On Sun, 1 Dec 2002, Sarad AV wrote:
> By principle of what?
By the principles of mathematics.
Godel used Principia Mathematica as a starting point. You might also.
> Isn't that the reason we call it 'undecidable',put it
> in an undeciable list which is the truth.
The problem description doesn't allow a third list, to create a third
list ouf of thin air would change mathematics from what we use today to
something else. The assumption of basic mathematics to be complete (see
definition) is that -all- strings will be either true or false.
Godel's does -not- say mathematics is incomplete, it says we can't prove
completeness -within- mathematics proper. To do so requires a
meta-mathematics of some sort.
> We can actually write these symbols down,it will be
> true for some and false for some
To write a string down to feed to your truth engine is one thing, to be
able to write it in either the 'true' or 'false' list is something
entirely different. Nobody cares about the first part, they care a great
deal about the second.
And no it won't be 'true for some, false for some'. The actual content of
the symbols is of -no interst-. We are trying to determine if the string
is legitimate within the axioms and their grammer, not it's absolute
context sensitive result.
Godel covers this in the first two (2) pages of his incompleteness work.
It's cheap, try it.
> eg: If we say-For a context free grammar G, L(G) is
> ambigious.
Then you've changed the rules in the middle of the game, and apparently
without realizing it.
What you are creating with that assertion is para-consistent logic. A
different beasty.
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