On Mon, 2 Dec 2002, Tyler Durden wrote:
> >That any particular string can be -precisely- defined as truth or false
> >as required by the definition of completeness, is what is not possible.
>
> Here we come down to what appears to be at the heart of the confusion as far
> as I see it. "True", depending on who's saying it (even in a discussion of
> Godelian Completeness), may be different. Mathematical types may define
> "true" as being "provably true", meaning something like "this statement can
> be derived from the other statements in my system by building up from logic
> plus the fundamental axioms".
If you're using different definitions of 'true' then you're not using the
same mathematics. You're in fact comparing apples and oranges. If you want
to compare something mathematically you -must- use the same axioms and
rules of derivation. The -only- discussion there is one of two parts:
- Is the sequence of applications/operators valid? (ie Proof)
- Is the sequence terminal, does it leave room for more derivation?
(ie Publish or Perish)
And no, there is zero confusion on what true means under Godel or Cauchy.
An individual (or a large group of them) may not understand it, but that
speaks to them, not it. I find that when I just can't 'get it' instead of
bitching about how hard it is or how little sense it makes, I look inward.
I ask myself what personality trait, learned behavior, or mode of thinking
is blocking my advancement? And then I try to deal with that. When I think
I've made progress I come back to the problem and take a crack at it
again. The reality is that most people have problems grasping concepts or
ideas because there is a conflict with other ideas/concepts they hold dear
and near. In most cases of mental block it is an emotional issue not an
intellectual one. People have a hard time learning not because they are
stupid but because they don't deal with their emotional landscape
effectively. The biggest problem most people have is lack of
self-confidence [1]. Western society is training their citizens to be
victims of authority (which is inherently against too rapid change as it
effects their stability via the law of unintended consequences, they
never grasp that simply because you 'own' something today is no right to
own it tomorrow. Nor does authority provide a rational for 'breaking
eggs'. They are afraid of uncertainty and chaos and want to control
'you' to minimize it, to 'their' best interests.). Eastern society has
already been there and done that.
Learning is auto-catalytic and iterative, it requires the ability to
question the most basic assumptions. Decarte's comments about open minds
being one which at least once questions everything comes to mind (though
to be clear I lean toward Hobbes myself).
Freedom -is- Security.
[1]
Ruckers Rules
1 Yes, there is a better way
2. Yes, -you- can do it
3. Seek the Gnarl!
--
____________________________________________________________________
We don't see things as they are, [EMAIL PROTECTED]
we see them as we are. www.ssz.com
[EMAIL PROTECTED]
Anais Nin www.open-forge.org
--------------------------------------------------------------------
