Re: The non-existence of "dark numbers"

On 3/23/2025 3:41 PM, WM wrote:

On 23.03.2025 19:23, Jim Burns wrote:

On 3/23/2025 1:23 PM, WM wrote:

Almost all elements follow upon every defined pair.

Yes,
that is a property of sets which
are their.own.only.inductive.subsets.

The reason that we know about these pairs
is not
that we come to their end, not in any sense.
>
The reason that we know about these pairs
is
that we have an indefinite description,
true of each one of infinitely.many pairs,

>
So you believe. Erroneously.

It makes no sense to say it is erroneous
for me to say
"I am discussing a thing of this description..."
When I make such a claim, watch me!
_There I am, discussing them_
When I say
"I am discussing a thing of this description..."
_that description_ is
an indefinite description of each one of
the things which I'm discussing.
This is a very important point, point which,
when I am discussing infinitely.many things,
is key to little, old finite me
gathering knowledge about infinite things.
Unfortunately,
it is such a blazingly.obvious point that
I find it difficult to convey how important it is.
It's a work.in.progress.

The reason that we know about these pairs
is that,
if a finite sequence has a false claim,
then it has a first.false claim,

>
But in case of darkness this cannot be seen.

Perhaps you (WM) haven't noticed that
that is a finite sequence of claims,
each claim of which can, in principle, be printed.
What could it possibly mean for a claim
printed out on dead tree
to be darkᵂᴹ?

Our ability is the product of long centuries
of intense effort by our best people.
If someone wakes up one morning and announces
"I'm going to repeat that work of centuries today"
and they _fail_ at their project,
they should not conclude, from that,
that all that previous work was in error.

>
Most of it concerns potential infinity
and is correct.

When you (WM) say 'actual infinity',
you refer to your own home.brewed 'actual infinity'
in which 'completing' elements
cannot be said to self.equal.
Sure, you (WM) say _their_ 'potential infinity'
is correct, but you don't know what that means.