A lógica de Brouwer e o príncipio ex falso quodlibet

Abstract

From both a historical and philosophical point of view, the development of intuitionist logic by Arend Heyting is usually justified as the formalization of L.E.J. Brouwers ideas on the nature of logic and its relationship with mathematical activity. It is shown, however, that a more adequate understanding of the conception of logic developed in Brouwers works render the admission of the principle of inference known as ex falso quodlibet problematic as axiom of a formal system which purports to be the codification of his ideas and also that the justifications presented in favor of the acceptance of this principle in intuitionist logic are not satisfactory from a brouwerian point of view. Thus, despite its traditional identification as the most adequate formal system to formally represent Brouwers conception of logic, it is maintained that intuitionist logic should not be considered as such. Finally, it is argued that minimal logic, which differs from intuitionist logic precisely by not admitting the above mentioned principle as axiom, would be a formal system more adequate than Heytings intuitionist logic to be taken as a formal image of Brouwers conception of logic