Re: How can the meaning of Goedel's unprovable statement descend from infinity?
- From: "david petry" <david_lawrence_petry@xxxxxxxxx>
- Date: 15 Feb 2006 16:17:41 -0800
mikeh106@xxxxxxxxxxx wrote:
I have thought hard about Goedel's Incompleteness Theorem since I
read a proof at age fifteen. My goal was to intuitively understand the
meaning of the unprovable statement. I now believe that while the
theorem is true, the statement is meaningless. It is just not the kind
of statement we would wish to prove in arithmetic.
Interesting. Godel showed, presumably, that if a formal system is
consistent, then there is no proof within that formal system that
proves that the formal system is consistent. However, if we insist that
the notion of proof must capture an intuitive notion of a "compelling
argument", then we realize that if we believe that the formal system
can prove anything at all, then at a minimum, we must already believe
that the formal system is consistent, (otherwise it could formally
prove anything, and hence it could prove nothing in the sense of a
compelling argument) -- the point being that Godel's theorem is already
implicit in our notion of belief. So maybe Godel's theorem is nothing
more than circular nonsense. However, currently, it is regarded as one
of the biggest advances in the field of logic in the twentieth century,
and any amateur who questions that will be denounced as a crackpot. So
my advice would be, unless you are certain that you want to get
involved with this topic, just ignore it and stay sane.
Anyway, I haven't actually read the rest of your article, and I don't
know if there is any argument of value there.
.
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- How can the meaning of Goedel's unprovable statement descend from infinity?
- From: mikeh106@xxxxxxxxxxx
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