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Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic

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Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic. / Kürbis, Nils.

In: Bulletin of the Section of Logic, Vol. 48, No. 4, 2019, p. 299-317.

Research output: Contribution to journalArticle

Harvard

Kürbis, N 2019, 'Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic', Bulletin of the Section of Logic, vol. 48, no. 4, pp. 299-317. https://doi.org/10.18778/0138-0680.48.4.04

APA

Kürbis, N. (2019). Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic. Bulletin of the Section of Logic, 48(4), 299-317. https://doi.org/10.18778/0138-0680.48.4.04

Vancouver

Kürbis N. Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic. Bulletin of the Section of Logic. 2019;48(4):299-317. https://doi.org/10.18778/0138-0680.48.4.04

Author

Kürbis, Nils. / Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic. In: Bulletin of the Section of Logic. 2019 ; Vol. 48, No. 4. pp. 299-317.

Bibtex Download

@article{666b6e9e2b804f92acbaf65f2bae3463,
title = "Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic",
abstract = "Sentences containing definite descriptions, expressions of the form {\textquoteleft}The F{\textquoteright}, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as {\textquoteleft}The F is G{\textquoteright}. 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 (K{\"u}rbis 2019), INFι is first compared to a system of Tennant{\textquoteright}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{\textquoteright}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",
author = "Nils K{\"u}rbis",
year = "2019",
doi = "https://doi.org/10.18778/0138-0680.48.4.04",
language = "English",
volume = "48",
pages = "299--317",
journal = "Bulletin of the Section of Logic",
issn = "0138-0680",
publisher = "Department of Logic, University of Lodz",
number = "4",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic

AU - Kürbis, Nils

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - definite descriptions

KW - binary quantifier

KW - term forming operator

KW - Lambert's Law

KW - intuitionist negative free logic

KW - natural deduction

U2 - https://doi.org/10.18778/0138-0680.48.4.04

DO - https://doi.org/10.18778/0138-0680.48.4.04

M3 - Article

VL - 48

SP - 299

EP - 317

JO - Bulletin of the Section of Logic

JF - Bulletin of the Section of Logic

SN - 0138-0680

IS - 4

ER -

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