[FOM] Geometry question

[Jay Sulzberger]

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
space.

http://en.wikipedia.org/wiki/Von_Neumann_algebra

oo--JS.