Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

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.
What others mean is no more than
a suggestion, a guess about what he means.
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.
If he weren't actively working to propagate
his ignorance, I'd be more.than.half inclined
to let him sleep.