Quotes About Intuitionism

Every Tuesday, James Fulton (and later, Orville Lever) stood in the downstairs drawing room and lectured on the intricacies of his science. Lectured on the implications of European maintenance deviations on Intuitionism, expounded on the gloom of the shaft and how it does not merely echo the gloom inside every living creature, but duplicates it perfectly. Afterwards there were mint juleps for everyone . . .

Respecting infinite sets, for example, Intuitionism is rabidly anti-Cantor and Formalism staunchly pro-Cantor, even though both Formalism and Intuitionism are anti-Plato and Cantor is a diehard Platonist. Which, migrainous or not, means we're back to metaphysics: the modern wrangle over math's procedures is ultimately a dispute over the ontological status of math entities.

If Hilbert's view prevails over intuitionism, as appears to be the case, then I see in this a decisive defeat of the philosophical attitude of pure phenomenology, which thus proves to be insufficient for the understanding of creative science even in the area of cognition that is most primal and most readily open to evidence – mathematics.

From an intuitionistic standpoint, mathematics, when correctly carried on, would not need any justification from without, a buttress from the side or a foundation from below: it would wear its own justification on its face.