Re: ONT Re: Changing Membership
From: "Jon Awbrey" <jawbrey@oakland.edu>
> How does it makes sense to talk about the relation
> between physical systems and mathematical systems?
The structures of a mathematical systems can represent the structures of a
physical systems. Just like the neural structures in your brain can
represent the self same physical system. We say that the representation of
the physical system by the mathematical system is more or less accurate
(true if you like) just in the proportion that the mathematical system can
predict events of the physical system. Embedded in that paragraph is my
definition of represent. You seem to use the word 'associated' for the same
relationship.
Just as we ~forget~ that our awareness's are entailed by the neural
representations in our brain and hence gives us the illusion that our
awareness walks among real physical objects, so a mathematical system can
~forget~ that it's structures are mere representations and function as if
they were the real things. So it can say that a real physical object is a
member of a set .. and make no apologies for its confusion.
The confusion of the map for the territory is when the actual mathematical
system is confused with the physical system. That does not happen unless it
makes a category error. Frequently parts of a mathematical system are used
to represent other parts of the mathematical system. I call that
reification and do not consider such reification to be any kind of
confusion; rather it is the mathematical system turning its eye (as it were)
on itself ... one neural analogy of that could be introspection.
... that is my humble opinion.
Seth Russell