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

In: The Hyperuniverse Project and Maximality

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  • Claudio Ternullo

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

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.

Suggested Citation

  • Claudio Ternullo, 2018. "Remarks on Buzaglo’s Concept Expansion and Cantor’s Transfinite," Springer Books, in: Carolin Antos & Sy-David Friedman & Radek Honzik & Claudio Ternullo (ed.), The Hyperuniverse Project and Maximality, pages 259-270, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-62935-3_12
    DOI: 10.1007/978-3-319-62935-3_12
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