Bulletin of the Section of Logic 48 (4):299-317 (2019)

Authors
Nils Kürbis
University of Lodz
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.
Keywords definite descriptions  binary quantifier  term forming operator  Lambert's Law  intuitionist negative free logic  natural deduction
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DOI 10.18778/0138-0680.48.4.04
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References found in this work BETA

A General Theory of Abstraction Operators.Neil Tennant - 2004 - Philosophical Quarterly 54 (214):105-133.
A Free Logic with Simple and Complex Predicates.Karel Lambert & Ermanno Bencivenga - 1986 - Notre Dame Journal of Formal Logic 27 (2):247-256.

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