Re: Source Code for OS?

[olcott <olcott@qwest.net>]

Quantum_Cat wrote:

> Hi Cooter,
>
>  *>> I've read Godel, Escher, Bach: An Eternal Golden Braid by Douglas R.
>  *>Hofstadter.
>  *>> While he focused primarily on recursion, self-reference, consiousness and
>  *>> artificial intelligence, he did and excellent job explaining Godel's
>  *>Theorem.
>  *>> From the premises through the design and finally to the proof.  I
>  *>recommend it.
>  *>> Lots of websites with reviews if you're interested.
>
>  *>Yes this is an excellent book. I have read many along these same lines.
>  *>Kurt's actual proof was so long and complex as to confuse even himself.
>
> I wouldn't know.  In any case, once someone makes a groundbreaking discovery,
> it's hardly optimized.  Others can and have come up with more concise proofs.
>
>  *>>
>  *>>  *>The study of English as a mathemtical formalism makes errors such as
>  *>the
>  *>>  *>Liar paradox, and Kurts Incompleteness theory much easier to see.
>  *>>
>  *>> Errors?  Still making that assertion?  *yawn*
>  *>>
>
>  *>Its so easy for me to see. For me its like  1 + 2 = 3. Yet not a one that I
>  *>have presented, has yet to see even the faintest glimmer.
>
> And this doesn't suggest something to you?  You've come so very close to seeing
> that what you regard as an error is in fact the whole point behind his theory,
> that I'm feeling frustrated for you.
>
>  *>> "This statement is a lie".  You can't prove it true or false in English OR
>  *>a
>  *>> derived system like Godel came up with. (for those of you still not
>  *>filtering
>  *>> Cooter and me, that's the Liar's Paradox...)
>  *>>
>
>  *>Neither can you prove that the following statement is true of false, and for
>  *>the same reason. On the next line after this sentence I will present a
>  *>statement and ask you to tell me whether it is true or false, and why?
>
> Ummm... You know, this has been _MY_ whole point, Cooter.  That there are
> statements which can not be proven true or false.  Therefore, the your assertions
> of an infallible "system" is in error.  Has the light finally come on?
>

The only purely analytical statements that can not be
proven true or false are merely ill formed statements...
Just like the statement "What time is it" can not
be proven true or false... The error of these ill formed
statements is mere too subtle for most to see...

There is no limitation placed on the set of knowledge
derived from the fact that one can not provide the
truth value of a sentence that has no truth value.

I am lying!
  What are you lying about?
I am lying about lying!
  What are you lying about lying about?
I am lying about lying about lying!
  What are you lying about lying about lying about?
I am lying abut lying about lying about lying...
  On and on forever recursive, thus ill formed.

Copyright P. L. Olcott 1997

Just like the statement...
I am going to!  (not I am going TOO)...
It lacks an object about which truth or falsity can pertain,
thus merely creates an ill formed statement.


>
>  *>What time is it?
>
>  *>Now was that statement true or false, and why?
>
> I believe Roy answered this as well or better than I could in his post.  I'll let
> that answer for me as well.
>
> Vogons For a Turlette Free Apple II Community!
>
> Quantum_Cat