From: Scott Roberts (jse885@earthlink.net)
Date: Tue Nov 30 2004 - 02:49:04 GMT
Platt,
> Guess we're talking past each other. Do you agree with the following
> statement from Ken Wilber (which includes a quote from Scientific
> American)?
>
> "The Incompleteness Theorem embodies a rigorous mathematical
demonstration
> that every encompassing system of logic must have at least one premise
> that cannot be proven or verified without contradicting itself.
This is correct.
Thus, 'it
> is impossible to establish the logical consistency of any complex
> deductive system except by assuming principles of reasoning whose own
> internal consistency is as open to question as that of the system
itself.'
This is strange. It is impossible to establish the logical consistency of
any sufficiently complex deductive system period. Godel's proof, strictly
speaking, shows that arithmetic is either inconsistent or incomplete. Since
no one in millenia of doing arithmetic has come up with an inconsistency,
it is generally assumed that arithmetic is consistenct, and hence
incomplete (hence the name of the theorem). So, yes, it is not established
that arithmetic is consistent, but I don't see what the point of the rest
of the sentence is. It is known that one cannot add further axioms in order
to come up with a complete system which includes arithmetic. Maybe that is
what the author is referring to.
> Thus logically, as well as physically, 'objective' verification is not
> mark of reality (except in consensual pretense). If all is to be
verified,
> how do you verify the verifier since he is surely part of the all?
No argument, but then who expects "all" to be verified? We live in an open
universe. Godel showed that mathematics is also necessarily open, but that
doesn't have any bearing on the non-mathematical universe. But where you
got the idea that "proof" has been "disproven" I just don't get. "2+2=4" is
a proven statement. No one disputes that it follows necessarily from the
axioms of arithmetic (that "mod 3" business that Erin mentioned uses
different axioms).
>
> > > I don't see where he views intellect as negative. He enjoys doing
> > > metaphysics.
> >
> > It's treated negatively in relation to DQ, as in the hot stove example,
or
> > in Ch, 29: "James had condensed this description to a single sentence:
> > "There must always be a discrepancy between concepts and reality,
because
> > the former are static and discontinuous while the latter is dynamic and
> > flowing." Here James had chosen exactly the same words Phaedrus had used
> > for the basic subdivision of the [MOQ]."
> >
> > Note that James has distinguished concepts from reality, with no
objection
> > from Phaedrus.
>
> I think Godel's Theorem and Wilber's interpretation of it are relevant to
> the issue you raise.
I don't. Mathematics is unique in that it is self-contained. It is not
about anything other than itself. Furthermore, intellect in general is not
constrained by mathematical logic, while any system that Godel's Proof
applies to is so constrained.
Intellect can never describe reality in full because
> intellect is part of the reality it tries to describe.
This is not because of Godel's Proof, since arithmetic doesn't describe
anything.
Just as we cannot
> get outside the present to define it, intellect cannot exclude itself
from
> its account of reality and still accurately reflect reality. But, that
> doesn't make intellect "negative." Its limits are simply a truism, even
if
> they can't be proven. :-)
What does this have to do with what I said? I said that Pirsig treats
intellect negatively *with respect to DQ*, that he treats it as covering up
DQ. Both you and Pirsig seem to think that intellect's primary function is
to describe. I don't. I think its primary function is to create, while
description is a partial means to that end. Any particular system will have
limits, of course. But intellect can create new systems. And, getting
esoteric, I think that when Intellect creates new systems, it creates
realities. As we do in a limited way.
>
> Intellect builds walls; DQ is "something that doesn't like a wall," to
> borrow from Robert Frost. Both are needed.
Intellect builds and tears down walls, so it is DQ as well as SQ. Without
distinctions (walls) there isn't anything. It is by building walls that one
gets reality. Otherwise, there is only chaos.
- Scott
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