Simplified Halting Problem Proof Rebuttal

[olcott]

A PhD computer science professor came up with a way to show that
Turing's halting problem proof is erroneous. I have simplified it for
people that know nothing about computer programming.

One thing that I found in my 20 year long quest is that self-
contradictory expressions are not true. “This sentence is not true.” is
not true and that does not make it true. As a corollary to this self-
contradictory questions are incorrect.

Linguistics understands that when the context of [who is asked] changes
the meaning of this question, this context cannot be correctly ignored.
When Jack's question is posed to Jack it has no correct answer.

Can Jack correctly answer “no” to this [yes/no] question?

Jack's question when posed to Jack meets the definition of an incorrect
question in that both answers from the solution set of {yes, no} are the
wrong answer.

*Simplified Halting Problem Proof*
Likewise no computer program H can say what another computer program D
will do when D does the opposite of whatever H says.

This meets the definition of an *incorrect decision problem instance*
When decision problem instance decider/input has no correct Boolean
value that the decider can return then this is stipulated to be an
incorrect problem instance.

We could also say that input D that does the opposite of whatever
decider H returns is an invalid input for H.

As everyone knows the technical term *undecidable* does not mean that
an algorithm is too weak to find the steps required to reach a correct
Boolean return value.

It actually means that no correct Boolean return value exists for this
decision problem instance.

Because people subconsciously implicitly refer to the original meaning
of undecidable [can't make up one's mind] they misconstrue a
decider/input pair with no correct Boolean return value from the decider
as the fault of the decider and thus not the fault of the input.


--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

[Richard Damon]

On 10/15/23 10:03 AM, olcott wrote:
> A PhD computer science professor came up with a way to show that
> Turing's halting problem proof is erroneous. I have simplified it for
> people that know nothing about computer programming.
>

Perhaps you should try to quote the ACTUAL proof, as your
"simplification" is truly broken.

My guess is you don't actually understand what the "PhD Computer Science
Professer" was actually saying, and he is not saying what you think he is.

> One thing that I found in my 20 year long quest is that self-
> contradictory expressions are not true. “This sentence is not true.” is
> not true and that does not make it true. As a corollary to this self-
> contradictory questions are incorrect.
>
> Linguistics understands that when the context of [who is asked] changes
> the meaning of this question, this context cannot be correctly ignored.
> When Jack's question is posed to Jack it has no correct answer.

Except that "Does the Program & Input described by the Input Halt when
it is run?" doesn't depend on who you ask it to.

>
> Can Jack correctly answer “no” to this [yes/no] question?

Which is just a dead Red Herring that you are flogging, showing your
lack of actual argument.

>
> Jack's question when posed to Jack meets the definition of an incorrect
> question in that both answers from the solution set of {yes, no} are the
> wrong answer.
>
> *Simplified Halting Problem Proof*
> Likewise no computer program H can say what another computer program D
> will do when D does the opposite of whatever H says.

So? That just means that all programs that try to be a Halt Decider will
get some questions wrong. Note, each decider gets a different problem wrong.

>
> This meets the definition of an *incorrect decision problem instance*
> When decision problem instance decider/input has no correct Boolean
> value that the decider can return then this is stipulated to be an
> incorrect problem instance.

Nope, the decision problem HAS a correct answer, it just isn't the one
that H gives. Thus your argument is based on a LIE.

For your H, the answer is YES, because H will say no, and thus the
"Pathological" program will halt.

>
> We could also say that input D that does the opposite of whatever
> decider H returns is an invalid input for H.
>

Then you have just defined that your system of computation is weaker
than the Turing system, so isn't Turing Complete.

You can't make a claim for "All Machines" and then exclude some.

> As everyone knows the technical term *undecidable* does not mean that
> an algorithm is too weak to find the steps required to reach a correct
> Boolean return value.
>
> It actually means that no correct Boolean return value exists for this
> decision problem instance.

Right, but the correct return value DOES exist, it is just that H
doesn't give it, so H is wrong.

