Intuitionistic logic considered as an extension of classical logic : some critical remarks

Javier Legris; Jorge A. Molina

Philosophia Scientiae (2001)

  • Volume: 5, Issue: 2, page 27-50
  • ISSN: 1281-2463

Abstract

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In this paper we analyze the consideration of intuitionistic logic as an extension of classical logic. This — at first sight surprising — point of view has been sustained explicitly by Jan Łukasiewicz on the basis of a mapping of classical propositional logic into intuitionistic propositional logic by Kurt Gödel in 1933. Simultaneously with Gödel, Gerhard Gentzen had proposed another mapping of Peano´s arithmetic into Heyting´s arithmetic. We shall discuss these mappings in connection with the problem of determining what are the logical symbols that properly express the idiosyncracy of intuitionistic logic. Many philosophers and logicians do not seem to be sufficiently aware of the difficulties that arise when classical logic is considered as a subsystem of intuitionistic logic. As an outcome of the whole discussion these difficulties will be brought out. The notion of logical translation will play an essential role in the argumentation and some consequences related to the meaning of logical constants will be drawn.

How to cite

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Legris, Javier, and Molina, Jorge A.. "Intuitionistic logic considered as an extension of classical logic : some critical remarks." Philosophia Scientiae 5.2 (2001): 27-50. <http://eudml.org/doc/103660>.

@article{Legris2001,
abstract = {In this paper we analyze the consideration of intuitionistic logic as an extension of classical logic. This — at first sight surprising — point of view has been sustained explicitly by Jan Łukasiewicz on the basis of a mapping of classical propositional logic into intuitionistic propositional logic by Kurt Gödel in 1933. Simultaneously with Gödel, Gerhard Gentzen had proposed another mapping of Peano´s arithmetic into Heyting´s arithmetic. We shall discuss these mappings in connection with the problem of determining what are the logical symbols that properly express the idiosyncracy of intuitionistic logic. Many philosophers and logicians do not seem to be sufficiently aware of the difficulties that arise when classical logic is considered as a subsystem of intuitionistic logic. As an outcome of the whole discussion these difficulties will be brought out. The notion of logical translation will play an essential role in the argumentation and some consequences related to the meaning of logical constants will be drawn.},
author = {Legris, Javier, Molina, Jorge A.},
journal = {Philosophia Scientiae},
language = {eng},
number = {2},
pages = {27-50},
publisher = {Éditions Kimé},
title = {Intuitionistic logic considered as an extension of classical logic : some critical remarks},
url = {http://eudml.org/doc/103660},
volume = {5},
year = {2001},
}

TY - JOUR
AU - Legris, Javier
AU - Molina, Jorge A.
TI - Intuitionistic logic considered as an extension of classical logic : some critical remarks
JO - Philosophia Scientiae
PY - 2001
PB - Éditions Kimé
VL - 5
IS - 2
SP - 27
EP - 50
AB - In this paper we analyze the consideration of intuitionistic logic as an extension of classical logic. This — at first sight surprising — point of view has been sustained explicitly by Jan Łukasiewicz on the basis of a mapping of classical propositional logic into intuitionistic propositional logic by Kurt Gödel in 1933. Simultaneously with Gödel, Gerhard Gentzen had proposed another mapping of Peano´s arithmetic into Heyting´s arithmetic. We shall discuss these mappings in connection with the problem of determining what are the logical symbols that properly express the idiosyncracy of intuitionistic logic. Many philosophers and logicians do not seem to be sufficiently aware of the difficulties that arise when classical logic is considered as a subsystem of intuitionistic logic. As an outcome of the whole discussion these difficulties will be brought out. The notion of logical translation will play an essential role in the argumentation and some consequences related to the meaning of logical constants will be drawn.
LA - eng
UR - http://eudml.org/doc/103660
ER -

References

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