Re: Godel Goofed? Nope.

[olcott <olcott@qwest.net>]

Quantum_Cat wrote:

> 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

Whoops (you forgot to consider "And Related Systems")
{Conventionally his theorem is taken to mean unprovable
within ANY possible system, rather than merely PM)...
(Besides if you are now claiming that it ONLY
applies to PM, then your original point (that my
system of infallible reasoning can not work) is lost)...

>
> 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.
>

Not at all Red Herring, the WHOLE point is the
Godel's Theorem specifically limits the possible
chances of my system of Infallible Reasoning,
if it ONLY applies to PM, then this point is
entirely lost. We both know that is applies to
more than PM (if it applies at all), so why bother
arguing against this self-evident truth?

>
>  *>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.
>

A Mathematical Mapping is the Mathematical
form of an Linguistic Analogy...

>
>  *>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.  ;)
>

Sure... In order for a Sentence to form a Valid Statement
there must be an Object that this Statement Specifically
refers to, for the Truth Value to be Attached.

EXAMPLE:
{George Washington was the first president of the United States}
In this case the object of the statement is {first president of the United States}.
If I would have said {George Washington was the}, it would
lack the object, thus fail to form a valid statement.


>
>  *>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
>

They still require OBJECTS to be complete...
Here is an example of an ill formed
mathematical "statement"

{1 + 1 =}
The analog in English would be the statements
{I am going to}
You are going to What?

>
> 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.
>

Mathematical Tautologies, not at all ill formed.

>