Remember, the question is NOT "What answer can H give ...?" but "Does
the Machine ... Halt?". The question is NOT about what the decider does,
but what the machine described by the input, and then the question of
can you make a machine that does that.

The answer to the second question is NO, there exists no machine that
correctly gives the answer to all inputs.

>
> Because people subconsciously implicitly refer to the original meaning
> of undecidable [can't make up one's mind] they misconstrue a
> decider/input pair with no correct Boolean return value from the decider
> as the fault of the decider and thus not the fault of the input.
>
>

No, YOU are the one stuck on the wrong definition. Halting is
Undecidable, as it is IMPOSSIBLE to make a Program that can give the
correct answer for all possible inputs. There is always a correct answer
to the question of does the program described by the input Halt, it is
just that for every decider we try, we can make an input it will get
wrong. Thus, the problem IS undecidable, and your logic is shown to be
invalid.

You are just proving your stupidity.

[olcott]

and that this is isomorphic to the HP decider/input pair
is the 100% complete essence of the whole proof.

[Richard Damon]

you are just showing your ignorance as you continiue to flog that dead
Red Herring.

I have shown you why they are different, and your failure to actually
address those points just becomes your admission that you are just a
liar to restate them.

The fact that Jack is volitional, and H isn't is a key factor. It makes
no sense to ask what value can an aready written program give to be
correct, when there is only one value that program can give, the one it
is programmed for.

Let me give a simple example, what value should x+1 be to for it to
equal y when x is 3 and y is 5?

The question in non-sense.

Just like asking what value can H give to be correct, since its answer
was determined when it was written, it can only give one answer, the one
it was programmed with, and if that is wrong, it is just wrong.

There IS a "Correct answer" to the question, H just doesn't give it.

You are just proving your ignorance and stupidity, and acknowledging you
that this to be true by not properly replying to the arguements.

Note, it is standard practice to presume that a rebutal not addressed
but dodged, is an admission that you don't have an answer to it.

You have just been confirming for ages that you understand your logic is
broken, but it is all you have, so you are going to cling to your
stupidity rather than try to learn something.

YOUR LOSS.

it is YOUR reputation that is destroyed, and your ideas ridiculed.

[olcott]

Both of the above two *are* essentially *self-contradictory questions*
when the full context of *who is asked* is understood to be a mandatory
aspect of the meaning of these questions.

[Richard Damon]

DEAD RED HERRING

>
> Likewise no computer program H can say what another computer program D
> will do when D does the opposite of whatever H says.

Which proves the Theorem. (since you asked the wrong question). The
ACTUAL question doesn't depend on who it is asked off, as it is
independent of who is trying to decide.

And we have the fact that H doesn't get a "choice" as to what to say, it
is fixed by it program. Thus, there can be a correct answer, but H just
doesn't say it because it was programmed "wrong" for this case.

Remember, H specifies a SPECIFIC sequence of deterministic instructions,
which means that H WILL give a specific answer for a specific input.

Thus D also becomes a SPECIFIC sequence of deterministic instructions
too. This D is thus based on that SPECIFIC program called H, so we can't
call anything else by that name.

It is thus possible to create another program that gives the right
answer, but that will have a different set of instructions so that new
program isn't H, but something else, like H1. And H1 can give the right
answer, but since D isn't the "pathological" input that the proof says
H1 would get wrong, that doesn't mean anything.

All of this breaks down if we try to do this to Jack, as jack being
volitional can't have his answer "predicted" by running a copy of him,
so we can't build a similar "pathological" question to ask him. Yes, a
question that explicitly references "itself" or "who it questions" can
lead to a contradiction, which is what your question does, but this
doesn't apply to the Halting Question, as it doesn't do that, only when
you LIE and try to alter it into your non-equivalent "equivalent" which
just proves you to be a liar.

>
> Both of the above two *are* essentially *self-contradictory questions*
> when the full context of *who is asked* is understood to be a mandatory
> aspect of the meaning of these questions.
>

Nope, but you are proving yourself too stupid to understand it.

