Carnap's theory of descriptions and its problems (Q969430)

\textit{R. Carnap} offered, e.g.\ in his [Meaning and necessity. A study in semantics and modal logic. Chicago: The University of Chicago Press (1947; Zbl 0034.00106)], not only a first-order modal logic, but also a theory of descriptions in its context. Unfortunately he chose, without explanation, two critical restrictions to the form of descriptions. Using self-predication principles, i.e.\ principles of the form \(\phi(\iota{x}\phi(x))\) for suitably chosen formulas \(\phi\), the author critically discusses previous approaches of \textit{D. Føllesdal} [Referential opacity and modal logic. London: Routledge (2004; Zbl 1118.03301)] and \textit{G. Martí} [J. Philos. Log. 23, No. 6, 575--593 (1994; Zbl 0812.03006)] to give the explanations which are missing in Carnap's presentation. He argues that Martí's solution of the problem is inadequate, and that Føllesdal's arguments partly fail, but can suitably be relaxed. However, also this author argues that Carnap's theory of descriptions is inadequate in dealing with improper descriptions.