Preintuitionism - Other Pre-Intuitionists

Other Pre-Intuitionists

The above examples only include the works of Poincaré, and yet Brouwer named other mathematicians as Pre-Intuitionists too; Borel and Lebesgue. Other mathematicians such as Hermann Weyl (who eventually became disenchanted with intuitionism, feeling that it places excessive strictures on mathematical progress) and Leopold Kronecker also played a role - though they are not cited by Brouwer in his definitive speech.

In fact Kronecker might be the most famous of the Pre-Intuitionists for his singular and oft quoted phrase, "God made the natural numbers; all else is the work of man."

Kronecker goes in almost the opposite direction from Poincaré, believing in the natural numbers but not the law of the excluded middle. He was the first mathematician to express doubt on non-constructive existence proofs. That is, proofs that show that something must exist because it can be shown that it is "impossible" for it not to.