Re: Godel proved maths inconsistent not incompleteness theorem

On Apr 16, 1:55 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Apr 15, 6:28 pm, Charlie-Boo <shymath...@xxxxxxxxx> wrote:

On Apr 15, 6:07 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
The claim that virtually all of ordinary mathematics can be formulated
in ZFC is not itself a formal mathematical claim. I've read a modest
amount of set theory, and then introductory abstract algebra,
topology, analysis, graph theory, and computability theory to see how
it can be formulated in ZFC.

Oh BS.  Nobody has published a formalization of computability theory
proofs (though trivial in CBL.)  

AGAIN you change the terms of the discussion. I said that the
mathematics can be formulated; I didn't say that someone belabored the
matter by printing out every single formula in the pure language of Z
set theory.

If you can formally prove prove any computability theorem using ZFC,
then no matter how big or complex it is, you could give a simple
(short) proof as an example, and give a detailed explanation of how
the big ones work. Saying it's too big to give doesn't make it.

C-B

I posted paragraphs worth of explanation of that matter
already.

What would the axioms and rules be?

We told you a thousand times already!

What would the formal proof of the Unsolvability of the Halting
Problem be like?  What would the logic be like?

I've told you already, in general. As to any specific result, just
define all the terminology in set theoretical terms (easy to do for
the halting problem since Turing machines are easily formulated in set
theory), then apply only axioms of set theory and first order logic to
prove the result in a manner that parallels any of the common informal
proofs.

You got no fuckin' answer but sarcasm and references that don't
contain ZF proofs claimed - not containing any ZF proofs at all.

You're lying about what I said, as I've made it clear over and over
the difference here. I didn't say the references contain ZF proofs.

I asked for a reference that contains formal ZF proofs of anything
outside of Arithmetic and Set Theory. You gave references. But then
I looked at them and they didn't have the proofs.

It's a waste of time to keep saying this. If you have a formal proof
as we are discussing, then start a thread saying that and include
them. Anything else is BS excuses.

C-B

I said they contain proofs that can be formulated in ZF.

Your problem is that you are schizophrenic.  On the face of it, you
claim that ZF does essentially everything we could ask for in
mathematics,

No, I did not say that. I said that it is claimed by knowledable
people that virtually all of ordinary mathematics can be formulated
and proven in ZFC and that in my own liimited study I have not yet
found a counterexample (and I even mentioned that I recall reading
some mathematicians differ by saying that there are some theorems in
some advanced areas that require visual proof).

If you don't believe that that
mathematics can be formulated in ZFC then you're welcome to stay
ignorant of it; meanwhile, the best I can do is to suggest that you
read the books like other people do; I have no interest in "proving"
for you what you would witness yourself if only you took some simple
steps toward an education in the subject of foundations of
mathematics.

MoeBlee

.

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