On Sep 28, 2008, at 1:34 AM, Rob Freeman wrote:
Thanks for the link to other work which relates Category Theory and
geometric physics. I'll check it out. Good to have independent
As I say, the actual solution using a geometric approach, whether in
physics, maths, or semantics, is not what interests me the most. What
I find interesting is that in all these domains of knowledge people
seem to be moving away from axiomatic/logical formulations, towards
formulation in terms of geometries, distortable continua, where
qualities in the system are not specified ab initio but as
distortions/mappings of something fundamentally indeterminate.
Which is not to say modeling semantics in terms of Category Theoretic
style "mappings" might not be useful, perhaps comparable to the move
from Newtonian to relativistic physics.
Or maybe to the move towards visual abstraction made by the Cubists in the 1920s, or to the rejection of tonality by the Second Viennese School, or even the Great Vowel Shift. When one looks at these things - and so many others - with a truly Open Mind, one is struck by the essentially indeterminately geometric nature of Change which underlies them all, and transcends - or perhaps one should say, undermines
- the narrow left-brain restrictions of mere logic. What we need here is a Holistic Universal Post-Quantum Topologo-Topos anti-Theory of Everything and Beyond! Then, maybe, we will be able to get some serious
ontology work done.