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  1. Higher‐order metaphysics.Lukas Skiba - 2021 - Philosophy Compass 16 (10):1-11.
    Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, propositions, and identity, (...)
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  • Reply to Florio and Shapiro.Øystein Linnebo & Agustín Rayo - 2014 - Mind 123 (489):175-181.
    Florio and Shapiro take issue with an argument in ‘Hierarchies Ontological and Ideological’ for the conclusion that the set-theoretic hierarchy is open-ended. Here we clarify and reinforce the argument in light of their concerns.
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  • Unrestricted quantification and extraordinary context dependence?Michael Glanzberg - 2021 - Philosophical Studies 180 (5-6):1-22.
    This paper revisits a challenge for contextualist approaches to paradoxes such as the Liar paradox and Russell’s paradox. Contextualists argue that these paradoxes are to be resolved by appeal to context dependence. This can offer some nice and effective ways to avoid paradox. But there is a problem. Context dependence is, at least to begin with, a phenomenon in natural language. Is there really such context dependence as the solutions to paradoxes require, and is it really just a familiar linguistic (...)
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  • Unrestricted quantification and extraordinary context dependence?Michael Glanzberg - 2023 - Philosophical Studies 180 (5):1491-1512.
    This paper revisits a challenge for contextualist approaches to paradoxes such as the Liar paradox and Russell’s paradox. Contextualists argue that these paradoxes are to be resolved by appeal to context dependence. This can offer some nice and effective ways to avoid paradox. But there is a problem. Context dependence is, at least to begin with, a phenomenon in natural language. Is there really such context dependence as the solutions to paradoxes require, and is it really just a familiar linguistic (...)
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  • Unrestricted Quantification.Salvatore Florio - 2014 - Philosophy Compass 9 (7):441-454.
    Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main arguments for (...)
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  • Against Cumulative Type Theory.Tim Button & Robert Trueman - 2022 - Review of Symbolic Logic 15 (4):907-49.
    Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...)
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  • Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
    Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...)
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