On 10/21/24 10:04 PM, olcott wrote:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the fact that >>> some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

Only if "can not be determined" means that there isn't an actual answer
to it,

Not that we don't know the answer to it.

For instance, the Twin Primes conjecture is either True, or it is False,
it can't be a non-truth-bearer, as either there is or there isn't a
highest pair of primes that differs by two.

The fact we don't know, and maybe can never know, doesn't make the
question incorrect.

Some truth is just unknowable.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

Right, and a question that we don't know (or maybe can't know) but is
either true or false, is not an incorrect question.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Does D halt, is not an incorrect question, as it will halt or not.

That the H that it was built from won't give the right answer is irrelevent.

You just don't understand what the terms mean, because you CHOSE to make youself ignorant, and thus INTENTIONALY made yourself into a pathetic
ignorant pathological lying idiot.

Sorry, but that is the facts.

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On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the fact that >>> some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.

Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

--
Mikko

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10/21/24 11:17 PM, olcott wrote:

On 10/21/2024 9:48 PM, Richard Damon wrote:

On 10/21/24 10:04 PM, olcott wrote:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the fact
that
some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

Only if "can not be determined" means that there isn't an actual
answer to it,

Not that we don't know the answer to it.

For instance, the Twin Primes conjecture is either True, or it is
False, it can't be a non-truth-bearer, as either there is or there
isn't a highest pair of primes that differs by two.

Sure.

So, you agree your definition is wrong

The fact we don't know, and maybe can never know, doesn't make the
question incorrect.

Some truth is just unknowable.

Sure.

And again.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

Right, and a question that we don't know (or maybe can't know) but is
either true or false, is not an incorrect question.

Sure.

So you argee again that you proposition is wrong.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Does D halt, is not an incorrect question, as it will halt or not.

Tarski is a simpler example for this case.
His theory rightfully cannot determine whether
the following sentence is true or false:
"This sentence is not true".
Because that sentence is not a truth bearer.

No, that isn't his statement, but of course your problem is you can't understand his actual statement so need to paraphrase it, and that loses
some critical properties.

That does not mean that True(L,x) cannot be defined.
It only means that some expression ore not truth bearers.

His proof does, the fact that you don't undetstand what he is talking
about doesn't make him wrong.

You asserting he is wrong becuase you don't understand his proof makes
you wrong, and STUPID.

That the H that it was built from won't give the right answer is
irrelevent.

You just don't understand what the terms mean, because you CHOSE to
make youself ignorant, and thus INTENTIONALY made yourself into a
pathetic ignorant pathological lying idiot.

Sorry, but that is the facts.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10/22/24 10:56 AM, olcott wrote:

On 10/22/2024 6:22 AM, Richard Damon wrote:

On 10/21/24 11:17 PM, olcott wrote:

On 10/21/2024 9:48 PM, Richard Damon wrote:

On 10/21/24 10:04 PM, olcott wrote:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the
fact that
some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

Only if "can not be determined" means that there isn't an actual
answer to it,

Not that we don't know the answer to it.

For instance, the Twin Primes conjecture is either True, or it is
False, it can't be a non-truth-bearer, as either there is or there
isn't a highest pair of primes that differs by two.

Sure.

So, you agree your definition is wrong

The fact we don't know, and maybe can never know, doesn't make the
question incorrect.

Some truth is just unknowable.

Sure.

And again.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

Right, and a question that we don't know (or maybe can't know) but
is either true or false, is not an incorrect question.

Sure.

So you argee again that you proposition is wrong.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Does D halt, is not an incorrect question, as it will halt or not.

Tarski is a simpler example for this case.
His theory rightfully cannot determine whether
the following sentence is true or false:
"This sentence is not true".
Because that sentence is not a truth bearer.

No, that isn't his statement, but of course your problem is you can't
understand his actual statement so need to paraphrase it, and that
loses some critical properties.

Haskell Curry species expressions of theory {T} that are
stipulated to be true:

   Thus, given {T}, an elementary theorem is an
   elementary statement which is true. https://www.liarparadox.org/Haskell_Curry_45.pdf

When we start with the foundation that True(L,x) is defined
as applying a set of truth preserving operations to a set
of expressions of language stipulated to be true Tarski's
proof fails.

