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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: Mon, 22 Apr 2024 07:29:34 -0400
Organization: i2pn2 (i2pn.org)
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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 
>>>>>>>>>>>>>>>>>>> of their
>>>>>>>>>>>>>>>>>>> meaning}
>>>>>>>>>>>>>>>>>>> is applying truth preserving operations to stipulated 
>>>>>>>>>>>>>>>>>>> truths.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> The axiomless, really does make for a richer 
>>>>>>>>>>>>>>>>>>>> accoutrement,
>>>>>>>>>>>>>>>>>>>> after metaphysics and the canon, why the objects of 
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