Re: Undecidability based on epistemological antinomies V2 --correct reasoning--

On 4/21/2024 6:52 PM, Richard Damon wrote:

On 4/21/24 5:38 PM, olcott wrote:

On 4/21/2024 4:19 PM, Richard Damon wrote:

On 4/21/24 3:34 PM, olcott wrote:

On 4/21/2024 1:42 PM, Ross Finlayson wrote:

On 04/21/2024 10:41 AM, olcott wrote:

On 4/21/2024 10:53 AM, Ross Finlayson wrote:

On 04/21/2024 08:16 AM, olcott wrote:

On 4/21/2024 9:17 AM, Ross Finlayson wrote:

On 04/20/2024 10:47 PM, 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."
>
>
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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.
>
>

>

>
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.
>
The use/mention distinction has that a type is a type is a type,
that an instance of a type is-or-is-not an instance of a type,
that it's an instance of a type and is an instance of a type.
>
Distinction and contradistinction, have it so for type inversion,
that the abstract and the concrete, model each other.
>
>
Then for geometry (of space) and algebra (of words), there's
basically that space is infinite and words finite,
there's though a space of words and words of space.
>
Then, type theory and category theory, make for great bodies
of relation of relation, that for most, theory is a relation
of relation, and that there is always a first-class abstraction,
theory, at all.
>
So, an ontology is just a sample of data in a science.
>
The "strong metonymy", is the idea that there's a true ontology.
Of course, it's not absent a metaphysical moment.
>
>

>
A complete
https://en.wikipedia.org/wiki/Ontology_(information_science)
is an accurate model of the actual world. Not the same thing at all
as an ontology from philosophy:
https://en.wikipedia.org/wiki/Ontology
>
There is definitely a true ontology even if every aspect of all of
reality is a figment of the imagination. You will never be able to
experience what seems to be the physical sensations of taking your
puppies elevator to his fifteenth floor.
>

>
So, you use quasi-modal logic but proved to yourself
it's not quasi-modal?
>
You proved to yourself.
>

>
If you understand that you cannot take the elevator to the fifteen
floor
of your puppy then you know that there are expressions that are
true on
the basis of their meaning. Quine could never get this.
>

One doesn't get a free pass from the argument and rhetoric
and discourse of the limits of ontology without an encompassing
reason and discourse on the completion of an ontology, a body of
knowledge, that seems an insufferable ignorance and it's not
invincible.
>

>
>
There are billions of things just like puppyies are
not fifteen story office buildings.
>

>
The usual notion of the quasi-modal model of the world,
sort of lacks contingency and temporality and a modality
everywhere, why it's called quasi-modal, because it's just
ignorant that it's not actually modal (temporal).
>

>
There is no reason why it can't have those things.
>

It's fair to say that Carnap and Quine and the Vienna school
and logical positivism after Boole and Shopenhauer and Derrida
sort of arrives at a big angsty withdrawal from a true theory
that's true with truth in it, while as well exploring the
a-letheia the traditional notion of disclosing what are not
un-truths, "remembering again for the first time", and all
these aspects of the canon of the technical philosophy that
are so because there's sort of before-Hegel and after-Hegel,
that Hegel's sort of included in before-Hegel, while at the
same time claimed by after-Hegel, that we are not new Hegelians.
>
Much like Kant leaves the Sublime _in_ the theory, as the
least "silver thread", connecting a proper metaphysics to
the physics and it's a science, Hegel makes for both a
fuller dialectic, and, besides Nothing, Hegel's a Platonist, too.
>
>
Then, with Wittgenstein and Nietzsche and Heidegger as,
"anti-Plato's, and Platonists again", then Gadamer arrives
at "Amicus Plato, period" and Badiou "you know, I'm a Platonist
again", what I think of your machine mind is that it doesn't
have a first-class mental maturity of an object sense of
objectivity.
>
You know, fifteen story buildings don't have thirteenth floors, ...,
in some places.
>

The point is that because Quine could not understand how we know
that all bachelors are unmarried he might not also accept that no
puppy is a fifteen story office buildings.
>

>
I can surely appreciate a grand ontology, yet, in terms of
the Ontological Commitment, and what one makes of an
Ontological Commitment, that fact that you have given yours
to a bitmap sort of arrives that being considered lacking
a more thorough and reasoned goal of "Ontological Commitment:
Reason, Rationality, the Purely Technically Philosophical,
and Science, and the Empirical, the Phenomenological",
is something that one can leave or keep, instead of being
just awash and adrift in the 0's and 1's.
>

It would be organized such the reasoning with formalized
natural language would be tree walks.
>

>
It may be all 0's and 1's down there, yet it's all
true and false up there, and here in the middle is
a sort of Objectivism.
>
What's above is as what is below,
a finite bitmap is so many scrawls
a stick, in the sand, of the beach, to reckon.
>
>
>
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>
>
>
That makes for "relevance logic", that syllogism only makes sense
in terms among common types.
>

