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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2
Date: Sat, 20 Apr 2024 16:05:13 -0500
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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,
> helps illustrate that deconstructive accounts work at the
> structuralist and constructivist again, what makes for that
> axiomatics is didactic, vis-a-vis, fundamentality.
> 
> Type and category are truly great ideas, it's true,
> and they're modeled as first-class after a deconstructive
> account of their concrete models, their abstract models.
> 
> Type, and category, have inversions, where for example
> a cat is a feline animal, while a lion is king of the beasts.
> 
> The most usual sorts of is-a and has-a are copulas, there
> are many sorts predicates of relation of relation, first-class.
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