Re: Yet another Attempt at Disproving the Halting Problem

[Marc Goodman]

No, there is a subtle but crucial difference between what you said,
and what would actually occur. My program still GETS the right
answer, and it sees that it is prohibited from providing this correct
answer to your f1() function, otherwise f1() would use this to change
its behavior, thus making this right answer into a wrong answer.
So for all practical purposes, adding this feedback loop effectively
disables the output mechanism. The halt analyzer still gets the correct
results.

You still think there are "correct results" here. There aren't.
The programs are in an indeterminate, contradictory state. The
correct answer is that the programs neither halt nor loop. They
do both, or neither, something clearly beyond the scope of a
Turing Machine. If your program reports "halt" it is wrong.
If your program reports "not halt" it is wrong.

The reason you don't get this is because you think you are
God and that there is Absolute Truth and that it is possible
to know everything in the universe, and any suggestion that
some things are intrinsically unknowable causes you to
go into a tizzy. You KNOW it can't be true, because you
DO know everything.

Do you agree or disagree with the following statement:
"It is possible that some things are intrinsically
unknowable?" If you answer, "no", then I can't imagine
that there's any point in anyone continuing this conversation
because you're philisophically incapable of "getting it."

 

[Eray Ozkural exa]

Ah so pointing out any errors that I have made in an objective
way, without resorting to disdain is not reasonable? So far it
seems I am mostly only getting disdain. I am not getting any
valid refutations.

To prove my point, I'll answer you.

What is the probability that all of the computer scientists who
responded to you have a poorer understanding of the problem than
yourself? (Hint: assume that there are 10 people who responded to you
independently)

Regards,

 

[Peter Olcott]

To prove my point, I'll answer you.

What is the probability that all of the computer scientists who
responded to you have a poorer understanding of the problem than
yourself? (Hint: assume that there are 10 people who responded to you
independently)

I will answer that question with another question.
What is the probability that the ad verecundiam fallacy is not an error of reasoning?
http://c2.com/cgi/wiki?AdVerecundiam

 

[Mitch Harris]

I will answer that question with another question.
What is the probability that the ad verecundiam fallacy is not an
error of reasoning?
http://c2.com/cgi/wiki?AdVerecundiam

in mathematics, very high. So that would make the answer to Eray's
question...?

Mitch

 

[Peter Olcott]

You still think there are "correct results" here. There aren't.

So if a program halts when it is executed, and the halt analyzer
determines this, then it is not correct?

The programs are in an indeterminate, contradictory state. The
correct answer is that the programs neither halt nor loop. They
do both, or neither, something clearly beyond the scope of a
Turing Machine.

Even with the high degree of GroupThink here you won't get a lot of
agreement on that one. You will find very few people here that will say
yes, I agree with that statement 100%. I have found that when people
here are direct disagreement, that they express it as:
"You could have stated that more clearly",
not wanting to upset the apple cart of group cohesiveness.

That you are wrong is very easy to see. A program either halts or it fails
to halt. There is no in-between third state. When one program attempts
to determine if another program halts, then there are three states:
(1) It Halts
(2) It does not halt
(3) You got me, I don't know if it halts or not.

 

[Marc Goodman]

So if a program halts when it is executed, and the halt analyzer
determines this, then it is not correct?

There are three cases:
A). The program halts - the halt analyzer should determine "halt."
B). The program doesn't halt - the halt analyzer should determine "not
halt."
C). The program is in a contradictory or inconsistent state - the halt
analyzer would be incorrect to return either "halt" or "not halt."

You seem to think that "halt" is always correct and everything
else is incorrect, no doubt because you think that a program that
exits is "working" while a program that infinite loops is broken.
This is not the case. Your program would have to be able to
correctly identify all three of the above cases to truly work,
but you STILL wouldn't have disproved Turing's proof because
Turing just showed that a Turing machine that must answer either
"halt" or "not halt" cannot recognize programs in case C.

Your program, if it exists must handle the following three
cases correctly:

int CaseA(TuringMachine *tm, InputString *is)
{
return(TRUE);
}

Your program should return "halts."

int CaseB(TuringMachine *tm, InputString *is)
{
while(TRUE);
return(FALSE) // never gets here
}

Your program should return "doesn't halt."

int CaseC(TuringMachine *tm, InputString *is)
{
if(Halts(tm, is)) {
while(TRUE);
return(FALSE); // never gets here
} else
return(TRUE);
}

Your program should correctly decide that the program
neither halts nor doesn't halt. If you do this, your
program is correct, but you havn't disproved the Turing's
proof of the Halting Problem.

