Intuitionistic logic considered as an extension of classical logic : some critical remarks
Philosophia Scientiae, Tome 5 (2001) no. 2, p. 27-50
Dans cet article, nous analysons la conception de la logique intuitionniste comme une extension de la logique classique. Ce point de vue - surprenant au premier abord - a été explicitement soutenu par Jan Łukasiewicz sur la base d'une projection de la logique propositionnelle classique dans la logique propositionnelle intuitionniste, réalisée par Kurt Gödel en 1933. Au même moment, Gerhard Gentzen proposait une autre projection de l'arithmétique de Peano dans l'arithmétique de Heyting. Nous discutons ces projections en lien avec le problème de la détermination des symboles logiques qui expriment adéquatement les idiosyncrasies de la logique intuitionniste. De nombreux philosophes et logiciens ne semblent pas suffisamment conscients des difficultés soulevées par le fait de considérer la logique classique comme un sous-système de logique intuitionniste. Un résultat de cette discussion sera de faire ressortir ces difficultés. La notion de traduction logique jouera un rôle essentiel dans l'argumentation, et nous esquisserons quelques conséquences concernant la signification des constantes logiques.
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.
@article{PHSC_2001__5_2_27_0,
     author = {Legris, Javier and Molina, Jorge A.},
     title = {Intuitionistic logic considered as an extension of classical logic : some critical remarks},
     journal = {Philosophia Scientiae},
     publisher = {\'Editions Kim\'e},
     volume = {5},
     number = {2},
     year = {2001},
     pages = {27-50},
     language = {en},
     url = {http://www.numdam.org/item/PHSC_2001__5_2_27_0}
}
Legris, Javier; Molina, Jorge A. Intuitionistic logic considered as an extension of classical logic : some critical remarks. Philosophia Scientiae, Tome 5 (2001) no. 2, pp. 27-50. http://www.numdam.org/item/PHSC_2001__5_2_27_0/

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