From Newsgroup: sci.lang

On 11/29/2025 5:55 AM, Alan Mackenzie wrote:

[ Followup-To: set ]

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/28/2025 4:54 PM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/28/2025 3:08 PM, Alan Mackenzie wrote:

dart200 <user7160@newsgrouper.org.invalid> wrote:

[ .... ]

*Within A new foundation for correct reasoning*

(a) Every element of the body of knowledge that can
be expressed in language is entirely composed of
(1) A finite set of atomic facts
(2) Every expression of language that is semantically
entailed by (1)
(b) a formal language based on Rudolf Carnap Meaning
Postulates combined with The Kurt G||del definition
of the "theory of simple types"
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944 >>>> Where every semantic meaning is fully encoded syntactically
as one fully integrated whole not needing model theory

We have now totally overcome G||del Incompleteness
and Tarski Undefinability for the entire body if
knowledge that can be expressed in language. It
is now a giant semantic tautology.

You can't "overcome" these theorems, since they're not obstacles.
They're fundamental truths.

I just showed the detailed steps making both of
them impossible in the system that I just specified.
A counter-example is categorically impossible.

Your construction is impossible, as proven by G||del's Incompleteness Theorem.

You didn't "show" anything. You just waved your hands and expect
everybody to accept your continually repeated falsehoods.

You can claim that my idea is impossible.
It is impossible to show that my idea is impossible.
A mere dogmatic assertion provides zero actual evidence
that I am incorrect.

A consistent finite set of basic facts of the world is possible.
This consistent finite set of basic facts of the world are
encoded in Rudolf Carnap Meaning Postulates thus fully
encoding all of these semantic meaning directly in the formal
language. The Meaning Postulates are arranged in a knowledge
ontology similar to a type hierarchy. The only inference
steps are semantic logical entailment performed syntactically.

You can declare that I must be wrong because it contradicts
what others have said, yet you cannot point out any actual
in any of the steps because there are none.

"this program loops forever iff it's decided that it halts"

As you also know, this is the contradiction reached in one of the proofs >>>>> of the Halting Theorem. This is also not the same as "This sentence is >>>>> false.", though it is inspired by that nonsense.

It is isomorphic.

Stop using mathematical terms you don't understand. There is no
isomorphism here. Your assertion is a category error.

I used that term correctly and you cannot actually
show otherwise.

I suggest you look up isomorphism in Wikipedia to find out what it
actually means.

The object in the Liar Paradox case is the sentence
the object in the halting problem case is the behavior
of the input. In each of these two cases the truth
is the opposite of whatever is said, thus the identical
structure.

They are isomorphic as abstract structures

None of these sentences/nonsenses limit our ability to understand truth. >>>>> They are part of the truth that we understand. They delineate
fundamental boundaries of what can be known and proven, in particular >>>>> that truth is more subtle than provability.

That is bullshit as I have just proven.

Every time you use the word "proven" you appear to be lying. I can't
recall any occurrence where you were telling the truth.

When a counter-example to my claim is categorically
impossible then I have proven this claim even if
you fail to understand that this is the generic
way that all actual proof really works.

It has nothing to do with my understanding, and a great deal to do with
your lack of it. You have not proven that a counter example to whatever
it is you're talking about is "categorically impossible".

You could not point out any specific error in the
details that I specified. You can only assert mere
baseless dogma that you believe that I am incorrect.

You can't,
since you lack the prerequisites to understand what constitutes a proof,
and you lack the mathematical foundations to be able to construct one.

I don't give a rat's ass about your narrow minded
learned by rote definitions of a proof are.

The most generic form of a proof is essentially
a semantic tautology.

Within the giant semantic tautology of knowledge that
can be expressed in language everything is proven or
not an element of this body.

Your scheme is limited indeed, in that it is not powerful enough to
represent unprovable propositions.

In other words "the entire body of knowledge that
can be expressed in language" uses big words that
you cannot understand?

What is left out of:
"the entire body of knowledge that can be expressed in language" ?

Arithmetic, for a start.

So you are trying to get away with saying that
knowledge of arithmetic cannot be expressed in language?

If that allegedly "entire body of knowledge"
was capable of doing arithmetic, G||del's Incompleteness Theorem would
apply to it.

Arithmetic is merely insufficiently expressive,
the body of knowledge that can be expressed in
language knows that.

That is a proof by contradiction that such a body of
knowledge cannot exist.

Not at all. Arithmetic is merely insufficiently expressive.
While you attempt to come up with counter-examples know
that dogma does not count.

A counter-example would be an element of knowledge
that can be expressed in language that:
(a) Cannot be expressed in language.
(b) Is not true. (All knowledge is true)

That is what I mean by counter-examples are
categorically impossible

[ .... ]

--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.lang

[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/29/2025 5:55 AM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/28/2025 4:54 PM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/28/2025 3:08 PM, Alan Mackenzie wrote:

[ .... ]

*Within A new foundation for correct reasoning*
(a) Every element of the body of knowledge that can
be expressed in language is entirely composed of
(1) A finite set of atomic facts
(2) Every expression of language that is semantically
entailed by (1)
(b) a formal language based on Rudolf Carnap Meaning
Postulates combined with The Kurt G||del definition
of the "theory of simple types"
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Where every semantic meaning is fully encoded syntactically
as one fully integrated whole not needing model theory
We have now totally overcome G||del Incompleteness
and Tarski Undefinability for the entire body if
knowledge that can be expressed in language. It
is now a giant semantic tautology.

