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Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic

Kürbis, N; (2019) Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic. Bulletin of the Section of Logic , 48 (4) pp. 299-317. 10.18778/0138-0680.48.4.04. Green open access

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Abstract

Sentences containing definite descriptions, expressions of the form `The F', can be formalised using a binary quantier that forms a formula out of two predicates, where ℩x[F;G] is read as `The F is G'. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INF℩ of intuitionist negative free logic extended by such a quantier, which was presented in [4], INF℩ is first compared to a system of Tennant's and an axiomatic treatment of a term forming ℩ operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INF℩ in which the G of ℩x[F;G] is restricted to identity. INF℩ is then compared to an intuitionist version of a system of Lambert's which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion.

Type: Article
Title: Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic
Open access status: An open access version is available from UCL Discovery
DOI: 10.18778/0138-0680.48.4.04
Publisher version: https://doi.org/10.18778/0138-0680.48.4.04
Language: English
Additional information: This work is licensed under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License.
Keywords: definite descriptions, binary quantifier, term forming operator, Lambert's Law, intuitionist negative free logic, natural deduction
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10093859
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