Modal translation: the relevance of worlds - Hanmer, Paul (2019)
Advanced or extraordinary modal sentences represent a challenge to the expressive adequacy of David Lewis’ (1968) modal translation scheme. Specifically, modal sentences that ought to be true (by the lights of genuine realism) are translated as false by the scheme, and vice versa. For example, the modal sentence “necessarily, there is a plurality of worlds” is true by the postulates of genuine realism but is interpreted as false by the scheme. The analysans is false because it states that at every world there is a plurality of worlds – that every world must have worlds as parts; however, Lewis states that worlds do not overlap (Lewis 1986a, page 2). The problem afflicts the genuine realist interpretation of sentences across several “domains of discourse” e.g. modal sentences about set theory, natural properties and propositions. In the absence of a mechanism to preserve the truth-value of advanced modal sentences the logical, semantic and expressive resources of modal translation may be confounded. It is imperative, therefore, that genuine realism secures an interpretation of advanced modal sentences capable of preserving their truth-value. We argue that the truth-value of advanced modal sentences can be preserved using the standard conceptual repertoire of genuine realism. The truth or falsity of advanced modal sentences can be preserved by a set-theoretic interpretation of their content. Furthermore, we are able to secure, as a component of modal translation, the use of the primitive predicate “x is in possible world y” (Lewis 1968 [1983], page 27). Hence, this solution is premised on the explicit use of the predicate expression “at a world w”. As such, we are able to distinguish our thesis from John Divers’ Redundancy Theory recommended by him as the solution most conducive to genuine realism.