Re: Tolerance of hate in Sci.Math

On Aug 3, 1:42 pm, Transfer Principle <wall...@xxxxxxxxx> wrote:
On Jul 30, 5:49 pm, Nosebleed <jazz...@hot mail.com> wrote:

On Jul 30, 3:19 pm, Transfer Principle <wall...@xxxxxxxxx> wrote:
There are some posters, whom I often call standard
theorists, who regularly call certain posters
"cranks" and belittle them, but such posters also
participate in threads in which standard theory is
discussed, threads that have nothing to do with
"cranks" at all. These posters, including Nosebleed,
Virgil, and others, are quite reasonable in threads
that have nothing to do with "cranks."
Anyway, cranks (who ignorantly, arrogantly, and persistently spread
misinformation and speciousness) deserved to be called 'cranks' and
to
be ridiculed.
No one deserves to be ridiculed and to do this a sci.math is a
disgrace to learning. --Musatov
Meanwhile, if a poster's attacks on cranks and especially SPAMMERS
are
justified, then the poster doesn't have to also post on other
subjects
in order to avoid a "zero respect" rating by me.
You should not respect anyone who attacks another poster.

That post, among several recent posts, seeks to answer
whether calling someone a "crank" is ever justified.
Calling someone a "crank" is never justified.

As I reach the second anniversary of my first post
here, I wonder, why am I here? What did I ever hope to
accomplish by posting at sci.math? Two years ago, I
saw how certain posters are called "cranks," and I
wanted to convince those who call them "cranks" that
the "crank" label is not justified. Obviously, the
post I quoted above shows that many posters still
consider the "crank" label to be justified.

The oldest post of mine (at least the oldest post I am
able to find on Google) was in a thread started by
tommy1729, called "A CHALLENGE TO VICTORIANS" (with
the name "Cantor" being another word for "standard
theorist"), in which the OP asked whether there is a
cardinal kappa such that 2^kappa = Aleppo_0. Along the
way, he suggested that Aleppo_1 =def 2^Aleppo_0, (as
opposed to be equivalent to Continuum Hypothesis) which
led to many posters calling him a "crank." And so this
attitude, in the minds of many, justifies the "crank"
label for tommy1729.

More recently, the poster WM claims that he has a
proof that PFC is inconsistent. Even I acknowledged
in that thread that Wm's proof of ~Con(PFC) is not a
valid proof. But then many posters wondered, why do I
refuse to take the next logical step, and accept that
the "crank" label for WM is justified?

The difference between most posters and myself is
that I'm willing to look past tommy1729's and Wm's
misconceptions about CH and ~Con(PFC) and look at
their desiderata for new theories. Most posters, on
the other hand, look only at their misconceptions
about CH and ~Con(PFC) and call them "cranks" for it,
thereby ignoring their desiderata for new theories.

The word "crank" is a thought-terminating cliche. As
soon as someone is called a "crank," nothing that
person says is taken seriously, not even if something
interesting comes out of what that person says.

I still think that underneath all the misconceptions
about PFC, there is a theory here, a theory that
might serve as a viable alternative to PFC yet
satisfy _some of_ the desiderata of many "cranks." I
want to be able to discuss this theory without
worrying about whether it matches _all of_ the
desiderata of a particular "crank" (including mutually
incompatible desiderata), and/or be accused of
misrepresenting the "_crank_" because the axioms I
give contradict something the particular "crank" said.

And so I give the following as my _own_ desiderata for
an alternate theory:

1. All the axioms of Z are to be retained except for
one -- the Axiom of Infinity. I want to change this
axiom but keep all the axioms of Z-Infinity.

This desideratum eliminates the problems I've had
recently with meteorology/shifting sets/three-valued
logic that arose in recent threads. I don't want to
make radical changes to Z -- in particular, I'd like
to keep the language of Z.

2. The new theory proves ~Infinity as a theorem but...
3. Adopting ~Infinity itself as an axiom is not
satisfactory, because I want the axiom to imply the
existence of a new set -- which I have often called
"alpha" in previous threads.

So alpha is supposed to be an infinite set, whose
existence not only fails to imply in Z-Infinity the
existence of a successor inductive set omega, but
actually proves that omega _isn't_ a set.

