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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --correct
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Date: Tue, 23 Apr 2024 13:59:48 -0500
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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.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>>>>>>>>>
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