In a recent paper, Wedgwood (2011) launches a simultaneous defense of intention recognition and a critique of the alleged neglect of cognition in interactional approaches to communicative interaction. In this paper, I argue that this simultaneous critique and defense is deeply flawed on a number of counts. First, the “looser” notion of intention that Wedgwood proposes glosses over and even confounds various levels or types of intention, and for this reason is ultimately not falsifiable. Second, in the course of his argumentation, he confounds intention with intentionality and agency. Third, his claim that a focus on “local” intentions offers a more “fine-grained” and “explanatory analysis” is completely unwarranted in light of close examination of the data at hand. I argue that such an approach instead generates speculation that is analytically unproductive, and, does not account for the cognitively interdependent inferences that underlie conversational interaction in addition to traditional monadic inferential processes. It is concluded that further discussions about the requirements that interaction places on cognition, including the question of the place of intention and intentionality can be productive, but only if researchers are cognizant of the different ways in which intention has been defined, and also the different analytical work to which intention is put by scholars in pragmatics.