Re: Source Code for OS?

[olcott <olcott@qwest.net>]

Quantum_Cat wrote:

> Hiya, Cooter.
>
>  *>> I know you're stuck on this fallacy that it's possible to _have_ full and
>  *>> complete analytical knowledge.  You presented mathematics as being in that
>  *>realm.
>  *>>
>  *>> I present my secret weapon.  Let's examine the concept and properties of
>  *>>the zero.  Yes, you can list all of it's properties.  Suppose you examine
>  *>>the property where any integer is divided by the zero.
>  *>>
>  *>> It's undefined.
>
>  *>This is "conventional wisdom"
>
> No, it's not.  ;)
>
>  *>yet as the denominator gets smaller the number gets bigger, therefore any
>  *>number divided by zero is actually defined as infinity.
>
> Nope.  The value may _approach_ infinity, but never becomes infinity.  I will
> demonstrate.
>
>  *> (which is not a number, but, a process).
>
> Good boy.  You are correct that infinity is not a number.  It isn't however, a
> process.
>
> Now my demonstration in the error in your assertion that a division by zero is
> defined as infinity.
>
> Take the operation 6/3=2.  The inverse is 2*3=6.  Comprehend?
>
> Now.  If 6/0=x, then 0*x=6.  Now one of the properties of zero is that a product
> of zero and any value is 0.  If as you state, that x=infinity, then
>
> 0 * infinity = 6
>
> An error.  THIS is why mathematicians have declared a division by zero as
> undefined.
>

They could have just as easily defined it as infinity,
and included that the reciprocal using infinity does
not work... It does not work because infinity is a
process rather than a number. Or perhaps because
of the unusual nature of this process, Infinity * 0 = 6...
This would superficially seem to cause a contradction
because that would result in an absurdity such
as 6 = 7... Or perhaps you may have even made your
point, that division by zero yields contradictory results
thus it remains undefined. This still is not a valid counter-
example for my claim...

>
> Odd that a brilliant theorist such as yourself has stumbled on one of the truly
> basic precepts of mathematics.  It casts a shadow on all your credibility.  ;)

Credibility is an invalid process. The scientific name for this
is surface validity, or in other words superficially how true
does the assertion seem to be, making sure that we do not
hear the person out...

>
>
>  *>> Definition- define: 1. To state precisely the meaning of (a word, etc) 2.
>  *>To
>  *>> describe the nature or properties of;explain;interpret. 3. To fix with
>  *>precision.
>  *>>
>  *>> There.  If there's ONE item in your "analytical knowledge" that can't be
>  *>known,
>  *>> then your assertion that it's possible to exhaustively prove every aspect
>  *>in this
>  *>> domain has been proven false.  This is that ONE item.  Sorry dude.
>
>  *>Except that I just refuted your attempt at one valid counter-example,
>
> Heh... attempted, and failed miserably.  ;)
>
> 0 * infinity = 6
>
> I should taunt you with that unmercifully.  ;)
>

Okay the example might be correct, but, then it does
not cut it as a counter-example. Your position is
that math creates things that are unknowable.
Well now we know that division by zero does not
work consistenly... That does not create anything
unknowable, thus does not refute my assertion
that the complete set of all analytical knowledge
can both be known, and verifed as correct.
Essentially that Kurt goofed is his famous
incompleteness theorem.

>
>  *> and your definition is "definition" is woefully inadequate.
>
> Got it from the dictionary.  If you have a better source, feel free to enlighten
> me.
>

How about from formal language theory?
In this cases its all about formal mathematical
mappings from one set of symbols to another.

>
>  *>Here's one a little better. The mathematical mapping of a precisely defined
>  *>set of concepts to a term, used as a place holder for this set of concepts.
>  *>(I am leaving out empiricism).
>
> Uh...  Are you sure you're getting enough sleep?  Perhaps your medication needs
> to be looked into?
>
> You've just defined "definition" using the phrase "precisely defined".  Let's try
> to avoid circular reasoning here, OK?  While your mind may be caught in a loop, I
> see no reason to join you in spinning your wheels.  ;)
>

Merely two entirely different words that are
spelled and pronounced the same, and have
similar, but, not identical meanings...

 par�a�dox    n.1. a statement or proposition that seems
self-contradictory or absurd but in reality expresses a
possible truth. 2. a self-contradictory and false proposition.

These two mutually exclusive sense meanings to the
same word spelling, are more accurately stated as
two different words with the same spelling. A more
precise way a delimiting the meaning of words
would be to call the first one paradox(1), and
the second one, paradox(2). Otherwise intelligent
people often get into completely endless arguments
over the meaning of a word, when for all practical
purposes these are two entirely different words,
that a spelled and pronounced the same.

