Definite Descriptions in Intuitionist Positive Free Logic

Logic and Logical Philosophy 30:1 (2020)
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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’.

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Author's Profile

Nils Kürbis
Ruhr-Universität Bochum

References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge: Harvard University Press.
Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.
The justification of deduction.Michael Dummett - 1978 - In Truth and other enigmas. Cambridge: Harvard University Press.

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