Re: Godel proved maths inconsistent not incompleteness theorem

On Tue, 25 Mar 2008 05:36:46 -0700 (PDT), Charlie-Boo
<shymathguy@xxxxxxxxx> said:
On Mar 24, 2:24 pm, Peter_Smith <ps...@xxxxxxxxx> wrote:
Peter Smith claims his book has my proofs, but see my reply - his
statements are not so. His proofs are an order of magintude
longer and more complex than mine.

Hardly. What I said was that some of the proof ideas you very vaguely
wave your armsat (e.g. about the unsolvability of the halting problem
entailing that the set of true sentences is not r.e.) are widely
available in the literature in properly worked out versions.

There is so much nonsense in just these 4 lines, where do I begin?
(Besides the fact that this is not what you said.)

1. What part of my proofs is vague and armwaving?

They are armwaving at every point at which you introduce a critical
notion requiring rigorous formal definition as an undefined primitive,
e.g., "recursive", "r.e.", "true", "sentence", "theorem", "Turing
Machine", "halts", "solvable", "representable", "expressible", etc etc.
They are vague when you supply them with nothing more than informal,
English interpretations.

2. "some of (my) proof ideas are available in the literature"? That's
bad?

No, of course not. What he's saying is that, in the literature, one can
find mathematically rigorous proofs of theorems for which you provide at
best vague and armwaving proofs.

Let's consider the negation of this statement: None of my proof
ideas are available in the literature. That would be preferable? But
then none of the proof ideas available in the literature would be used
in my proofs and CBL wouldn't be doing the job of capturing their
proofs!

You are literally saying that it is wrong if CBL formalizes proofs
that have been published!

No, he's really not saying that at all. He's saying that what you are
calling a formalization of those proofs isn't really.

Of course some of my proof ideas are available in the literature. In
other words, some of the proof ideas in the literature are available
in CBL! In fact, a ton of them are. Isn't that a good thing??

It might be if they were worked out in CBL with anything like the
necessary rigor found in the literature.

As far as your book goes, honestly, the proof that the true sentences
are not enumerable is WAY more complex than necessary. I can prove
this theorem in numerous ways (see my postings - will post them again
if you'd like to discuss this) and they are ALL much shorter and
simpler than all of the gyrations (7 or 8 steps) that you go through.
And this is just the first of the proofs that you say are mine. No,
it isn't my proof. It's way the heck longer and more complicated than
the CBL proof of this theorem - all of the CBL proofs I have given, in
fact.

The CBL proofs are formal, simpler and numerous in number.

Your proofs do not have the content you claim for them due to the
problems noted. They are shorter and simpler because they are lacking
all of the necessary infrastructure that a real proof of the results in
question requires. Your theorems simply don't have the content you
think they have.

You provide one long messy proof and you say that is better than CBL's
numerous simpler proofs?????????

Well, it isn't quite right to say his proofs are *better*, because yours
aren't really proofs of the results in question at all. They are at
best stubs that you might be able to fill in by adding all of the
necessary infrastructure that is worked out in detail in books like
Peter's.

Can you (anyone) prove me wrong?

I believe I have pointed out exactly what is wrong with CBL above and in
several recent posts.

You like to brag about your book (no problem - I thanked you for the
interesting reference) but are you honest enough to admit something is
shown to be superior? Because I'm not a fucking professor and you
will lie, cheat and steal to the end of time to deny credit to anyone
outside of your peers.

Really, that's just quite ridiculous.

(Look through journals and see how academia dominates publishing.
Where are the mathematical geniuses who don't have a job working for a
college or university?)

Lots of terrific mathematicians work for IBM, Microsoft, NIST, NSA, and
lots of other government and private organizations. Many of them
publish regularly in academic journals.

.