Intuitionistic Logic Considered as An Extension of Classical Logic: Some Critical Remarks

JAVIER LEGRIS JORGE MOLINA

PHILOSOPHIA SCIENTIAE

Kimé

Lugar: Paris; Año: 2001 vol. 5 p. 27 - 50

1281-2463

In this paper we analyze the consideration of intuitionistic logic as an extension of classical logic. This point of view has been sustained explicitly by Jan Lukasiewicz on the basis of a mapping of classical propositional logic into intuitionistic propositional logic due to Kurt Gödel in 1933. Simultaneously with Gödel, Gerhard Gentzen had proposed another mapping pf 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.