[FOM] Geometry question
jays at panix.com
Wed Nov 23 00:53:56 EST 2005
On Mon, 21 Nov 2005, A.P. Hazen wrote:
> 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."
> Allen Hazen
> Philosophy Department
> University of Melbourne
von Neumann and Murray worked on what is now called "pointless geometry".
A pointless geometry is a geometry without atoms. Here "geometry" means a
lattice which looks something like the lattice of subspaces of a vector
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