Maybe if you tried responding to my actually rebuttal, and not just
restating your flawed position you might sound a bit smarter.

Until then, you are just proving yourself to be a self-deluded idiot
that is totally ignorant about what he is talking about.

Maybe the problem is that your don't have any real intelligence of your
own, so are trying to make "artificial" intelligence smarter than it
actually is.

[olcott]

There is a very simple principle here:
Self-contradictory questions have no correct answer only
because there is something wrong with the question.

Both Jack's question posed to Jack and input D
to program H that does the opposite of whatever
H says are SELF-CONTRADICTORY QUESTIONS.

bool True_False_Decider("This sentence is not true")

It does not matter whether a human or a deterministic
program determines the result in both cases a correct
answer does not exist.

[Richard Damon]

On 10/15/23 8:26 PM, olcott wrote:

> There is a very simple principle here:
> Self-contradictory questions have no correct answer only
> because there is something wrong with the question.
>
> Both Jack's question posed to Jack and input D
> to program H that does the opposite of whatever
> H says are SELF-CONTRADICTORY QUESTIONS.
>
> bool True_False_Decider("This sentence is not true")
>
> It does not matter whether a human or a deterministic
> program determines the result in both cases a correct
> answer does not exist.
>

Which means you need a MEANINGFUL contradictory question.

Note, ANY quesiton of the form "What answer can program X give to be
correct for problem Y?" is not meaningful as there is only one answer
that program X CAN give, and that is the answer that it gives when run.
Any other answer just is impossible for THAT program to give.

Thus, if you allow that sort of question, NO problem is
non-contradictory. So you are just showing that you logic is meaningless.

IF we ACTUALLY look at your question, What answer can H give to answer
the Halting Question for program P?" The answer is Halting (even though
it gives non-halting) because the program P includes its own copy of H,
and thus the original instruction stream of that original H, so when you
imagine H changing, it doesn't change P.

Yes, the question of What answer can Halt Decider H give to answer about
the input built off of that decider H would be a self-contradictory
statement, but that isn't the halting question.

Thus, all you are doing is proving you have no understanding about what
a program is, and your argument is just flawed.

Your logic system seems to be built on seeing how many logical fallacies
you can build into your argument.

Since you haven't shown that the ACTUAL Halting Question meets your
requirement, you are just admitting you are a stupid liar that is making
up fallacious arguments.

Maybe some day you will grow up beyond the mental age of two, and
actually try to respond to the rebuttal given. Until then you are just
showing your immaturity and ignorance.

YOU are a source of "disinformation" and promoting the causes you claim
to be fighting. Which just make you more stupid.

[olcott]

We can see that both of the above questions are self-contradictory thus
the reason that they cannot be answered is that there is something wrong
with the question.

[olcott]

This eliminates the https://en.wikipedia.org/wiki/Shell_game
Of the infinite set of definitions for H where some D does
the opposite of whatever Boolean value that this H returns
none of them provides a Boolean value corresponding to the
behavior of any D.

Because I have stipulated infinite sets there cannot possibly
be some other H or D that has not already been addressed.

[Richard Damon]

What is "Self-Contradictory" about the actual Halting Question:

"Does the machine represented by the input to the decider Halt in a
finite number of steps?"

Please show a case where a SPECIFIC machine halts and does not halt (or
=neither Halts or does not Halt) exists.

Note, SPECIFIC machine. Not a set of Decider / Input combinations, as
that isn't what the question asks. The question is about a SPECIFIC input.

And the proof builds that SPECIFIC input from a SPECIFIC decider, and
specifically shows that that one specific decider is wrong for this
particual input.

Since for EVERY SPECIFIC decider that might be imagined, we CAN
construct such SPECIFIC input, we can safely say that no decider exists
that can correctly answer for all inputs.

We can also show that for all possible inputs, there does exist a
decider that happens to get that input correctly (we just don't know
which decider it is until we know the answer), thus we know the question
has a possible answer.

