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

Nils Kürbis
University of Lodz
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
Categories (categorize this paper)
DOI 10.18778/0138-0680.48.4.04
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

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.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

On the Philosophical Foundations of Free Description Theory.Karel Lambert - 1987 - History and Philosophy of Logic 8 (1):57-66.
Definite Descriptions and Negative Existential Quantifiers.Paul Elbourne - 2018 - Philosophical Studies 175 (7):1597-1612.
Definite Descriptions: Language, Logic, and Elimination.Norbert Gratzl - 2009 - In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. pp. 355.
Are “Attributive” Uses of Definite Descriptions Really Attributive?Ilhan Inan - 2006 - Kriterion - Journal of Philosophy 20 (1):7-13.
Interpretations of Intuitionist Logic in Non-Normal Modal Logics.Colin Oakes - 1999 - Journal of Philosophical Logic 28 (1):47-60.
A Topological Logic of Action.Krister Segerberg - 1984 - Studia Logica 43 (4):415 - 419.
Co-Extensive Theories and Unembedded Definite Descriptions.Alex Barber - 2005 - In Reinaldo Elugardo & Robert J. Stainton (eds.), Ellipsis and Nonsentential Speech. Springer. pp. 185–201.
Free Logic: Selected Essays.Karel Lambert - 2002 - Cambridge University Press.
Incomplete Symbols — Definite Descriptions Revisited.Norbert Gratzl - 2015 - Journal of Philosophical Logic 44 (5):489-506.


Added to PP index

Total views
20 ( #483,223 of 2,326,738 )

Recent downloads (6 months)
20 ( #31,810 of 2,326,738 )

How can I increase my downloads?


My notes