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

On 11/18/2024 07:46 AM, Jim Burns wrote:

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?
>
>

I already did you keep clipping it.
Why don't you look back about the last three
posts and see an example where an inductive argument
FAILS and is nowhere finitely "not.first.false",
that it yet FAILS. So, it's a counterexample,
and illustrates why what's not.first.false must
also be not.ultimately.untrue to not FAIL.
Then about Russell's retro-thesis and "there are
no standard models of integers", there are theories
like Finsler's and Boffa's with NONE.
Only fragments or extensions, ....
And they DO say Russell is a lie. Just, politely,
most people don't push the point.
Anyways you keep dropping the points in
the deliberations and contemplations put
forth here for formal reasoning, it's
considered a faux pas in the usual sense
of the refusing to refuse the mathematical,
that being wrong.