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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --correct
 reasoning--psychosis--
Date: Wed, 24 Apr 2024 13:18:27 -0500
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On 4/24/2024 12:34 PM, Ross Finlayson wrote:
> On 04/24/2024 08:57 AM, olcott wrote:
>> On 4/24/2024 10:07 AM, Ross Finlayson wrote:
>>> On 04/23/2024 11:59 AM, olcott wrote:
>>>> On 4/23/2024 12:55 PM, Ross Finlayson wrote:
>>>>> On 04/23/2024 09:24 AM, olcott wrote:
>>>>>> On 4/22/2024 6:29 AM, Richard Damon wrote:
>>>>>>> On 4/22/24 12:18 AM, olcott wrote:
>>>>>>>> On 4/21/2024 9:02 PM, Richard Damon wrote:
>>>>>>>>> On 4/21/24 8:53 PM, olcott wrote:
>>>>>>>>>> On 4/21/2024 6:52 PM, Richard Damon wrote:
>>>>>>>>>>> On 4/21/24 5:38 PM, olcott wrote:
>>>>>>>>>>>> On 4/21/2024 4:19 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 4/21/24 3:34 PM, olcott wrote:
>>>>>>>>>>>>>> On 4/21/2024 1:42 PM, Ross Finlayson wrote:
>>>>>>>>>>>>>>> On 04/21/2024 10:41 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 4/21/2024 10:53 AM, Ross Finlayson wrote:
>>>>>>>>>>>>>>>>> On 04/21/2024 08:16 AM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 4/21/2024 9:17 AM, Ross Finlayson wrote:
>>>>>>>>>>>>>>>>>>> On 04/20/2024 10:47 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 4/20/2024 10:39 PM, Ross Finlayson wrote:
>>>>>>>>>>>>>>>>>>>>> On 04/20/2024 02:05 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 4/20/2024 3:07 PM, Ross Finlayson wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 04/19/2024 02:36 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2024 4:04 PM, Ross Finlayson wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 04/19/2024 11:23 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2024 11:51 AM, Ross Finlayson wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 04/17/2024 10:57 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/17/2024 9:34 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> "...14 Every epistemological antinomy can
>>>>>>>>>>>>>>>>>>>>>>>>>>>> likewise be used
>>>>>>>>>>>>>>>>>>>>>>>>>>>> for a
>>>>>>>>>>>>>>>>>>>>>>>>>>>> similar
>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability proof..." (Gödel 1931:43-44)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> is literally true whether or not Gödel meant it
>>>>>>>>>>>>>>>>>>>>>>>>>>>> literally.
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Since it
>>>>>>>>>>>>>>>>>>>>>>>>>>>> <is>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> literally true I am sure that he did mean it
>>>>>>>>>>>>>>>>>>>>>>>>>>>> literally.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Parphrased as*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Every expression X that cannot possibly be 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> true
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or false
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proves
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system F cannot correctly determine
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> whether X is
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> true or
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which shows that X is undecidable in F.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is easy to understand that 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> self-contradictory
>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean
>>>>>>>>>>>>>>>>>>>>>>>>>>>> unprovable and
>>>>>>>>>>>>>>>>>>>>>>>>>>>> irrefutable, thus meeting the definition of
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Incomplete(F).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Which shows that F is incomplete, even 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> though X
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cannot
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proposition in F because propositions must be
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> true or false.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A proposition is a central concept in the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> philosophy of
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language,
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics, logic, and related fields, often
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> characterized as
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> primary
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> bearer of truth or falsity.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Proposition
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Most common-sense types have "the truth is the
>>>>>>>>>>>>>>>>>>>>>>>>>>> truth is the
>>>>>>>>>>>>>>>>>>>>>>>>>>> truth"
>>>>>>>>>>>>>>>>>>>>>>>>>>> then
>>>>>>>>>>>>>>>>>>>>>>>>>>> as with regards to logical positivism and a
>>>>>>>>>>>>>>>>>>>>>>>>>>> sensitive,
>>>>>>>>>>>>>>>>>>>>>>>>>>> thorough,
>>>>>>>>>>>>>>>>>>>>>>>>>>> comprehensive, reasoned account of rationality
>>>>>>>>>>>>>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>> fundamental
>>>>>>>>>>>>>>>>>>>>>>>>>>> objects of the logical theory, makes for again a
>>>>>>>>>>>>>>>>>>>>>>>>>>> stonger
>>>>>>>>>>>>>>>>>>>>>>>>>>> logical
>>>>>>>>>>>>>>>>>>>>>>>>>>> positivism, reinvigorated with a minimal "silver
>>>>>>>>>>>>>>>>>>>>>>>>>>> thread" to a
>>>>>>>>>>>>>>>>>>>>>>>>>>> metaphysics, all quite logicist and all quite
>>>>>>>>>>>>>>>>>>>>>>>>>>> positivist, while
>>>>>>>>>>>>>>>>>>>>>>>>>>> again structuralist and formalist, "the truth is
>>>>>>>>>>>>>>>>>>>>>>>>>>> the truth
>>>>>>>>>>>>>>>>>>>>>>>>>>> is the
>>>>>>>>>>>>>>>>>>>>>>>>>>> truth".
