-grained, non-set-theoretical entities face pressure to be slot theorists. I note that slots permit a natural account of the notion of adicy. I then consider a series of ‘slot-free’ accounts of that notion (...) |
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Presupposing that most predicates do not correspond directly to genuine relations, I argue that all genuine relations are symmetric. My main argument depends on the premise that there are no brute necessities, interpreted so as to require logical and metaphysical necessity to coincide for sentences composed entirely of logical vocabulary and primitive predicates. Given this premise, any set of purportedly primitive predicates by which one might hope to express the facts about non-symmetric relations order their relata will generate an objectionable (...) |
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Do non‐symmetric relations apply to the objects they relate in an order? According to the standard view of relations, the difference between aRb and bRa obtaining, where R is non‐symmetric, corresponds to a difference in the order in which the non‐symmetric relation R applies to a and b. Recently Kit Fine has challenged the standard view in his important paper ‘Neutral Relations’ arguing that non‐symmetric relations are neutral, lacking direction or order. In this paper I argue that Fine cannot account (...) |
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The full-text of this article is not currently available in ORA, but you may be able to access the article via the publisher copy link on this record page. N.B. Prof Williamson is now based at the Faculty of Philosophy, University of Oxford. |
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In this paper I present a formal language in which complex predicates stand for properties and relations, and assignments of denotations to complex predicates and assignments of extensions to the properties and relations they denote are both homomorphisms. This system affords a fresh perspective on several important philosophical topics, highlighting the algebraic features of properties and clarifying the sense in which properties can be represented by their extensions. It also suggests a natural modification of current logics of properties, one in (...) |
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States of affairs involving a non-symmetric relation such as loving are said to have a relational order, something that distinguishes, for instance, Romeo’s loving Juliet from Juliet’s loving Romeo. Relational order can be properly understood by appealing to o-roles, i.e., ontological counterparts of what linguists call thematic roles, e.g., agent, patient, instrument, and the like. This move allows us to meet the appropriate desiderata for a theory of relational order. In contrast, the main theories that try to do without o-roles, (...) |
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The history of the idea of predicate is the history of its emancipation. The lesson of this paper is that there are two more steps to take. The first is to recognize that predicates need not have a fixed degree, the second that they can combine with plural terms. We begin by articulating the notion of a multigrade predicate: one that takes variably many arguments. We counter objections to the very idea posed by Peirce, Dummett's Frege, and Strawson. We show (...) |
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In this paper I rehearse two central failings of traditional possible world semantics. I then present a much more robust framework for intensional logic and semantics based liberally on the work of George Bealer in his book Quality and Concept. Certain expressive limitations of Bealer's approach, however, lead me to extend the framework in a particularly natural and useful way. This extension, in turn, brings to light associated limitations of Bealer's account of predication. In response, I develop a more general (...) |
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In the ordinary way of representing relations, the order of the relata plays a structural role, but in the states themselves such an order often does not seem to be intrinsically present. An alternative way to represent relations makes use of positions for the arguments. This is no problem for the love relation, but for relations like the adjacency relation and cyclic relations, different assignments of objects to the positions can give exactly the same states. This is a puzzling situation. (...) |
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Is there an explanation of why the state of x's bearing the non-symmetric binary relation R to y is different from its differential opposite, the state of y's bearing R to x? One traditional view has it that the explanation is that non-symmetric relations hold of objects in an essentially directional way, ordering the relevant relata. We call this view ‘directionalism’. Kit Fine has suggested that this approach is subject to significant metaphysical difficulties, sufficient to motivate seeking an alternative analysis. (...) |
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There is a standard view of relations, held by philosophers and logicians alike, according to which we may meaningfully talk of a relation holding of several objects in a given order. Thus it is supposed that we may meaningfully—indeed, correctly—talk of the relation loves holding of Anthony and Cleopatra or of the relation between holding of New York, Washington, and Boston. But innocuous as this view might appear to be, it cannot be accepted as applying to all relations whatever. For (...) |
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Realists about universals face a question about grounding. Are things how they are because they instantiate the universals they do? Or do they instantiate those universals because they are how they are? Take Ebenezer Scrooge. You can say that Scrooge is greedy because he instantiates greediness, or you can say that Scrooge instantiates greediness because he is greedy. I argue that there is reason to prefer the latter to the former. I develop two arguments for the view. I also respond (...) |
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I argue that it is intuitive and useful to think about composition in the light of the familiar functionalist distinction between role and occupant. This involves factoring the standard notion of parthood into two related notions: being a parthood slot and occupying a parthood slot. One thing is part of another just in case it fills one of that thing's parthood slots. This move opens room to rethink mereology in various ways, and, in particular, to see the mereological structure of (...) |
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v. 1. Nominalism and realism.--v. 2. A theory of universals. |
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Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. However, the apparatus of modern logic does not allow a place for them. Thomas McKay here explores the enrichment of logic with non-distributive plural predication and quantification. His book will be (...) |
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In this book, Linda Wetzel examines the distinction between types and tokens and argues that types exist (as abstract objects, since they lack a unique ... |
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Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) |
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This work presents a version of the correspondence theory of truth based on Wittgenstein's Tractatus and Russell's theory of truth and discusses related metaphysical issues such as predication, facts and propositions. Like Russell and one prominent interpretation of the Tractatus it assumes a realist view of universals. Part of the aim is to avoid Platonic propositions, and although sympathy with facts is maintained in the early chapters, the book argues that facts as real entities are not needed. It includes discussion (...) |
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