Quantification: Natural Language versus the Predicate Calculus
The absence of plural referring expressions from the predicate calculus forces quantification to function in the calculus in a way that is significantly different from the way it functions in natural language. When we quantify, we refer to a plurality of particulars, and say that specific quantities of them are such-and-such; quantification involves reference to a plurality. Natural language accomplishes this kind of reference by means of plural referring expressions, which designate the plurality, or pluralities, about which something is said. And by using different expressions, natural language can refer to different pluralities. By contrast, since the predicate calculus uses concepts only as predicates, it has no plural referring expressions. The plurality about which something is said by its sentences has to be presupposed, and different sentences cannot specify different pluralities. In natural language, pluralities are introduced and specified by means of plural referring expressions; in the predicate calculus, a plurality, which is unspecified by the sentence, is introduced by presupposing a domain of discourse.