1. Scope Theory vs. Lexical Theory of Even

The focus particle even introduces an implicature (or a presupposition) that is not available with a corresponding sentence without even; (1a) implies that Book A is unlikely to be read (the unlikely reading), although such an implication does not arise with John read Book A.1 It has been argued that this is due to a scalar presupposition of even (henceforth, ScalarP) (Karttunen and Peters 1979): assuming that even is a sentential operator, as in (1b), even presupposes that the relevant proposition p is the least likely proposition among the alternatives in C (a silent restrictor variable), as in (1c).2,3 The alternatives obtain by replacing the focused element with elements of the same type. For example, in (1b), C denotes a set of propositions obtained by replacing Book A with elements of the same type