David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 9 (1):1-12 (1988)
This paper begins by pointing out that the Aristotelian conception of continuity (synecheia) and the contemporary topological account share the same intuitive, proto-topological basis: the conception of a ?natural whole? or unity without joints or seams. An argument of Aristotle to the effect that what is continuous cannot be constituted of ?indivisibles? (e.g., points) is examined from a topological perspective. From that perspective, the argument fails because Aristotle does not recognize a collective as well as a distributive concept of a multiplicity of points. It is the former concept that allows contemporary topology to identify some point sets with spatial regions (in the proto-topological sense of this term). This identification, in turn, allows contemporary topology to do what Aristotle was unwilling to do: to conceive the property of continuity, as well as the properties of having measure greater than zero and having n- dimension, as emergent properties. Thus, a point set can be continuous (connected) although none of its subsets of sufficiently smaller cardinality can be. Finally, the paper discusses the manner in which a topological principle, viz., the principle that none of the singletons of points of a continuum can be open sets of that continuum, captures certain aspects of the Aristotelian proto-topological conception of the relation between points and continua. E.g., for both Aristotle and contemporary topology, points in a continuum exist simple as limits of the remainder of the continuum: their singletons have empty ?interiors? and, hence, they are not ?chunks? (topologically, regular closed set) of the continuum
|Keywords||No keywords specified (fix it)|
|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
Samuel Levey (2003). The Interval of Motion in Leibniz's Pacidius Philalethi. Noûs 37 (3):371–416.
D. F. M. Strauss (2010). The Significance of a Non-Reductionist Ontology for the Discipline of Mathematics: A Historical and Systematic Analysis. [REVIEW] Axiomathes 20 (1):19-52.
Similar books and articles
Iraj Kalantari & Allen Retzlaff (1979). Recursive Constructions in Topological Spaces. Journal of Symbolic Logic 44 (4):609-625.
Anne Newstead (2001). Aristotle and Modern Mathematical Theories of the Continuum. In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang.
Roberto Casati (2009). Does Topological Perception Rest on a Misconception About Topology? Philosophical Psychology 22 (1):77 – 81.
Athanassios Tzouvaras (1997). The Order Structure of Continua. Synthese 113 (3):381-421.
Dieter Spreen (1998). On Effective Topological Spaces. Journal of Symbolic Logic 63 (1):185-221.
Thomas Mormann (1998). Continuous Lattices and Whiteheadian Theory of Space. Logic and Logical Philosophy 6:35 - 54.
S. Salbany & Todor Todorov (2000). Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications. Journal of Symbolic Logic 65 (4):1836-1840.
Steffen Lewitzka (2007). Abstract Logics, Logic Maps, and Logic Homomorphisms. Logica Universalis 1 (2):243-276.
Peter Roeper (1997). Region-Based Topology. Journal of Philosophical Logic 26 (3):251-309.
Added to index2009-08-27
Total downloads38 ( #44,275 of 1,099,034 )
Recent downloads (6 months)2 ( #175,277 of 1,099,034 )
How can I increase my downloads?