Re: Godel proved maths inconsistent not incompleteness theorem

On Apr 22, 5:55 pm, herbzet <herb...@xxxxxxxxx> wrote:
Charlie-Boo wrote:
herbzet wrote:
Charlie-Boo wrote:
herbzet wrote:
Charlie-Boo wrote:
Daryl McCullough wrote:
Charlie-Boo says...

Why is it *bad* that the ZF proof of
the Pythagorean theorem is only a few lines long?

It isn't.  If you mean why isn't it ok to define what you're trying to
prove and then you have a one line proof, I assume you know the answer
to that.

No, I have no idea what you are going on about,
and I don't think you really know what you are
asking for, either.

And I think you're a horse's ass for making personal attacks during
what should be an intelligent discussion of principles of Mathematics.

And I think that _you're_ a horse's ass.  A _giant_ horse's ass.

What intellegent discussion of "priciples of Mathematics" are you
referring too?

What does "intellegent" mean?  http://dictionary.reference.com/browse/intellegent

Oh!  A spelling flame! What an masterly riposte!

I'm crushed!

But isn't that ironice as all get out? "intellegent" LOL

It's even . . . self-referential. Do you see how? It is an example
of a non-self-descriptive word. "English" is self-descriptive.
"Intellegent" is non-self-descriptive. So the question is: Is "non-
self-descriptive" self-descriptive? What's the answer? The answer
is . . . another paradox!!

Surely not this discussion.

Boy are you right on that one.

Glad you admit how stupid you are.





Would it be ok to define the sum of the angles of a triangle to be 180
degrees?  Or to define the distance between two points to be the
square root of the sum of the squares of the difference between the
two coordinates?  That is the distinction I am talking about - use vs.
misuse of definitions.

Defining the sum of the angles of a triangle to be equal to two
right angles is a perfectly good postulate equivalent to the parallel
postulate -- idiot.

Setting up a definition when there is already an axiom for it is a
perfectly good thing to do?

You really can't process plain english when it doesn't suit you to,
can you?

Charlie asks an irrelevant question, #1.

Who's Charlie?  I'm C-B, remember?

For the set of all ordered pairs of real numbers <x,y>, there's
nothing at all to prevent us from defining a distance metric D
between two elements <a, b> and <c,d>  D = sqrt |((a - c)^2 - (b - d)^2))|.
Under this metric the set of ordered real number pairs is Euclidean.
Idiot.

How does that illustrate the power of ZF when the whole proof is one
line: "By definition"?

You didn't answer the question.

Because it is irrelevant, as I pointed out.

 The answer is that it doesn't, so the
proof given has no relevance.

Defining a distance metric is not a one line proof of the Pythagorean
theorem;

Put the vertex at the origin and two sides colinear with the x and y
axes. Then the definition of the distance between the two non-vertex
points is the Pythagorean Theorem. qed

your question is irrelevant, and your answer to your question is
irrelevant.

Squirt more ink, squid.

I fill up about 1-3 pages per day with just new ideas. (I wonder if
anyone else here keeps stacks of papers containing only new ideas?) So
yes, I do squirt (a lot of ink.)

Charlie asks an irrelevant question #2.

I thought you were talking about "use vs. misuse of definitions," not
"illustrating the power of ZF".  Moving the goal posts?

I gave an example of misuse of definitions.

No, you didn't.  You just think you did.

 You are confused.

 <snort!>  

No, you are terminally confused about formal systems.  The evidence of this
is overwhelming over the past two years I've been reading sci.logic.

I have likely developed more axiomatizations of existing systems than
anyone else in the history of the planet. What is the world's record
(outside of me)? CBL is an abstraction from at least 5-6
axiomatizations. I have posted at least 5 different proofs of
incompleteness - and the number continues to grow. I no longer prove
Godel's or Rosser's theorems per se. I prove the general theorem of
there being incompleteness, with the axioms used being either Godel's,
Rosser's, some combination or really different, premises. (Of course
they never expressed their proofs axiomatically - who has? I mean
actually gave a formal proof, as opposed to saying they can?)

You are incapable of explaining, over the course of _two years_
(at _least_) an object as inherently simple as a formal deductive
system (which CBL, supposedly, is).

Inherently simple? The problem is that it's so new and different,
people have a hard time weaning themselves away from their old ideas
and security blankets.

Proof: You can't name one person, besides yourself, who understands,
or can explain, CBL.  

Flip through these messages and you'll see one or two.

Furthermore, you are acting as if, despite your four years of
honor's math and 800 SAT's, you have never heard of analytic
geometry. (Hint: Descartes invented it).

What's wrong with acting?

Therefore you have no right to complain and anything you say is
meaningless and incoherent babble.  The proof?  By definition.  (And
remember, you like and specifically approve of proofs based on 1
definition.)

Oh, yeah.  That makes a lot of sense.  _I'm_ confused, not you.  Right.

