Moebius schrieb:

Am 22.04.2024 um 21:36 schrieb Jim Burns:

However, deleting context courts confusion,
as you have noticed.

That's why I tend to use (i.e. stick to) standard notation and common
notions (in this context).

Folks and people are different, the more in societies with more plurality.

:-)

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Jim Burns schrieb:

On 4/26/2024 10:37 AM, WM wrote:

Le 26/04/2024 à 01:11, Jim Burns a écrit :

On 4/25/2024 4:03 PM, WM wrote:

If all smaller numbers are doubled,
then there is no place for
the doubled numbers below ω.

If n is below ω
then n can be counted to from 0
then n⋅2 can be counted to from n

That is true for definable numbers
but not for the last numbers before ω.

If any number below n canNOT be counted to from 0
then n itself canNOT be counted to from 0

Thus,
each number which CAN be counted to from 0
is not above
any number which canNOT be counted to from 0

By definition,
ω is between
numbers which CAN be counted to from 0 and
numbers which canNOT be counted to from 0

Imagine being someone who denies that definition of ω

Because the following isn't a claim about ω
you (the denier) should still admit:
if n can be counted to from 0
then n*2 can be counted to from n
then n*2 can be counted to from 0 (through n)

If ω exists as defined,
then doubling never crosses ω
(from CAN to canNOT)

Even if ω doesn't exist as defined,
then doubling never crosses
_where ω would be if ω existed_
(from CAN to canNOT)

ω is NOT a simply.humongous.instance of
the numbers 0 1 2 3 ...
ω marks a boundary between domains with
different descriptions (CAN and canNOT).

Imagine being someone who denies that
ω marks that boundary.
With or without the marker,
the domains (CAN and canNOT) remain
the domains (CAN and canNOT).

This is really well put!

Unfortunately, WM is not interested in our ideas of (our) math and
logic but in his own (mostly read up upon) ideas and his flexible
and willingly deformable "true logic" which a "normal" person can
even "feel" -- but even more is WM interested in (we) WHAT folks
CLAIM and STATE about (our) math, more than about that math itself.

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Am 01.05.2024 23:46:38 Moebius schrieb:

Am 30.04.2024 um 15:12 schrieb WM:

If n is before ω then n⋅2 is before ω. (*)

That is not true.

Doch, doch, Mückenheim, das ist wahr.

Für den Beweis brauchen wir lediglich 2 (im Rahmen der ML beweisbare) Tatsachen:

(1) n < ω <-> n e IN

und

(2) An e IN: n⋅2 e IN ,

sowie die Definition:

(3) x is /before/ y iff x < y.

Nun der Beweis von (*):

Es gelte "n is before ω", d. h. mit (3): n < ω. Mit (1) folgt daraus n e
IN und daher mit (2) n⋅2 e IN. Mit (1) folgt daraus n⋅2 < ω und mit (3) dann "n⋅2 is before ω". Wir haben mithin also gezeigt, dass "If n is before ω then n⋅2 is before ω" gilt. qed

passt... (oder auf 'nntp': ack)

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Am 02.05.2024 00:46:01 Jim Burns schrieb:

On 4/26/2024 3:27 PM, Tom Bola wrote:

Jim Burns schrieb:

ω is NOT a simply.humongous.instance of
the numbers 0 1 2 3 ...
ω marks a boundary between domains with
different descriptions (CAN and canNOT).

Imagine being someone who denies that
ω marks that boundary.
With or without the marker,
the domains (CAN and canNOT) remain
the domains (CAN and canNOT).

This is really well put!

Thank you for saying so.
It's a nice change from
what I usually hear about me.

Unfortunately,
WM is not interested in
our ideas of (our) math and logic
but in his own (mostly read up upon) ideas and
his flexible and willingly deformable "true logic"
which a "normal" person can even "feel" --
but even more is WM interested in
WHAT (we) folks CLAIM and STATE about (our) math,
more than about that math itself.

You might think I'm on a fool's quest.

No! Why...

You might even be correct to think that.
But what it is I am trying to do is address
the reasons WM thinks what he thinks,
whatever those reasons are.

I think it's possible that
WM thinks that
a mathematical claim is mathematical because
of the great certainty with which it is expressed.

I think it's possible that
WM thinks that
_he_ has been playing by The Rules, even though
_we_ have been cheating,
by overriding his mathematizingᵂᴹ certainties
with "proofs" (WM uses deprecating quote marks).

You are simply "as correct as possible" which is
Math and what is how Math should be.

I think it's possible that
WM has no objection
to the run.of.the.mill claims about
the first.upper.bound of
numbers which can be counted.to from 0
(and things like that) as long as
those claims are not made using symbols
such as ω ℕ ℵ₀ which
WM has made his mathematizedᵂᴹ claims about.

I think that WM has a very fixed idea of the
"world of math" which is fixed by nature and
not a creation of culture in the mind of men
which WM thinks is given by THE ONE real nature
and by THE ONE true logic which can ONLY be
detected and "seen" rather than defined and
built. WMs thinking is manic, he has no more
choice in his days...

