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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --correct
 reasoning--
Date: Tue, 23 Apr 2024 21:47:10 -0400
Organization: i2pn2 (i2pn.org)
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On 4/23/24 12:24 PM, 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.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> We do not merely assume that a "dead rat" is not 
>>>>>>>>>>>>>>>>>>>>> any type of
>>>>>>>>>>>>>>>>>>>>> "fifteen story office building" we know that it is a
>>>>>>>>>>>>>>>>>>>>> self-evident
>>>>>>>>>>>>>>>>>>>>> truth.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Expressions of language that are stipulated to be 
>>>>>>>>>>>>>>>>>>>>> true for the
>>>>>>>>>>>>>>>>>>>>> sole purpose of providing semantic meaning to 
>>>>>>>>>>>>>>>>>>>>> otherwise totally
>>>>>>>>>>>>>>>>>>>>> meaningless finite strings provide the ultimate 
>>>>>>>>>>>>>>>>>>>>> foundation of
>>>>>>>>>>>>>>>>>>>>> every
>>>>>>>>>>>>>>>>>>>>> expression that are true on the basis of its meaning.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> The only other element required to define the 
>>>>>>>>>>>>>>>>>>>>> entire body of
>>>>>>>>>>>>>>>>>>>>> {expressions of language that are true on the basis 
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