Remarks on Buzaglo's concept expansion and Cantor's transfinite
pp. 259-270
in: Carolin Antos, Radek Honzik, Claudio Ternullo, Sy D. Friedman (eds), The hyperuniverse project and maximality, Berlin, Springer, 2018Abstract
Historically, mathematics has often dealt with the "expansion' of previously accepted concepts and notions. In recent years, Buzaglo (The logic of concept expansion, 2002) has provided a formalisation of concept expansion based on forcing. In this paper, I briefly review Buzaglo's logic of concept expansion and I apply it to Cantor's "creation' of the transfinite. I argue that, while Buzaglo's epistemological considerations fit well into Cantor's conceptions, Buzaglo's logic of concept expansion might be unsuitable to justify the creation of the transfinite in terms of a logically rigorous derivation of concepts.
