Re: Replacement of Cardinality (infinite middle)

On 08/11/2024 12:30 PM, Chris M. Thomasson wrote:

On 8/11/2024 11:39 AM, Ross Finlayson wrote:

On 08/11/2024 11:30 AM, Jim Burns wrote:

On 8/10/2024 7:05 PM, Moebius wrote:

Am 11.08.2024 um 00:47 schrieb Chris M. Thomasson:

On 8/10/2024 3:43 PM, Moebius wrote:

>

Hint: Let's "consider" the real line:
>
...|-----|-----|-----|-----|--..
   0     1     2     3     4
>
[Now] omega is not a point on this line. :-P

>
"Out of scope", perhaps? Is that okay?

>
Somehow. :-P
>
I guess, JB would say:
"If we don't consider omega,
we don't consider omega."
:-P

>
I think I can make a good case for that.
>
----
I propose that
each split F,H of the line is situated in the line
== the line has a point last.in.F or first.in.H
>
It follows that
each positive point is separated from 0
by some finite /n
otherwise, contradiction follows.
>
If each positive point has a reciprocal,
then each point has a finite reciprocal,
and no point is ω
>
----
Georg Cantor did not get up one morning and ask,
"How can I piss off Wolfgang Mückenheim decades from now?"
>
We often have reasons for things being how they are,
the weirder they seem, the better the reasons,
because, no, those who made it that way
are not actually trying to piss you off.
They have (had) better things to do.
>
>
>

>
Did Cantor wake up on morning "why am I in an insane asylum?"

>
Shit happens? ;^) lol.
[...]

Yeah, it's like one time I was walking across the quad
with Professor R., mathematics. I brought up infinity
and he smiled and said "Thinking about infinity makes
people nuts". I laughed and agreed.
There is though that 0, 1, and infinity are all the numbers
needed to start a mathematics, so, at some point it's
easier to deal with the multiple meanings and deconstructive
accounts of infinity as a purely rational exercise, than for
example explaining the human condition, man's inhumanity
to man, a world when things don't make sense, injustice,
the machinery of fear, warring impulses, or why the only
book on mental health is full of disorders.
Then, that infinity requires deductive analysis and a
deconstructive account as of the elements of a theory
of truth, itself, for a strong mathematical platonist in
the milieu of strong logicist positivism, some people
don't have it.
Yet, it can be acquired, an object-sense word-sense number-sense
that includes real infinity, and it requires language, it requires
a vocabulary and exposure to the language of logic and mathematics,
and a facility in abstraction, and quite much so, reason.
This way there can be a true theory without paradoxes,
without apeiron yet with the entelechia and res and
the verum and the certum, the continuum.
... A One of them. "A Theory"
"It's OK."