Mind 126 (502):499--528 (2017)

Authors
Stephan Kraemer
Universität Hamburg
Abstract
On its intended interpretation, logical, mathematical and metaphysical discourse sometimes seems to involve absolutely unrestricted quantification. Yet our standard semantic theories do not allow for interpretations of a language as expressing absolute generality. A prominent strategy for defending absolute generality, influentially proposed by Timothy Williamson in his paper ‘Everything’, avails itself of a hierarchy of quantifiers of ever increasing orders to develop non-standard semantic theories that do provide for such interpretations. However, as emphasized by Øystein Linnebo and Agustín Rayo, there is pressure on this view to extend the quantificational hierarchy beyond the finite level, and, relatedly, to allow for a cumulative conception of the hierarchy. In his recent book, Modal Logic as Metaphysics, Williamson yields to that pressure. I show that the emerging cumulative higher-orderist theory has implications of a strongly generality-relativist flavour, and consequently undermines much of the spirit of generality absolutism that Williamson set out to defend.
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DOI 10.1093/mind/fzv187
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References found in this work BETA

Everything.Timothy Williamson - 2003 - Philosophical Perspectives 17 (1):415–465.
Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
Toward a Theory of Second-Order Consequence.Augustín Rayo & Gabriel Uzquiano - 1999 - Notre Dame Journal of Formal Logic 40 (3):315-325.

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Citations of this work BETA

Unrestricted Quantification and the Structure of Type Theory.Nicholas K. Jones & Salvatore Florio - 2021 - Philosophy and Phenomenological Research 102 (1):44-64.

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