Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity)

On 01/02/2025 08:47 AM, Jim Burns wrote:

On 1/1/2025 7:28 PM, Ross Finlayson wrote:

On 01/01/2025 01:14 PM, Jim Burns wrote:

On 07/29/2024 12:44 PM, Ross Finlayson wrote:

On 07/29/2024 05:32 AM, Jim Burns wrote:

On 7/28/2024 7:42 PM, Ross Finlayson wrote:

>

about ubiquitous ordinals

>
What are ubiquitous ordinal?

>

So, "ubiquitous ordinals"
is exactly what it says.

>
It's surprising
how unhelpful some answers can be.

>

I'd so hope to be helpful,
it's categorized under virtue
somewhere between
thrifty and reverent or reverent and clean,
so I'd wonder,
is it, "un-helpful", in,
"can't think it", or,
"keep thinking it", or,
"keeps rebooting".

>
'Unhelpful' as in
"empty of new information".
>
--  It says what it says.
Yes, and ... ?
>
unhelpful.
⎛ I yam what's I yam
⎝ an' dat's all that I yam.
>
helpful.
⎛ I'm strong to the finich
⎜ 'cause I eats me spinach.
⎜ I'm Popeye the Sailor Man
⎝ <toot toot>.
>
----

it's categorized under virtue
somewhere between
thrifty and reverent or reverent and clean,

>
I'm thinking more of the Gricean maxim
"Be informative".
https://en.wikipedia.org/wiki/Cooperative_principle
>
Philosopher Paul Grice describes
the behavior which those in a conversation
engage in and assume others engage in.
>
The problem I have with calling that a virtue
is that,
for a too.large.fraction of people,
that is an argument against being helpful,
virtue having been redefined to be
in opposition to virility.
>
>

"Well-Order the Universe" is
what "ubiquitous ordinals" is.
Which, you snipped?
It makes for a model of set theory
where "powerset is successor is order type",
thusly where the Powerset Theorem
holds different, as it were.
It makes for how set theory can be
having at least three models of continuous domains,
defined as having "extent density gaplessness measure",
or "extent density completeness measure",
continuous domains, about continuous topologies,
which are their own initial and final topologies.
Yet, you still haven't addressed that
"not.ultimately.untrue" is as important
as "not.first.false" in accounts of inference.
To be, ..., "not ultimately untrue".