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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2
Date: Fri, 19 Apr 2024 16:36:13 -0500
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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.
> 
> 

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer