Refuting Gödel's 1931 Incompleteness Theorem in one sentence

[Arising_uk]

... You could publish this in every journal and win the Nobel Prize and the Turing award and you still can't convince me.
...

Oh now c'mon.

[Univalence]

... You could publish this in every journal and win the Nobel Prize and the Turing award and you still can't convince me.
...

Oh now c'mon.

Epaulettes mean nothing in epistemology.

Results do.

I know what results in this field look like.

There is an objective criterion for this claim.

[PeteOlcott]

... You could publish this in every journal and win the Nobel Prize and the Turing award and you still can't convince me.
...

Oh now c'mon.

Epaulettes mean nothing in epistemology.

Results do.

I know what results in this field look like.

Here is a bridge between the two. My publication will include the source code for
TM H and TM H^ and a complete execution trace of TM H on input pair: (H^, H^).

This execution trace will show every state transition of the UTM executing H and H^
as well as every change to the state of this UTM's tape.

After I completed the algorithm for doing this December 13, 2018 between 6:00 and 8:00 PM
(I still have my original notes. I scanned a copy of them for posterity).
it took me a few more months to write the source code for H and H^.

[Univalence]

Oh now c'mon.

Epaulettes mean nothing in epistemology.

Results do.

I know what results in this field look like.

Here is a bridge between the two. My publication will include the source code for
TM H and TM H^ and a complete execution trace of TM H on input pair: (H^, H^).

This execution trace will show every state transition of the UTM executing H and H^
as well as every change to the state of this UTM's tape.

After I completed the algorithm for doing this December 13, 2018 between 6:00 and 8:00 PM
(I still have my original notes. I scanned a copy of them for posterity).
it took me a few more months to write the source code for H and H^.

You don’t need to provide the input - that is my job.

You just need to provide the algorithm. All your algorithm needs to do is examine a previously-unseen input and return Boolean True when the input will halt and Boolean False when it won’t.

[PeteOlcott]

Epaulettes mean nothing in epistemology.

Results do.

I know what results in this field look like.

Here is a bridge between the two. My publication will include the source code for
TM H and TM H^ and a complete execution trace of TM H on input pair: (H^, H^).

This execution trace will show every state transition of the UTM executing H and H^
as well as every change to the state of this UTM's tape.

After I completed the algorithm for doing this December 13, 2018 between 6:00 and 8:00 PM
(I still have my original notes. I scanned a copy of them for posterity).
it took me a few more months to write the source code for H and H^.

You don’t need to provide the input - that is my job.

You just need to provide the algorithm. All your algorithm needs to do is examine a previously-unseen input and return Boolean True when the input will halt and Boolean False when it won’t.

The input is only a single example of a TM that exactly matches the specification
for H^ thus unequivocally proving that the pattern specified by the conventional halting
problem proofs does not actually prevent halting from being decidable.

The claim of the conventional halting problem proofs is that a certain pattern
makes halting undecidable in every instance of that pattern.

Refuting this only requires one instance of the exact same pattern where halting
is shown to be decidable. Once the pattern is broken it cannot be reestablished again.

[Univalence]

Here is a bridge between the two. My publication will include the source code for
TM H and TM H^ and a complete execution trace of TM H on input pair: (H^, H^).

This execution trace will show every state transition of the UTM executing H and H^
as well as every change to the state of this UTM's tape.

After I completed the algorithm for doing this December 13, 2018 between 6:00 and 8:00 PM
(I still have my original notes. I scanned a copy of them for posterity).
it took me a few more months to write the source code for H and H^.

You don’t need to provide the input - that is my job.

You just need to provide the algorithm. All your algorithm needs to do is examine a previously-unseen input and return Boolean True when the input will halt and Boolean False when it won’t.

The input is only a single example of a TM that exactly matches the specification
for H^ thus unequivocally proving that the pattern specified by the conventional halting
problem proofs does not actually prevent halting from being decidable.

The claim of the conventional halting problem proofs is that a certain pattern
makes halting undecidable in every instance of that pattern.

Refuting this only requires one instance of the exact same pattern where halting
is shown to be decidable. Once the pattern is broken it cannot be reestablished again.

Peter, have you solved the general case of the halting problem or not?

If you have you should be indifferent to the input!

I should be able to give you ANY programmatic expression and your algorithm can determine if it halts or not.

It seems to me you are beginning to backtrack on your claims...

[PeteOlcott]

You don’t need to provide the input - that is my job.

You just need to provide the algorithm. All your algorithm needs to do is examine a previously-unseen input and return Boolean True when the input will halt and Boolean False when it won’t.

The input is only a single example of a TM that exactly matches the specification
for H^ thus unequivocally proving that the pattern specified by the conventional halting
problem proofs does not actually prevent halting from being decidable.

The claim of the conventional halting problem proofs is that a certain pattern
makes halting undecidable in every instance of that pattern.

Refuting this only requires one instance of the exact same pattern where halting
is shown to be decidable. Once the pattern is broken it cannot be reestablished again.

Peter, have you solved the general case of the halting problem or not?

If you have you should be indifferent to the input!

I should be able to give you ANY programmatic expression and your algorithm can determine if it halts or not.

It seems to me you are beginning to backtrack on your claims...

I have not written a program that is all knowing about halting decidability.

I have refuted all of the conventional halting problem proofs by showing one instance
of halting decidability that has been proven to be categorically impossible.

[Univalence]

The input is only a single example of a TM that exactly matches the specification
for H^ thus unequivocally proving that the pattern specified by the conventional halting
problem proofs does not actually prevent halting from being decidable.

The claim of the conventional halting problem proofs is that a certain pattern
makes halting undecidable in every instance of that pattern.

