In this paper, we argue against theories that seek to sever external arguments from verbs such as Kratzer (1996), as well as Bale's (2007) generalization that only intransitive and not transitive verbs take their external arguments directly. Using subjectless presuppositions introduced by again, we show that subjectless presuppositions are permitted with optionally intransitive verbs only when they appear with an optional internal argument. These facts are not predicted by approaches like Kratzer's, where external arguments associate with intransitive verbs via Event Identification, nor are they predicted by those having the verb root directly introduce the external argument, such as Bale's. Rather, we propose that the availability of subjectless presuppositions is not determined by the lexical semantics of the verbal root, but by the syntactic structure in which a root is embedded. In so doing, we propose that verbal roots take thematic roles as arguments, along with an individual and event argument. These thematic roles are introduced by functional heads within the verbal projection, such as little v and Voice, and verbal roots take these thematic role denotations directly as arguments. This allows us to account for the apparent flexibility of these verbs in allowing for subjectless presuppositions with optional arguments, and further develops a novel theory of root denotations and argument structure.