You can't "overcome" these theorems, since they're not obstacles.
They're fundamental truths.

I just showed the detailed steps making both of
them impossible in the system that I just specified.
A counter-example is categorically impossible.

Your construction is impossible, as proven by G||del's Incompleteness
Theorem.
You didn't "show" anything. You just waved your hands and expect
everybody to accept your continually repeated falsehoods.

You can claim that my idea is impossible.

I no longer remember which idea that is.

It is impossible to show that my idea is impossible.

Given that your ideas strongly tend to violate firmly established
mathematical results, there is no such impossibility as you assert. Note
that if you hold established results to be false, you have the burden of
proof. At no time in this newsgroup have you met this obligation.

A mere dogmatic assertion provides zero actual evidence
that I am incorrect.

I don't need to provide evidence. As just written, the burden of proof
is on your side.

A consistent finite set of basic facts of the world is possible.

There are many such finite sets, but none of them are complete, and they
cannot be complete. This was demonstrated by mathematicians in the early
20th century.

This consistent finite set of basic facts of the world are
encoded in Rudolf Carnap Meaning Postulates thus fully
encoding all of these semantic meaning directly in the formal
language. The Meaning Postulates are arranged in a knowledge
ontology similar to a type hierarchy. The only inference
steps are semantic logical entailment performed syntactically.

This is a will o' the wisp, as much as Frege's or Russell and Whitehead's
much more modest attempts to formalise all of mathematics were.

You can declare that I must be wrong because it contradicts
what others have said, yet you cannot point out any actual
in any of the steps because there are none.

As I keep saying, the burden of proof is on your side. The three mathematicians just mentioned failed because what they were attempting
was fundamentally impossible. That was not yet understood in the early
years of the twentieth century, but it is firm knowledge now. What you
are insisting can be done is a superset of these impossibilities.
There is a lot of hubris involved here, and seemingly not a little
personal insecurity, in someone who cannot accept reality as it is.

"this program loops forever iff it's decided that it halts"

As you also know, this is the contradiction reached in one of the proofs >>>>>> of the Halting Theorem. This is also not the same as "This sentence is >>>>>> false.", though it is inspired by that nonsense.

[ .... ]

None of these sentences/nonsenses limit our ability to understand
truth. They are part of the truth that we understand. They
delineate fundamental boundaries of what can be known and proven,
in particular that truth is more subtle than provability.

That is bullshit as I have just proven.

Every time you use the word "proven" you appear to be lying. I can't
recall any occurrence where you were telling the truth.

When a counter-example to my claim is categorically
impossible then I have proven this claim even if
you fail to understand that this is the generic
way that all actual proof really works.

It has nothing to do with my understanding, and a great deal to do with
your lack of it. You have not proven that a counter example to whatever
it is you're talking about is "categorically impossible".

You could not point out any specific error in the
details that I specified. You can only assert mere
baseless dogma that you believe that I am incorrect.

The "details" you "specified" were just hand-waving nonsense, not based
on any firm logical or mathematical results. Therefore they can be
justifiably disregarded.

You can't, since you lack the prerequisites to understand what
constitutes a proof, and you lack the mathematical foundations to be
able to construct one.

I don't give a rat's ass about your narrow minded learned by rote
definitions of a proof are.

Neither do I. Not relevant, since I don't have any such learned by rote definitions of a proof.

The most generic form of a proof is essentially a semantic tautology.

That's neither here not there, being too abstract to be of use.

Within the giant semantic tautology of knowledge that
can be expressed in language everything is proven or
not an element of this body.

Your scheme is limited indeed, in that it is not powerful enough to
represent unprovable propositions.

In other words "the entire body of knowledge that
can be expressed in language" uses big words that
you cannot understand?
What is left out of:
"the entire body of knowledge that can be expressed in language" ?

Arithmetic, for a start.

So you are trying to get away with saying that
knowledge of arithmetic cannot be expressed in language?

I'm saying that any system of knowledge in which G||del's Incompleteness Theorem doesn't apply is either inconsistent or incapable of doing
arithmetic.

If that allegedly "entire body of knowledge"
was capable of doing arithmetic, G||del's Incompleteness Theorem would
apply to it.

Arithmetic is merely insufficiently expressive, the body of knowledge
that can be expressed in language knows that.

No, the body of knowledge that can be represented as you envisage
wouldn't come up to the level of a stone-age person.

That is a proof by contradiction that such a body of
knowledge cannot exist.

Not at all.

How can you say that? You don't understand proof by contradiction,
remember?

Arithmetic is merely insufficiently expressive.
While you attempt to come up with counter-examples know
that dogma does not count.

I don't know what you mean by dogma. I'm talking about proven results
like 2 + 2 = 4. You're just ignorant, because you don't have the
background needed to test these results, but you reject them just because
you don't like them. You're an idiot, in other words.

A counter-example would be an element of knowledge
that can be expressed in language that:
(a) Cannot be expressed in language.
(b) Is not true. (All knowledge is true)

That would indeed be a counter example. But given there is no suspicion
that such a construct of knowledge could be complete, no proof, no
attempt at a proof, there is nothing to give a counter example to.

That is what I mean by counter-examples are
categorically impossible

Your complete system of knowledge is categorically impossible.

--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning" computable.
This required establishing a new foundation
for correct reasoning.

--
Alan Mackenzie (Nuremberg, Germany).
--- Synchronet 3.21a-Linux NewsLink 1.2