We overcome Tarski Undefinability the same way that ZFC
overcame Russell's Paradox. We replace the prior foundation
with a new one.

https://liarparadox.org/Tarski_275_276.pdf

So, DO THAT then, and show what you get.

So, just as Z and F did, and went through ALL the logical proofs to show
what you could do with there rules, write up your complete set of rules
and then show what can be done with it.

You have been told this for years, but don't seem to understand, perhaps because you don't understand the basics well enough to actually do that.

Note, it isn't just the summary you will find on the informal sites that
you need to do, but the FORMAL PROOF that is in their academic papers.

Papers you probably can't understand.

And not, that since you are moving to a more basic level, of changing
the fundamental rules of the logic, you can't just assume any of the
existing logic principles still work.

This may well be the sort of thing where it takes 20 pages to show that
2 + 3 = 5 at the fundamental level of defining what + means.

That does not mean that True(L,x) cannot be defined.
It only means that some expression ore not truth bearers.

His proof does, the fact that you don't undetstand what he is talking
about doesn't make him wrong.

You asserting he is wrong becuase you don't understand his proof makes
you wrong, and STUPID.

That the H that it was built from won't give the right answer is
irrelevent.

You just don't understand what the terms mean, because you CHOSE to
make youself ignorant, and thus INTENTIONALY made yourself into a
pathetic ignorant pathological lying idiot.

Sorry, but that is the facts.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the fact that >>>>> some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.

Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

--
Mikko

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10/24/24 12:07 PM, olcott wrote:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the
fact that
some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.

Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability. It does eliminate undecidability
and not bothering to look at it is no actual rebuttal.

So, you admit that you haven't actually rebutted any of the errors
pointed out in your logic, as saying they are not interesting isn't
actually a rebuttal.

Thus you admit that nothing you have said has any useful basis.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the fact that
some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.

Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.

No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty. Ae also know
that a good foundation to computability does not eliminate
undecidablility but proves it, and also proves uncomputablility
of various functions.

Whether some foundation can be correct or what it would mean to
call it so is a different problem.

It does eliminate undecidability
and not bothering to look at it is no actual rebuttal.

You may say so but you don't offer any good argument to support
that claim. Instead you offer various indications that you will
never present a good argument about anything.

--
Mikko

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10/25/24 10:37 AM, olcott wrote:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the >>>>>>>>> fact that
some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that >>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>> theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there >>>>>>>> is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory >>>>>> leaves several important question unanswered. There are infinitely >>>>>> may different groups and group axioms must be true in every group. >>>>>>
Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.

No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

Then you plan to do the work to show this?

Or do you think ZF only wrote down there rules and said to everyone,
just believe us, this fixes everything.

Of course, my guess is you have on idea how to do that, as you don't
understand how the logic works.

I am not sure if you understand what is needed to even properly define
your initial set of axioms to build your logic on.

And by changing the rules of logic, you need to rederive the rules of
logic under your system, and then show that they are at least as useful
as the classical one.

ZF had the advantage that it was well known that "Naive" set theory was
broken, and so people were looking for something to replace it.

Until you can actually demonstrate that something logictians want is
broken, you have a major uphill battle.

The fact that many systems are incomplete, and many problems turn out to
be uncomputable isn't a problem in logic, as it has been shown to be a
pretty natural proerty following from the power of the logic system to
express more than can be actually known.

All I can see is your logic system tries to work by limiting what can be
talked about, to keep things under that threshold where capability to
express grows faster than the capability to know does, which leads to
those properties.

I am also not sure if your ideas are really knew, as there are a number
of theories of restricted logic, and you haven't been about to define
yours well enough to compare them. I am not sure YOU even undertstand
what you want well enough to actually definie it to do so.

Ae also know
that a good foundation to computability does not eliminate
undecidablility but proves it, and also proves uncomputablility
of various functions.

Whether some foundation can be correct or what it would mean to
call it so is a different problem.

It does eliminate undecidability
and not bothering to look at it is no actual rebuttal.

You may say so but you don't offer any good argument to support
that claim. Instead you offer various indications that you will
never present a good argument about anything.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 2024-10-25 14:37:19 +0000, olcott said:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the fact that
some expressions of language are simply not truth bearers.

