ABSTRACT
There are various arguments in favour of, or against, each of these options of logical representation, but we shall not dwell on the pros and cons in more detail because this would require a careful analysis (see Bealer [4] and Halbach [16]). Instead we are going to concentrate on a particular problem affecting modalities if regarded as unary predicates of sentences, i.e., according to the extensionalist version of the predicate view from above. This position has been held and defended most notably by Quine [24, 23]. We think that there would be very good reasons for preferring this account if it was not threatened by inconsistency: Montague [21] was the first to notice that the predicate version of the acknowledged modal system T is inconsistent if it is joined with arithmetic. This is due to the existence of self-referential expressions, which is a consequence of Godel’s diagonalisation lemma, which is in turn derivable from even weak systems of arithmetic. From this Montague concluded:
Thus if necessity is to be treated syntactically, that is, as a predicate of sentences, as Carnap and Quine have urged, then virtually all of modal logic [ . . . ] must be sacrificed.
