Roots of Incorrect Reasoning

From: Bruno Marchal <>
Date: Fri, 10 Jan 2003 09:11:21 +0100

Henry Sturman <> 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.


And At 14:48 +1100 9/01/2003, Brett Hall <> 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!

More on the modal logic at
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).
Received on Fri Jan 10 2003 - 03:11:29 PST

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