ABSTRACT
Versions of AR are often conceived and presented with the provision of an applied PW-semantics for quantified modal logic (QML) as the immediate aim.1 Indeed, it is often the case, and especially in the earlier period of the literature, that the conceptual and ontological intentions of AR PW-semanticists are invisible to the reader. I begin this chapter by revisiting the ‘intuitive’ application that Kripke (1963) suggests for his own semantics.2 Many hold that, when measured against compelling modal intuitions and other independent sources of modal opinion, the intuitive application does well in outcome – i.e. in the patterns of modal theses that it validates. Yet philosophically, the intuitive application is variously and seriously problematic, if not downright unacceptable, from an AR standpoint. The challenge to AR is to provide an applied semantics for QML that matches the intuitive application in the acceptability of its outcomes for modal validity but which is also, at least from the AR standpoint, philosophically satisfactory. The philosophical problems emerge as follows.
