From: Colin Hales (colin@versalog.com.au)
Date: Sat Jun 15 2002 - 03:20:36 MDT
scerir wrote:
>
> > Well ;-) sorry, but my statement was really a claim
> > that there *aren't* any "rigorous guidelines to suggest
> > to one that an apparently completely rational argument
> > may have a whole in it".
> > Lee
>
> Ah. Somebody wrote something about it.
> Bertrand Russell, "Vagueness", Australian Journal of Philosophy, 1,
> 1923.
> Max Black, "Vagueness, an exercise in logical analysis", Philosophy of
> Science, 4, 1937.
> As far as I remember vagueness in legal arguments is a very
> interesting subject (lots of books too).
> s,
>
You really have to watch out for the meaning of the word 'rational'.
It's a Philosophical rainbow AFAICT.
eg Have a look at Dennett's 'Intentional Stance'.
Ch4 "Making sense of ourselves".
The word 'rational' is a linguistic attempt at nailing down an
absolute standard of behaviour. In common fuzzy day-to-day
human usage it works pretty well. But every time you get empirical
with the word it vapourises. Relative terms such as the word
'consistent' seems more useful. In the legal
profession it would allude to the use of 'precedent'.
In a social/cultural setting it would allude to 'convention'.
In science/mathematics it takes on a Godel-ish meaning.
"Changing One's Mind" is a loaded statement. It says that
a mental state has changed, not something in the world, except
in as much as the holder of the changed belief's behaviour
is subsequently altered. Using the external world's rules
to describe it would seem unwise: The logician's approach is
trying to describe the behavour of a consistent system.
Don't use it on the mind!
There is absolutely no reason to assume that the
computational models of the world in the mind have the attributed
consistency of the world on which they are based. Indeed
I think that the inconsistency may be one source of the
great power of the mind. Anything goes.
The vagueness and inconsistency of the middle-east, being
the net effect of inconsistent minds interacting for millenia
would seem to present an intractable mathematical problem
from this point of view.
It's interesting that this thread started with a proof of
2 = 1 which revolves around the mathematically 'irrational'
use of "0" or, another way, the mathematically
inconsistent behaviour that ensues when systems of mathematics
are inadvertently augmented by allowing operations
normally excluded. We live in the belief that when we keep
our systems of mathematics 'consistent' that they are
therefore empowered to accurately describe our universe. The proof of this
would appear to be that we have never found any proven example
of inconsistency in the real world. Yet.
Are we missing something as a result? It's an issue I
think about sometimes. Is there a place and/or a time when
the 'irrational' operations involving zero are OK?
The obvious ones: the Big Bang or maybe the very small or the very large
or perhaps _the_ biggee - why there is anything at all
.ie. not Nothing. The 'irrational' use of zero may prove productive
in this area.
regards,
Colin
______________________
aside {
I wrote a 'frippery' humour piece on this recently.
Basically: 0 = Thing + (-Thing) generates either
a Thing universe or a -Thing universe because there simply
isn't enough energy (ie infinite energy needed) to maintain a perfect
0 (Nothing). The resulting tiny errors in Thing and -Thing cancellation
causes a universe of Thing or -Thing, but not both. It generates
a bedrock for formal logic:
(ref the “Law of Non-Contradiction: X is TRUE if NOT {X and NOT X} is TRUE”)
or Nothing = NOT (Thing and (-Thing)) :-)
If anyone's interested in reading it, let me know.
190K .pdf. 3 pages. 2800 words
"Colin goes nuts trying to make Nothing"
I'd appreciate the feedback.}
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