Quantification and Second-Order Monadicity

Abstract

The first part of this paper reviews some developments regarding the apparent mismatch between the logical and grammatical forms of quantificational constructions like 'Pat kicked every bottle'. I suggest that (even given quantifier-raising) many current theories still posit an undesirable mismatch. But all is well if we can treat determiners (words like 'every', 'no', and 'most') as second-order monadic predicates without treating them as predicates satisfied by ordered pairs of sets. Drawing on George Boolos's construal of second-order quantification as plural quantification, I argue that we can and should view determiners as predicates satisfied (plurally) by ordered pairs each of which associates an entity with a truth-value (t or f). The idea is 'every' is satisfied by some pairs iff every one of them associates its entity with t. It turns out that this provides a kind of explanation for the "conservativity" of determiners. And it lets us say that concatenation signifies predicate-conjunction even in phrases like 'every bottle' and 'no brown dog'.