The author proposes a new variant of semantic minimalism combining anti-intentionalism (the view according to which the semantic content of uttered sentences is independent of speaker intentions) with the rejection of propositionalism (the view according to which the semantic content of uttered sentences always reaches the level of a proposition, i.e. a content potentially figuring as the object of an attitude). Investigating the specifics of demonstrative expressions as a touchstone for her minimalist account, by decoupling the notion of a truth-condition from that of a proposition the author manages to stay within the bounds of a truth-conditional account, while taking into account that the referents of demonstrative expressions cannot be determined without reference to speaker intentions.