From: Lee Corbin (lcorbin@tsoft.com)
Date: Sat Jun 15 2002 - 09:48:02 MDT
Colin writes
> 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.
That happens with practically *every* word. Words are
extremely slippery. As I like to say, "Words are like
ball-bearings on a skating rink: to get anywhere to
you have to tread carefully and be especially wary of
putting too much weight on any one of them."
However, on the SL4 list several people wrote very
clearly about "rationality":
"Rational goals are those that result from
some logical thought process." ---Gordon Worley
and
"A system X is rational *relative to a system Y* if
the conclusions it draws are (in Y's judgment) about
as accurate as possible given the constraints on X's
cognitive abilities". ---Ben Goertzel
(Gordon and Ben would immediately stress that their
statements are to be taken as tacit characterizations
only, certainly not definitions.)
Colin continues
> Relative terms such as the word 'consistent' seems more
> useful.
Yes, indeed! At least in many discussions, it will be
far easier to identify consistency than rationality.
> "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.
Of course. How the hell could it be otherwise? We
really "change our minds" whenever we learn anything,
but the phrase is reserved for replacing something that
we now think of as incorrect with something we now
consider right. Example: "Planets orbit the sun
in ellipses" packs about as much truth in a sentence
as is possible, but that sentence was as equally true on
the day in 87 A.D. that Ptolemy was born as it was the
day that Newton was born. The only difference was that
in between, astronomers changed their minds about what
was true. Ptolemy was wrong, and Kepler was right.
> 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...
> The vagueness and inconsistency of the middle-east, being
> the net effect of inconsistent minds interacting for millennia
> would seem to present an intractable mathematical problem
> from this point of view.
I completely agree.
> 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 [sic] of this would appear to be that we have
> never found any proven example of inconsistency in the
> real world. Yet.
Yeah, and we cannot even conceive of one.
> 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
> .i.e.. not Nothing. The 'irrational' use of zero may prove productive
> in this area.
There are some cases also in calculus where careful
division by zero facilitates the evaluation of limits.
But I didn't spend quite enough time on it to know
whether tight guidelines on this dangerous (and dumb)
operation could be found.
> 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,
Yes, anyone who supposes that lawyers ever win cases
by submitting absolutely logical arguments wouldn't
appear to understand how language and reality work.
Lee
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