Authors
Nils Kürbis
University of Lodz
Abstract
This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions recommended here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’.
Keywords Free logic  Definite descriptions  Proof theory  Normalisation  Intuitionist logic  Binary quantifiers  Term forming operators
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DOI 10.12775/llp.2020.024
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References found in this work BETA

Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.
Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.
A Natural Extension of Natural Deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
Proof and Falsity: A Logical Investigation.Nils Kürbis - 2019 - Cambridge, UK: Cambridge University Press.

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