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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: Sat, 20 Apr 2024 20:39:43 -0700
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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,
>> 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
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