Re: Is the Halting Problem merely an ill-formed question?
- From: Nam Nguyen <namducnguyen@xxxxxxx>
- Date: Mon, 23 Oct 2006 04:39:25 GMT
george wrote:
Peter Olcott wrote:An ill-formed question is any question that requires an answer from a solution
set where no correct answer exists within this solution set.
No, it isn't, dumbass.
There are all kinds of questions asking whether something exists
in some set. If it turns out that the answer is no, it doesn't, then
that
obviously does NOT mean the question was ill-formed. If the question
were ill-formed, then it could not be clearly and correctly answered
negatively.
One example of an ill-formed question is
No it isn't, dumbass.
the following: "How tall are you green or blue?".
That is an ill-formed "question" because it is ill-formed, PERIOD.
It is, therefore, NOT a question. Putting a question mark at the
end of something does not make it a question. There are plenty
of other criteria that have to be met first. What you ACTUALLY MEANT
to say here was, "How tall are you? Green or blue?". Which is, of
course,
actually, TWO questions. What you are CALLING "ill-formed" here is
actually a type-conflict or a SORT-conflict. This is easy to create in
natural
language but in formal languages it RARELY occurs because a lot of
the most commonly-used first-order formal theories ARE SINGLE-SORTED,
i.e., EVERYthing in the domain is of ONE type. For example, in Peano
Arithmetic, EVERYthing is a number. In Zermelo-Fraenkel set theory,
EVERYthing is a set. And in logic generally, EVERYthing is a SENTENCE
which is either TRUE OR FALSE, NOT green or blue.
Thus, when somebody asks you "What does LoopIfHalts(LoopIfHalts)
return?" and you say, "an exception", YOU are the one who is answering
"How tall are you?" with "Green" or "blue". THAT is NOT one of the
POSSIBLE
answers! It either halts or it doesn't; those are the ONLY two
possible
answers.
Another type of ill-formed question is requiring an answer to be in form
impossible for the respondent to correctly provide.
That, again, is possible in natural language but simply not relevant
in logic, simply because THERE ARE NO responders. A TM does
NOT respond. It just runs. On EVERY input, it just either halts or
it doesn't. At every moment, its tape just says what it says.
One example of this would be
requiring a mute person to answer
a question only in the form of verbal spoken
communication.
You're just being stupid. TMs ARE NOT mute.
THEY CAN write on their tapes.
void LoopIfHalts(string SourceCode) {
if ( WillHalt(SourceCode, SourceCode) == TRUE )
while (TRUE) // loop forever
;
else
return;
}
This reflects some ignorance of how "if" works in C.
You never say if(whatever)==TRUE.
To be fair, one should never say "never" here. What he *actually*
said is if (whatever == TRUE) which, for clarity, one should use;
all it would take is to define: #define FALSE 0, and
#define TRUE !(FALSE).
You just say if(whatever) { doit }.
One surely could choose this option (I did that quite often).
Though I suspect this style is used more often by the "system"
programmers than the commercial ones.
int WillHalt(string SourceCode, string InputData) {
if (MalignantSelfReference(SourceCode, InputData))
return MALIGNANT_SELF_REFERENCE;
if ( TheProgramWillHalt(SourceCode, InputData) )
return TRUE;
else
return FALSE;
}
The problem here is simply that You Can't Write
"Malignant self reference". You CAN'T usually TELL
that a malignant self reference is happening.
TMs don't make any distinction between void and and int
as result-types. They write on their tapes and they halt or
they don't. If you want to write a halting-problem for C-programs,
well, that is going to be a different problem.
LoopIfHalts(LoopIfHalts);
I propose this assertion, every variation of the above example that attempts to
prove the conclusion of the Halting Problem forms at least one of the two
specified types of ill-formed questions.
Well, they don't. Not that you know what an ill-formed question is
anyway.
It is not my burden of proof to show
that the Halting Problem is solvable, I am only at most attempting to show the
prior proofs concluding that it is unsolvable may be incorrect.
The problem with proofs is that they are ALL syntactically PROVABLE to
be correct. The correctness of a proof NEVER HAS ANYTHING TO DO WITH
ANY natural-language notions OF ANY kind, whether about well-formed
questions OR ANYthing else. They're ALL JUST PATTERN-matching.
Because of this, I am not required to show that the function
MalignantSelfReference(SourceCode, InputData) is computable.
Everything that is computable is provably computable.
Since the burden can in fact be met, YOU ARE obligated to meet it.
This function will continue to be assumed to be computable,
unless and until anyone provides a
specific example showing that it is not computable in a specific instance.
It's not computable in EVERY GENERAL instance, dumbass.
The assumption that it is computable ENTAILS A CONTRADICTION.
THAT *is* a proof.
--
-----------------------------------------------------
What we call 'I' is just a swinging door which moves
when we inhale and exhale.
Shunryu Suzuki
----------------------------------------------------
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