Michael Kremer Marti on Descriptions in Carnap ’ S S 2

This note is a friendly amendment to Marti’s analysis of the failure of Føllesdal’s argument that modal distinctions collapse in Carnap’s logic S2. Føllesdal’s argument turns on the treatment of descriptions. Marti considers how modal descriptions, which Carnap banned, might be handled; she adopts an approach which blocks Føllesdal’s argument, but requires a separate treatment of non-modal descriptions. I point out that a more general treatment of descriptions in S2 is possible, and indeed is implicit in Marti’s informal discussion, and that this treatment also blocks Føllesdal’s argument. Further, I show by a semantic argument that no revised version of Føllesdal’s argument could establish a collapse of modal distinctions. This note is a friendly amendment to Marti’s recent analysis1 of the failure of Føllesdal’s argument that modal distinctions collapse in Carnap’s modal logic S2. Føllesdal’s argument turns on the treatment of descriptions. Marti considers how descriptions containing modal operators, which Carnap banned from his system, might be handled; she adopts an approach to such descriptions which blocks Føllesdal’s argument, but is restricted to modal descriptions and requires a separate treatment of non-modal descriptions. I point out that a more general treatment of descriptions in Carnap’s logic is possible, and indeed is implicit in Marti’s informal discussion, and that this treatment also blocks Føllesdal’s argument for the collapse of modal distinctions. Further, I show by a semantic argument that no revised version of Føllesdal’s argument could establish such a collapse of modal distinctions. I will assume familiarity with Marti’s paper in the interest of brevity. Carnap’s contextual analysis of non-modal descriptions took the form: Q(ιxPx) =df ∃y(∀x(Px↔ x = y) &Qy) ∨ (C) (∼ ∃y∀x(Px↔ x = y) &Qa∗).2 As Marti points out, there is a difficulty in extending (C) to modal descriptions. For example, on (C) descriptions of the form ιx Px will denote a∗ in almost all cases (see below). The problem here can be brought out by considering the condition: