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

Stephan Kraemer
Universität Hamburg
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.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1093/mind/fzv187
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 60,750
Through your library

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.

View all 11 references / Add more references

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.

Add more citations

Similar books and articles

Sets, Properties, and Unrestricted Quantification.Øystein Linnebo - 2006 - In Gabriel Uzquiano & Agustin Rayo (eds.), Absolute Generality. Oxford University Press.
Unrestricted Quantification.Salvatore Florio - 2014 - Philosophy Compass 9 (7):441-454.
Beyond Plurals.Agustin Rayo - 2006 - In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. pp. 220--54.
Absolute Generality.Agustín Rayo & Gabriel Uzquiano (eds.) - 2006 - Oxford University Press.
Unlimited Possibilities.Gonçalo Santos - 2011 - In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications.
Numbers and Everything.Gonçalo Santos - 2013 - Philosophia Mathematica 21 (3):297-308.
Absolute Identity and Absolute Generality.Timothy Williamson - 2007 - In Gabriel Uzquiano & Agustin Rayo (eds.), Absolute Generality. Oxford University Press. pp. 369--89.
Unrestricted Unrestricted Quantification: The Cardinal Problem of Absolute Generality.Gabriel Uzquiano - 2006 - In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. pp. 305--32.
Introduction.Agustin Rayo & Gabriel Uzquiano - 2006 - In Agustin Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press.
Semantic Values in Higher-Order Semantics.Stephan Krämer - 2014 - Philosophical Studies 168 (3):709-724.
Williamson on Modality.Juhani Yli-Vakkuri & Mark McCullagh - 2016 - Canadian Journal of Philosophy 46 (4-5):453-851.
Russell’s Leibnizian Concept of Vagueness.Larry M. Jorgensen - 2011 - History of Philosophy Quarterly 28 (3):289-301.


Added to PP index

Total views
144 ( #71,090 of 2,438,720 )

Recent downloads (6 months)
6 ( #113,053 of 2,438,720 )

How can I increase my downloads?


My notes