Your trying to link the question to requiring a SPECIFIC program to
giving the right answer is flawed as I explained, as that arguement
could be used to say that ANY question is "self-contradictory", as there
will always exist SOME program P that will give the wrong answer, so the
fact that this particular H does isn't special.

And as been shown, we CAN modify H to produce a new program that will
get the right answer for this particular input (since the SPECIFIC input
was SPECIFICALLY built on the SPECIFIC original H, and doesn't magically
change when we define a new H).

Note, your magically changing input isn't even a valid program, as it
can't be run on its own, since then there isn't an "H" for it to call.
Thus proving you are totally ignorant about what a program is.

You are just confirming your stupidity.

[Richard Damon]

So, you are admitting that you don't understand what a program is.

A program is NOT a "Set of Programs", so you argument just fails.

Or, it could be said that your argument PROVES the statement of the
Halting Theorem, as you show that No H can exist that correctly answer
the question: "Does the machine represented by the input to the decider
Halt in finite time?"

Thus, your claimed refutal actually turns out to be a proof of the thing
you are trying to refute.

You are just showing that your logical ability is so bad that you refute
yourself with your own words.

[olcott]

Input D to termination analyzer H where D does the
opposite of whatever Boolean value that H returns
is self-contradictory for H in exactly the same
way that Carol's question is self-contradictory
for Carol.

[Richard Damon]

Nope. The determinacy of H make it not so.

There IS an answer to the actual question, so the actual question is not
self-contradictory,

What is self-contradictory about asking:

"Does the program D(D) Halt When Run?"

since it does (since this D was built on the H that you say returns 0
from H(D,D)

This is what the call to H(D,D) refers to, since that is the DIRECT
MEANING of the question:

Does the Program, represented by the input, Halt when run.

The input is D,D which is the representation of D(D)

You are just basing your whole argument on a LIE that you are allowed to
change the question to something that in nonsensical to claim the
original quesiton in nonsensical.

YOU LOSE

You are admitting that by not actually reply to my points, and your
refusal to reply to the message and quote them show that.

You are just a chicken liar, who needs to hold on to your falsehoods,
because you can't stand what the truth tells you. You are going to spend
eternity being tormented by your lies and fears.

Such is the fate of all liars.

[olcott]

Each element of the infinite set of every possible encoding of H
is a program. I am sure that you already knew this.

[Richard Damon]

Yes, an no element of that set meets the requirement of a Halt Decider,
and every input to all the sets has a definite answer to the ACTUAL
question (does the input represent a machine that will halt on its given
input), so your argument fails.

All your question done is prove that fact, so it doesn't REFUTE the
Halting Theorem claim that no correct Halt Deciders can exist, but
PROVES it.

The fact that you seem to think that a statement proving a Theorem,
Refutes it, shows you are stupid.

To think you can replace a question with a different one that has a
(subtly) different meaning shows your think logical fallacies are good
logic, again proving your stupidity.

The fact that you continue to not quote the statement you are replying
to shows that you know your arguments are incorrect, and they can't
stand being put up against the rebuttals give, proving you are just a
deceitful liar.

In short, you are admitting to being a source of the disinformation that
you claim to be fighting, making you a Hypocrite.

Face it, you have ruined your life and are going to spend eternity
facing your errors.


Also note just because your set of H is infinite, doesn't mean it
contains ALL of the possible Halt Deciders, there are infinite sets that
are proper subsets of other infinite sets, and due to the (perhaps
confusing to small minds like yours) fact that some mathematics works
differently on infinite number, your logic just fails.

[olcott]

Each element of the set of every possible combination of H and input D
where D does the opposite of of whatever Boolean value that H returns
<is> the infinite set of every halting problem decider/input pair.

Neither return value of true/false is correct for each decider/input
pair because each element <is> a self-contradictory question.

This eliminates the https://en.wikipedia.org/wiki/Shell_game

where gullible fools can honestly believe that there are HP
instances that have not been accounted for.

People stuck in rebuttal mode may try to claim that an infinite set
of program/input pairs have zero elements that are programs, yet this
is very obviously quite foolish.

