The Monist 79 (1):148--80 (1996)

Dean Zimmerman
Rutgers University - New Brunswick
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”?
Keywords Analytic Philosophy  Contemporary Philosophy  General Interest  Philosophy of Mind  Philosophy of Science
Categories (categorize this paper)
ISBN(s) 0026-9662
DOI 10.5840/monist19967918
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

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

Theories of Masses and Problems of Constitution.Dean W. Zimmerman - 1995 - Philosophical Review 104 (1):53-110.
Scattered Objects.Richard Cartwright - 1975 - In Keith Lehrer (ed.), Analysis and Metaphysics. Reidel. pp. 153-171.

View all 15 references / Add more references

Citations of this work BETA

Location and Mereology.Cody Gilmore - 2013 - Stanford Encyclopedia of Philosophy.
Simples and Gunk.Hud Hudson - 2007 - Philosophy Compass 2 (2):291–302.
Indefinite Divisibility.Jeffrey Sanford Russell - 2016 - Inquiry: An Interdisciplinary Journal of Philosophy 59 (3):239-263.

View all 24 citations / Add more citations

Similar books and articles

Hudson on Location. [REVIEW]Josh Parsons - 2008 - Philosophy and Phenomenological Research 76 (2):427 - 435.
Objects, Their Parts, and Essences.Karol Polcyn - 2012 - Filozofia Nauki 20 (3).
Zeno Objects and Supervenience.Simon Prosser - 2009 - Analysis 69 (1):18 - 26.
Henry More and Nicolas Malebranche's Critiques of Spinoza.Jasper Reid - 2015 - European Journal of Philosophy 23 (3):764-792.
Simply Possible.Theodore Sider - 2000 - Philosophy and Phenomenological Research 60 (3):585-590.
On Stages, Worms, and Relativity.Yuri Balashov - 2002 - Royal Institute of Philosophy Supplement 50:223-.
Relativity and Persistence.Yuri Balashov - 2000 - Philosophy of Science 67 (3):562.
Composition as a Fiction.Gideon Rosen & Cian Dorr - 2002 - In Richard Gale (ed.), The Blackwell Companion to Metaphysics. Blackwell. pp. 151--174.
Endurantist and Perdurantist Accounts of Persistence.Maureen Donnelly - 2011 - Philosophical Studies 154 (1):27 - 51.
A Tale of Two Simples.Joshua Spencer - 2010 - Philosophical Studies 148 (2):167 - 181.
Parts and Wholes.Kris McDaniel - 2010 - Philosophy Compass 5 (5):412-425.


Added to PP index

Total views
1,167 ( #3,232 of 2,403,328 )

Recent downloads (6 months)
72 ( #9,672 of 2,403,328 )

How can I increase my downloads?


My notes