Cantor's paradise
Cantor's Paradise is an expression of the Hilbert program that David Hilbert used at a commemorative event of the Westphalian Mathematical Society in honor of Karl Weierstrass on June 4, 1925 in Münster to describe the set theory and the infinite cardinal numbers that Georg Cantor had developed. The context of Hilbert's comment was his opposition to what he saw as the reductive attempts of Luitzen Egbertus Jan Brouwer : a description of what kind of mathematics was acceptable.
"1. Wherever there is only the slightest prospect, we want to carefully track down fruitful conceptual formations and conclusions, and cultivate, support and make them usable. Nobody should be able to drive us out of the paradise that Cantor created for us.
2. It is necessary to establish consistently the same certainty of reasoning as is present in ordinary lower number theory, which no one doubts and where contradictions and paradoxes arise only from our inattentiveness.
Obviously, these goals can only be achieved if we succeed in fully enlightening us about the essence of the infinite . "
literature
- David Hilbert: About the infinite. Mathematische Annalen, 95 (1), 1926, pp. 161-190.