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Something About Everything: Universal Quantification in the Universal Sense of Universal Quantification

In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute generality. New York: Oxford University Press. pp. 98--148 (2006)

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  1. Linnebo on Analyticity and Thin Existence.Mark Povich - 2024 - Philosophia Mathematica 32 (3):332–357.
    In his groundbreaking book, Thin Objects, Linnebo (2018) argues for an account of neo-Fregean abstraction principles and thin existence that does not rely on analyticity or conceptual rules. It instead relies on a metaphysical notion he calls “sufficiency”. In this short discussion, I defend the analytic or conceptual rule account of thin existence.
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  • Rules to Infinity: The Normative Role of Mathematics in Scientific Explanation.Mark Povich - 2024 - Oxford University Press USA.
    One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should not be thought of as describing, in any substantive sense, (...)
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  • Categoricity by convention.Julien Murzi & Brett Topey - 2021 - Philosophical Studies 178 (10):3391-3420.
    On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order and Zermelo’s quasi-categoricity theorem (...)
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  • Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.Jared Warren - 2020 - New York, USA: Oxford University Press.
    What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...)
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  • (1 other version)The Semantic Foundations of Philosophical Analysis.Samuel Elgin - manuscript
    I provide an analysis of sentences of the form ‘To be F is to be G’ in terms of exact truth-maker semantics—an approach that identifies the meanings of sentences with the states of the world directly responsible for their truth-values. Roughly, I argue that these sentences hold just in case that which makes something F is that which makes it G. This approach is hyperintensional, and possesses desirable logical and modal features. These sentences are reflexive, transitive and symmetric, and, if (...)
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  • Quantification and Paradox.Edward Ferrier - 2018 - Dissertation, University of Massachusetts Amherst
    I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...)
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  • Generality, Extensibility, and Paradox.J. P. Studd - 2017 - Proceedings of the Aristotelian Society 117 (1):81-101.
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  • Necessarily Maybe. Quantifiers, Modality and Vagueness.Alessandro Torza - 2015 - In Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics, and Language. (Synthese Library vol. 373). Springer. pp. 367-387.
    Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...)
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  • Quantifiers and Quantification.Gabriel Uzquiano - 2014 - Stanford Encyclopedia of Philosophy.
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  • Plurals.Agustín Rayo - 2007 - Philosophy Compass 2 (3):411–427.
    Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.
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  • The Metasemantics of Indefinite Extensibility.Vera Flocke - 2021 - Australasian Journal of Philosophy 99 (4):817-834.
    ABSTRACT Generality relativism is the view that any domain of quantification can always be expanded. The view promises to resolve a broad range of paradoxes, but, without an explanation of how domains expand, it sounds very mysterious. Proponents of linguistic versions of generality relativism try to demystify the view by likening domain expansions to semantic change. They think that domains expand when we re-interpret certain terms so that, upon re-interpretation, the quantifiers range over more things. This article makes trouble for (...)
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  • Dadaism: Restrictivism as Militant Quietism.Tim Button - 2010 - Proceedings of the Aristotelian Society 110 (3pt3):387-398.
    Can we quantify over everything: absolutely, positively, definitely, totally, every thing? Some philosophers have claimed that we must be able to do so, since the doctrine that we cannot is self-stultifying. But this treats restrictivism as a positive doctrine. Restrictivism is much better viewed as a kind of militant quietism, which I call dadaism. Dadaists advance a hostile challenge, with the aim of silencing everyone who holds a positive position about ‘absolute generality’.
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  • Open-endedness, schemas and ontological commitment.Nikolaj Jang Lee Linding Pedersen & Marcus Rossberg - 2010 - Noûs 44 (2):329-339.
    Second-order axiomatizations of certain important mathematical theories—such as arithmetic and real analysis—can be shown to be categorical. Categoricity implies semantic completeness, and semantic completeness in turn implies determinacy of truth-value. Second-order axiomatizations are thus appealing to realists as they sometimes seem to offer support for the realist thesis that mathematical statements have determinate truth-values. The status of second-order logic is a controversial issue, however. Worries about ontological commitment have been influential in the debate. Recently, Vann McGee has argued that one (...)
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  • Anything and Everything.Patrick Dieveney - 2013 - Erkenntnis 78 (1):119 - 140.
    Some novel solutions to problems in mathematics and philosophy involve employing schemas rather than quantified expressions to formulate certain propositions. Crucial to these solutions is an insistence that schematic generality is distinct from quantificational generality. Although many concede that schemas and quantified expressions function differently, the dominant view appears to be that the generality expressed by the former is ultimately reducible to the latter. In this paper, I argue against this view, which I call the 'Reductionist view'. But instead of (...)
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  • (1 other version)The Semantic Foundations of Philosophical Analysis.Samuel Z. Elgin - 2023 - Review of Symbolic Logic 16 (2):603-623.
    I provide an analysis of sentences of the form ‘To beFis to beG’ in terms of exact truth-maker semantics—an approach that identifies the meanings of sentences with the states of the world directly responsible for their truth-values. Roughly, I argue that these sentences hold just in case that which makes somethingFalso makes itG. This approach is hyperintensional and possesses desirable logical and modal features. In particular, these sentences are reflexive, transitive, and symmetric, and if they are true, then they are (...)
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  • Grim’s arguments against omniscience and indefinite extensibility.Laureano Luna - 2012 - International Journal for Philosophy of Religion 72 (2):89-101.
    Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...)
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  • Absolutely general knowledge.Rachel Elizabeth Fraser & Beau Madison Mount - 2020 - Philosophy and Phenomenological Research 103 (3):547-566.
    Philosophy and Phenomenological Research, Volume 103, Issue 3, Page 547-566, November 2021.
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  • Quantification and Metaphysical Discourse.Patrick Dieveney - 2013 - Theoria 80 (4):292-318.
    It is common in metaphysical discourse to make claims like “Everything is self-identical” in which “everything” is intended to range over everything. This sort of “unrestricted” generality appears central to metaphysical discourse. But there is debate whether such generality, which appears to involve quantification over an all-inclusive domain, is even meaningful. To address this concern, Shaughan Lavine and Vann McGee supply competing accounts of the generality expressed by this use of “everything.” I argue that, from the perspective of the metaphysician, (...)
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