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NNTP-Posting-Date: Sun, 17 Nov 2024 18:41:27 +0000
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-standard)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 17 Nov 2024 10:41:58 -0800
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On 11/17/2024 10:35 AM, Jim Burns wrote:
>
>> > > On 11/16/2024 02:22 AM, Jim Burns wrote:
>> > >> On 11/15/2024 9:52 PM, Ross Finlayson wrote:
>> > >>> On 11/15/2024 02:37 PM, Jim Burns wrote:
>> > >>>> On 11/15/2024 4:32 PM, Ross Finlayson wrote:
>> >
>> > >>>>> Ah, yet according to Mirimanoff,
>> > >>>>> there do not exist standard models of integers,
>> > >>>>
>> > >>>> If it is true that
>> > >>>> our domain of discourse is a model of ST+PQ
>> > >>>> then it is true that
>> > >>>> our domain of discourse holds a standard integer.model.
>> > >>>> What is Mirimanoff's argument that
>> > >>>> it doesn't exist?
>> > >>>
>> > >>> Mirimanoff's? Russell's Paradox.
>> > >>
>> > >> ST+PQ does not suffer from claiming
>> > >> that the set of all non.self.membered sets
>> > >> is self.membered or claiming it isn't.
>> > >>
>> > >> While I am at it,
>> > >> ZFC does not suffer from claiming
>> > >> that the set of all non.self.membered sets
>> > >> is self.membered or claiming it isn't,
>> > >> and
>> > >> ordinal.theory=Well.Order
>> > >> does not suffer from claiming
>> > >> that the set of all non.self.membered sets
>> > >> is self.membered or claiming it isn't.
>
>> > On 11/16/2024 12:07 PM, Ross Finlayson wrote:
>>
>> >> you have ignored Russell his paradox and so on
>
> On 11/17/2024 1:52 AM, Ross Finlayson wrote:
>> On 11/16/2024 10:11 PM, Ross Finlayson wrote:
>>> On 11/16/2024 09:59 PM, Ross Finlayson wrote:
>>>> On 11/16/2024 09:56 PM, Jim Burns wrote:
>
>>>>> ⎛ The modern study of set theory was initiated by
>>>>> ⎜ Georg Cantor and Richard Dedekind in the 1870s.
>>>>> ⎜ However,
>>>>> ⎜ the discovery of paradoxes in naive set theory,
>>>>> ⎜ such as Russell's paradox,
>>>>> ⎜ led to the desire for
>>>>> ⎜ a more rigorous form of set theory
>>>>> ⎝ that was free of these paradoxes.
>>>>>
>>>>> https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
>
>>>> How about Finsler and Boffa?
>
> Meaning:
> how about non.well.founded set theories?
>
> ⎛ I learned a new word recently: 'sanewashing'.
> ⎜
> ⎜ For example,
> ⎜ it is sanewashing
> ⎜ when I snip context in which
> ⎜ you call me a liar for stating facts
> ⎜ accessible to Wikipedia.level research.
> ⎜
> ⎜ I don't wish to dwell on my sanewashing.
> ⎜ I doubt that anyone beyond you (RF) or me
> ⎜ would find it the least bit interesting if I did.
> ⎜ I only note it in passing for the benefit of
> ⎝ the future, when the cockroaches evolve archeologists.
>
> On a lighter note,
> 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.
>
> The more.interesting reason is that
> ST+PQ and ZFC and well.ordering
> do not suffer from Russell's {S:S∉S}
> _by design_
>
> Without looking up what Mirimanoff or
> Finsler or Boffa have to say about
> non.well.founded set.theories,
> I am confident that their theories
> do not suffer from Russell's {S:S∉S}
> _by design_
>
> Because they know that, otherwise,
> they would be talking gibberish.
>
> 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.

Mirimanoff says so, too.

Then there's also the "not.first.false is
not necessarily not.ultimately.untrue" bit,
and the demonstration of the "yin-yang ad-infinitum"
bit, then also as with regards to doubling-spaces
and halving spaces and the continuum in mathematics.