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This paper compares Hilbert’s -terms and Russell’s approach to indefinite descriptions, Russell’s indefinites for short. Despite the fact that both accounts are usually taken to express indefinite descriptions, there is a number of dissimilarities. Specifically, it can be shown that Russell indefinites - expressed in terms of a logical ρ-operator - are not directly representable in terms of their corresponding -terms. Nevertheless, there are two possible translations of Russell indefinites into epsilon logic. The first one is given in a language with classical -terms. The second translation is based on a refined account of epsilon terms, namely indexed -terms. In what follows we briefly outline these approaches both syntactically and semantically and discuss their respective connections; in particular, we establish two equivalence results between the epsilon calculus and the proposed ρ-term approach to Russell’s indefinites.
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Arbitrary Reference.Wylie Breckenridge & Ofra Magidor - 2012 - Philosophical Studies 158 (3):377-400.
Completeness of Indexed Varepsilon -Calculus.G. E. Mints & Darko Sarenac - 2003 - Archive for Mathematical Logic 42 (7):617--625.

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