I explore two alternatives to post-suppositions for generating cumulative readings of sentences with multiple modified numerals. The first uses higher-order dynamic generalized quantifiers (GQs), functions whose ‘trace’ is itself typed as a dynamic GQ. Such functions, though a hop-and-a-skip up the type hierarchy from dynamic GQs, are already available to any standard-issue Montagovian dynamic semanticist, and dealing with them compositionally requires nothing beyond whatever machinery already underwrites quantifiers in object position, scope ambiguity, and so on (though the analysis is presented using a handy continuations-oriented tower notation). I build on this theory by exploring a type-theoretic elaboration of it (technically, in terms of subtype polymorphism) that rules out arguably unattested ‘pseudo-cumulative’ readings.
Second, I show that these steps (higher-order dynamic GQs subtyping) are unnecessary if the usual ‘point-wise’ dynamic semantics of Dynamic Predicate Logic or Compositional DRT, where propositions are typed as relations on assignments, is replaced with an update semantics, where propositions are typed as functions from sets of assignments into sets of assignments. Conservative update-semantic meanings for modified numerals — direct analogs of their point-wise counterparts — automatically yield cumulative readings and fail to derive pseudo-cumulative readings. This gives an argument for an update semantics in the anaphoric domain (so far as I know the first of its kind).
I compare these two kinds of analyses with each other and consider their relation to post-suppositions in semantic theory more generally, concluding: (i) the theories canvassed here have modest empirical advantages over post-suppositions; (ii) the update-theoretic account offers the most direct route to an empirically adequate analysis of modified numerals; (iii) the reasons for this turn out to be specific to modified numerals; theories of other ‘post-suppositional’ phenomena are better formulated with higher-order GQs.