Re: Replacement of Cardinality (ubiquitous ordinals)

On 7/30/2024 4:56 PM, Ross Finlayson wrote:

On 07/30/2024 11:18 AM, Jim Burns wrote:

[...]

>
The idea that there's one theory for all this theory,
has that otherwise there isn't
and you're not talking about any of them.

If I remember correctly,  your (RF's) name for
not.talking about
what's outside the domain of discussion
is hypocrisyᴿꟳ.
That sounds like you're delivering a value.judgment:
that we _should not_ not.talk about
what's outside the domain of discussion,
that we _should not_ for example, not.talk about
_all_ triangles when we discuss whether
the square of its longest side equals
the sum of the squares of the two remaining sides.
However,
it is because we are hypocriticalᴿꟳ (in your sense?)
that such discussions produce results.
"Conclusions", if you like.
We make finite.length.statements which
we know are true in infinitely.many senses.
We can know they are so because
we have narrowed our attention to
those for which they are true without exception.
Stated once, finitely, for infinitely.many.
Non.hypocrisyᴿꟳ (sincerityᴿꟳ?) throws that away.