On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider with infinite resources.

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.

/Flibble

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On Mon, 21 Apr 2025 17:08:49 -0700, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider
with infinite resources.

That's not what I asked, and it's not interesting.

Do I need to ask the question again, or can you go back and find what I wrote?

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.

That's your assertion. One more time, you're free to construct a new mathematical system with that as an axiom. Such a new system is less
useful and less interesting than the one in which the proof of the insolubility of the Halting Problem was constructed, which is about computations that can be completed in a finite number of steps.

Finite number of steps? See Flibble's Law.

/Flibble

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On 4/21/25 7:41 PM, Mr Flibble wrote:

On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider with infinite resources.

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits infinite analysis of that behavior in its decidability scope.

/Flibble

Which is just a false statement, and thus a LIE.

We don't know if Goldbach's Conjecture can be SOLVED using a Simulating
Halt Decider with infinite resources, as we don't know that such a
machine will ever give an answer.

Note, a machine checking every number, will NEVER reach its final state
if the conjecture is true. So even given unbounded time, it still
doesn't answer.

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On 4/21/25 7:52 PM, olcott wrote:

On 4/21/2025 5:08 PM, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

This document refutes Alan Turing’s 1936 proof of the undecidability of >>> the halting problem, as presented in “On Computable Numbers, with an
Application to the Entscheidungsproblem” (Proceedings of the London
Mathematical Society, 1936), by leveraging the assumption that self-
referential conflation of a halt decider and its input constitutes a
category (type) error. The refutation argues that Turing’s proof, which >>> relies on a self-referential construction, is invalid in a typed system
where such conflation is prohibited.

You're acknowledging that it's an "assumption".

Sure, *if* you **assume** that "self-referential conflation of a
halt decider and its input constitutes a category (type) error",
then Turing's proof is invalid in a system where that assumption
is true (if your terms can be rigorously defined).

Of course Turing's proof wasn't intended to be interpreted in such
a system, and there is no actual self-reference.  If Turing's proof
actually relied on self-reference, you might have a valid claim.
The proposed halt decider does not operate on itself, or on a
reference to itself; it operates on a modified copy of itself.

Are you ever going to answer my questions about Goldbach's
Conjecture?

[SNIP]

Computer Science Professor Eric Hehner PhD
and I all seem to agree that the same view
that Flibble has is the correct view.

And many more disagree, so you are out voted so you argument by
authority fails.

Sorry, you are just showing you don't understand what you are talking about.

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On Mon, 21 Apr 2025 20:49:06 -0400, Richard Damon wrote:

On 4/21/25 7:41 PM, Mr Flibble wrote:

On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider
with infinite resources.

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.

/Flibble

Which is just a false statement, and thus a LIE.

We don't know if Goldbach's Conjecture can be SOLVED using a Simulating
Halt Decider with infinite resources, as we don't know that such a
machine will ever give an answer.

Note, a machine checking every number, will NEVER reach its final state
if the conjecture is true. So even given unbounded time, it still
doesn't answer.

It has infinite resources as per Flibble's Law so doesn't have to give an answer in finite time, i.e. it doesn't have to give an answer.

/Flibble

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On 4/21/25 9:16 PM, Mr Flibble wrote:

On Mon, 21 Apr 2025 20:49:06 -0400, Richard Damon wrote:

On 4/21/25 7:41 PM, Mr Flibble wrote:

On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider
with infinite resources.

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.

/Flibble

Which is just a false statement, and thus a LIE.

We don't know if Goldbach's Conjecture can be SOLVED using a Simulating
Halt Decider with infinite resources, as we don't know that such a
machine will ever give an answer.

Note, a machine checking every number, will NEVER reach its final state
if the conjecture is true. So even given unbounded time, it still
doesn't answer.

It has infinite resources as per Flibble's Law so doesn't have to give an answer in finite time, i.e. it doesn't have to give an answer.

