From: Lee Corbin (lcorbin@tsoft.com)
Date: Tue Jun 18 2002 - 10:50:38 MDT
Rafal writes
> Harvey Newstrom wrote:
> > A mathematical formula does not contain real people. A book does not
> > contain real people.
I think that Harvey's point was that a book does not contain
*living* people. In effect all the careful descriptions of
people that reside in some extremely special large integers,
while they are indeed *descriptions* of people possibly
living possibly dead, they themselves are at best *dead*.
> > A map does not contain real towns with real people.
> > A photograph does not contain real people.
Yes, only *descriptions* of real people---a completely different
thing!
> > Merely describing people with words, math or pictures does not
> > mean they are consciously living outside of any physical reality.
Yes!
> > This argument is just word play. It confuses the map with the
> > territory.
I guess so.
### It depends on whether you think math is the map, or the territory.
Well, I always think of mathematics as consisting mainly
of relationships *between* the "map" (as you and Harvey
are calling the domain) and the territory (the range).
You are failing to acknowledge that Harvey was completely
correct.
### Since in most cases it is the mathematicl structures that are
### discovered first (and then applied to physics, sometimes quite
### serendipitously), it is quite reasonable to think that they are not
### inventions, but discoveries - independent of the minds that contain
### their representations, just like the land of America was there long
### before anybody mapped it.
Yes. Anyone who believes that mathematics consists
of discoveries rather than inventions is a mathematical
realist, (or mathematical platonist). Thank computers
for saving us from the evil clutches of the nominalists
and formalists.
### The mere description of physical reality using mathematical
### means is just an afterthought for the pure mathematician.
Well, yes, but I think that mathematicians more than
ever acknowledge their debt to inspiration from physics
and from physical reality.
Lee
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