Constructive Versus Ontological Construals of Cantorian Ordinals

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Abstract:

In a recent paper, Kit Fine offers a reconstruction of Cantor's theory of ordinals. It avoids certain mentalistic overtones in it through both a non-standard ontology and a non-standard notion of abstraction. I argue that this reconstruction misses an essential constructive and computational content of Cantor's theory, which I in turn reconstruct using Martin-Löf's theory of types. Throughout, I emphasize Kantian themes in Cantor's epistemology, and I also argue, as against Michael Hallett's interpretation, for the need for a constructive understanding of Cantorian 'existence principles'.

Document Type: Research Article

DOI: http://dx.doi.org/10.1080/0144534031000079324

Publication date: January 1, 2003

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