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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2
Date: Sun, 21 Apr 2024 07:19:32 -0400
Organization: i2pn2 (i2pn.org)
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On 4/21/24 1:47 AM, 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 
>>>>> nature
>>>>> of mathematical axioms, they too must be semantic tautologies.
>>>>>
>>>>>> There's nothing wrong with Tertium Not Datur,
>>>>>> for the class of predicates where it applies.
>>>>>>
>>>>>> Which is not all of them.
>>>>>>
>>>>>>
>>>>>
>>>>
>>>> Leafing through Badiou's "Second Manifesto ... on Philosophy",
>>>> he sort of arrives at again "I am a Platonist, yet a sophisticated
>>>> not a vulgar one".
>>>>
>>>> It seems quite a development when after Badiou's "First Manifesto ..."
>>>> twenty years prior, that in the maturation of his philosophical
>>>> development he came again to arrive at truth as its own truth.
>>>>
>>>> Tautology, identity, and equality, are not necessarily the same
>>>> thing, with regards to deconstructive accounts, and the distinction
>>>> of extensionality and intensionality, for sameness and difference,
>>>> with regards to affirmation and negation, in usual modes of
>>>> predicativity and quantifier disambiguation.
>>>>
>>>
>>> A semantic tautology is a term that I came up with that self-defines the
>>> logical positivist notion of analytic truth. It seems that most people
>>> succumbed to Quine's nonsense and decided to simply "not believe in"
>>> {true on the basis of meaning}.
>>>
>>> We know that the living animal {cat} is not any type of {fifteen
>>> story office building} only because of {true on the basis of meaning}.
>>>
>>>>
>>>> Geometry arising as natural and axiomless from "a geometry of
>>>> points and spaces" from which Euclid's geometry justly arises,
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