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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 14:34:35 -0500
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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".
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> We cannot really understand the notion of true on the basis of
>>>>>>>>>> meaning
>>>>>>>>>> by only examining how this applies to real numbers. We must
>>>>>>>>>> broaden
>>>>>>>>>> the scope to every natural language expression.
>>>>>>>>>>
>>>>>>>>>> When we do this then we understand that a "dead rat" is not any
>>>>>>>>>> type
>>>>>>>>>> of "fifteen story office building" is a semantic tautology that
>>>>>>>>>> cannot
>>>>>>>>>> possibly be false.
>>>>>>>>>>
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