/Flibble

first, "Flibbles's Law" hasn't been proven, so it can't be invoked.

Second, Not answering even after an infinite time is not the same as
answering after an infinite time.

If you claim that not answering after an infinite time is answering then
a Flibble Halt Decider is simple, return 1, as ALL programs will do no
worse than not answering.

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On Mon, 21 Apr 2025 18:27:15 -0700, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

On Mon, 21 Apr 2025 17:08:49 -0700, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's
Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider
with infinite resources.

That's not what I asked, and it's not interesting.

Do I need to ask the question again, or can you go back and find what
I wrote?

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.

That's your assertion. One more time, you're free to construct a new
mathematical system with that as an axiom. Such a new system is less
useful and less interesting than the one in which the proof of the
insolubility of the Halting Problem was constructed, which is about
computations that can be completed in a finite number of steps.

Finite number of steps? See Flibble's Law.

Yes, finite number of steps. I saw Flibble's Law. It doesn't interest
me, nor does proof by tedious repetition.

What does or does not interest you is of little consequence. Flibble's Law stands.

/Flibble

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On Mon, 21 Apr 2025 21:37:59 -0400, Richard Damon wrote:

On 4/21/25 9:16 PM, Mr Flibble wrote:

On Mon, 21 Apr 2025 20:49:06 -0400, Richard Damon wrote:

On 4/21/25 7:41 PM, Mr Flibble wrote:

On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's
Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider
with infinite resources.

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.

/Flibble

Which is just a false statement, and thus a LIE.

We don't know if Goldbach's Conjecture can be SOLVED using a
Simulating Halt Decider with infinite resources, as we don't know that
such a machine will ever give an answer.

Note, a machine checking every number, will NEVER reach its final
state if the conjecture is true. So even given unbounded time, it
still doesn't answer.

It has infinite resources as per Flibble's Law so doesn't have to give
an answer in finite time, i.e. it doesn't have to give an answer.

/Flibble

first, "Flibbles's Law" hasn't been proven, so it can't be invoked.

Flibble's Law is an axiom.

Second, Not answering even after an infinite time is not the same as answering after an infinite time.

There is no "after" an infinite time so as per Flibble's Law no answer has
to be given.

If you claim that not answering after an infinite time is answering then
a Flibble Halt Decider is simple, return 1, as ALL programs will do no
worse than not answering.

As per Flibble's Law no answer has to be given, the problem is the problem
not the analysis of the problem.

/Flibble

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On 4/22/25 8:22 AM, Mr Flibble wrote:

On Mon, 21 Apr 2025 18:27:15 -0700, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

On Mon, 21 Apr 2025 17:08:49 -0700, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's
Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider
with infinite resources.

That's not what I asked, and it's not interesting.

Do I need to ask the question again, or can you go back and find what
I wrote?

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits >>>>> infinite analysis of that behavior in its decidability scope.

That's your assertion. One more time, you're free to construct a new
mathematical system with that as an axiom. Such a new system is less
useful and less interesting than the one in which the proof of the
insolubility of the Halting Problem was constructed, which is about
computations that can be completed in a finite number of steps.

Finite number of steps? See Flibble's Law.

Yes, finite number of steps. I saw Flibble's Law. It doesn't interest
me, nor does proof by tedious repetition.

What does or does not interest you is of little consequence. Flibble's Law stands.

/Flibble

Only in the Flibbleverse, which others don't care about.

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On 4/22/25 8:21 AM, Mr Flibble wrote:

On Mon, 21 Apr 2025 21:37:59 -0400, Richard Damon wrote:

On 4/21/25 9:16 PM, Mr Flibble wrote:

On Mon, 21 Apr 2025 20:49:06 -0400, Richard Damon wrote:

On 4/21/25 7:41 PM, Mr Flibble wrote:

On Mon, 21 Apr 2025 15:08:34 -0700, Keith Thompson wrote:

Are you ever going to answer my questions about Goldbach's
Conjecture?

