To Continue With Continuity

Metaphysica 6 (2):91-109 (2005)
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Abstract

The metaphysical concept of continuity is important, not least because physical continua are not known to be impossible. While it is standard to model them with a mathematical continuum based upon set-theoretical intuitions, this essay considers, as a contribution to the debate about the adequacy of those intuitions, the neglected intuition that dividing the length of a line by the length of an individual point should yield the line’s cardinality. The algebraic properties of that cardinal number are derived pre-theoretically from the obvious properties of a line of points, whence it becomes clear that such a number would cohere surprisingly well with our elementary number systems.

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References found in this work

Parts: A Study in Ontology.Peter Simons - 1987 - Oxford, England: Oxford University Press.
Parts: A Study in Ontology.Peter Simons - 1987 - Oxford, England: Clarendon Press.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford, England: Oxford University Press.
Parts : a Study in Ontology.Peter Simons - 1987 - Revue de Métaphysique et de Morale 2:277-279.
Cantorian Set Theory and Limitation of Size.Michael Hallett - 1984 - Oxford, England: Clarendon Press.

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