Re: Godel proved maths inconsistent not incompleteness theorem

On Mar 12, 12:11 pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
On Mar 11, 1:07 pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
On Mar 10, 4:04 pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
MoeBlee <jazzm...@xxxxxxxxxxx> writes:
On Mar 10, 12:11 pm, Charlie-Boo <shymath...@xxxxxxxxx> wrote:
On Mar 10, 6:47 am, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:

Be a sport,

When have I not?  (Unsubstantiated innuendo?)

(1) No, he didn't insinuate that you're not a sport. (2) But the
answer to your question includes such instances as never getting back
to me as to the purpose of your question about set theory that I
answered in full (our very first discussion), and not recognizing the
examples given to you of theorems of mathematics proven by ZFC.

By the way, did you ever figure out how to prove in Z set theory that
if a set and its complement are recursively enumerable then the set is
recursive?

got to be easy --
just feed it into CBL and turn the handle, AIUI.

What's with the Z?  You want it in CBL?  It's probably trivial.  I
think it's an axiom, in fact.

you *think* it's an axiom?

Name 2 authors who agree on what the ZF axioms are (or for that
matter, the CBL axioms).

For the first, Takeuti and Zaring.

I think they're brothers.

For the second, how come *you* don't know?

where can I find the list of all CBL axioms?

Here:

1. Program Synthesis e.g. for PHP programs

"e.g." doesn't cut it.

Please read the rest and comprehend. There are an infinite number of
programming languages. I show the axioms for one enough to synthesize
a useful program nobody else has ever synthesized, the test for being
a factor.

People who write about a Program Synthesis system without reference to
the programming language are already BSing you. The axioms depend on
the language.

(I synthesize two different programs, that use differemt algorithms,
something those who translate one programming language into another
cannnot do. I can also complement each request: list all factors or
list all nonfactors, something else inputting a program cannot do as
you can input a program to list all prgrams that halt but you cannot
input the complement.)

So, there is no complete list of CBL axioms;

See above.

far from being a dinky
little system like ZF, it's not even properly defined to start with.

ZF does nothing useful. It's axioms are not even enough to decide any
useful question about sets. What it does do is to show silly little
statements about sets that we already know are true. What new fact -
or any fact the least bit subtle - has it shown?

The real intent was to say they fixed the Russell Paradox because it
is all formal, but what they have is no solution as it doesn't provide
the facilities needed in an axiomatization: to be able to decide
questions about Set Theory. (CBL decides numerous questions about all
sorts of branches of CS.)

What new facts has ZF shown us? Rememeber, that's ZF, the 8 or 10
axioms.

(The real source of the problem is that they are inconsistent about
what a wff can contain. "Can a wff contain a reference to something
that is not a set?" The Russell Paradox occurs because they are
inconsistent on this question. Pick an answer (yes or no) and there
is no Paradox if you keep that answer in mind. They never thought of
it because they didn't even know there was such a thing as a non-set.
In fact, some still say to this day that "Everything is a set."!! {x|
~(x e x)} is not.

This is common in "Paradoxes" e.g. Unexpected Exam/Hanging and God
Paradox are the same. "Can we expect more than once?" is not
addressed and is inconsistently implied and refuted by the logic
used. This is all shown clearly by CBL, which is why I am able to
post so many proofs of theorems of Godel/Rosser/Turing et. al. One
proof generated by CBL was called the shortest one for Godel-1 by an
author of a book on Godel's Theorems, and I immediately provided a
shorter one - so that must be unpublished so far (outside of Google
Groups.)

C-B

--
Alan Smaill- Hide quoted text -

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