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Plainly, modeling bodies of knowledge is at 
>>>>>>>>>>>>>>>>>>>>>>>>>>> least
>>>>>>>>>>>>>>>>>>>>>>>>>>> two things,
>>>>>>>>>>>>>>>>>>>>>>>>>>> one is a formal logical model, and another is a
>>>>>>>>>>>>>>>>>>>>>>>>>>> scientific
>>>>>>>>>>>>>>>>>>>>>>>>>>> model,
>>>>>>>>>>>>>>>>>>>>>>>>>>> as with regards to expectations, a statistical
>>>>>>>>>>>>>>>>>>>>>>>>>>> model.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> For all the things to be in one modality, is
>>>>>>>>>>>>>>>>>>>>>>>>>>> that,
>>>>>>>>>>>>>>>>>>>>>>>>>>> as a
>>>>>>>>>>>>>>>>>>>>>>>>>>> model of
>>>>>>>>>>>>>>>>>>>>>>>>>>> belief, is that belief is formally unreliable,
>>>>>>>>>>>>>>>>>>>>>>>>>>> while at the
>>>>>>>>>>>>>>>>>>>>>>>>>>> same
>>>>>>>>>>>>>>>>>>>>>>>>>>> time, reasoned and rational as for its own inner
>>>>>>>>>>>>>>>>>>>>>>>>>>> consistency
>>>>>>>>>>>>>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>>>>>>>>>>>>>> inter-consistency, all the other models in the
>>>>>>>>>>>>>>>>>>>>>>>>>>> entire modal
>>>>>>>>>>>>>>>>>>>>>>>>>>> universe,
>>>>>>>>>>>>>>>>>>>>>>>>>>> temporal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Axioms are stipulations, they're assumptions, 
>>>>>>>>>>>>>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>>>>>>>>>>>>>> there are
>>>>>>>>>>>>>>>>>>>>>>>>>>> some
>>>>>>>>>>>>>>>>>>>>>>>>>>> very well-reasoned ones, and those what follow
>>>>>>>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>>>>>>>> reflections on
>>>>>>>>>>>>>>>>>>>>>>>>>>> relation, in matters of definition of structural
>>>>>>>>>>>>>>>>>>>>>>>>>>> relation, and
>>>>>>>>>>>>>>>>>>>>>>>>>>> the first-class typing, of these things.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> In epistemology (theory of knowledge), a
>>>>>>>>>>>>>>>>>>>>>>>>>> self-evident
>>>>>>>>>>>>>>>>>>>>>>>>>> proposition is
>>>>>>>>>>>>>>>>>>>>>>>>>> a proposition that is known to be true by
>>>>>>>>>>>>>>>>>>>>>>>>>> understanding its
>>>>>>>>>>>>>>>>>>>>>>>>>> meaning
>>>>>>>>>>>>>>>>>>>>>>>>>> without proof
>>>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Self-evidence
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> In the case of the correct model of the actual
>>>>>>>>>>>>>>>>>>>>>>>>>> world
>>>>>>>>>>>>>>>>>>>>>>>>>> stipulations
>>>>>>>>>>>>>>>>>>>>>>>>>> are not assumptions. In this case stipulations
>>>>>>>>>>>>>>>>>>>>>>>>>> are the
>>>>>>>>>>>>>>>>>>>>>>>>>> assignment of
>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning to otherwise totally meaningless
>>>>>>>>>>>>>>>>>>>>>>>>>> finite
>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
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