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NNTP-Posting-Date: Wed, 24 Apr 2024 17:34:07 +0000
Subject: Re: Undecidability based on epistemological antinomies V2 --correct
 reasoning--
Newsgroups: comp.theory,sci.logic
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Wed, 24 Apr 2024 10:34:11 -0700
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On 04/24/2024 08:57 AM, olcott wrote:
> On 4/24/2024 10:07 AM, Ross Finlayson wrote:
>> On 04/23/2024 11:59 AM, olcott wrote:
>>> 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
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