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Gratzl, Norbert (2009): Definite Descriptions: Language, Logic, and Elimination. In: Hieke, Alexander; Leitgeb, Hannes (eds.) : Reduction – Abstraction – Analysis Proceedings of the 31th International Ludwig Wittgenstein-Symposium in Kirchberg 2008. Publications of the Austrian Ludwig Wittgenstein Society. New Series., Ontos Verlag pp. 353-361
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Definite descriptions are in the focus of philosophical discussion at least since Russell's famous paper "On Denoting". We present in this paper a logic with descriptions in Russell's spirit. The formulation, however, is closely related to Schütte's development of predicate logic, i.e. the formulation of the calculus uses positive- and negative-parts. With respect to this slightly more sophisticated formulation it is possible to formalize Russell's convention that is originally stated in the metalanguage of his theory of descriptions within our calculus. In this paper we prove an elimination theorem for this calculus.