Fredagskollokvium: Øystein Linnebo: Conceptions of the infinite

Aristotle famously distinguished the potential from the actual infinite, defending the former while rejecting the latter. Two millennia later, the subject was transformed by Cantor, who developed a deep and fruitful mathematical theory of actual infinities. In classical mathematics, the potential infinite has now almost entirely been eliminated in favor of the Cantorian “transfinite”. I argue that this is a mistake. I also discuss whether the infinite really exists and to what extent there are objective truths about it.