[Richard Damon]

Right.

You have an infinite number of deciders, each being given a different
input, so you have an infinite number of instances of the Halting Problem.

You are just showing that NONE of your decider give the right answer,
which supports the Halting Theorem

>
> Neither return value of true/false is correct for each decider/input
> pair because each element <is> a self-contradictory question.
>

Wrong, for EVERY input, there is a correct answer, it just isn't the one
that its H gives. Thus, NONE of the questions are contradictory.

So, the fact that 1 + 1 = 2, but 2 + 2 = 4 means that addition is
contraditory? That is two different problems with different answers?

You are just proving your stupidity.

> This eliminates the https://en.wikipedia.org/wiki/Shell_game
> where gullible fools can honestly believe that there are HP
> instances that have not been accounted for.
>

Nope. Each element has a DIFFERENT input, so it is a DIFFERENT question.

> People stuck in rebuttal mode may try to claim that an infinite set
> of program/input pairs have zero elements that are programs, yet this
> is very obviously quite foolish.
>

Maybe if you try to actually answer the rebuttals you would look so stupid.

[olcott]

"Wrong, for EVERY input, there is a correct answer"

For every halting problem decider/input pair there
is no correct Boolean value that can be returned
by this decider because this input to this pair
is a self-contradictory thus incorrect question
for this decider.

The some other decider can answer some other question
is no rebuttal at all.

An input D to a decider H1 having no pathological relationship
to this decider is an entirely different question than this
same input input to decider H that has been defined to do the
opposite of whatever value that H returns.

[Richard Damon]

But that isn't the question, the question is, "does the machine
represented by the input halt?"

THAT question has an answer.

Your whole arguement is based on LIES.

>
> The some other decider can answer some other question
> is no rebuttal at all.
>
> An input D to a decider H1 having no pathological relationship
> to this decider is an entirely different question than this
> same input input to decider H that has been defined to do the
> opposite of whatever value that H returns.
>
>

Nope, same input, the same description of the same machine, so same
question and same answer.

WHy does it matter WHO you ask does 1+1=2 ?

It is a fundamental fact that D(D) will Halt (since its copy of H(D,D)
returns 0)

You are just proving your are a lying stupid idiot that doesn't
understand what he is talking about but who makes up lies to try and get
his way.

[olcott]

Does machine D halt on input D?
Is a self-contradictory question for H when D is defined
to do the opposite of whatever Boolean value that H returns
and not a self-contradictory question for H1.

That D contradicts H and does not contradict H1
proves that these are two different questions.

[Richard Damon]

Yes.

> Is a self-contradictory question for H when D is defined
> to do the opposite of whatever Boolean value that H returns

Why is it "self-contradictory?" What "Self" did it contradict.

D contradics H, not "itself".

> and not a self-contradictory question for H1.
>
> That D contradicts H and does not contradict H1
> proves that these are two different questions.
>

Nope.

Since D(D) Halts ALWAYS the answer to, "does it halt?", is YES.

ALWAYS.

Even for H

Remember, H was defined too, so H does what H always did. and is wrong.

Nothong "Self-Contradictory", just WRONG, as are you.

You are just proving yourself to be a lying idiot.

[olcott]

That H(D,D) cannot possibly return either Boolean
value that corresponds to the direct execution of any
D that is defined to do the opposite of whatever value
that H returns proves that the decider/input pair is
self-contradictory for this decider.

When D does the opposite of whatever H says this
<is> self-contradictory in the same way that
"This sentence is not true." contradicts itself.

[Richard Damon]

So, you are just admitting that you don't understand your own argument
or how programs work.

You clearly don't understand what the *self* in self-contradictory
means, maybe because your ego is just too big that you think you are
everything.

I guess that is why you think you are God. YOU AREN'T.

H(D,D) Must ALLWAYS return the value it return, and H exists first,
before D possibly can.

You claim is basically the same as saying that Tic-Tac-Toe in an invalid
game because there isn't a strategy to win it.

