Indivisible Parts and Extended Objects: Some Philosophical Episodes from Topology’s Prehistory

The Monist 79 (1):148--80 (1996)
Download Edit this record How to cite View on PhilPapers
Physical boundaries and the earliest topologists. Topology has a relatively short history; but its 19th century roots are embedded in philosophical problems about the nature of extended substances and their boundaries which go back to Zeno and Aristotle. Although it seems that there have always been philosophers interested in these matters, questions about the boundaries of three-dimensional objects were closest to center stage during the later medieval and modern periods. Are the boundaries of an object actually existing, less-than-three-dimensional parts of the object—that is, are solids bounded by two-dimensional surfaces, surfaces by one-dimensional “edges” or “physical lines”, edges by dimensionless “simples”? If not, how does a perfectly spherical object manage to touch a perfectly flat object—what part of the sphere is in immediate contact with the plane, if the sphere has no unextended parts? But if such parts be admitted, are we not then saddled with “actual infinities” of simples, lines, and surfaces spread throughout each continuous object—the boundaries of all the object’s internal parts? Does it help to say that these internal boundaries exist only “potentially”?
(categorize this paper)
PhilPapers/Archive ID
Upload history
Archival date: 2015-11-21
View other versions
Added to PP index

Total views
1,284 ( #3,557 of 65,772 )

Recent downloads (6 months)
43 ( #19,933 of 65,772 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.