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Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)299-317
JournalBulletin of the Section of Logic
Volume48
Issue number4
DOIs
Published2019

Documents

  • KurbisIotaNatDedIntII

    KurbisIotaNatDedIntII.pdf, 133 KB, application/pdf

    Uploaded date:09 Mar 2020

    Version:Accepted author manuscript

King's Authors

Abstract

Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[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 INFι of intuitionist negative free logic extended by such a quantifier, which was presented in (Kürbis 2019), INFι is first compared to a system of Tennant’s and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INFι in which the G of ιx[F, G] is restricted to identity. INFι 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.

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