Re: Proper class.Proper class ?

Jonathan Hoyle wrote:
I don't have to believe that they are all competent and honest. I only
need to believe that some of them are, and observe that they all pretty
much agree on this point.

Then why ask why I should get a different answer from this newsgroup if
your statement refers to only some of its participants?

They don't refer to just some of them. All professional mathematicians
agree on this point.

How do you know what all of them believe?

If, as you say, you don't have to believe they are all competent and
honest, then they might as well be stupid liars, so their opinion is of
limited value, isn't it?

How does their agreeing make them not wrong?

Because they all have read the proofs.

But can't a person read a proof and then draw erroneous conclusions
about it?

What prompted the development of ZFC in the first place?

You act as if this were a contraversial topic.

How did I act like that? I didn't say anything about popular
opinion.

It is not, and has not been for over a century.

On what basis can you make that claim?

On the basis that the entirity of the professional mathematical and
logical community agree.

How do you know that they all agree?

I'm a Mathematician and I don't agree.

If there is no controversy, then why are there so many alternatives
(ZF, ZFC, NF, NFU, MK, NBG, etc.)? That is quite the opposite of your
claim of it not being controversial.

You seem to think that because there are multiple axiomatic systems fo
set theory that therefore there must be some contraversy. Nothing can
be further from the truth.

If there is controversy as to what the solution should be, then people
would propose alternate solutions to what has been published,
wouldn't they? How is the current situation any different from that?

Professional logicians are may work in any
one of them. Just as there exists both Euclidean and Non-Euclidean
Geometries,

Those are different theories, not different axiomatizations of the same
theory.

It is ironic that you would refer to "basic introductory literature
of set theory" when essentially all such discussions talk about the
various opposing opinions as to how to axiomatize set theory - a
direct contradiction to your claim that there is no controversy.

Never once have I alluded to "various opposing opinions as to how to
axiomatize set theory".

Who said you did?

That different axiomatic systems exist is
true. However, there are "no opposing opinions" about them. Logicians
and mathematicians agree that they are each valid in their own system.

If the problem is adequately solved, why do they need to come up with
additional solutions?

Although there will always be crackpots (such as yourself),

I beg your pardon? What is that supposed to mean?

That you are a crank. For more detailed information on what that
means, go to http://www.crank.net and look up the section on
Mathematical cranks.

What have you seen that makes you invoke that notion?

the professional mathematical and logical community agrees.

What specifically demonstrates that?

All of their publications for over a century.

Have you read them all?

Yet you again refer to popular opinion - is that a basis for a
scientific conclusion?

I am not referring to popular opinion. I am referring to mathematical
proofs that have been confirmed by the professional mathematical
community en masse.

Isn't that just an expression of their opinion? Isn't it possible
(in principle) that someone might disagree?

"In philosophical discussion, the merest hint of dogmatic certainty as
to finality of statement is an exhibition of folly." - Alfred North
Whitehead

Do you believe Whitehead?

<remaining rant snipped>

You wrote, "And it has been proven that NBG Set Theory (in which
classes are defined) is equi-consistent with ZFC, So it is valid."

I replied, "Valid in what sense? Simply declaring that two things
are equivalent doesn't prove that either of them is of value."

How is that a rant? Is asking a question a rant?

Does simply declaring that two things are equivalent in fact prove that
either of them is of value?

C-B

Jonathan Hoyle
Eastman Kodak

.

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