Path: ...!local-3.nntp.ord.giganews.com!Xl.tags.giganews.com!local-1.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Wed, 01 Jan 2025 18:10:37 +0000
Subject: Re: Replacement of Cardinality (ubiquitous ordinals)
Newsgroups: sci.logic,sci.math
References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp>
 <881fc1a1-2e55-4f13-8beb-94d1f941b5af@att.net>
 <vg44QVKbPSR4U0Tq71L-fg5yqgM@jntp>
 <85194aeb-1b24-4486-8bcc-4dcd43b4fd2f@att.net>
 <HVudnVg62uHETjv7nZ2dnZfqn_ednZ2d@giganews.com>
 <HVudnVo62uGFSDv7nZ2dnZfqn_ednZ2d@giganews.com>
 <tR-dnU_G9dTXSjv7nZ2dnZfqn_WdnZ2d@giganews.com>
 <2e188e21-4128-4c76-ba5d-473528262931@att.net>
 <NQednW9Dop2vbDr7nZ2dnZfqn_SdnZ2d@giganews.com>
 <7d074e06-497a-4c38-9b34-fcded370ec75@att.net>
 <Yz6dnZrQj9Lf3zX7nZ2dnZfqn_udnZ2d@giganews.com>
 <305754ad-bf86-44e7-95a5-f6059b8869da@att.net>
 <78CcnZMbf6XDzjT7nZ2dnZfqn_udnZ2d@giganews.com>
 <ef6e9a26-4899-41a5-ade7-5ab5a3d654d0@att.net>
 <SIacnYBQM_GoSjf7nZ2dnZfqnPSdnZ2d@giganews.com>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Wed, 1 Jan 2025 10:10:41 -0800
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101
 Thunderbird/38.6.0
MIME-Version: 1.0
In-Reply-To: <SIacnYBQM_GoSjf7nZ2dnZfqnPSdnZ2d@giganews.com>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Message-ID: <aD2dnaiNTPWAGOj6nZ2dnZfqn_QAAAAA@giganews.com>
Lines: 82
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-28Poz8NFVjASYi8C/tFJQSt+9wL4xdt7/WqFtCx1f5pyC3IeJ6IP/y2j+QVe8FkTSxj+8E66pbIgWUL!0KaIdMGOJlvq7BpWxo81on+WKRe2argmENqbPwt2hmICTKirOTiererux3Sk0xK1wscQSHzP7HQ=
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
Bytes: 4880

On 07/31/2024 05:30 PM, Ross Finlayson wrote:
> On 07/31/2024 01:21 PM, Jim Burns wrote:
>> On 7/30/2024 4:56 PM, Ross Finlayson wrote:
>>> On 07/30/2024 11:18 AM, Jim Burns wrote:
>>
>>>> [...]
>>>
>>> The idea that there's one theory for all this theory,
>>> has that otherwise there isn't
>>> and you're not talking about any of them.
>>
>> If I remember correctly,  your (RF's) name for
>> not.talking about
>> what's outside the domain of discussion
>> is hypocrisyᴿꟳ.
>>
>> That sounds like you're delivering a value.judgment:
>> that we _should not_ not.talk about
>> what's outside the domain of discussion,
>> that we _should not_ for example, not.talk about
>> _all_ triangles when we discuss whether
>> the square of its longest side equals
>> the sum of the squares of the two remaining sides.
>>
>> However,
>> it is because we are hypocriticalᴿꟳ (in your sense?)
>> that such discussions produce results.
>> "Conclusions", if you like.
>>
>> We make finite.length.statements which
>> we know are true in infinitely.many senses.
>>
>> We can know they are so because
>> we have narrowed our attention to
>> those for which they are true without exception.
>> Stated once, finitely, for infinitely.many.
>>
>> Non.hypocrisyᴿꟳ (sincerityᴿꟳ?) throws that away.
>>
>>
>
> You're talking about a field, I'm talking about foundations.
>
> ... Of which there is one and a universe of it.
>
> Then, when these examples of just carrying forward inductive
> inference get out, they do. That there's a class of expressions
> that are outside of tertium non datur is always a thing.
>
> Let's talk about completions and the infinite limit and
> the continuum limit, there's always an inductive counterargument
> that it's not so, not complete, not the sum, not continuous.
>
> About triangles and right triangles, and classes and sets in
> an ordinary theory like ZFC with classes, now your theory has
> classes that aren't sets.
>
> That analysis is sometimes catalysis, for anaphora and cataphora,
> is a thing, and two things.
>
> In foundations, there's a universe to account for,
> there's nothing outside, or vice-versa, ..., and vice-versa.
>
>
> Then ubiquitous ordinals you can also find in where, for example,
> "ordering theory" is fundamental instead of "set theory", it's
> a theory altogether with entirely different elements, then with
> the decriptive approach of model theory, making models and giving
> them names, the "equi-interpretability" here has that simply
> the ordering theory's a bit simpler than set theory, and in
> a fundamental theory the elements are simple.
>
> So, hypocrisy, like Russell's retro-thesis, a restriction of
> comprehension that goes along with other axioms that would
> build for themselves a confounding confusing conflating
> consterning counter-example, doesn't just go without saying.
>
>
> Yeah, my mathematical conscience demands that hypocrisy is bad.
>
>