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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 11:24:03 -0500
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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 
>>>>>>>>>>>>>>>>>>>> of their
>>>>>>>>>>>>>>>>>>>> meaning}
>>>>>>>>>>>>>>>>>>>> is applying truth preserving operations to 
>>>>>>>>>>>>>>>>>>>> stipulated truths.
>>>>>>>>>>>>>>>>>>>>
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