Two applications of dynamic constructivism: Brouwer’s continuity principle and choice sequences in formal topology

Abstract

We are here to celebrate a master, namely L. E. J. Brouwer, and one hundred years from the birth of his intuitionism. I believe that the best way to keep Brouwer alive is to try and go beyond Brouwer himself. That is why it seems proper to start with this interesting quote from Leonardo da Vinci. To go beyond Brouwer means to learn his lesson, but also try to fix his mistakes and to soften (in ourselves) some hardness in his personality. And in this way to keep him alive. To confine Brouwer into the prison of what he has materially written, would mean to kill him (again).

Tristo è quel discepolo che non avanza il suo maestro. Leonardo da Vinci¹

Miserable is that disciple who does not go beyond his master