Schlenker, Philippe. 2007. "Properties, Plurals and Paradox"
(manuscript, 16 pages, UCLA & Institut Jean-Nicod).
paper in pdf]
Abstract: 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.