Re: Godel proved maths inconsistent not incompleteness theorem

On Mar 24, 12:35 pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
On Mar 17, 10:55 am, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
On Mar 17, 8:47 am, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Chris Menzel <cmen...@xxxxxxxxxxxxxxxxxxxx> writes:
On Sat, 15 Mar 2008 01:25:35 -0700 (PDT), Charlie-Boo
<shymath...@xxxxxxxxx> said:
...
...the ZF axioms aren't used to prove anything outside of simple,
fairly obvious, statements about sets.  

Ignorant codswallop.  I gave you three examples (of thousands):

1. Every singular limit ordinal k with cofinality < card(k) lacks the
Souslin property.  

2. The Stone Representation theorem (every Boolean Algebra is
isomorphic to a field of sets)

3. Every normal function on the ordinals has arbitrarily large fixed
points.

(Refutations welcome.)

Where "welcome" = "ignored".

Also ignored was my pointer posted earlier to a machine-checked proof
of Tarski's fixed point theorem,

(Actually, I asked for a little evidence and am still waiting.)

read the article;

What does it mean for a proof to be machine-checked and how does that
prove the theorem?  As I said before, that only shows that someone
typed in the right syntax for that system.  It doesn't say anything
about what the input represents or how it relates to the theorem.

read the article;
if you want clarification, read the book that describes the
theoretical basis for the (implemented and generally accessible)
system in which the results are proved.

You can start by stating the formal representation that they used and
proved for these theorems.  Then I would be very interested in these
proofs that use only the ZF axioms.

read the article.

and the theory of recursive
functions, both in ZF.

How does one prove "the theory of recursive functions"?  What doe that
theorem state?

Read the article.

Where does someone talk about "proving the theory of recursive
functions"?

Why are you quoting yourself?

You can find from the article easily enough what results from the theory
of recursive functions are proved, should you deign to read it.

What the books and articles do, if they give anything at all, is to
list a humongous formalism and say that proves the theorem.  The
problem is, a formal proof doesn't consist of just a formalism.  It
must also contain a mapping from that formalism to an "actual" proof -
something that shows us that the theorem must in fact be true.

You asked for proofs that use ZF, explicitly.
Here they are, should you deign to look.

This is back to the same old BS that Einstein warned us about (see
quote elsewhere.)  Showing a bunch of equations doesn't prove
anything.  You have to show how that equates to a proof of THAT
PARTICULAR THEOREM.

What it shows, contrary to your assertion, is that results like
the Tarski fixed-point theorm can be, and have been, formalised
in ZF and proved.  You asked for the formal representations
and proofs in ZF -- stop moaning when you get what you asked for.

Do your own work,

I didn't do the work so the claim is not substantiated and whoever
made the claim is not giving an honest mathematical proof.  I'm not
sure why it's "my work".  The consequence of not substantiating a
claim of a mathematical nature is that its author is deficient.  I
didn't make the claim.

The work in question is actually reading a short article and making an
effort to understand it, rather than asking others to explain it to
you, when you are perfectly capable of understanding it yourself.

If you wanted to ...

Ok, if I track down that article and it doesn't do as you say, what is
my compensation? How about, "Alan Smaill is a liar when it comes to
Mathematical Logic and shouldn't be believed."?

(I'm still trying to get my money back for Peter Smith's book.)

C-B

I don't even think such a substantiation exists, myself.

there are none so blind as those that do not wish to see.

C-B

--
Alan Smaill
.

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