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Universal Universal Quantification

In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Oxford, England: Oxford University Press UK (2003)

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  1. A completeness theorem for unrestricted first- order languages.Agustin Rayo & Timothy Williamson - 2003 - In J. C. Beall (ed.), Liars and heaps: new essays on paradox. New York: Oxford University Press.
    Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents and the syntactic differences between their non-logical constituents, treated as (...)
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  • Beyond Plurals.Agust\’in Rayo - 2006 - In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute generality. New York: Oxford University Press. pp. 220--54.
    I have two main objectives. The first is to get a better understanding of what is at issue between friends and foes of higher-order quantification, and of what it would mean to extend a Boolos-style treatment of second-order quantification to third- and higherorder quantification. The second objective is to argue that in the presence of absolutely general quantification, proper semantic theorizing is essentially unstable: it is impossible to provide a suitably general semantics for a given language in a language of (...)
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