David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang (2001)
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Anne Newstead & Franklin James (2008). On the Reality of the Continuum. Philosophy 83 (1):117-28.
Michael J. White (1988). On Continuity: Aristotle Versus Topology? History and Philosophy of Logic 9 (1):1-12.
Michael Dummett (2000). Is Time a Continuum of Instants? Philosophy 75 (4):497-515.
Kai Hauser (2002). Is Cantor's Continuum Problem Inherently Vague? Philosophia Mathematica 10 (3):257-285.
Anne Newstead (1997). Actual Versus Potential Infinity (BPhil Manuscript.). Dissertation, University of Oxford
Geoffrey Hellman & Stewart Shapiro (2013). The Classical Continuum Without Points. Review of Symbolic Logic 6 (3):488-512.
Matthew E. Moore (2007). The Genesis of the Peircean Continuum. Transactions of the Charles S. Peirce Society 43 (3):425 - 469.
Edward G. Belaga (forthcoming). Retrieving the Mathematical Mission of the Continuum Concept From the Transfinitely Reductionist Debris of Cantor’s Paradise. Extended Abstract. International Journal of Pure and Applied Mathematics.
Philip Ehrlich (2012). The Absolute Arithmetic Continuum and the Unification of All Numbers Great and Small. Bulletin of Symbolic Logic 18 (1):1-45.
Edward G. Belaga, Halfway Up To the Mathematical Inﬁnity I: On the Ontological & Epistemic Sustainability of Georg Cantor’s Transﬁnite Design.
Dougal Blyth (2000). Platonic Number in the Parmenides and Metaphysics XIII. International Journal of Philosophical Studies 8 (1):23 – 45.
Wolfgang Achtner (2005). Infinity in Science and Religion. The Creative Role of Thinking About Infinity. Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 47 (4):392-411.
Gregory H. Moore (2011). Early History of the Generalized Continuum Hypothesis: 1878—1938. Bulletin of Symbolic Logic 17 (4):489-532.
Mark van Atten, Dirk van Dalen & And Richard Tieszen (2002). Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuumt. Philosophia Mathematica 10 (2):203-226.
Added to index2011-03-03
Total downloads290 ( #5,313 of 1,781,456 )
Recent downloads (6 months)42 ( #17,545 of 1,781,456 )
How can I increase my downloads?