Goldbach's Conjecture can be solved using a Simulating Halt Decider
with infinite resources.

Flibble's Law:

If a problem permits infinite behavior in its formulation, it permits >>>>> infinite analysis of that behavior in its decidability scope.

/Flibble

Which is just a false statement, and thus a LIE.

We don't know if Goldbach's Conjecture can be SOLVED using a
Simulating Halt Decider with infinite resources, as we don't know that >>>> such a machine will ever give an answer.

Note, a machine checking every number, will NEVER reach its final
state if the conjecture is true. So even given unbounded time, it
still doesn't answer.

It has infinite resources as per Flibble's Law so doesn't have to give
an answer in finite time, i.e. it doesn't have to give an answer.

/Flibble

first, "Flibbles's Law" hasn't been proven, so it can't be invoked.

Flibble's Law is an axiom.

Then you are admitting that you aren't talking about the system you
claim to be talking about, as it doesn't have that axiom.

All you are doing is showing that lie PO, you are living in a fantasy
world where the real truth doesn't matterm.

Second, Not answering even after an infinite time is not the same as
answering after an infinite time.

There is no "after" an infinite time so as per Flibble's Law no answer has
to be given.

Sure there is. Their are Transfinite Ordinals, so there IS an order past infinity.

If you claim that not answering after an infinite time is answering then
a Flibble Halt Decider is simple, return 1, as ALL programs will do no
worse than not answering.

As per Flibble's Law no answer has to be given, the problem is the problem not the analysis of the problem.

/Flibble

Then the Flibbleverse doesn't know how to define a decider, and has just
blown itself up in self-contradictions.

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On 4/25/25 12:31 PM, olcott wrote:

On 4/25/2025 3:46 AM, Mikko wrote:

On 2025-04-24 15:11:13 +0000, olcott said:

On 4/23/2025 3:52 AM, Mikko wrote:

On 2025-04-21 23:52:15 +0000, olcott said:

Computer Science Professor Eric Hehner PhD
and I all seem to agree that the same view
that Flibble has is the correct view.

Others can see that their justification is defective and contradicted
by a good proof.

Some people claim that the unsolvability of the halting problem is
unproven but nobody has solved the problem.

For the last 22 years I have only been refuting the
conventional Halting Problem proof.

Trying to refute. You have not shown any defect in that proof of the
theorem. There are other proofs that you don't even try to refute.

Not at all. You have simply not been paying enough attention.

Once we understand that Turing computable functions are only
allowed to derived their outputs by applying finite string
operations to their inputs then my claim about the behavior
of DD that HHH must report on is completely proven.

Youy have your words wrong. They are only ABLE to use finite algorithms
of finite string operations. The problem they need to solve do not need
to be based on that, but on just general mappings of finite strings to
finite strings that might not be described by a finite algorithm.

The mapping is computable, *IF* we can find a finite algorith of
transformation steps to make that mapping.

You just don't seem to understand that diffence between Requirements and Capability.

Yes, it doesn't make much sense to ask about if we can compute something
that we know can not be, but many non-computable problems, like Halting,
were first suppoed to be computable, and solutions were looked for, when
the, in hind sight obvious, counter example that shows it can't be was
found.

In fact, your argument just shows that the problem, as actually stated
is impossible to do, but you misuse that to say that means you get to
change the question. THAT is a fundamental lie in your logic. The
question, "Does the machine+input described by the input halt when run?"
is a perfectly valid question. The fact that it turns out that it is
impossible to write a program that can do this for all inputs, doesn't
make the question suddenly invalid. It says the question is
non-computable, and thus no Halt Deciders exist.

This DOES have great impact on much of logic, as a related property of
this that exists in any logic system that has the needed propeties of
the Natural Numbers having statements that are true but not provable.

This turns out to be an attribute that comes out of the creation of
countable infinities which just breaks some of our common notions of how
things should work, but end up must being true in those systems.

