Everything, and then some

Krämer, S. (2017) Everything, and then some. Mind, 126(502), pp. 499-528. (doi: 10.1093/mind/fzv187)

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’ (2003), 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 (2012), 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 (2013), 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kraemer, Dr Stephan
• Authors: Krämer, S.
• Subjects: B Philosophy. Psychology. Religion > B Philosophy (General); B Philosophy. Psychology. Religion > BC Logic
• College/School: College of Arts & Humanities > School of Humanities > Philosophy
• Journal Name: Mind
• Publisher: Oxford University Press
• ISSN: 0026-4423
• ISSN (Online): 1460-2113
• Published Online: 30 September 2016
• Copyright Holders: Copyright © 2016 Krämer
• First Published: First published in Mind 126(502): 499-528
• Publisher Policy: Reproduced in accordance with the publisher copyright policy