The lecture will examine some different conceptions of the infinity, from Aristotle to Georg Cantor (1845-1918) and beyond. The ancient distinction between actual and potential infinity will be explained, along with some arguments against the possibility of actually infinite collections. These arguments were eventually rejected by most philosophers and mathematicians as a result of Cantor’s elegant and successful theory of actually infinite collections. I outline a modernized version of the ancient notion of potential infinity, which is compatible with Cantor’s central insights, and which promises to be a useful philosophical and mathematical tool.
Øystein Linnebo: "What is infinity?"
Øystein Linnebo is a Professor of Philosophy at the University of Oslo. His main research interests are in the philosophies of logic and mathematics, metaphysics and the philosophy of science. He is particularly interested in questions concerning ontology, individuation, essence, reference (especially to abstract objects), necessity and of necessary truths. He has recently published two books, Philosophy of Mathematics (Princeton University Press, 2017) and Thin Objects: An Abstractionist Account (Oxford University Press, 2018).
Published June 27, 2022 8:42 AM
- Last modified Sep. 16, 2022 10:37 AM