>
Yes exactly no one else could get this because they try
to hide their ignorance with insults and disparagement.
>

Also for "relevance logic" is that "Ex Falso Quodlibet and
Material Implication" are _not_ a thing, and that a contradiction
about un-related/ir-relevant things say absolutely _nothing_
about things.
>

>
Yes that is the exact error of modern logic.
{The Moon is made of Green Cheese} proves {Donald Trump is God}
In both the principle of explosion and valid deductive inference.
>
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion
nevertheless to be false.https://iep.utm.edu/val-snd/
>
Thus enabling 'from falsehood, anything [follows]';
https://en.wikipedia.org/wiki/Principle_of_explosion
>

I.e., "Russell is not the Pope, and Russell never was the Pope".
>
That works just fine for usual "common-sense" types, and
it really even reflects on "common" and "sense", and it's
why there's "relevance logic" at all from what otherwise
was just usual analysis because "classical quasi-modal
logic" has "EFQ+MI" and Principle of Explosion instead
of "Ex Falso Nihilum".
>
So, one needn't have a "greater ontology" to establish
that the housecat or juvenile canine and the office tower
or a steamboat, while each things, have distinct properties
which effect their relations in usual enough is-a/has-a senses
or as with regards to any other collections of tuples in classes
and individuals and predicates that affect descriptions of
relations, which of course must be non-circular and
non-contradictory.
>

>
The purpose of the greater knowledge ontology that already exists
in the minds of most people is to provide computations with human
reasoning. LLM systems have already computed in a few months what
would take humans millions of man-years.
>

It seems then first you put down the quasi-modal for
relevance logic its much more sensible framework,
then at least common-sense is much less insulted.
>

>
The https://en.wikipedia.org/wiki/Cyc project already spent
1000 labor years fully formalizing all common sense. Without
the help of LLM systems it would take millions of labor years
to formalize the rest of human general knowledge.
>

>
My usual biggest gripe is about EFQ+MI which

>
I am not sure what you mean by MI.
>

seems totally insouciant if not duplicitous,
and absolutely un-necessary, then about Tertium
Non Datur gets involved the multi-valent, and
the temporal and so on, then besides the usual
notions of of sputniks of quantification of the
usual roots of "logical" paradox, a deconstructive
account after modern fundamental formalisms
results a quite better approach to modern foudnations,
also modern fundamental formalist foundations.

>
The sum total of all human general knowledge can be encoded
in mostly in formalized natural language propositions. Some
of this must be formalized using other formal languages.
One can explain the details of writing C programs in English
yet needs some actual C mixed into the explanation.
>
We don't really need multi-valent logic. Mostly what we need
is an enormously large number of axioms that are stipulated
to have the Boolean value of true.
>
We can compress the space required for these axioms and make
them much easier to process in an inheritance hierarchy knowledge
ontology. We also refrain from directly encoding and facts of the
world that can be derived from other facts of the world.
>
{Cats} <are> {Animals}
{Animals} <are> {Living Things}
thus no need to store
{Cats} <are> {Living Things}
>
This is already in the knowledge ontology inheritance hierarchy.
UML Inheritance {cat} ▷ {animal} ▷ {Living Thing}
>
>
>
>
>

>
>
A usual idea of a more robust deduction is also
that the premises have to be drawable as random
draws and that it results the same deduction
regardless the order of the draws.
>

>
I have not idea what this could possibly mean.
{Cats} <are> {Animals} can only be deduced from the
axiom {Cats} <are> {Animals}.
>

So, I don't agree that being "valid deductive inference",
it not being sound given arbitrary order-senstive premises.
>

>
This is valid deductive inference as shown by my analysis above:
{The Moon is made of Green Cheese} proves {Donald Trump is God}
>

That is, a robust and sound and valid deductive inference,
has to be the same from any angle and any draw or any
serialization of the premises (or "premisses").
>

>
If we don't somehow have some aspects of semantic relevance
directly encoded into our notion of formal systems of logic then we get
{The Moon is made of Green Cheese} proves {Donald Trump is God}
>

>
The "EFQ+MI" is "Ex False Quodlibet plus Material
Implication", where "Material Implication" is neither
"material" nor "implication" and "not p, or q" does
not have a "truth value", and doesn't belong in
a "truth table",

