History and Philosophy of Logic 24 (1):45-63 (2003)
AbstractIn 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?
Added to PP
Historical graph of downloads
References found in this work
Citations of this work
No citations found.
Similar books and articles
Intentionality Versus Constructive Empiricism.F. A. I. Buekens & F. A. Muller - 2012 - Erkenntnis 76 (1):91-100.
Constructive Mathematics in Theory and Programming Practice.Douglas Bridges & Steeve Reeves - 1999 - Philosophia Mathematica 7 (1):65-104.
The Generalised Type-Theoretic Interpretation of Constructive Set Theory.Nicola Gambino & Peter Aczel - 2006 - Journal of Symbolic Logic 71 (1):67 - 103.
A System of Abstract Constructive Ordinals.W. A. Howard - 1972 - Journal of Symbolic Logic 37 (2):355-374.