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Numbers and Everything

Philosophia Mathematica 21 (3):297-308 (2013)

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  1. The Inexpressibility Objection.Filippo Costantini - 2018 - Kriterion - Journal of Philosophy 32 (2):25-46.
    In this paper, we offer a contribution to the discussion of one of the most important objections against a relativist position in the absolute generality debate. The inexpressibility objection accuses the generality-relativist of not being able to coherently express her own position. First, we examine Glanzberg’s attempt to reply to this objection and we show that it fails. Second, we study the prospects of generalizing the relativist position. In particular, we analyze Fine’s and Linnebo’s modal approaches and we argue that, (...)
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  • Dummett on Indefinite Extensibility.Øystein Linnebo - 2018 - Philosophical Issues 28 (1):196-220.
    Dummett’s notion of indefinite extensibility is influential but obscure. The notion figures centrally in an alternative Dummettian argument for intuitionistic logic and anti-realism, distinct from his more famous, meaning-theoretic arguments to the same effect. Drawing on ideas from Dummett, a precise analysis of indefinite extensibility is proposed. This analysis is used to reconstruct the poorly understood alternative argument. The plausibility of the resulting argument is assessed.
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  • Quantifiers and Quantification.Gabriel Uzquiano - 2014 - Stanford Encyclopedia of Philosophy.
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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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