>
I totally agree with you on this. All of the other people on
these forums take the steps of logic as forming their own
foundation and thus are inherently correct even when they
derive nonsense.
>
I would replace implication with is a necessary consequence of.
Making the unary operator □ also be applied to binary relations.
∃!fluffy ∈ Cats | (Fluffy □ Animal).
>
They simply stipulate that the nonsense that they derive cannot
possibly be nonsense on basis of their religious belief that the
steps of logic are inherently infallible.
>
They then go on to assert that anyone that does not hold this
religious belief is totally ignorant about logic. They never
realize that the issue is their own ignorance of the philosophy
of logic.
>

with regards to why a usual "model"
in such a setting also isn't a model and usual "monotonicity"
in such a setting also isn't and a usual "entails"
in such a setting also isn't, that being why what

>
A is a necessary consequence of B: A □ B seems to be entails.
>

you'll find in the field called "Comte's Boole's Russell's
logical positivism's 'classical' logic" is renamed its
more proper appellation "classical _quasi-modal_ logic".
>
This is like, "ass|u|me", and "e fq mi", both considered
bad ideas.
>

>
You are almost the only one that every agreed with me on this.
The only other one the agreed that EFQ is nonsense had their
answer voted down to oblivion on SE. Logicians and Mathematicians
have the firmly held religious belief that the rules of logic
are inherently infallible and utterly ridicule anyone that
fully understands all of the reasoning that proves otherwise.
>
When this proof is presented to them they put their hands
over their ears making sure to not hear a single word while
shouting your stupid fool you don't know logic at all.
>

The premises, of deductive inference, if they're in

a given order, _is another premise_, and when they're _not_,
then those _are not_.
>

Every sequence of inference steps must be in the proper order
or there is no connection between inference steps.
>

>
The idea of "Large Language Model" is largely bunk,
a model of reasoning can be very compact.
Just having an arithmetic/vector coding of associated
values in types, is just an addressing scheme.
>

>
It is not actually largely bunk.
It has the key issue that it lies its ass off.
https://en.wikipedia.org/wiki/Hallucination_(artificial_intelligence)
>
Technology like this is the only feasible way that we can
populate a knowledge ontology of the general knowledge of
the actual world.
>
This dialogue proves that it has the equivalent of human understanding
that undecidable decision problems are really nothing more than yes/no
questions defined to have no correct yes/no answer.
https://www.liarparadox.org/ChatGPT_HP.pdf
>

>
Schroedinger's cat, now, helps explores in concept
the nature of indeterminism, and why, inference and
reasoning is first-class, not follow-the-red-dot.
>

>
>

>
What you get into is the box and circle modalities,
about when the transfer principle applies and
a heap is a heap is a heap or the Sorities,
matter of definition, not a paradox, disambiguated
in its quantifiers by disambiguating the universal quantifier,
into for: any/each/every/all, existential as unique or not,
the result _direct implication_ carries and with
ALL of De Morgan's rules of logic, simplifies things,
and excludes any sort "paradox".
>
That a cat has a kingdom and a genus and species vis-a-vis
being in a class of a kingdom and genus and speciesas is-a, just
reflects that is-a and has-a are only about the predicates
and relations, predicate logic and the predicate calculus,
and the resulting logic large of relations, and not necessarily
to be confused with Tarski's "cylindrical" bits when for
example there is algebraic GEOMETRY and ALGEBRAIC geometry
and they're _two, different things_.
>
I usually like to frame predicates as 'has-a' instead of
'is-a', because, things change, and "is" just "is".
>
It's all relations of course, predicates is relations.
>
>
I often have said "anybody who buys or shills Material Implication
is a fool or a fraud". The _direct_ implication, or just plain
old implication, first of all fills all of De Morgan's rules of logic
both ways, and, does not need "Material Implication", which is neither,
at all.
>
>
Russell: was never, the Pope.
>
>
>
Things have Types. So, one should be familiar with C.S. Peirce
and the Lambda Calculus, yet, in the logic of the universals and
particulars, there is the besides Type Inversion, there are as
well quantifier ambiguities, simply courtesy quantification
and schemes or schemas, to be resolved with quantifier disambiguation
and the correct and adequate book-keeping of contingency the
modality in predication the relation a stroke, evaluation.
>
(Judgment.)

>
The Bottom line that you seem to be avoiding is that there really
are expressions that are {true on the basis of meaning}.

>
SOME statements are true based on their "meaning" (as you are defining it), not all.
>
Not ALL True statements are True based on the meaning of their words.
>
Agaim, you are falling for the fallacy of proof by example.
>
The Pythagorean Theorem isn't True by the meaning of the words, but its truth comes out of the Truth makers of Plane Geometry and a series of valid connections from them to the Theorem.
>

>
We really cannot take the elevator of a puppy to the fifteenth
floor of this puppy and this is {true on the basis of meaning}.
>
The majority of people that were convinced there is no such thing
as {true on the basis of meaning} on the basis that Quine utterly
failed to understand how we know that bachelors are unmarried are
simply wrong.

