This article investigates the nature of argumenthood and adjuncthood, through an examination of the behaviour of the internal arguments of two classes of motion verbs in English. A highly modular view is put forth, in which three separate distinctions influencing argument-like or adjunct- like behaviour must be recognized: aspectual versus thematic licensing, structural versus inherent case assignment, and referentiality versus non-referentiality. Of these three, only referentiality is a graded rather than a binary distinction. The distinction between aspectual and thematic licensing is developed and elucidated. A picture emerges in which aspectual structure may itself be thematically licensed by a verb, and this aspectual structure may have its own arguments, which are then indirectly licensed by the verb. Cognate objects and Romance measure phrases are also discussed in light of these theoretical conclusions.