Re: Godel proved maths inconsistent not incompleteness theorem

On Mon, 17 Mar 2008 18:28:27 +0000 (UTC), Chris Menzel
<cmenzel@xxxxxxxxxxxxxxxxxxxx> wrote:

On Mon, 17 Mar 2008 09:58:29 -0700 (PDT), MoeBlee <jazzmobe@xxxxxxxxxxx>
said:
On Mar 16, 8:01 pm, Chris Menzel <cmen...@xxxxxxxxxxxxxxxxxxxx> wrote:
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".

Wow, Charlie-Boo is STILL making that challenge and IGNORING replies.

And still unable to see that CBL is just Magickal Thinking. E.g., in
CBL, "P(I)" just *means* "P is recursive", where "recursive" appears to
be an undefined primitive; "YES(x,y)" just *means* "Turing Machine x
halts yes on input y", but one looks in vain for the definition of a
Turing Machine and what it is for one to halt on a given input. Simply
*declaring* those expressions to mean the complex concepts that he
intends them to mean is his idea of an adequate formal theory, simply
because he has no clue what a formal theory *is*.

So it would appear.

Of course he could prove us wrong by writing that CBL proof
checker - that would prove that CBL is in fact "formal" in the
required sense.

(Not that CB cares, but the point is that the axioms and rules
need to be clearly defined, and clearly defined _only_ in terms
of the _syntax_, with no reference to what anything "means",
so that one can determine whether a proof is correct by just
looking at the syntactic structure of the lines in the proof,
_without_ knowing what anything "means".

Which of course is exactly why writing a proof-checker
would be compelling evidence that we're all wrong about
CBL, because the computer _doesn't_ know what anything
means.)

But instead of
educating himself -- he certainly seems smart enough to learn the
material -- he appears to be stuck in the illusion that his work is
simply too innovative and original to be accepted by a mathematical
community that is blinded by its ossified traditions. Pity that. I
mean, I'd really *like* the guy to have the pleasures of learning and
appreciating the actual mathematics he's groping toward. I guess that's
why I keep responding in off moments.

David C. Ullrich
.

Relevant Pages

  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... what should be an intelligent discussion of principles of Mathematics. ... points is the Pythagorean Theorem. ... CBL is an abstraction from at least 5-6 ... there being incompleteness, with the axioms used being either Godel's, ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... what should be an intelligent discussion of principles of Mathematics. ... points is the Pythagorean Theorem. ... CBL is an abstraction from at least 5-6 ... there being incompleteness, with the axioms used being either Godel's, ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ...  How does this tethering happen in real mathematics? ... any evidence that CBL is tethered in the same way to computation at ... with axioms written in CBL, as I have done and described for PA. ... From that point onward, PR refers to the set of theorems, ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... what should be an intelligent discussion of principles of Mathematics. ... points is the Pythagorean Theorem. ... CBL is an abstraction from at least 5-6 ... all I have to do is to also steal Peano's Axioms and say they ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ...  How does this tethering happen in real mathematics? ... Well, "tethering", as I was using it, is a relation between a formal ... axioms for group theory and the class of groups that those axioms pick ... And that's exactly what CBL is doing. ...
    (sci.logic)