Re: Is the Halting Problem merely an ill-formed question?



"Daryl McCullough" <stevendaryl3016@xxxxxxxxx> wrote in message
The unsolvability
of the halting problem is simply the claim that there is no
computer program that computes this function. Bringing up
"ill-formed questions" or "malignant self-reference exceptions"
or whatever is simply admitting that there is no computer program
that computes this function.

Peter Olcott wrote:
That may be correct,

Make up your mind.
If it is correct then you've been lying and proving your stupidity all
this time, and you owe the world at large an apology.

yet, only for exactly the same reason that it is impossible
for you to correctly provide me with your height when I limit the solution set
to the colors of (Blue, and Green}.

No, dumbass, it is NOT for the same reason.
The reason in YOUR case is because blue and green are NOT heights.
The height question has an answer of type number while blue and green
have type color, and normally, these types are disjoint.

There is NOTHING analogous to that going on in the case of the halting
problem. You think there is a well-defined question as to whether some
TM H does or doesn't halt on some input P. This is NOT what is going
on.
What is actually going on is that H DOESN'T EXIST IN THE FIRST PLACE.

Whether you like it or not, ALL questions about whether TM M halts on
input I
have {T,F} as the answer-type. Nobody is making anything ill-formed by
"limiting"
the answer TO this type! THIS IS the type of the answer!
You tried to make a WELL-formed question, "What is X's height?",
ill-formed
by limiting the solution set to a type OTHER than number. But the
question IS
well-formed with a NATURAL type for its solution-set.
"Does M halt on I?", where M names a TM THAT ACTUALLY EXISTS
(and I is an input string over that TM's finite alphabet), is ALWAYS
a well-formed question and the answer is ALWAYS of type boolean.
You CANNOT make the question ill-formed by stipulating a different
answer-
type -- NO MATTER what type you stipulate, the ACTUAL ANSWER ALWAYS
REMAINS of type boolean. So, obviously, WE would never be stupid
enough
to TRY anything that stupid. Stipulating a different answer-type, a
type
disjoint from the required one, and thereby making the question
ill-formed,
is what YOU are doing.

What WE are doing is like limiting the answer to "How tall are you?" to
be a number
of centimeters. What YOU are doing is like limiting the answer to "how
tall are
you?" to {blue,green}. "Malignant-self-reference" IS NOT an
answer-type for
the halting question about any ACTUAL TM on any ACTUAL finite
input-string.

The inability to provide a correct answer to
an ill-formed question, only because the question itself is ill-formed should
not have been elevated to one of the foundations of computer science.

You don't know *** about what an "ill-formed question" is.

.

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