Remarks on Buzaglo’s Concept Expansion and Cantor’s Transfinite

Claudio Ternullo ()
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Claudio Ternullo: University of Vienna, Kurt Gödel Research Center for Mathematical Logic

A chapter in The Hyperuniverse Project and Maximality, 2018, pp 259-270 from Springer

Abstract: Abstract 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-62935-3_12

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DOI: 10.1007/978-3-319-62935-3_12

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