Re: How about Self-Inconsistency
Hi Yang,
I don't know how much more I want to debate this point (that knowledge is
necessarily inconsistent.)
If you, or others, have a particular interest, it may be better to continue
off-line.
But for now, just to sketch the arguments again...
On Sunday 03 April 2005 09:59, Yang wrote:
> Hi, Rob:
> We cannot deduce that a system may be greater than itself from what
> Goedel has said since he has thrown away self-referencing.
I thought it was Bertrand Russell who tried to expunge all self-reference
(from his Principia) and that Goedel trumped him by showing self-reference
was unavoidable (in Russell's Principia.)
Have a look at it again, and if it still seems it is Goedel who shuns
self-reference, write to me and we can compare references.
Anyway, on the broader point of relevance to knowledge representation. I don't
know if Goedel's theorem can be interpreted as a mathematical proof that
knowledge is necessarily incomplete and inconsistent. I just find the
parallels tantalizing, and recommend it as an interesting study for those who
are inclined.
> ... Anyway, what we are concerned is whether it may affect our
> practices.
I agree. Philosophy is interesting, but it has its limitations. As I said in a
discussion elsewhere, "We don't know what air is at root, either, but if the
plane flies that is one consolation."
The "consistent knowledge" model does not fly.
Philosophy aside, even maths aside, it just seems reasonable to me that it
would not fly, either.
Understood in a certain way the expectation of consistency just appears
nonsensical.
To me demanding to "know" objective truth is like demanding to "know" which
single order in a population of people lines them up in every possible way
simultaneously (according to age, IQ, tennis scores... all at the same time.)
A child will tell you it can't be done. The process of lining people up just
doesn't work that way. It is unavoidably multiple in nature.
Why shouldn't "knowledge" work like that? Indeed, isn't it reasonable to
imagine that (orderings) is exactly how it does work?
Wouldn't it explain the observable facts nicely if that was the way
"knowledge" worked?
-Rob