>
>  *>>  *>Example... to know that unicorns do not exist anywhere requires
>  *>omniscience.
>  *>>
>  *>> If omniscience is a meaningful concept.
>
>  *>It precisely means the present possession of the universal set of knowledge.
>
> Putting words in order like that may give the appearance of meaning, but still
> lack meaning.  And example:
>
> Your "universal set" is analogous to the unacceptable contradiction: "The set of
> all sets.".  Try a Venn diagram of THAT.  ;)
>

A precise definition of the universal set is very easy.
The complementary set to the empty set... Just because
something can not be diagrammed, forms no indication
that it is not valid... Example try to draw either a line
or a ray from geometry...

>
> So, if your definition of omniscience contains a contradition, it must be
> meaningless.
>
>  *>> When you compare it's presumed
>  *>> properties with others like "free will",
>
>  *>Because of the socialization process very little (if any) free will actually
>  *>exists.
>
> Perhaps, but the universe is chaotic enough to cast doubt on predetermination as
> well.
>
>  *>> you quickly find mutually exclusive
>  *>> concepts.  One or the other must be correct, but they both can't.  And
>  *>there is
>  *>> no possible way to tell which IS correct.  Godel's Incompleteness Theorem
>  *>again.
>
>  *>> And you.  ;)  And this was YOUR assertion.  YOU prove that he erred.
>
>  *>So far everyone that I have attempted to explain this to
>  *>(many dozens) were so attached to their religious conviction that he was
>  *>correct, that none of them could manage to focus enough attention on my
>  *>point to as much as hear it far less than understand it.
>
> Um... Perhaps you might consider that if you see something that no one else sees,
> that there may be a possibility that you are delusional?  Hmmm?
>
>  *>Suffice it to say that Godel makes an analogous error as the so called "Liar
>  *>Paradox" if you can't get it from this, you never will.
>
> Sigh.  Yes.   He demonstrates that any and all sufficiently powerful systems
> contains the analogous "Liar's Paradox", demonstrating a contradiction.
>

I can say that I flew my dog for a drive, but, this
does not invalidate English... Necessarily requiring
a contradiction would be another matter.

>
> Perhaps you should consider the methods used in proofs...(direct, indirect ..
> i.e. contrapositive, contradiction).  There are plenty of web sources that would
> cost you nothing and might enlighten you on what Godel has done here.
>
>  *>> That was the point, Cooter... Any sufficiently powerful system can
>  *>generate a
>  *>> self-reference which will collapse into a contradiction.  This precludes
>  *>any
>  *>> further determination of truth or falsehood.  Therefore, there are truths
>  *>or
>  *>> falsehood which are impossible to prove.
>
>  *>Here is another one. Go buy me a pack of cigarettes from the first store
>  *>that you come to, that never has, and never will sell cigarettes. You must
>  *>buy these directly from this store, AND they must not sell them to you...
>  *>(Another way to phrase the barber paradox)...
>
>  *>Here is an even simpler version, provide me with at least three numbers that
>  *>are numerically greater than five AND numerically less than three... They
>  *>must also be pre-existing integer numbers, and can ONLY come form the set
>  *>{7, 8, 9}.
>
> The Barber Paradox leads to a proof by Contradiction just as the Liar's Paradox
> does.  Your number example would be disproved using the same method.
>

The barber paradox, like, nearly every one (or every one)
of these linguistic paradoxes, merely represent ill formed
statements, not impossibly difficult ones. To show that it
is possible to make an ill-formed statement does not
limit the power of language at all, nor attainable truth.

>
>  *>>  *>With analytical truth ALL can be fully known by the mere meaning of the
>  *>>  *>words, thus within this domain the possibility of error can be utterly
>  *>>  *>eliminated.
>  *>>
>  *>> Division by zero.  Undefined.  Gotcha.
>
>  *>I just defined it, (infinity) Gotcha back...
>
> 0 * infinity = 6
>
> Nice try anyway.  ;)
>
>  *>> Yup.  And unlike most other schools of thought, science is
>  *>self-correcting.  It
>  *>> approaches the truth at a much faster rate than ever observed by mental
>  *>> gymnastics of Kant and Augustine.  Because we recognise the most common
>  *>mistakes,
>  *>> and take care to take them into account.
>
>  *>Unless its every bit of all of it is entirely based on a most fundamental
>  *>premise that turns out to be untrue... In that case you are merely getting
>  *>closer and closer to more self consistent illusions. It could be the actual
>  *>truth that nothing at all from science is true at all.
>
> Could be.  That's the nature of science.  So far, it's working pretty damn well.