Aristotle and modern mathematical theories of the continuum

In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang (2001)
  Copy   BIBTEX


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.



External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On Continuity: Aristotle versus Topology?Michael J. White - 1988 - History and Philosophy of Logic 9 (1):1-12.
Is time a continuum of instants.Michael Dummett - 2000 - Philosophy 75 (4):497-515.
Is Cantor's continuum problem inherently vague?Kai Hauser - 2002 - Philosophia Mathematica 10 (3):257-285.
Actual versus Potential Infinity (BPhil manuscript.).Anne Newstead - 1997 - Dissertation, University of Oxford
The classical continuum without points.Geoffrey Hellman & Stewart Shapiro - 2013 - Review of Symbolic Logic 6 (3):488-512.
The genesis of the Peircean continuum.Matthew E. Moore - 2007 - Transactions of the Charles S. Peirce Society 43 (3):425 - 469.
Chapter.John Bell - manuscript
Platonic number in the parmenides and metaphysics XIII.Dougal Blyth - 2000 - International Journal of Philosophical Studies 8 (1):23 – 45.
Infinity in science and religion. The creative role of thinking about infinity.Wolfgang Achtner - 2005 - Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 47 (4):392-411.


Added to PP

2,203 (#3,769)

6 months
267 (#8,086)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Anne Newstead
Swinburne University of Technology

Citations of this work

Quantity and number.James Franklin - 2013 - In Daniel Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. London: Routledge. pp. 221-244.
Avicenna on Mathematical Infinity.Mohammad Saleh Zarepour - 2020 - Archiv für Geschichte der Philosophie 102 (3):379-425.

Add more citations

References found in this work

No references found.

Add more references