Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic
Bulletin of the Section of Logic (2019)
- Volume: 48, Issue: 4
- ISSN: 0138-0680
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topNils Kürbis. "Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic." Bulletin of the Section of Logic 48.4 (2019): null. <http://eudml.org/doc/295568>.
@article{NilsKürbis2019,
abstract = {Sentences containing definite descriptions, expressions of the form `The F', can be formalised using a binary quantier that forms a formula out of two predicates, where ℩x[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 INF℩ of intuitionist negative free logic extended by such a quantier, which was presented in [4], INF℩ is first compared to a system of Tennant's and an axiomatic treatment of a term forming ℩ operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INF℩ in which the G of ℩x[F;G] is restricted to identity. INF℩ 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.},
author = {Nils Kürbis},
journal = {Bulletin of the Section of Logic},
keywords = {definite descriptions; binary quantifier; term forming operator; Lambert's Law; intuitionist negative free logic; natural deduction},
language = {eng},
number = {4},
pages = {null},
title = {Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic},
url = {http://eudml.org/doc/295568},
volume = {48},
year = {2019},
}
TY - JOUR
AU - Nils Kürbis
TI - Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic
JO - Bulletin of the Section of Logic
PY - 2019
VL - 48
IS - 4
SP - null
AB - Sentences containing definite descriptions, expressions of the form `The F', can be formalised using a binary quantier that forms a formula out of two predicates, where ℩x[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 INF℩ of intuitionist negative free logic extended by such a quantier, which was presented in [4], INF℩ is first compared to a system of Tennant's and an axiomatic treatment of a term forming ℩ operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INF℩ in which the G of ℩x[F;G] is restricted to identity. INF℩ 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.
LA - eng
KW - definite descriptions; binary quantifier; term forming operator; Lambert's Law; intuitionist negative free logic; natural deduction
UR - http://eudml.org/doc/295568
ER -
References
top- [1] M. Fitting and R. L. Mendelsohn, First-Order Modal Logic, Dordrecht, Boston, London, Kluwer, 1998. https://doi.org/10.1007/978-94-011-5292-1
- [2] Andrzej Indrzejczak, Cut-free modal theory of definite descriptions, [in:] G. Metcalfe, G. Bezhanishvili, G. D'Agostino and T. Studer (eds.), Advances in Modal Logic, Vol. 12, pp. 359–378, London, College Publications, 2018.
- [3] Andrzej Indrzejczak, Fregean description theory in proof-theoretical setting, Logic and Logical Philosophy, Vol. 28, No. 1 (2018), pp. 137–155. http://dx.doi.org/10.12775/LLP.2018.008
- [4] N. Kürbis, A binary quantifier for definite descriptions in intuitionist negative free logic: Natural deduction and normalisation, Bulletin of the Section of Logic, Vol. 48, No. 2 (2019), pp. 81–97.https://doi.org/10.18778/0138-0680.48.2.01
- [5] K. Lambert, A free logic with simple and complex predicates, Notre Dame Journal of Formal Logic, Vol. 27, No. 2 (1986), pp. 247–256. https://doi.org/10.1305/ndjfl/1093636615
- [6] K. Lambert, Free logic and definite descriptions, [in:] E. Morscher and A. Hieke (eds.), New Essays in Free Logic in Honour of Karel Lambert, Dordrecht, Kluwer, 2001. https://doi.org/10.1007/978-94-015-9761-6_2
- [7] E. Morscher and P. Simons, Free logic: A fifty-year past and an open future, [in:] E. Morscher and A. Hieke (eds.), New Essays in Free Logic in Honour of Karel Lambert, Dortrecht, Kluwer, 2001. https://doi.org/10.1007/978-94-015-9761-6_1
- [8] N. Tennant, Natural Logic, Edinburgh, Edinburgh University Press, 1978.
- [9] N. Tennant, A general theory of abstraction operators, The Philosophical Quarterly, Vol. 54, No. 214, pp. 105–133. https://doi.org/10.1111/j.0031-8094.2004.00344.x
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