Hi everybody,
It seems Bruno's argument is a bit rich for some of us to digest, so I
decided to keep talking by posing another issue.
By Godel's argument we know that every sufficiently powerful system of logic
would be incomplete, and recently there has been much argument to make human
an exception; that's because we see the truth of Godelian statements (i.e.
This sentence is unprovable in this system)
Let's call such a system S1, and call another (powerful enough in Godel's
sense) system S2. and suppose S2 structurally is able to give statements
about the statements in S1. What does it mean? Consider S2 as a being
able examine some statements in S2 via some operators and get the
result(like function calls).
My claim is:
1.
S2, is able to see the truth of the Godelian statements in S1, and in some
sense:
"S2 is complete against the statements of S1", because it can see that S1 at
last wont be able to evaluate our Godelian statement and so the statement
would be correct.
2.
We humans are vulnerable to the Godelian statements like all other logical
systems. We have our paradoxes too.
Consider the same Godelian statement for yourself as a system (i.e. "You
can't prove me" or some similar sentences like "This sentence is false")
3.in the first claim consider the first system to have the same attitude
toward the second one, I mean let there be a loop (some how similar to
Hofstadter's Strange loops as the foundation of self)
Is it complete of not?
--
Mohsen Ravanbakhsh.
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Received on Tue May 22 2007 - 06:58:06 PDT