[FOM] Geometry question
a.hazen at philosophy.unimelb.edu.au
Sun Nov 20 22:37:26 EST 2005
A. Mani writes
> I would like to know of surveys in axiomatic theories of geometries
>which do not allow for conceptions of points, lines and surfaces.
------I'm not going to try to answer. But if I WERE going to try to
answer, I would start by looking at Roberto Casati and Achille
Varzi's "Parts and Places: the structure of spatial representation"
(MITP 1999: ISBN 0-262-03266-X), and citations therein. There has
been a fair bit of work on "pointless" approaches to topology in
fairly recent times. Casati and Varzi survey some of it. Of their
references, I have a feeling (vague memory from reading the book and
from conversation with Varzi) that the paper by Gerla in F.
Buekenhout, ed., "Handbook of Incidence Geometry" (Elsevier: 1995),
pp. 1015-1031 **might** be a good starting place.
C & V's book has useful discussion of a variety of problems, and
describe two dozen or so axiomatic theories: several of them
"mereotopologies" which try to develope mereology and some
geometrical or topological stuff simultaneously, with a primitive
notion of "connectedness."
University of Melbourne
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