Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-standard)

On 11/17/2024 1:41 PM, Ross Finlayson wrote:

On 11/17/2024 10:35 AM, Jim Burns wrote:

how about Finsler or Boffa or Mirimanoff or
non.well.founded set theories?
Do they show that ST+PQ or ZFC or ordinals
suffer from Russell's {S:S∉S}?
>
No. They do not show that.
>
The less.interesting reason that they don't
is that
they are different domains of discourse.
⎛ 0 < 1/2 < 1 does not show that
⎜ there is an integer between 0 and 1
⎝ because 1/2 isn't an integer.
>
That less.interesting reason seems to
lie close to the heart of your objection.
You (RF) seem to not.believe that
things can be not.referred to.
>
In that respect,
I don't see what I can do for you.
I will continue to not.refer to
what I choose to not.refer to.

You (RF) seem to argue that
☠⎛ they cannot not.refer to Russell's {S:S∉S}
☠⎜ and therefore they ARE talking gibberish
☠⎝ and a standard model of the integers not.exists.
>
☠( and anyone who disagrees with that is a liar.

>
It is so that
that is what I argue, for, yes.

I see at least two ways in which 'argue'
might be used in our discussion here.
'Argue.1' and 'argue.2' are distinguished by
their order.in.discussion with respect to
⎛ a FINITE SEQUENCE OF CLAIMS, each claim of which
⎝ is true.or.not.first.false.
A large part, the important part of
what.I.want.to.say is supported by
⎛ A FINITE SEQUENCE OF CLAIMS, each claim of which
⎜ is true.or.not.first.false  is
⎜ a FINITE SEQUENCE OF CLAIMS, each claim of which
⎝ is true.
I emphasize that
it is THE CLAIMS in that sequence which
are finitely.many,  and
it is EACH CLAIM in that sequence which
either is true or is after a false claim.
It is important enough that
I would really like to hear from you,
Ross Finlayson,
either that you agree
or what your objections are,
so that I can address them.
I plan to turn to your argument
once we have finished with
⎛ A FINITE SEQUENCE OF CLAIMS, each claim of which
⎜ is true.or.not.first.false  is
⎜ a FINITE SEQUENCE OF CLAIMS, each claim of which
⎝ is true.
What do you have to say about that, Ross?