Even with the high degree of GroupThink here you won't get a lot of
agreement on that one.

Yes I will. Look at the program again. If it loops, it halts.
If it halts, it loops. It must return the same result on the
same input, but it can't (this is not your extra special program
that knows about when it's being called, this is just the plain
old normal version that Turing talked about). Why do you
think it should halt when it clearly says, "Loop on this
input if I would halt on this input?"

Either your program must return the right answer for this
program, or your program isn't correctly deciding whether
all program/input pairs will halt or not.

You will find very few people here that will say

yes, I agree with that statement 100%. I have found that when people
here are direct disagreement, that they express it as:
"You could have stated that more clearly",
not wanting to upset the apple cart of group cohesiveness.

Try reading Go:del, Escher, Bach: an Eternal Golden Braid
for a good, informal, easy to read introduction to
the issues here.

That you are wrong is very easy to see. A program either halts or it fails
to halt.

See the above. Does it halt or not? You mistakenly seem
to think it halts. You are wrong.

There is no in-between third state. When one program attempts

to determine if another program halts, then there are three states:
(1) It Halts
(2) It does not halt
(3) You got me, I don't know if it halts or not.

Which of these three classes would you say the program CaseC
falls into?

 

[Karl Heinz Buchegger]

No, there is a subtle but crucial difference between what you said,
and what would actually occur. My program still GETS the right
answer, and it sees that it is prohibited from providing this correct
answer to your f1() function, otherwise f1() would use this to change
its behavior, thus making this right answer into a wrong answer.

You might want to study the examples posted to you.
In f1() contra f2() there is not one single feedback
loop involved.

The halt analyzer still gets the correct
results.

I don't see how this can be true.

So for all practical purposes, adding this feedback loop effectively
disables the output mechanism. The halt analyzer still gets the correct
results.


void WillHalt(string program, string input)
{
bool halt;
//
// do some calculations to compute halt;
cout << halt << endl;
}

void f1(string program, string input)
{
bool halt;
//
// do some calculations to compute halt; // see notes
while (halt);
}

cout << WillHalt(f1) // outputs true
cout << WillHalt(f2) // outputs true

*** NOTES ***
The invocation of the halt analyzer from the specific context
of f1() will not return true. From this specific context it will
see that returning true will be used by f2() to make true an
incorrect answer, thus refrain from returning true within this
specific context.

Wow. AI !

 

[Eray Ozkural exa]

in mathematics, very high. So that would make the answer to Eray's
question...?

I think I'll just make a calculation that is highly optimistic for
Peter.

If we assume that the probability one computer scientist has poorer
understanding of the halting problem than Peter is 0.7, then for 10
people, it becomes about 0.282, around 3%, for 10 independent
responses. Not a very high probability, but I think in reality it
is much less than that...

Cheers,

 

[Eray Ozkural exa]

I will answer that question with another question.
What is the probability that the ad verecundiam fallacy is not an error of reasoning?
http://c2.com/cgi/wiki?AdVerecundiam

Thanks for making my point.

You didn't read that page, did you?

The page says that argument from authority is:

----------------------------------------------------

Sometimes correct, because:

* X may be in fact proven; or sufficiently well-demonstrated that it
is near-universally regarded as fact. (Then you point to the study)

* Expert community may in fact agree that X is true.

----------------------------------------------------

Note that this is exactly the case with your argument here, and the
responses that have been given to you.

BTW, my question does not really use argument from authority (in an
unreliable way). It uses an argument of knowledge coupled with a
community argument.

I'll make it easier for you. What is the probability that one of the
computer scientists who responded to you have a poorer understanding
of the halting problem than your royal self? %100 %90? %80? %70? %60?
%50? Pick one. (All of these choices are optimistic for you)

After your potential reply or your silent approval, it will be
established that there is no need to respond to you any further.

Cheers,

 

[Acme Diagnostics]

I think I'll just make a calculation that is highly optimistic for
Peter.

