Properties, plurals and paradox
It has been argued that an objectual semantics for plurals falls victim to Russell’s paradox, and that a nominalistic semantics should therefore be preferred (Boolos 1984); similar considerations have sometimes been extended to other types of abstract reference, in particular to property talk. We suggest that this line of argument is mistaken: deeply entrenched features of ordinary language guarantee that property and plural talk do give rise to paradoxes. In the case of properties, the grammar of English is untyped, which makes it straightforward to generate a paradox. In the case of plurals, it is badly typed, which means that paradoxes can be generated, but in complicated ways. In both cases, the problem is not to avoid paradoxes but to model them. We conclude that an objectual semantics is entirely in order, but that it must be developed within a trivalent semantics suited to a paradoxical object language.
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