A formal theory is undecidable if there is no Turing machine that >>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>> theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there >>>>>>>> is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory >>>>>> leaves several important question unanswered. There are infinitely >>>>>> may different groups and group axioms must be true in every group. >>>>>>
Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.

No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

No, not in the same way. ZFC is a useful set theory for many purposes.
You don't offer any useful theory for any purpose.

--
Mikko

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10/26/24 8:59 AM, olcott wrote:

On 10/26/2024 2:52 AM, Mikko wrote:

On 2024-10-25 14:37:19 +0000, olcott said:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring >>>>>>>>>>> the fact that
some expressions of language are simply not truth bearers. >>>>>>>>>>

A formal theory is undecidable if there is no Turing machine that >>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>> is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory >>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>
Another possibility is that a theory is poorly constructed: the >>>>>>>> author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is >>>>>>>> incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.

No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

No, not in the same way.

Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.

Nope, because is set theory, the "self-reference" was only directly
available in the definition of a set. By disallowing the set itself to
be in the set of things it can contain, ZF eleminated the problem.

For computations we have the problem that BY DEFINITION they need to be
able to handle "ANY" finite input string.

And, since any computation can be expressed as a finite string, we can
not exclude as the input, a string that represents the program (or
contains which incudes the program as part of the input).

The problem gets compounded in that there aren't just a "few" inputs
that could repreesent the program,

When we disallow the Liar Paradox then Tarski cannot derive
the first state of his proof and his proof fails.

But he shows that you can, and thus your claim fails. All you are saying
is that if we take "all" to not mean "all" we might be able to do
something, but since all does mean all, that can't apply.

Tarski's Liar Paradox from page 248
   It would then be possible to reconstruct the antinomy of the liar
   in the metalanguage, by forming in the language itself a sentence
   x such that the sentence of the metalanguage which is correlated
   with x asserts that x is not a true sentence.
   https://liarparadox.org/Tarski_247_248.pdf

By which he shows that the language itself has been shown to support the representation of the Liar's Paradox, and thus it *IS* a valid input.

Formalized as:
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x https://liarparadox.org/Tarski_275_276.pdf

adapted to become this
x ∉ Pr if and only if p  // line 1 of the proof

Here is the Tarski Undefinability Theorem proof
(1) x ∉ Provable if and only if p       // assumption (see above)
(2) x ∈ True if and only if p              // Tarski's convention T
(3) x ∉ Provable if and only if x ∈ True. // (1) and (2) combined
(4) either x ∉ True or x̄ ∉ True;      // axiom: ~True(x) ∨ ~True(~x)
(5) if x ∈ Provable, then x ∈ True;  // axiom: Provable(x) → True(x) (6) if x̄ ∈ Provable, then x̄ ∈ True;  // axiom: Provable(~x) → True(~x)
(7) x ∈ True
(8) x ∉ Provable
(9) x̄ ∉ Provable

ZFC is a useful set theory for many purposes.
You don't offer any useful theory for any purpose.

If we had a True(L, x) that worked consistently and L
is formalized natural language then we could refute
all of the dangerous lies made for political gain in
real time before they gained any traction.

But Tarski shows that a True((L, x), defined to work on ALL x that are expressable in L, can not be defined, as there exists some x that it can
not have a consistent value for.

Your logic requires that ALL doesn't actually mean ALL, and thus your
logic system is just not consistently defined.

Because we don't have this it looks like there is a
good chance we will be seeing the rise of the Fourth
Reich in a few days.

You just don't understand cause and effect it seems.

It is YOUR type of thinking that is fueling those dangers, so consider
yourself part of the problem.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10/26/24 5:57 PM, olcott wrote:

On 10/26/2024 10:48 AM, Richard Damon wrote:

On 10/26/24 8:59 AM, olcott wrote:

On 10/26/2024 2:52 AM, Mikko wrote:

On 2024-10-25 14:37:19 +0000, olcott said:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring >>>>>>>>>>>>> the fact that
some expressions of language are simply not truth bearers. >>>>>>>>>>>>

A formal theory is undecidable if there is no Turing machine >>>>>>>>>>>> that
determines whether a formula of that theory is a theorem of >>>>>>>>>>>> that
theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>> there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group >>>>>>>>>> theory
leaves several important question unanswered. There are
infinitely
may different groups and group axioms must be true in every >>>>>>>>>> group.

Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
does not eliminate undecidability.

