Re: Replacement of Cardinality (effective bounds)

On 08/24/2024 03:39 PM, Jim Burns wrote:

On 8/24/2024 4:50 PM, Ross Finlayson wrote:

On 08/24/2024 11:08 AM, FromTheRafters wrote:

WM has brought this to us :

Le 23/08/2024 à 20:06, joes a écrit :

>

The unit fractions don’t reach 0.

>
Of course not.
Therefore they must cease before.

>
Why must they cease at all?

>
He can just axiomatize it so,
saying that there's a rule.

>
Yes,
he can axiomatize it so.
However,
axioms set what the conversation is about.
>
Yes,
WM can change what his conversation is about.
So can you. So can anyone.
WM cannot change what his conversation is about while
keeping it part of the unchanged conversation.
>
I'm not declaring a rule,
anymore than it's a rule that circles are round.
It is how it is.
>
Suppose, purely hypothetically, that I have accused
all Germans of being assholes, and
WM intends to push back against this foul calumny.
"There are many very nice Norwegians", he says.
>
My advice would be to not.make this argument,
that its effect would be pretty much the opposite of
what WM might want for an effect.
>
There are striking parallels between
axiomatizing it so (changing what's discussed),
and a different country (changing what's discussed).
>
Yes, clearly, WM can do it.
Much less clear is why WM would do it.
>
>

Still, you can just look at it that he has a speech impediment,
and in some generous reading he's the only go-between that
somehow you must explain in his terms, what's in your terms.
So here, it's simplest as a system of bounds, modeled in
the unbounded, instead of just a usual system of no bounds,
modeled in the unbounded. I.e. it's just the sort of
opposite that you've chosen or have a natural or imposed
sort of slur about whether they're bounds in the unbounded
or not-bounds in the un-bounded.
Anyways you've declared many times that you're quite deaf
to claims that Russell's axiom is in any way false, so,
I'm not quite sure what it is that will make it so that
anyone who'd care to try and follow your argument would
have to always insert a slate of boilerplate argument
in front of any quantification over a domain or Russell's
receipt as it were, this is just another one or two,
one with "least non-zero indivisible" and another with
"greater fixed-point", either though of course one
might arrive at for its own sake.
Hausdorff, Skolem, ....