The Classical Continuum without Points
Keyword(s):
The Real
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This chapter develops a “semi-Aristotelian” account of a one-dimensional continuum. Unlike Aristotle, it makes significant use of actual infinity, in line with current practice. Like Aristotle, this account does not recognize points, at least not as parts of regions in the space. The formal background is classical mereology together with a weak set theory. The chapter proves an Archimedean property, and establishes an isomorphism with the Dedekind–Cantor structure of the real line. It also compares the present framework to other point-free accounts, establishing consistency relative to classical analysis.
2013 ◽
Vol 6
(3)
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pp. 488-512
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