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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: Sun, 21 Apr 2024 16:38:00 -0500
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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 reason
>>>>>>>>>>>>>>> and rationality, "arise" from axiomless deduction, 
>>>>>>>>>>>>>>> naturally.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Then, our axiomatics and theory "attain" to this, the truth,
>>>>>>>>>>>>>>> of what is, "A Theory", at all.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> One good theory.  (Modeling all individuals and 
>>>>>>>>>>>>>>> contingencies
>>>>>>>>>>>>>>> and their models of belief as part of the world of theory.)
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> One good theory, "A Theory: at all", we are in it.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> A catalog and schema and dictionary and the finite is only
>>>>>>>>>>>>>>> that,
>>>>>>>>>>>>>>> though.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> "Bigger:  not always worse."
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> "Understanding" doesn't mean much here
>>>>>>>>>>>>> except lack thereof, and hypocrisy.
>>>>>>>>>>>>>
>>>>>>>>>>>>> We only have "true axioms" because in
>>>>>>>>>>>>> all their applications they've held up.
>>>>>>>>>>>>> They "withstand", and, "overstand".
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
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