  Since we are evaluating (6) with regard to the intended interpretation of its language, the w-extension of ‘P’ that is returned by its intension, for any world w, is the (perhaps empty) set of John's pets in w and that of ‘M’ is the set of mammals in w. Hence, if w is a world where John has a pet canary — COBOL, say — COBOL is in the w-extension of ‘P’ but not that of ‘M’ , i.e., ‘∀x(Px → Mx)’ is false at w and, hence, by the truth condition (9), (6) is false at the actual world — that is, (6) is false simpliciter, as it should be. 