Re: how (point at infinity)

On 6/15/2024 12:45 PM, Ross Finlayson wrote:

On 06/15/2024 09:35 AM, Moebius wrote:

[...]

>
I.e., singularities in closed theories,
are multiplicities in more open theories.

It is an essential aspect of mathematics that,
when we are discussing a thing or things,
we are not discussing a different thing or things.
That's a principle with wider application, I think,
but mathematics is simply impossible without it.
Consider the set of finite von Neumann ordinals.
None of them are infinite.
Amazing! Fantastic! A tour de force!
Not.
But,
using the knowledge that none of them are infinite,
we explore the infinity of them by means of
our not.first.false telescope.
That is not an exploration of more open theories
about infinite von Neumann ordinals as well,
even though those are theories we could explore.
We _could_ explore them, but we _aren't_
Not right now.