If we assume that the probability one computer scientist has poorer
understanding of the halting problem than Peter is 0.7, then for 10
people, it becomes about 0.282, around 3%, for 10 independent
responses. Not a very high probability, but I think in reality it
is much less than that...

I noticed "independent."

Larry

 

[Howard]

SEE RIGHT HERE IS ANOTHER EXAMPLE! I ONLY SAID NOT
TO REPORT THE RESULT TO THE FUNCTION BEING ANALYZED,
AND YOU LEAP TO THE STUPID CONCLUSION WITHOUT
EVER PAYING ANY ATTENTION TO WHAT I AM SAYING!
I HAVE POSTED EXACTLY WHAT I MEAN BY THIS FOR
SEVERAL WEEKS. THE ADDRESS IS NOT HARD TO REMEMBER
ITS WWW.HALTING-PROBLEM.COM HOW THE HELL DO
YOU EXPECT TO REFUTE ME IF YOU DON'T EVEN KNOW
WHAT I AM SAYING ???

I smile and walk away, quite satisfied to leave my opponent screaming in
anger.

:-D

-Howard

 

[Peter Olcott]

I smile and walk away, quite satisfied to leave my opponent screaming in
anger.

:-D

-Howard

You presume.

 

[Marc Goodman]

Peter, you still haven't answered this question.
If you assume WillHalt exists and gives the correct
answer, what will WillHalt answer for CaseA, CaseB, and
CaseC below?

If you say that CaseC should have the same answer as
CaseA or CaseB, then please explain why you think that
two cases that clearly should have different answers
have the same answer.

If you say that CaseA, CaseB, and CaseC should have
different answers, then please explain why this has
anything to do with the statement, "WillHalt must
correctly answer "Yes" or "No" for any Turing Machine
and input string."

Or, you could just go away.

 

[Eray Ozkural exa]

Peter, you really should have a look at my post below. Do you know
when argument from authority can be valid?

Cheers,

 

[Simon G Best]

Yet this is not at all what the respondent had claimed.

Yes it is. Dave Vandervies was just putting it "More precisely".

It is not at all true that no halt analyzer can possibly exist.

According to your definition of "halt analyzer", but not Turing's.

The Halting Problem does not say that.

The Halting Problem says:-

'Given a Turing Machine, T, and an input, x, would T halt on x? Solve
this problem for the general case where T may be any possible Turing
Machine, and x may be any possible input.'

*That's* what the Halting Problem is.

The Halting Problem is *not* Turing's proof that there is no general
solution to this problem. The Halting Problem is *not* Turing's method
of proof, either.

The most that the Halting Problem says is that
this Halt analyzer won't work correctly in every possible instance.

(Bearing in mind that you're using your own definition of "Halt
analyzer",) I'm glad you're now conceding that Turing's proof was
correct

Simon

 

[Simon G Best]

Whoops! I thought the post I was responding to was a new post. It
wasn't. My ISP's newsfeeds don't seem to be that good :-(

 

[Peter Olcott]

(Bearing in mind that you're using your own definition of "Halt
analyzer",) I'm glad you're now conceding that Turing's proof was
correct

Simon

Yet I dispute this conclusion. using the method that I propose
a halt analyzer can be constructed from an ordinary Turing Machine
that is not prohibited from providing correct results for every
possible input. Or at least not prohibited in the sense of the
proof that this is (was considered to be) impossible.

 

[Peter Olcott]

Peter, you really should have a look at my post below. Do you know
when argument from authority can be valid?

Within deduction it is never valid.
Only deduction can guarantee that it always provides correct results. It is
considered to be valid inductive inference, yet inductive inference can not
guarantee correct results. Deduction can not err, induction can err.

 

[Peter Olcott]

I think that I have already answered a more abbreviated
version of this. If you are the one that reformed it to
a more concise version, I took great care in answering
your question. My answer to you, was the key point that
I made tonight.

 

[Eray Ozkural exa]

Within deduction it is never valid.
Only deduction can guarantee that it always provides correct results. It is
considered to be valid inductive inference, yet inductive inference can not
guarantee correct results. Deduction can not err, induction can err.

It has nothing to do with deduction or induction, Peter.

It is apparent that you cannot even understand what is written on the
very page that you cite yourself. It is established, probably for the
100th time, that there is no need to respond to you, by any person on
this group.

People, please do not talk to this net.kook. This guy is just as
hopeless as Arthur T. Murray.