We investigate the interaction of structural and contextual constraints on the on-line generation of three types of Scalar Implicature, (a) the disjunction: “A or B” >> “either A or B but not both”, (b) the partitive NP: “some of the Fs”>> “at least one but not all of the Fs” and (c) ad hoc context dependent scales. In theoretical linguistics, according to the structural approach (Chierchia, 2004; Levinson 2000) Scalar Implicatures (SIs) are generated whenever certain constraints on the semantic properties of the linguistic structure are satisfied. According to the pragmatic approach, structural properties are a necessary but not sufficient condition, since for SIs to be generated there ought to be further contextual constraints (Carston, 1998; Recanati, 2003; Sperber & Wilson, 1995). The linguistic debate can be addressed experimentally, but studies in this small but growing area are not reaching a consensus. Single sentence truth value judgment tasks (Bott & Noveck, 2004; Noveck & Posada, 2003) and studies on the visual-world eye-tracking paradigm (Storto & Tanenhaus, 2005; Huang & Snedeker, 2005) support the pragmatic approach but do not explicitly manipulate discourse context constraints. Text comprehension studies that do so (Bezuidenhout & Cutting, 2002; Bezuidenhout & Morris, 2004, Breheny, Katsos & Williams in press) have been ambivalent. We present one off-line and three on-line text comprehension experiments that address the previous shortcomings and conclude in favor of the pragmatic approach. The linguistic debate is related to the psycholinguistic discussion of the factors that constrain sentence processing. We discuss our findings with regards to the modular versus interactive nature of the human parser.