According to one view of linguistic information (Karttunen, 1974; Stalnaker, 1974), a speaker can convey contextually new information in one of two ways: (a) by "asserting" the content as new information; or (b) by "presupposing" the content as given information which would then have to be "accommodated." This distinction predicts that it is conversationally more appropriate to assert implausible information rather than presuppose it (e.g., von Fintel, 2008; Heim, 1992; Stalnaker, 2002). A second view rejects the assumption that presuppositions are accommodated; instead, presuppositions are assimilated into asserted content and both are correspondingly open to challenge (e.g., Gazdar, 1979; van der Sandt, 1992). Under this view, we should not expect to find a difference in conversational appropriateness between asserting implausible information and presupposing it. To distinguish between these two views of linguistic information, we performed two self-paced reading experiments with an on-line stops-making-sense judgment. The results of the two experiments--using the presupposition triggers "the" and "too"--show that accommodation is inappropriate (makes less sense) relative to non-presuppositional controls when the presupposed information is implausible but not when it is plausible. These results provide support for the first view of linguistic information: the contrast in implausible contexts can only be explained if there is a presupposition-assertion distinction and accommodation is a mechanism dedicated to reasoning about presuppositions.