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  1. Collapse and the Varieties of Quantifier Variance.Matti Eklund - 2021 - In James Miller (ed.), The Language of Ontology.
    The aim of the paper is to bring clarity regarding the doctrine of quantifier variance (due to Eli Hirsch), and two prominent arguments against this doctrine, the collapse argument and the Eklund-Hawthorne argument. Different versions of the doctrine of quantifier variance are distinguished, and it is shown that the effectiveness of the arguments against it depends on what version of the doctrine is at issue. The metaontological significance of the different versions of the doctrine are also assessed. Roughly, quantifier variance (...)
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  • Ontology, Set Theory, and the Paraphrase Challenge.Jared Warren - forthcoming - Journal of Philosophical Logic:1-18.
    In many ontological debates there is a familiar challenge. Consider a debate over X s. The “small” or anti-X side tries to show that they can paraphrase the pro-X or “big” side’s claims without any loss of expressive power. Typically though, when the big side adds whatever resources the small side used in their paraphrase, the symmetry breaks down. The big side plus small’s resources is a more expressively powerful and thus more theoretically fruitful theory. In this paper, I show (...)
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  • Conciliatory Metaontology, Permissive Ontology, and Nature's Joints.David Mokriski - forthcoming - Synthese.
    According to the conciliatory view in metaontology, there are multiple possible languages corresponding to the popular positions in ontology. In each of these languages, the term ‘exists’ expresses a distinct “existence-like” property, and consequently the claims associated with each of the rival ontological positions come out true in some such language. Species of the conciliatory view can be distinguished based on claims about how the various existence-like properties are related vis-à-vis metaphysical naturalness. On some versions, all of the existence-like properties (...)
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  • Quantifier Variance, Mathematicians’ Freedom and the Revenge of Quinean Indispensability Worries.Sharon Berry - forthcoming - Erkenntnis:1-18.
    Invoking a form of quantifier variance promises to let us explain mathematicians’ freedom to introduce new kinds of mathematical objects in a way that avoids some problems for standard platonist and nominalist views. In this paper I’ll note that, despite traditional associations between quantifier variance and Carnapian rejection of metaphysics, Siderian realists about metaphysics can naturally be quantifier variantists. Unfortunately a variant on the Quinean indispensability argument concerning grounding seems to pose a problem for philosophers who accept this hybrid. However (...)
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  • Notational Variance and Its Variants.Rohan French - 2019 - Topoi 38 (2):321-331.
    What does it take for two logics to be mere notational variants? The present paper proposes a variety of different ways of cashing out notational variance, in particular isolating a constraint on any reasonable account of notational variance which makes plausible that the only kinds of translations which can witness notational variance are what are sometimes called definitional translations.
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  • Quantifier Variance.Eli Hirsch & Jared Warren - 2019 - In The Routledge Handbook of Philosophy of Relativism. New York: pp. 349-357.
    Quantifier variance is a well-known view in contemporary metaontology, but it remains very widely misunderstood by critics. Here we briefly and clearly explain the metasemantics of quantifier variance and distinguish between modest and strong forms of variance (Section I), explain some key applications (Section II), clear up some misunderstandings and address objections (Section III), and point the way toward future directions of quantifier-variance-related research (Section IV).
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  • Conventionalism, Consistency, and Consistency Sentences.Jared Warren - 2015 - Synthese 192 (5):1351-1371.
    Conventionalism about mathematics claims that mathematical truths are true by linguistic convention. This is often spelled out by appealing to facts concerning rules of inference and formal systems, but this leads to a problem: since the incompleteness theorems we’ve known that syntactic notions can be expressed using arithmetical sentences. There is serious prima facie tension here: how can mathematics be a matter of convention and syntax a matter of fact given the arithmetization of syntax? This challenge has been pressed in (...)
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  • Quantifier Variance and the Demand for a Semantics.Eli Hirsch & Jared Warren - 2019 - Philosophy and Phenomenological Research 98 (3):592-605.
    In the work of both Matti Eklund and John Hawthorne there is an influential semantic argument for a maximally expansive ontology that is thought to undermine even modest forms of quantifier variance. The crucial premise of the argument holds that it is impossible for an ontologically "smaller" language to give a Tarskian semantics for an ontologically "bigger" language. After explaining the Eklund-Hawthorne argument (in section I), we show this crucial premise to be mistaken (in section II) by developing a Tarskian (...)
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  • Quantifier Variance Dissolved.Suki Finn & Otávio Bueno - 2018 - Royal Institute of Philosophy Supplement 82:289-307.
    Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance is not an (...)
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  • Quantifier Variance and Indefinite Extensibility.Jared Warren - 2017 - Philosophical Review 126 (1):81-122.
    This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in requiring nonstandard assumptions about (...)
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  • Sider on the Epistemology of Structure.Jared Warren - 2016 - Philosophical Studies 173 (9):2417-2435.
    Theodore Sider’s recent book, “Writing the Book of the World”, employs a primitive notion of metaphysical structure in order to make sense of substantive metaphysics. But Sider and others who employ metaphysical primitives face serious epistemological challenges. In the first section I develop a specific form of this challenge for Sider’s own proposed epistemology for structure; the second section develops a general reliability challenge for Sider’s theory; and the third and final section argues for the rejection of Siderean structure in (...)
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