Actually solving the Halting Problem requires making a computer
program that is literally all knowing about program termination.

Which is provably impossible.

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On 2025-04-25 10:31, olcott wrote:

Once we understand that Turing computable functions are only
allowed to derived their outputs by applying finite string
operations to their inputs then my claim about the behavior
of DD that HHH must report on is completely proven.

You're very confused here.

Computable functions are *functions*. That is, they are mappings from a
domain to a codomain, neither of which are required to be strings.
Functions don't involve finite string operations at all.

What distinguishes a computable function from other functions is that it
is possible to implement an algorithm which computes that function. That algorithm might involve string operations, but the algorithm is not the function anymore than the function is the algorithm.

The halting *function* is a mapping from the set of computations (not
strings) to the set of boolean values (also not strings). A given
computation maps to true if and only if it is finite.

A halt *decider* (were such a thing possible) would be an algorithm
which computes the halting function. Such an algorithm (assuming we're
talking in terms of Turing Machines) would have to encode the elements
of the halting function's domain as strings, but the mapping it computes
would still be from the computations which those strings represent to
their associated boolean values.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

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On 4/25/25 5:46 PM, olcott wrote:

On 4/25/2025 11:54 AM, Richard Damon wrote:

On 4/25/25 12:31 PM, olcott wrote:

On 4/25/2025 3:46 AM, Mikko wrote:

On 2025-04-24 15:11:13 +0000, olcott said:

On 4/23/2025 3:52 AM, Mikko wrote:

On 2025-04-21 23:52:15 +0000, olcott said:

Computer Science Professor Eric Hehner PhD
and I all seem to agree that the same view
that Flibble has is the correct view.

Others can see that their justification is defective and contradicted >>>>>> by a good proof.

Some people claim that the unsolvability of the halting problem is >>>>>> unproven but nobody has solved the problem.

For the last 22 years I have only been refuting the
conventional Halting Problem proof.

Trying to refute. You have not shown any defect in that proof of the
theorem. There are other proofs that you don't even try to refute.

Not at all. You have simply not been paying enough attention.

Once we understand that Turing computable functions are only
allowed to derived their outputs by applying finite string
operations to their inputs then my claim about the behavior
of DD that HHH must report on is completely proven.

Youy have your words wrong. They are only ABLE to use finite
algorithms of finite string operations. The problem they need to solve
do not need to be based on that, but on just general mappings of
finite strings to finite strings that might not be described by a
finite algorithm.

The mapping is computable, *IF* we can find a finite algorith of
transformation steps to make that mapping.

There are no finite string operations that can
be applied to the input to HHH(DD) that derive
the behavior of of the directly executed DD thus
DD is forbidden from reporting on this behavior.

Of course there is a finite string transformation that can be applied to
the input of HHH(DD), ie the code of DD, as that transformation is the transformation defined by the x86 language, or the FULL AND COMPLETE
emulation of the input DD.

It just is a fact that this isn't the transformation that HHH does, but
is what HHH1 does.

It is forbidden for the same reason that
int sum(int x, int y) { return x + y; }
sum(3,2) IS NOT ALLOWED TO REPORT ON THE SUM OF 5 + 7.

But the input to HHH is the object code of DD, not what that does. It is
HHH's job to figure out what it does.

Just like sum(3,20 is given the number 3 and 2, and it needs to figure
out what the sum of those numbers are.

Remember, you have stipulated that the input DD includes the code
defined by Halt7.c, so HHH has been given all the code of itself. This
is enough information to determine the behavior, as HHH1 shows, it is
just that HHH doesn't do that, and DD capitalizes on that error in HHH
to make it wrong.

Now, of course if you make some different decider, say UTM that doesn't
do that abort, then DDUTM which calls that UTM instead of HHH, will
cause UTM(DDUTM) to not answer, and thus fail to be a decider, showing
that DDUTM acheived its goal.

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