Refuting this only requires one instance of the exact same pattern where halting
is shown to be decidable. Once the pattern is broken it cannot be reestablished again.

Peter, have you solved the general case of the halting problem or not?

If you have you should be indifferent to the input!

I should be able to give you ANY programmatic expression and your algorithm can determine if it halts or not.

It seems to me you are beginning to backtrack on your claims...

I have not written a program that is all knowing about halting decidability.

I have refuted all of the conventional halting problem proofs by showing one instance
of halting decidability that has been proven to be categorically impossible.

Pete, have you solved the general case of the halting problem?

Do you have a universal algorithm which can determine if a program will halt?

Yes or no.

[PeteOlcott]

Peter, have you solved the general case of the halting problem or not?

If you have you should be indifferent to the input!

I should be able to give you ANY programmatic expression and your algorithm can determine if it halts or not.

It seems to me you are beginning to backtrack on your claims...

I have not written a program that is all knowing about halting decidability.

I have refuted all of the conventional halting problem proofs by showing one instance
of halting decidability that has been proven to be categorically impossible.

Pete, have you solved the general case of the halting problem?

Do you have a universal algorithm which can determine if a program will halt?

Yes or no.

No. I have refuted all of the conventional halting problem proofs thus opening the
door for the halting problem to be solved.

99.99% of solving the halting problem is proving that it is not impossible
and the rest is conventional computer programming using the model that I
established.

Thus it is not too much poetic license to say that I solved the halting
problem by merely providing a single counter-example of halting decidability
that conforms to the conventional halting problem proof pattern of undecidability.

[Univalence]

No. I have refuted all of the conventional halting problem proofs thus opening the
door for the halting problem to be solved.

99.99% of solving the halting problem is proving that it is not impossible
and the rest is conventional computer programming using the model that I
established.

Thus it is not too much poetic license to say that I solved the halting
problem by merely providing a single counter-example of halting decidability
that conforms to the conventional halting problem proof pattern of undecidability.

It is too much poetic license. It is a hasty generalization.

A single counter-example which detects a particular manifestation of non-halting behaviour (how did you decide that the pattern is non-halting to begin with? Did you use an Oracle perhaps?) is not a universal solution to all non-halting patterns.

A counter-example is insufficient evidence for your grandiose claim. You need to provide a solution for the universal case. Where you produce a generic algorithm and I produce the input.

And I should hope you can produce such a thing, because even languages which promise totality aren't making the claims you are making, because in order to guarantee termination they give up Turing-completeness.

[PeteOlcott]

No. I have refuted all of the conventional halting problem proofs thus opening the
door for the halting problem to be solved.

99.99% of solving the halting problem is proving that it is not impossible
and the rest is conventional computer programming using the model that I
established.

Thus it is not too much poetic license to say that I solved the halting
problem by merely providing a single counter-example of halting decidability
that conforms to the conventional halting problem proof pattern of undecidability.

A single counter-example which detects a particular manifestation of non-halting behaviour (how did you decide that the pattern is non-halting to begin with? Did you use an Oracle perhaps?) is not a universal solution to all non-halting patterns.

And I should hope you can produce such a thing, because even languages which promise totality aren't making the claims you are making, because in order to guarantee termination they give up Turing-completeness.

(1) It refutes one instance of the the generic pattern of the general case Thus refuting
other instances of this generic pattern merely requires using other instance of the refutation pattern.
In other words I figured out how to solve the halting problem. To actually solve the
halting problem only requires using my method plus conventional programming.

(2) How do you leap to any conclusion regarding Turing completeness ?

[Univalence]

(1) It refutes one instance of the the generic pattern of the general case Thus refuting
other instances of this generic pattern merely requires using other instance of the refutation pattern.
In other words I figured out how to solve the halting problem. To actually solve the
halting problem only requires using my method plus conventional programming.

Hence - hasty generalization. If you claim that it solves the general case and I provide you with a counter-example then clearly it doesn't.

(2) How do you leap to any conclusion regarding Turing completeness ?

Because that's the only way to achieve totality.

Total functional programming (also known as strong functional programming,[1] to be contrasted with ordinary, or weak functional programming) is a programming paradigm that restricts the range of programs to those that are provably terminating

.....

These restrictions mean that total functional programming is not Turing-complete.

[PeteOlcott]

(1) It refutes one instance of the the generic pattern of the general case Thus refuting
other instances of this generic pattern merely requires using other instance of the refutation pattern.
In other words I figured out how to solve the halting problem. To actually solve the
halting problem only requires using my method plus conventional programming.

Hence - hasty generalization. If you claim that it solves the general case and I provide you with a counter-example then clearly it doesn't.

(2) How do you leap to any conclusion regarding Turing completeness ?

Because that's the only way to achieve totality.

Total functional programming (also known as strong functional programming,[1] to be contrasted with ordinary, or weak functional programming) is a programming paradigm that restricts the range of programs to those that are provably terminating

.....

These restrictions mean that total functional programming is not Turing-complete.

I have answered this question three times now. The system keeps erasing it.

I have refuted one instance of the general case of the halting problem thus providing the
means to refute every other case using conventional programming and my refutation pattern.

So the broadest claim that I can fully make (after my work has been fully validated)
is that I figured out how to solve the halting problem.

This has nothing to do with Turing completeness.

[Univalence]

I figured out how to solve the halting problem.

This has nothing to do with Turing completeness.

If you are not solving the halting problem in the context of Turing-complete languages then you aren't solving the halting problem.

You are solving something else.

[Univalence]

I have refuted one instance of the general case

This is an oxymoron.

providing the means to refute every other case using conventional programming and my refutation pattern.

Total functional programming languages already do that. They detect almost all non-halting functions.

Almost.