Lecture by Øystein Linnebo: ‘The potential infinite’ 

Abstract
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 favour of the Cantorian “transfinite”. By reflecting on the set-theoretic paradoxes, this talk argues that an important role remains for the potential infinite. It also explores how the notion should be understood and developed mathematically.

Dr Øystein Linnebo is lecturer of Philosophy at Birkbeck (University of London). He obtained his PhD from Harvard University in 2002. Linnebo’s main research interests are in the philosophies of logic and mathematics, metaphysics and the philosophy of language. He is particularly interested in questions concerning ontology, individuation, essence, reference (especially to abstract objects), necessity and knowledge of necessary truths.
  

ZENO lectures

The ZENO lecture series is organised by the research institute of Philosophy, ZENO.

Attendance to this lecture is free and no registration is required. More information: http://zenolectures.phil.uu.nl/