>
I don't think many people think that there are no statements that are true by the nature of the meaning of the words, just that the "meaning of the words" can't be the only criteria.
>

>
I never restricted it this way (to the meaning of words)

 THen you DO accept that Godel's G is a true statement by its meaning since there does not exist any number g that satisfies the defined Primitive Recursive Relationship?
 And this can be established by the infinite sequence of steps of checking every Natural Number against that relationship, which is the classical meaning of Semantically true,
 

How do we use this to show that we know it is true that we
cannot take the elevator of a puppy to its fifteenth floor?
When you say
 > checking every Natural Number against that relationship, which is the
 > classical meaning of Semantically true,
you totally ignore 99.9999999% of semantics.
That it like saying counting to three is ALL of mathematics.

And thus is can not be a epistemological antinomy.
 

Observe that, in terms of the standard interpretation
(∀x2) ¬𝒫𝑓 (x2, ⌜G⌝) says that there is no natural number
that is the Gödel number of a proof in K of the wf G, which is equivalent to asserting that there is no proof in K of G.
Hence, G is equivalent in K to an assertion that G is unprovable
in K. In other words, G says “I am not provable in K”.
This is an analogue of the liar paradox: “I am lying”
(that is, “I am not true”). However, although the liar paradox
leads to a contradiction, Gödel (1931) showed that G is an
undecidable sentence of K. We shall refer to G as a Gödel
sentence for K. (Mendelson: 2015:208)
Mendelson, Elliott 2015. Introduction to Mathematical Logic sixth edition CRC Press Taylor & Francis Group Boca Raton, FL
When G says “I am not provable in K”.
any proof of G in K requires a sequence of inference
steps in K that prove that they themselves do not exist.
Meta_K can see this and confirms that G is unprovable in K.
*Gödel's proof hides all of these details*

I never even restricted on on the basis of the:
>
*Principle of compositionality*
In semantics, mathematical logic and related disciplines, the principle
of compositionality is the principle that the meaning of a complex
expression is determined by the meanings of its constituent expressions
and the rules used to combine them.
https://en.wikipedia.org/wiki/Principle_of_compositionality
>
I have *always* meant the 100% perfectly totally complete
meaning that also includes the full discourse context.

 How does that show that the Pathagorean Theorem is true?
 The question isn't determining the "Meaning of the Words" which is what the full discourse context would provide, but the sequence of the logical arguement that proves it, which is something which goes beyound "meaning" of the words.
 

>
Do you think that it is possible to:
take the elevator of a puppy to the fifteenth floor of this puppy?
or would the total meaning of the expression make that impossible?

 Nope. WHich is a fallacy of proof by example.
 Note, all your examples go to the most primiative form of logic, which if that is all you have, can be complete because it will be finite.
 

>
Maybe my example would have given Quine a clue about how we know
that all bachelors are unmarried. He is the one that convinced
most of the world that {true on the basis of meaning} is vacuous
and he did this almost entirely on the basis that he could not
understand exactly how we know that all bachelors are unmarried.
>
{true on the basis of meaning} is only relations between finite
strings thus excludes direct observations of things in the world.
>
*Two Dogmas of Empiricism*
https://www.ditext.com/quine/quine.html

  Since none of this relates to Formal logic or undecidability or incompleteness, I will presume that you are just admitting that you have no answers to the replys and are just working on Red Herring.
  Note, Quine doesn't say that we can't show that all bachelors are unmarried, but that bachelor and unmarried are not SYNONYMS replaceable with each other, and that logic that is based on that is too imprecise, and we need to better define the rules of logic when doing such things.
 The key point here is that while the classical definition of a bachelor is a never married man (though some uses of the words might include a man that was married but now nolonger has a wife), the word "unmarried" also has ranges of meaning from "never married" to "currently not married" and thus the two words can't be considered truely equivalent words.
 It seems, your problem is that you just don't understand the nuances of the papers, and in your stupidity assume this means the other people are just wrong, when the error is on YOUR part.
 

The bottom line of all of this (even if my summation is not
precisely accurate) is the Quine convinced most people that
{true on the basis of meaning} is not a viable notion.
It has never been the case that the precise nuances of detail
have ever mattered at all. It has always been the case that
the gist of the matter is crucial.
{True on the basis of meaning} is the actual ultimate foundation
of correct reasoning.

To re-iterate, every challenge I have put to you, asking you to defend your position has been ignored, and I will treat that as your admission that you have no response, and an admission that you accept that your claim is invalid, and thus that you repeated making the disproven claims are just proof of your being a liar and an idiot (for thinking people will believe your lies).
 

>

>
We must establish {true on the basis of meaning} as the ultimate
foundation of correct reasoning before we can begin to point out
how modern logic diverges from correct reasoning.
>

>
Then your concept of "Correct Reasoning" can't handle fundamental true statements like the Pythagorean Theorem, or even that 2 + 3 = 5, as these are not true JUST by the meaning of the words.
>

>

 

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