David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press 20-44 (2006)
There are four broad grounds upon which the intelligibility of quantification over absolutely everything has been questioned—one based upon the existence of semantic indeterminacy, another on the relativity of ontology to a conceptual scheme, a third upon the necessity of sortal restriction, and the last upon the possibility of indefinite extendibility. The argument from semantic indeterminacy derives from general philosophical considerations concerning our understanding of language. For the Skolem–Lowenheim Theorem appears to show that an understanding of quanti- fication over absolutely everything (assuming a suitably infinite domain) is semantically indistinguishable from the understanding of quantification over something less than absolutely everything; the same first-order sentences are true and even the same first-order conditions will be satisfied by objects from the narrower domain. From this it is then argued that the two kinds of understanding are indistinguishable tout court and that nothing could count as having the one kind of understanding as opposed to the other.
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Citations of this work BETA
J. P. Studd (2012). The Iterative Conception of Set: A (Bi-)Modal Axiomatisation. Journal of Philosophical Logic 42 (5):1-29.
Benjamin Schnieder (2010). Inexpressible Properties and Grelling's Antinomy. Philosophical Studies 148 (3):369 - 385.
Salvatore Florio (2014). Unrestricted Quantification. Philosophy Compass 9 (7):441-454.
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