And if there was, it would still be an invalid game, because it one
player could always win, the other player can't also have a winning
stratagy,

The problem here is the Halt Desider Designer needs to move first and
make the Halt Decider, then the challenger gets to make the input. And
this game the second player wins.

It isn't a "Self-Contradictory" problem, it is a problem that isn't
computable, as are most problems.

You just are too stupid to understand that.

[Richard Damon]

On 10/16/23 10:52 PM, olcott wrote:

>

> That H(D,D) cannot possibly return either Boolean
> value that corresponds to the direct execution of any
> D that is defined to do the opposite of whatever value
> that H returns proves that the decider/input pair is
> self-contradictory for this decider.
>
> When D does the opposite of whatever H says this
> <is> self-contradictory in the same way that
> "This sentence is not true." contradicts itself.
>

H(D,D) can only return 1 value, becuase of how it is programed.

It is a category error to talk about H returning anything other than
what it is programmed to do.

You clearly don't understand how programs work

You don't even seem to know what "Self" means.

You don't understand how logic works.

You are just continuing to prove that you are nothing but a hypocritical
lying idiot.

You claim to want to fight disinformation, but you spread it yourself.

You going down in history as a laughing stock.

[olcott]

I told the computer science professor about
the loophole you found in his work.

[Richard Damon]

Some how I don't believe you.

A "Real" Conputer Science Professor wouldn't be trying to do this as
they know better.

And if the actually WERE going to try to do this, they would keep it
totally secret until they submitted the paper to a Journal so they could
get the credit.

[olcott]

is a self-contradictory thus incorrect question when posed
to Jack.

Jack's question <is> precisely isomorphic to this question:
"Does your input halt on its input?" when posed to H on input
D such that D does the opposite of whatever Boolean value that
H returns.

That people have been well indoctrinated into the belief that
the halting problem is correct any anyone saying otherwise is
crazy has them ignore all of the facts and short-circuit to a
counter-factual conclusion.

[Richard Damon]

So, you continue to beat this dead Red Herring.

> Jack's question <is> precisely isomorphic to this question:
> "Does your input halt on its input?" when posed to H on input
> D such that D does the opposite of whatever Boolean value that
> H returns.

Which is a Red Herring, because that isn't the halting problem question,
an in fact, is a non-sense quesiton in this context.

Since H is a DEFINED program, talking about it doing anything becides
what it is actually programmed to do is meaningless.

That is like saying "If 1+2 was 5, then ....", which is clearly non-sense.

You CAN pull that sort of thing OUTSIDE the specific problem, and ask if
it is possible to find some H that can get the right answer for the
problem it creates, and there, the answer of No, you can not create an H
that gives the right answer just becomes the proof of the Halting
Theorem, that no such program exist. It doesn't show that any particular
problem question was somehow invalid, because every Halting Problem
Question (Does the machine described by this input Halt?) has a correct
answer, it just isn't the answer that the decider that this input was
built on gives.

So, you are showing your stupidity by claiming that your have disprove
the theorem when you have actually just proved it, which shows you just
don't understand how logic (or truth) works.

>
> That people have been well indoctrinated into the belief that
> the halting problem is correct any anyone saying otherwise is
> crazy has them ignore all of the facts and short-circuit to a
> counter-factual conclusion.
>
>

Nope, YOUR have gas-lit yourself into belieiving your own lies and thus
can't face the facts. This is highlighted by the fact that you don't
even TRY to answer the rebuttals. This just confirms that you know you
don't have an answer to them are just using the fallacy of ignoring the
truth. In other words, you are admitting defeat, but then continue to
dig your own grave.

You have proved to the world that you totally don't understand about how
logic works, about what Truth means. You also seem to be telling it that
Disinformation is an acceptable practice, since this is what you are
using to proclaim your "vital" message, in other words, you are just
sabotaging your own stated goals.

IF you will TRY to even answer the errors pointed out, with ACTUAL
FACTS, not just more of your puffed up statements, then maybe we can
talk. Untill then, I will just smack down your repeated lies with strong
words.