(Note for Mr. Literalist: the immediately above is sarcasm.)

 CBL is used to prove it by that reasoning.
                        ^^
What is the reference of this indefinite pronoun?

If that is a proof of the Pythagorean Theorem based entirely on ZF
then ...

No, "that" (the definition) is not a proof of the Pythagorean
Theorem, so we can dump the consequent clause.

<snip>

Whether CBL proves the Pythagorean theorem or not is, of course, a
complete mystery to me and everyone else.

I don't know that anyone asked. But you are ALL missing the obvious
when you ask if it can prove what you claim some other system e.g. ZF
can prove.

1. Where did ZF get the axiom "There exists a zero." etc.?
2. Since ZF stole it, why can't CBL?
3. I.e. if I wanted to show that CBL proves what people think ZF
proves, all I have to do is to also steal Peano's Axioms and say they
are part of CBL. Now is that a worthless exercise or what?
4. But I don't - why? Because CBL is designed for Metamathematics,
not Mathematics. I don't add functionality outside of that in order
to keep it at a high level and thus incredibly efficient at creating
theorems.

You asked whether ZF proves the Pythagorean
theorem (when point, line, etc. are interpreted as
particular types of sets). The answer is: yes, it's
provable in just a few lines. Every standard theorem
about Euclidean geometry is provable.

Ok, here's a simple one: For any finite set of points in a plane there
is a line that contains all of them or exactly two of them.

Yessuh, Massa Charles, we be gettin' right on it!  Anything you
wants, suh!

Being asked to substantiate a mathematical statement is equivalent to
a racist joke?

Charlie asks irrelevant question #3.  You're the joke.

It is a very nice theorem from Geometry that can't be proven by
declaring one definition.

It's a theorem?  Prove it.  Formally.  No BS.  From Euclid's axioms.
No omitted "lemmas".  I don't think you know what you're talking about.  

It is certainly a theorem. I though I was supposed to be the dumb one
here? And I never said anything about proving it with an axiomatic
system myself.

No referring me to BS texts either, that don't give the formal proof
in full.

Put up or admit you're a liar.

I'm a liar because I said that for any finite set of points in a plane
there is a line that contains all of them or exactly two of them? Is
that what you believe? Here's your shovel (not just to follow behind
the elephants that parade around here - to dig your own grave.)

I think that a healthier attitude than being so cavalier as to declare
all of Mathematics to be provable by ZF is to:

1. Ask what can be proven in ZF.

2. Drop the idea that ZF’s 10 axioms have anything to do with it
(outside of Set Theory).  It’s all from Peano’s Axioms and the use of
sets to represent real numbers.

3. Recognize that Peano’s Axioms amount to the 3 relations of
addition, multiplication and TRUE (the universal set) being
representable (without reference to the actual axioms.)

Fantastic idiocy.  You just haven't a clue, do you?

The above (including what you snipped) is true.  Peano's Axioms do in
fact imply that these 3 relations are representable, and vice versa.

I was referring to all three of your assertions.

Btw, how do the Peano axioms imply the representability of
"the universal set"?

ISANUMBER(x) is provable for all x in the universal set by induction,
so that ISANUMBER(x) represents the universal set.

ISANUMBER(0) is "There is a zero" and (all x)ISANUMBER(x) =>
ISANUMBER(suc(x)) is "For every number there is a successor." so (all
x)ISANUMBER(x) is provable by Induction.

So ISANUMBER(x) =def Ey[y = x]?

Well, I would hope that x=x actually. (Although that old dictum is
not actually true.) Insert a few select spaces in the name and maybe
you'll see what ISANUMBER means.

 This represents "the universal set"
"without reference to the actual axioms"?

That's deep stuff, Charlie.

*blush*

The problem is that you are too dumb to think of important significant
discoveries in Mathematics or Metamathematics like the above that I
thought of, so you wine and cry about other things.

Yes, I'm crying in my wine:http://dictionary.reference.com/browse/wine.

Sorry, that doesn't make you any smarter.  You need to read up on the
subject. At your level, that would be a kindergarten book on how to
count.

Ah, well -- in vino veritas.

In contrast, I am so smart that I discovered that a fundamental axiom
of computing is ~LT(I,x) which means, "We can count to any given
number."  This is a quite remarkable discovery with significant
implications regarding foundations of Mathematics and
Metamathematics.

Yes, exciting stuff.

To discover that one of the 3 or 4 axioms of the Theory of Computation
is what children learn in the 1st grade is not exciting?

 And people took my picture at the NIST meeting
because I am so smart and they like me.  The only time you ever had
your picture taken in public was for the same reason they took
pictures of Pee-wee Herman in a movie theatre.

That's funny -- there's a picture of me hanging in a restaurant
right down the street.  Did they hang that picture of Pee-Wee in
a restaurant?

Don't know - I was at the NIST convention at the time.

I'd stop eating there if I were you.

I won't say what I was eating. (Rank has its privileges.)

C-B

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