Here's another.
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Message-ID: <359454C3.C440F143@qlink.queensu.ca>
Date: Fri, 26 Jun 1998 22:11:15 -0400
From: Eric Boyd <6ceb3@qlink.queensu.ca>
Organization: Religious Engineers Inc.
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To: "Gifford, Nate F" <giffon@SDCPOS3B.DAYTONOH.ncr.com>
Subject: Re: virus: Locker Room Talk
References: <199806251830.OAA26381@qlink.queensu.ca>
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Hi,
"Gifford, Nate F" <giffon@SDCPOS3B.DAYTONOH.ncr.com>
> In fact aren't there infinite non-Euclidean geometries?
> How do you know the one you picked is the one true geometry?
I'm not sure. If I remember correctly, there are only TWO non-euclidean
geometry's, but I have to admit I'm not sure.
Irregardless, you can tell if you have the "true" one by how well it
predicts what you see around you. The buck always stops with reality, at
least in science. Of course, in mathematics, one can just assume it's
truth and use that to discover properties of that system (which may be
useful even if we don't live in a universe like that)
> Yeah ... and that universe has nothing to do with Newtonian
> Mechanics, Relativistic Mechanics, Euclidean geometry or Non Euclidean
> geometry. The map is not the territory. There are NO models of the
> universe which are FULLY true ... unless you contend the universe
> models itself ....
You may define "true" however you like, but *I* think that it's most useful
to declare "truth" as a *relationship* between the model and
that-which-is-to-be-modelled (Objective Reality). In a certain sense, my
definition of truth is NOT a boolean operator, more like a fuzzy logic
kinda thing, but I still think that it's (theoretically) possible to build
a model with a truth value of "1".
> Didn't Herr Godel prove we won't?
"Here is a restatement of Godel's Theorem:
Within any formal system there are unrational statements
which are reasonable but which it is impossible for
the system to rationalize."
(I've lost the attribution to this quote, but suspect Reed Konsler)
Now this issue interests me very much. I need to acquire a much better
understanding of the proof itself to know how much of limitation it will
be. For instance, exactly how "formal" does a system have to be to apply
Godel's theorem? Does it really matter that you cannot *PROVE* (in the
mathematical sense) the statement true, inside the system, so long as you
can tell that it is? How much "contradiction" do you have to accept in
your starting axioms to avoid the conclusion of the theorem? How did
Godel establish the EXISTENCE of the statement that cannot be proven? Does
the proof detail a way in which to derive this one statement for any given
set of axioms, or it is merely an existence proof? How does Godel's proof
establish the TRUTH of that one statement, if, by his own proof, even the
formal system in question cannot prove it true?
I plan to read the original proof, although I may have to wait till I get
back to the math department at QueensU in order to find it. (and I may
have to wait until I have a deeper mathematical background, although I hope
not)
> In which case by Epsilon proof we're both right. Unless you
> say I'm wrong in which case we can both be wrong.
I don't know your position well enough to make any claims about it's over
all truth value.
ERiC
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