In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang (2001)
AbstractThis 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.
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Citations of this work
An Aristotelian Realist Philosophy of Mathematics: Mathematics as the science of quantity and structure.James Franklin - 2014 - London and New York: Palgrave MacMillan.
Quantity and number.James Franklin - 2014 - In Daniel D. Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. New York, USA: Routledge. pp. 221-244.
Avicenna on Mathematical Infinity.Mohammad Saleh Zarepour - 2020 - Archiv für Geschichte der Philosophie 102 (3):379-425.
How can a line segment with extension be composed of extensionless points?Brian Reese, Michael Vazquez & Scott Weinstein - 2022 - Synthese 200 (2):1-28.
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