Intuitionism in the context of "L. E. J. Brouwer"

Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of excluded middle and double negation elimination, which are fundamental inference rules in classical logic.

Formalized intuitionistic logic was originally developed by Arend Heyting to provide a formal basis for L. E. J. Brouwer's programme of intuitionism. From a proof-theoretic perspective, Heyting’s calculus is a restriction of classical logic in which the law of excluded middle and double negation elimination have been removed. Excluded middle and double negation elimination can still be proved for some propositions on a case by case basis, however, but do not hold universally as they do with classical logic. The standard explanation of intuitionistic logic is the BHK interpretation.

Giovanni Papini (9 January 1881 – 8 July 1956) was an Italian journalist, essayist, novelist, short story writer, poet, literary critic, and philosopher. A controversial literary figure of the early and mid-twentieth century, he was the earliest and most enthusiastic representative and promoter of Italian pragmatism. Papini was admired for his writing style and engaged in heated polemics. Involved with avant-garde movements such as futurism and post-decadentism, he moved from one political and philosophical position to another, always dissatisfied and uneasy: he converted from anti-clericalism and atheism to Catholicism, and went from convinced interventionism – before 1915 – to an aversion to war. In the 1930s, after moving from individualism to conservatism, he finally became a fascist, while maintaining an aversion to Nazism.

As one of the founders of the journals Leonardo (1903) and Lacerba (1913), he conceived literature as "action" and gave his writings an oratory and irreverent tone. Though self-educated, he was an influential iconoclastic editor and writer, with a leading role in Italian futurism and the early literary movements of youth. Working in Florence, he actively participated in foreign literary philosophical and political movements such as the French intuitionism of Bergson and the Anglo-American pragmatism of Peirce and James. Promoting the development of Italian culture and life with an individualistic and dreamy conception of life and art, he acted as a spokesman for Roman Catholic religious beliefs.