Wed Feb 27, 2019
234 Moses Hall, 6–7:30 PM
|Working Group in the History and Philosophy of Logic, Mathematics, and Science
Stewart Shapiro (Ohio State University)
Superplurals, Groups, and Paradox
There are two views regarding definite plurals like “the students” in
The students gathered around the teacher. According to singularism, “the students” refers to a certain set-like
object, and (1) will be true if that set-like object has the cumulative property of gathering around the teacher. According to pluralism, “the students” refers to a primitive multiplicity of individuals, as familiar from plural logic, and (1) will be true if that multiplicity has that same cumulative property.
Singularism is the predominant view within linguistic semantics and pluralism is at least the received view among philosophers and logicians who invoke plurals. The latter is due in large part to the influence of George Boolos. The primary argument against singularism is that the view is prone to Russell’s paradox. Semanticists are, of course, aware of this threat of paradox, as illustrated by Fred Landman’s “First Amendment” for semantics:
The right to solve Russell’s Paradox some other time shall not be restricted.
The first purpose of this paper is to review the empirical data that supports linguistic singularism. The issue concerns the so-called “super-plurals”. The second, and main purpose, of the paper is to discharge the First Amendment and provide a potentialist theory of groups—the semantic value of plural expressions. On this theory, though it is always possible to form a group from a plurality, it is not necessary that we do so. The view ties in with both the nature of potential infinity generally and the recursive or generative nature of natural languages.