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Am 02.05.2024 20:00:50 Jim Burns schrieb:

On 5/1/2024 7:32 PM, Tom Bola wrote:

Am 02.05.2024 00:46:01 Jim Burns schrieb:

I think it's possible that
WM has no objection
to the run.of.the.mill claims about
the first.upper.bound of
numbers which can be counted.to from 0
(and things like that) as long as
those claims are not made using symbols
such as ω ℕ ℵ₀ which
WM has made his mathematizedᵂᴹ claims about.

mathematizedᵂᴹ == expressed with utter.certainty

I'm not saying that utter.certainty mathematizes.
I'm saying that WM thinks it mathematizes.

I think that WM has a very fixed idea of the
"world of math" which is fixed by nature and
not a creation of culture in the mind of men
which WM thinks is given by THE ONE real nature
and by THE ONE true logic which can ONLY be
detected and "seen" rather than defined and
built.

I have tried to accommodate
the "seen.only" view of mathematics with my
little "only.not.first.false" backgrounder.
A finite sequence with no first false claim
is "seen" and must be with no false claim.

If I have had any success at all with that approach,
it appears to be no more than partial.

----
I find a recent pair of claims useful for
the purpose of theorizing what.WM.means.

<WM<JB>>

If n can be counted to from 0
then n⋅2 can be counted to _from n_
then n⋅2 can be counted to from 0 _through n_

That is true.

If n is before ω
then n⋅2 before ω

That is not true.

</WM<JB>>
Date: Tue, 30 Apr 24 13:12:48 +0000

WM _rejected my definition_
but didn't _reject my math_

My guess is that,
whether WM is aware of it or not,
he follows this line of thought:
| Infinitenessⁿᵒᵗᐧᵂᴹ is weird.
| Infinitenessⁿᵒᵗᐧᵂᴹ is wrong.
| Infinitenessᵂᴹ is not infinitenessⁿᵒᵗᐧᵂᴹ.
| ω first infiniteᵂᴹ ordinal is not infiniteⁿᵒᵗᐧᵂᴹ.
| Stepping back from ω is to darkᵂᴹ numbers.
| Any discord which the darkᵂᴹ brings forth is darkᵂᴹ
| and cannot affect the visibleᵂᴹ

Yep, and WM (frequently) changes parts of his persuasions forth
and back at volatile touches of his mental impulses on his
guidelines of own "natural", "true", "clear", "right",..., feelings.

WM will say that
ω is the first infiniteᵂᴹ ordinal,
but he does NOT mean that
ω is the first infiniteⁿᵒᵗᐧᵂᴹ ordinal.

WM rejects the idea that there is "actual infinity" which is
realized in nature and WM rejects it also in the any mental space
because it is "wrong logic" and idiocy (but he tends to "allow"
for the idea of "potential infinity").
WMs philosophy is like ultrafinitistic while he is too dense for any
mathematic thinking which he lacks to basically understand altogether)...

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Am 03.05.2024 11:07:00 Jim Burns schrieb:

On 5/2/2024 2:49 PM, Tom Bola wrote:

Am 02.05.2024 20:00:50 Jim Burns schrieb:

WM will say that
ω is the first infiniteᵂᴹ ordinal,
but he does NOT mean that
ω is the first infiniteⁿᵒᵗᐧᵂᴹ ordinal.

WM rejects the idea that
there is "actual infinity" which
is realized in nature

WM rejects
∀j:∃k≠j: j<k
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
¬∃k:∀j≠k: j<k

If I recall correctly, the reason he's given is
actual infinity or potential infinity
but
that only flies if "infinite" means
"more than one"

and WM rejects it also
in the any mental space because
it is "wrong logic" and idiocy
(but he tends to "allow" for
the idea of "potential infinity").

It seems to me that
there is less going on there,
going on either correctly or incorrectly,
than there appears to be at first.

WM call various things
"actually infinite" and "potentially.infinite".
What does he mean by those terms?
NOT "What does Cantor mean? Euclid mean?"

WM alters definitions to whatever suits him.

That's one of the worst point of WMs idiocy.

What others mean is no more than
a suggestion, a guess about what he means.

Yes, for him: what he (clearly logically) "sees".

I look at how things get labelled.
"Actual infinity" is used to disagree with
the mathematical.industrial.complex.
"Potential infinity" is used to agree with
the mathematical.industrial.complex.
And that's the whole of it.

| ∀j:∃k≠j: j<k
| ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
| ¬∃k:∀j≠k: j<k
|
denies darkᵂᴹ numbers
Therefore,
"something something actual infinity".
Oh! We matheologians are so silly.
Wolfgang Mückenheim wins again.

But
there is nothing about infinity of any kind
in the derivation.
WM doesn't care.
He has his two permission slips, which
excuse him from thinking about any of this.

WMs philosophy is like ultrafinitistic
while he is too dense for any mathematic thinking
which he lacks to basically understand altogether)...

I have a strong suspicion that
WM's philosophies are
roll.over.and.go.back.to.sleep and under.no.circumstances.bother.me.with.that.

I have trouble accepting that
WM is literally unable to follow this,
but
I can imagine that,
after 30+ years of shielding his ignorance,
he is unwilling to get rid of it.

He never, never was willing - on the contrary is that
another main issue of how his (random) thinking works.

If he weren't actively working to propagate
his ignorance, I'd be more.than.half inclined
to let him sleep.

It doesn't make much of a difference in this strange world... ;)

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