[FOM] Geometry question

Andre.Rodin@ens.fr Andre.Rodin at ens.fr
Mon Nov 21 16:33:53 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.
> A.P. Hazen writes:
> ------ 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.

You might also check P. T. Johnstone: The point of pointless topology. Bulletin
American Mathematical Society, 8(1):41--53, 1983 and Giovanni Sambin's page on
Formal Topology. http://www.math.unipd.it/~sambin/maths-formaltopology.html

Pointless approaches to topology are developing in mathematics already during
few decades, and it is a great pity that many philosophers interested in this
issue don't take these important developments into account...
Andrei Rodin
Ecole Normale Superieure

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