From: ian glendinning (psybertron@gmail.com)
Date: Wed Sep 28 2005 - 12:26:23 BST
Scott, (Platt mentioned) may I pick up one one aspect ...
You used the expression "wont stay still"
You also used a number of apparent opposites inside / outside, north /
south poles ... Platt suggested that "relative" quality solves the
problem of worrying which end / side you're on.
Thinking out loud.
There is something in this.
It's a topological problem (as the mobius-strip / klein-bottle
paradoxical examples illustrate), so..
... rather than worry which end of a dichotomy you're at, just move up
a level (topologically / dimensionally) and worry about which
dimension or axis you're in (or which "aspect" you're considering.) In
the Mobius / Klein example it's "surface" in the north / south example
it's "line".
Position (value) in that dimension can then be considered "conjugate"
something uncertain individually but certain in combination - like
Heisenberg's classic position and velocity or the classic wave /
particle duality. In the Mobius / Klein case you know you have the
"surface" aspect, but the values inside or outside are merely a matter
of perspective, and it's possible to have some combinations of both
(apparently contradictory values) at the same time.
Just a thought, I too am struggling with contradictory identity.
Regards
Ian
PS1 Platt, remind me, in which thread did I leave you dangling with
the "quality of explanation" question ?
PS2 Scott, some of your logical relations there are looking like
"Quines" ? (or anti-Quines)
On 9/18/05, Scott Roberts <jse885@cox.net> wrote:
> Case,
>
> Case said:
> The Klein bottle is an example of a surface that really does not have a
> front and back or an inside and outside. It is a more complicated version of
> a Mobius strip which is a piece of paper with only one side.
>
> Scott:
> Right, so there is contradiction only if one insists that a surface have a
> distinct front and back. One need not insist on it.
>
> Case asked:
> How do the Laws of Form treat logical paradoxes. I thought it was kind of a
> condensed version of the Principia Mathematica. Both were over my head.
>
> Scott:
> By analogy to complex numbers. The formula "x = -1/x" has no real number
> solution, since substituting 1 on the right side gives -1, and
> substituting -1 gives 1. This is the same pattern as in trying to apply
> 'true' or 'false' to the statement 'this statement is false'. If true, then
> it is false, if false, then it is true. So in analogy to the introduction in
> algebra of the imaginary number i = square root of -1, Spencer Brown
> introduces an imaginary logic state, in addition to the states true and
> false. And just as i turns out to be useful, indeed necessary, in some
> physical applications -- that is, it is more than a gimmick, so the
> imaginary logic state turns out to be useful as well. One might say that a
> statement like 'this statement is false', whose truth value is 'imaginary',
> represents an oscillation: "if true, then false, then true, then false...."
>
> - Scott
>
>
>
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