Re: Godel Goofed? Nope.

[Quantum_Cat <quantum-no-spam@cotse.com>]

Hiya, Cooter.

 *>> The Liar's Paradox and Godel's Incompleteness Theorem share similarities. 
 *>I will
 *>> state both here for clarity.
 *>>
 *>> Liar's Paradox: "This statement is false"
 *>>
 *>> Godel's Sentence G in his proof, when translated is equivalent to:
 *>>
 *>> "This statement of number theory does not have any proof in the system of
 *>> Principia Mathemetica"
 *>>

 *>Matthew T. Russotto: The Goedel theorem is analagous to "This statement
 *>cannot be proven"

 *>http://www.miskatonic.org/godel.html From this link, (and common knowledge)
 *>and even your prior statements, it is obvious that your translation is quite
 *>inaccurate as to the scope of the theorem.

You are familiar with the title of Godel's paper?  "On Formally Undecidable 
Propositions Of Principia Mathematica And Related Systems".

Since we are referring to Godel's Theorem, and he limited it's scope to PM, I 
will do so as well.  Therefore, the accuracy of my translation is adequate for 
our purposes.  If you want the actually statement in German, I'm sure you can 
find it.  If you want it in English,  Try page 17 of GEB.  The mathematical 
symbols involved make it difficult or impossible to post it meaningfully here.

 *>The scope extends beyond PM...

Red Herring.  Please stick to the topic at hand.

 *>Please try again...

Give some thought before making unfounded assertions.  ;)

 *>> Now, the only similarity between these statements is that both of them are
 *>self-
 *>> referal.  The Liar's Paradox in English, and Godel's Proof in
 *>Godel-numbering.
 *>>
 *>> For your assertion to be correct, you would need a one to one mapping of
 *>your
 *>> analogy to Godel's Theorem.  This was phrased as: "Only if the analogy is
 *>> perfect.  Which it is not." by Matthew Russotto in a previous post.

 *>"This statement cannot be proven"
 *>"This statement is false"

 *>The analogy (mathematical mapping)

Analogies and mathematical mappings aren't synonymous.  Please stop trying to 
cloud the issues by misusing terms.

 *>that I claim is that both of these sentences are ill formed statements for
 *>the same reason of self reference. 

You make the claim that statements of self reference are ill formed, and ill 
formed statements are self referal.  Circular reasoning.  Perhaps now is the time 
for you to disclose your definition of "ill formed" in order to avoid this 
fallacy in the future.  ;)

 *>Statements require an object to attach the truth value to, they must be
 *>about something, or they are not well formed statements.

Wrong.  But I see your problem.  A statement in English requires a subject.  Roy 
pointed this out to you when you presented those dippy false analogies earlier.  
If you remember.  ;)

Mathematical statements *DON'T* have to be about something.  They just are.  An 
example.

1+1=2

3>2

0 * anything = 0

These are the types of statements Godel used in his proofs.  He used the notation 
and rules of inference of PM in his proof.

Your entire trouble with Godel's Theorem appears to be a misunderstanding on the 
use of the mathematical term "statement" and confusing it with the more general 
usage of the word.

Quite an easy fix.  ;)

 *>Try to address this very sharply focused point directly with specific
 *>reasoning. 

Too bad it wasn't as sharply focused as you thought.  

 *>You are doing much better at this now, I trust that you can do this...

But of course I did.  ;)

 *>Here are some suggestions for you to attack my position.
 *>(1) Statements do not have to be about anything.

Mathematical statements.

 *>(2) Self reference does not invalidate that a sentence is a statement.

Don't confuse mathematical statements with sentences or vice versa.

 *>(3) One of these two involves self reference and the other does not.

They are both self referal.

 *>(4) "This statement cannot be proven" does not represent Godel's theorem
 *>accurately, here is why...

You will find the text of Godel's paper at:

http://www.ddc.net/ygg/etext/godel/godel3.htm

I offer it as evidence.  You will find that he did limit it to PM, which your 
comment left out.  Therefore, your statement doesn't represent Godel's Theorem 
accurately.

This will give you the opportunity to actually read the proof before making any 
more unfounded assertions about its validity.  ;)


And I notice that my prophesies were remarkably accurate.  Odd that you chopped 
them.  ;)

Vogons For a Turlette Free Apple II Community!

Quantum_Cat