Re: how

On 6/20/2024 9:36 PM, Ross Finlayson wrote:

On 06/20/2024 05:18 PM, Jim Burns wrote:

We can learn this in our 13.7×10⁹.year.old universe.

>
You know about 30 years about
it was only 13.4, billion years old.

What?
So now it should only be 13,400,000,030 years old?
Is that it?
https://www.youtube.com/watch?v=F7khLBcH-2A
It's not the years, honey, it's the mileage.
The arc of reports of the age of the universe
has some of my favorite numbers to quote, because
they show how far we've come in
a metaphorical eye.blink.
The Wiki tells me 13.787±0.020 10⁹.years now and
NASA says, before 1999, between 7 and 20 10⁹.years.
https://en.wikipedia.org/wiki/Age_of_the_universe
https://imagine.gsfc.nasa.gov/science/featured_science/tenyear/age.html

Imagine the simplest sort of argument that
deduction immediately solves, yet induction
never does.
"Not ultimately untrue."

You and I only appear to be communicating.
What I know, as induction,
either transfinite or cisfinite,
in a mathematical context, _is_ deduction.

If you reject that, then remember that
the usual Axiom of Infinity isn't just
naming the second constant of ZF after
the empty set: it's also a restriction
of comprehension because naive comprehension
makes it extra-ordinary.

Here's what I think I know.
Unrestricted comprehension says
{y:P(y)} exists.
I avoid self.contradicting sets by
calling them meta.sets, and
having only sets in meta.sets.
(or maybe it's plural quantification).
ZFC replaces unrestricted comprehension with
specification, {x e A: P(x)} exists  and
replacement, {f(x): x e A} exists,
where A exists.
I see that unrestricted comprehension makes
the axiom of infinity redundant.
I don't think of that as it being part of
unrestricted comprehension, but it's not hard
to find disagreements I consider more important.