Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]

On 3/28/2025 3:34 AM, WM wrote:

Am 28.03.2025 um 02:02 schrieb Moebius:

Am 27.03.2025 um 21:11 schrieb WM:

Am 26.03.2025 um 23:18 schrieb Moebius:

Am 26.03.2025 um 22:38 schrieb Alan Mackenzie:

WM <wolfgang.mueckenheim@tha.de> wrote:

The number of [...] rooms in Hilbert's hotel
is infinite but [...] grow[s].

>
No, it doesn't.

>
And the number of guests?

>
Is still the same: aleph_0.
>
It's just the "reality" (->Cantor) of guests
that has grown by one. :-)

>
Set theory cannot describe reality. :-(

Set theory describes the Cantorian reality of sets.
Set theory makes claims certainly true about
what set theory's claims are true about.
Which, granted, is circular.
But is also certainly true.

Mathematics is expected to
be able to describe reality. :-)

Some of mathematics is known to not.describe
Wignerian reality.
Sorting the "good" description from the "bad" is
what observation and experiments are for.
Observation and experiments underdetermine
Wignerian reality.
Mathematical theories of physical reality associate
(observed) Wignerian reality with
(necessary) Cantorian reality, which associates with
(predicted) Wignerian reality.
The only part of _that scheme_ which we are
(mostly) discussing is the Cantorian.reality.part.
Other discussions are possible.
Do we "really" observe our observations,
or are we brains in vats being tricked by
some all.powerful demon?
Why are our
Wignerian(Cantorian(Wignerian))) predictions
so good? Etc.
Cantorian descriptions are certainly true about
what they describe.
That's a very low bar to get over,
but they don't need more.
Cantorian consequences are certainly true about
whatever they're about
IF
they are claims (somewhere, anywhere) in
a finite sequence of claims with no first.false claim.
My claim about Cantorian consequences is NOT
a claim about, for example, photon scattering.
It is a claim about
claims about, for example, photon scattering.
Specifically, it is about finite sequences of claims,
whatever they're about.
In a finite sequence of things,
if a thing x has property P
then some thing y is first having property P.
That's true, because of what 'finite' means,
even if the things are _claims_
  about some indefinite one.of.infinitely.many
and Property P is being.false.