Aristotle and modern mathematical theories of the continuum

In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang (2001)
Authors
Anne Newstead
University of Sydney
Abstract
This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open versus closed intervals is discussed. Finally, it is suggested that one reason there is a common structure between Aristotle's account of the continuum and that found in Cantor's definition of the real number continuum is that our intuitions about the continuum have their source in the experience of the real spatiotemporal world. A plea is made to consider Aristotle's abstractionist philosophy of mathematics anew.
Keywords Aristotle's theory of the continuum  Brouwer  real numbers  infinity  Cantor
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