Domains of Discourse

Logique Et Analyse 117 (17):173-176 (1987)
Abstract
Suppose there is a domain of discourse of English, then everything of which any predicate is true is a member of that domain. If English has a domain of discourse, then, since ‘is a domain of discourse of English’ is itself a predicate of English and true of that domain, that domain is a member of itself. But nothing is a member of itself. Thus English has no domain of discourse. We defend this argument and go on to argue to the same conclusion without relying on the supposition that English is a language which contains the predicate ‘is a domain of discourse of English’.
Keywords domains  universal set  axiom of regularity
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