 This thread—that quantifier expressions signify second-order relations—was not picked up by any of Aristotle’s medieval followers (as far as we know). Instead, they picked up on the fact that the two terms have different status: the first combines with the quantifier expression to form a noun phrase (as we now say), which is the subject of the sentence, whereas the second is a verb phrase constituting the predicate. This led them to focus on what the subject—all men, some dogs, no sailors—signified, which conceptually seems to be a harder question. One might surmise that all men signifies every man (or the set of men), and that some dogs signifies some particular dog, but what about no sailors? In fact, one can show that approaches like these are doomed to  failure.[5]  The modern “solution” is that noun phrases signify sets of sets of individuals, so that, for example some dogs signifies the set of sets containing at least one dog—but that appears to require a more abstract and mathematical approach to semantics than the idea, which is at least implicit in Aristotle, that quantifier phrases signify relations between (the denotations of) terms.