Re: Undecidability based on epistemological antinomies V2

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)
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is literally true whether or not Gödel meant it literally. Since it <is>
literally true I am sure that he did mean it literally.
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*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.
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It is easy to understand that self-contradictory mean unprovable and
irrefutable, thus meeting the definition of Incomplete(F).
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Which shows that F is incomplete, even though X cannot possibly be a
proposition in F because propositions must be true or false.
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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
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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".
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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Then, our axiomatics and theory "attain" to this, the truth,
of what is, "A Theory", at all.
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One good theory.  (Modeling all individuals and contingencies
and their models of belief as part of the world of theory.)
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One good theory, "A Theory: at all", we are in it.
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A catalog and schema and dictionary and the finite is only that, though.
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"Bigger:  not always worse."
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 "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