Now I wonder, what sort of set could alpha be? As we
keep in mind that all the axioms of Z other than
Infinity are available, we consider the following:

x1ex0, x2ex1, x3ex2, x4ex3, ...

This is an infinitely descending chain. Now we know
that in Z, such chains don't exist because of the
Axiom of Foundation/Regularity. But -- as I've
pointed out before -- Foundation only states that
every nonempty set is disjoint with one of its
elements, and that the axiom alone doesn't disprove
the existence of infinitely descending chains, or
even cycles such as:

hey, ye

For if x={y} and y={x} (with ~x=y), both x and y
are disjoint with their lone elements. Rather, it's
{x,y} -- which is a set via by Pairing -- which
fails to be disjoint with its elements. Similarly,
it's not necessarily x0, x1, x2, etc., which fail
to be disjoint with their elements, but rather:

chi = {x0, x1, x2, x3, x4, ...}

So unless we can prove that chi is a set, the chain
of sets x0, x1, x2, etc., can still be infinitely
descending without contradicting Foundation!

Now in Z, we can prove chi is a set. To prove it,
we start with omega which exists via Infinity, then
use the Replacement Schema to replace 0 with x0, 1
with x1, 2 with x2, and so on. But in Z-Infinity,
we can't prove chi is a set -- instead, we conclude
from the existence of the chain x0, x1, x2, ...
that omega _isn't_ a set, since if it were a set,
we could apply Replacement to it to obtain chi,
which violates Foundation.

So alpha can be a set which contains all of the
sets x0, x1, x2, ..., as elements, plus extra
elements disjoint with alpha. Notice that chi can't
be a definable subset of alpha -- that is, there is
no formula phi such that:

{alphabet | phi(x)} = chi

for then we could apply Separation Schema to obtain
chi, which violates Foundation.

So our axiom would look something like:

"There is a set with an infinitely descending chain."

But that's English, not the language of ZF. And this
is where I'm stumped -- I can't find an axiom which
states that an infinitely descending chain exists,
yet doesn't imply that omega exists or invite the
use of Separation to isolate the chain.

The best I can do is try a "mohair" trick -- let the
primitive symbol V represent the chain and write:

~V=0 & Ex (~x=0 & At ((ye & ye) -> E (zen & ex & zen)))

and then restrict Separation to formulas phi that
don't mention the symbol V. But this isn't very
elegant at all -- I'd like to be able to avoid extra
primitive symbols like V, and keep the other axioms
of Z the way they are without relativistic them to
V or mentioning V at all.

I expect no one to help me write an axiom that does
satisfy all of my desiderata. The "cranks" won't
help, since my desiderata aren't identical to _all_
of their own desiderata. Also, the non-"cranks" will
not help me either, since I have spent the last two
years antagonizing them as my enemies and besides,
their "help" would consist of pointing me to some
book I can't access anyway.

So it appears that I'm on my own here. Still, I hope
to accomplish much more with this theory than I did
trying to convince posters not to call each other a
"crank," since it doesn't appear that they'll stop
using that five-letter word anytime soon.

--Musatov
.

Relevant Pages

  • new-idears Re: .9 repeating
    ... I would definitely killfile some posters. ... crank chasers draw the word ... "crank" to talk about crank chasers. ... I wish the psychology science would come up with a better term for ...
    (sci.math)
  • Re: Tolerance of hate in Sci.Math
    ... "cranks" and belittle them, but such posters also ... whether calling someone a "crank" is ever justified. ... axiom but keep all the axioms of ZF-Infinity. ... The new theory proves ~Infinity as a theorem but... ...
    (sci.math)
  • Re: Would it matter if ZF was inconsistent?
    ... So the use of the word "crank" to describe WM is ... but unfortunately other posters besides MoeBlee ... "crank" would agree with MoeBlee's reason for doing so. ... a question about _probability_, not definiteness. ...
    (sci.logic)
  • Re: irrational number continuum
    ... the reasons for using those words.) ... MoeBlee's conception that certain posters need to be called ... self-deluded, arrogant, or incompetent a crank may be, ... if I were to agree with Marshall completely, ...
    (sci.logic)
  • Re: how to list all of the real numbers
    ... theory, etc., I have never seen him challenge set theory. ... One can be a crank about subjects other than ... of course, the Axiom of Infinity. ...
    (sci.math)
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