[FOM] Geometry question

A.P. Hazen 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."


Allen Hazen
Philosophy Department
University of Melbourne

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