No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

No, not in the same way.

Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.

Nope, because is set theory, the "self-reference"

does exist and is problematic in its several other instances.
Abolishing it in each case DOES ELIMINATE THE FREAKING PROBLEM.

Yes, IN SET THEORY, the "self-reference" can be banned, by the nature of
the contstruction.

In Computation Theory it can not, without making the system less than
Turing Complete, as the structure of the Computations fundamentally
allow for it, and in a way that is potentially undetectable.

You don't seem to understand that fact, but the fundamental nature of
being able to encode your processing in the same sort of strings you
process makes this a possibility.

Dues to the nature of its relationship to Mathematics and Logic, it
turns out that and logic with certain minimal requirements can get into
a similar situation.

Your only way to remove it from these fields is to remove that source of "power" in the systems, and the cost of that is just too high for most
people, thus you plan just fails.

Of course, you understanding is too crude to see this issue, so it just
goes over your head, and your claims just reveal your ignorance of the
fields.

Sorry, that is just the facts, that you seem to be too stupid to understand.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 2024-10-26 12:59:33 +0000, olcott said:

On 10/26/2024 2:52 AM, Mikko wrote:

On 2024-10-25 14:37:19 +0000, olcott said:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the fact that
some expressions of language are simply not truth bearers. >>>>>>>>>>

A formal theory is undecidable if there is no Turing machine that >>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>> is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory >>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>
Another possibility is that a theory is poorly constructed: the >>>>>>>> author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is >>>>>>>> incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.

No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

No, not in the same way.

Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.

There is no self reference in a formal theory. Expressions of a formal
theory don't refer.

--
Mikko

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10/26/24 9:22 PM, olcott wrote:

On 10/26/2024 8:04 PM, Richard Damon wrote:

On 10/26/24 5:57 PM, olcott wrote:

On 10/26/2024 10:48 AM, Richard Damon wrote:

On 10/26/24 8:59 AM, olcott wrote:

On 10/26/2024 2:52 AM, Mikko wrote:

On 2024-10-25 14:37:19 +0000, olcott said:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in >>>>>>>>>>>>>>> ignoring the fact that
some expressions of language are simply not truth bearers. >>>>>>>>>>>>>>

A formal theory is undecidable if there is no Turing >>>>>>>>>>>>>> machine that
determines whether a formula of that theory is a theorem >>>>>>>>>>>>>> of that
theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>>>> there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y >>>>>>>>>>>>> cannot be determined to be yes or no then the question >>>>>>>>>>>>> itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group >>>>>>>>>>>> theory
leaves several important question unanswered. There are >>>>>>>>>>>> infinitely
may different groups and group axioms must be true in every >>>>>>>>>>>> group.

Another possibility is that a theory is poorly constructed: the >>>>>>>>>>>> author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is >>>>>>>>>>>> incompatible with decidability, for example arithmetic. >>>>>>>>>>>>

An incorrect question is an expression of language that >>>>>>>>>>>>> is not a truth bearer translated into question form. >>>>>>>>>>>>>
When "X a formula of theory Y" is neither true nor false >>>>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer. >>>>>>>>>>>>

Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>>>> some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>>>> all the same thing as the corrected foundation to computability >>>>>>>>> does not eliminate undecidability.

No, but we already know that you don't offer anything interesting >>>>>>>> about foundations to computability or undecidabilty.

In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

No, not in the same way.

Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.

Nope, because is set theory, the "self-reference"

does exist and is problematic in its several other instances.
Abolishing it in each case DOES ELIMINATE THE FREAKING PROBLEM.

Yes, IN SET THEORY, the "self-reference" can be banned, by the nature
of the contstruction.

That seems to be the best way.

It works for sets, but not for Computations, due to the way things are
defined.

In Computation Theory it can not, without making the system less than
Turing Complete, as the structure of the Computations fundamentally
allow for it,

Sure.

So, you ADMIT that your computation system you are trying to advocate is
less than Turing Complete?

That means that the Halting Problem isn't a problem.

and in a way that is potentially undetectable.

I really don't think so it only seems that way.

Of course it is.

The method of assigning meaning to the symbols can be done is a
meta-system that the system doesn't know about, and thus its meaning is unknowable to the logic system.

You don't seem to understand that fact, but the fundamental nature of
being able to encode your processing in the same sort of strings you
process makes this a possibility.

