Two types of indefinites: Hilbert & Russell

Gratzl, Norbert and Schiemer, Georg (13. April 2017): Two types of indefinites: Hilbert & Russell. In: IfCoLog Journal of Logics and their Applications, Vol. 4, No. 2: pp. 333-348

Abstract

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 (indexed) epsilon calculus and the proposed ρ-term approach to Russell’s indefinites.

• Item Type: Journal article
• EU Funded Grant Agreement Number: 675415
• EU Projects: Horizon 2020 > Marie Skłodowska Curie Actions > Marie Skłodowska-Curie Innovative Training Networks > 675415: Diaphora: Philosophical Problems, Resilience and Persistent Disagreement
• Form of publication: Publisher's Version
• Keywords: Indefinite descriptions, epsilon terms, choice semantics, Hilbert, Russell
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic; Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Diaphora: Logic and Paradox
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 100 Philosophy and Psychology > 160 Logic
• Annotation: 978-1-84890-234-3
• Language: English