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NNTP-Posting-Date: Sun, 21 Apr 2024 18:42:07 +0000
Subject: Re: Undecidability based on epistemological antinomies V2
Newsgroups: comp.theory,sci.logic
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 21 Apr 2024 11:42:22 -0700
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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.
>>>>>>>>>
>>>>>>>>> When we understand this then we have much deeper insight into the
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