Abstract:

On the “Embracing Revenge” view (see Cook [2008], Cook [2009]), truth values are proxies for relations that can hold between language and the world. A full appreciation of the ‘Revenge’ phenomenon suggests that there is a proper class of such relations (and hence a proper class of truth values) and that, further, concepts such as Truth Value, Statement, and Language are indefinitely extensible (and thus that absolutely general quantification is impossible). Here I shall show how the framework deals with a recent worry formulated by Greg Restall [2008]: That languages with arbitrary infinitary conjunction (or disjunction) allow one to reconstruct a variant of the Curry paradox.

Cook, R. [2009], “What is a Truth Value, and How Many Are There?”, Studia Logica 92 (special issue on truth values): 183 – 201.

Cook, R. [2008], “Embracing Revenge: On the Indefinite Extensibility of Language”, in Revenge of the Liar, JC Beall (ed.), Oxford, Oxford University Press: 31 – 52.

Restall, G. [2008], “Curry’s Revenge: The Costs of Non-Classical Solutions to the Paradoxes of Self-Reference”, in Revenge of the Liar, JC Beall (ed.), Oxford, Oxford University Press: 262 - 271.