Full plural logic
Alex Oliver, Timothy Smiley · Oxford University Press eBooks · 2016
Abstract This chapter presents a second topic neutral system of plural logic, full plural logic. It is obtained from the mid-plural system of the previous chapter by allowing plural variables to be bound by quantifiers and also by an operator symbolizing plurally unique description. Naturally, there are great gains in expressive power. The price is the loss of axiomatizability. A partial axiomatization is presented which combines the axioms for mid-plural logic with plural versions of those for singular logic. A plural version of comprehension is derived from the resulting axioms, and versions of plural choice are discussed.