Re: Godel proved maths inconsistent not incompleteness theorem

In article
<9df49f3b-9476-475f-97c8-ffc2c184fd89@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Charlie-Boo <shymathguy@xxxxxxxxx> wrote:
[cut]
And if my description is in fact poorly written, tell me what wording
is unclear. I will glady - eagerly - try to make it more
intelligible.

I find it hard to understand CBL because you usually give all the things
that CBL can do. Such a presentation forces me to try to see how all
that fits together and raises questions for me that concern this
inter-relation between all these things. But, I would prefer to
concentrate on just one of the things that CBL can do and work from
there.

I would like to chose "Set Theory" of the many things that CBL does.
I think it would help to present CBL with regards to "Set Theory" only.

I quote from a former post of yours:

==========================
5. Set Theory
We can state most of the standard axioms of Set Theory pretty easily.
Many are theorems from more primitive axioms than those given in
print.  For example, Pairing is theorem EQ(I,x)vEQ(J,x) from axioms
EQ(I,x) for every thing there is a set that contains just it, and P,Q
=> PvQ the union of two sets is a set.  Comprehension is P/SE , Q/TW
=> P^Q/SE.
When you formalize these axioms in CBL you notice that they refer to
other mathematical objects like functions and wffs, without giving
axioms (formal definitions) for them.  And remember that not being
exact about what a wff consists of is what gets us in trouble with the
Russell Paradox.
==========================


Request 1: What is the starting explanation of how CBL does "Set
Theory"? Keep it brief; I can ask you to expand on it further later.
From that former post that I mentioned above, I suspect that you will
give the axioms, terms, etc that form the basis of CBL Set Theory.

Request 2: I object to the wording "axioms (formal definitions)" above.
For me, "axiom" does not mean "formal definition." I think the standard
terminology is that "functions are primitive" something. I forget what
that "something" is.

Request 3: If you can, include Pairing that you mentioned above, unless
it will take pages to get to that point (if so, we can come to pairing
later after request 1 is done).
.

Relevant Pages

  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... concentrate on just one of the things that CBL can do and work from ... I think it would help to present CBL with regards to "Set Theory" only.. ... We can state most of the standard axioms of Set Theory pretty easily. ... I am not interested how CBL generate theorems of set theory. ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... I find it hard to understand CBL because you usually give all the things ... I think it would help to present CBL with regards to "Set Theory" only. ... We can state most of the standard axioms of Set Theory pretty easily. ... You mean how do I generate theorems of set theory? ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... concentrate on just one of the things that CBL can do and work from ... I think it would help to present CBL with regards to "Set Theory" only. ... We can state most of the standard axioms of Set Theory pretty easily. ... I am not interested how CBL generate theorems of set theory. ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... I find it hard to understand CBL because you usually give all the things ... I think it would help to present CBL with regards to "Set Theory" only. ... We can state most of the standard axioms of Set Theory pretty easily. ... You mean how do I generate theorems of set theory? ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... you are using them in a standard way in CBL. ... assertion that the set of theorems is ... Any system where PR being the set of theorems satisfies the axioms. ... theorems or truths of any given system besides your say so. ...
    (sci.logic)