It does not make these things undetectable, it merely
allows failing to detect.

No, it makes things undetectable, unless you allow the system to just
reject ALL statements, even if they are not actually "self-referential"
to be considered "bad".

Dues to the nature of its relationship to Mathematics and Logic, it
turns out that and logic with certain minimal requirements can get
into a similar situation.

I think that I can see deeper than the Curry/Howard Isomorphism.
Computations and formal systems are in their most basic foundational
essence finite string transformation rules.

You don't undertstand what you see.

Part of the problem is that while Compuation Theory and Formal Logic
System do have large parts that are just finite string transformation
rules, they have other parts that are not.

Your only way to remove it from these fields is to remove that source
of "power" in the systems, and the cost of that is just too high for
most people, thus you plan just fails.

Detection then rejection.

But since detection is impossible, you can not get to rejection.

Once you allow the creation of the statement, you can't reject it later
and still have the claim of handling "All".

Of course, you understanding is too crude to see this issue, so it
just goes over your head, and your claims just reveal your ignorance
of the fields.

Sorry, that is just the facts, that you seem to be too stupid to
understand.

In other words you can correctly explain every single detail
conclusively proving how finite string transformation rules
are totally unrelated to either computation and formal systems.

That isn't what I said, and just proves your stupidity.

You mind is just too small to handle these discussions.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10/27/24 9:29 AM, olcott wrote:

On 10/27/2024 3:27 AM, Mikko wrote:

On 2024-10-26 12:59:33 +0000, olcott said:

On 10/26/2024 2:52 AM, Mikko wrote:

On 2024-10-25 14:37:19 +0000, olcott said:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring >>>>>>>>>>>>> the fact that
some expressions of language are simply not truth bearers. >>>>>>>>>>>>

A formal theory is undecidable if there is no Turing machine >>>>>>>>>>>> that
determines whether a formula of that theory is a theorem of >>>>>>>>>>>> that
theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>> there
is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group >>>>>>>>>> theory
leaves several important question unanswered. There are
infinitely
may different groups and group axioms must be true in every >>>>>>>>>> group.

Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
does not eliminate undecidability.

No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

No, not in the same way.

Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.

There is no self reference in a formal theory. Expressions of a formal
theory don't refer.

Godel says otherwise.

In Godel, the reference is "self", but a big circle that gets back to
its start.

He shows that Mathematics is capable of expressing that level of
recursive referencing.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 2024-10-27 13:29:19 +0000, olcott said:

On 10/27/2024 3:27 AM, Mikko wrote:

On 2024-10-26 12:59:33 +0000, olcott said:

On 10/26/2024 2:52 AM, Mikko wrote:

On 2024-10-25 14:37:19 +0000, olcott said:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:

On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:

On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:

On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:

The whole notion of undecidability is anchored in ignoring the fact that
some expressions of language are simply not truth bearers. >>>>>>>>>>>>

A formal theory is undecidable if there is no Turing machine that >>>>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>>>> is not. No third possibility.

After being continually interrupted by emergencies
interrupting other emergencies...

If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
itself is somehow incorrect.

There are several possibilities.

A theory may be intentionally incomplete. For example, group theory >>>>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>>>
Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.

Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.

An incorrect question is an expression of language that
is not a truth bearer translated into question form.

When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.

Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.

See my most recent reply to Richard it sums up
my position most succinctly.

We already know that your position is uninteresting.

Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
does not eliminate undecidability.

No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

No, not in the same way.

Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.

There is no self reference in a formal theory. Expressions of a formal
theory don't refer.

Godel says otherwise.

No, he doesn't. Terms of formal system can be interpreted as references
but an interpretation is not a part of the formal theory. The word
"formal" means that only a form is defined but not any meaning. For
example, the meanings of the terms are not needed in order to determine
whether a finite sequence of finite strings is a proof.

There is a common interpretation of the symbols of Peano arithmetic:
the constant 0 means the empty set and the successor of the set X is
the set X ∪ {X}, and the meanings of the other operators follow from
that and their defining axioms; usually but not always the range of
meanings is restricted to the smallest collection of sets that contains
the exmpty set and the successor of every member. With this interpretation, every term refers to a set so no term refers to itself or any other term
or any formula.

--
Mikko

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)