Henry Sturman <[EMAIL PROTECTED]> wrote in the FOR list:
I think most people are crazy, at least to some extent, perhaps this is
some random evolutionary flaw. Does anyone have a possible explanation for
how or why a human mind might evolve where a large percentage of people
display incorrect reasoning? There's a lot of bad thinking you see in many
areas from economics to morality to MWI. Most people are good in practical
application of thinking tasks but bad in fundamental insights.
<snip>
And At 14:48 +1100 9/01/2003, Brett Hall <[EMAIL PROTECTED]> commented
Whatever the answer to the central question posed [above], it seems to be a
trait of all living organisms to make mistakes and perhaps this says
something about the quest for artificial intelligence. Organisms gain
knowledge from making mistakes - but only insofar as they remember those
mistakes, an are able to accomodate this new knowledge in such a way that it
meshes well with what else they know.
Mmmh ...
I see you don't remember the first (non trivial) theorem of mathematical
psychology: Godel's second incompleteness theorem:
(Where I identify "pretending" or "making" with "proving", noted by [],
and I interpret the Falsity f by a mistake.).
-[]f -> <>[]f
In french:
Not making mistakes implies the possibility of making mistakes
Logically equivalent: (cf -[] = <>- ; -<> = []- ; p->q = -q->-p, etc.)
[]-[]f -> []f
In french:
Pretending I don't make mistakes implies making a mistake.
Today's "machine" (and animals) are not introspective enough to
acknowledge their mistakes. Are humans so good at it? I guess a little
bit better.
But that's the kind of things which can be infinitely ameliorated. Forever.
(in Computerland).
Alan Forester wrote also in this context:
Animals *are* guesses - human beings *make* guesses.
I agree. And human beings *are* guesses too. Guesses making guesses.
And I guess it would be foolish for humans to take for granted they
are God's last word. Perhaps they are. But if they takes that for
granted then *certainly* they are not!
Bruno
More on the modal logic at http://www.escribe.com/science/theory/m1417.html
Note that I note []p the old Bp, the constant propositional truth T is the
same as the negation of the constant propositional -f, etc.
I recall Smullyan's "Forever Undecided" introduces both elementary
classical propositional calculus and the godel-lob psychology of
self-reference. (Note that it works on machine but also on weaker
notion of self-referential being, but I limit myself to machines).
