TY  - JOUR
TI  - Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic
EP  - 317
AV  - public
Y1  - 2019/12/31/
KW  - definite descriptions
KW  -  binary quantifier
KW  -  term forming operator
KW  -  Lambert's Law
KW  -  intuitionist negative free logic
KW  -  natural deduction
ID  - discovery10093859
N2  - 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.
PB  - Uniwersytet Lodzki (University of Lodz)
N1  - This work is licensed under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License.
IS  - 4
VL  - 48
SP  - 299
JF  - Bulletin of the Section of Logic
A1  - Kürbis, N
SN  - 2449-836X
UR  - https://doi.org/10.18778/0138-0680.48.4.04
ER  -