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Mathematical undecidability is an unsound notion V2

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olcott

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Oct 22, 2023, 8:57:32 PM10/22/23
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This is the essence of an alternative proof related to
the halting problem

*It seems that everyone agrees with this*
(a) When the halting problem is defined with a program
specification that requires an H to report on the behavior
of the direct execution of D(D) that does the opposite of
whatever Boolean value that H returns then this is an
unsatisfiable program specification.

(b) *An unsatisfiable program specification is merely*
*the inability to do the logically impossible thus places*
*no actual limit on anyone or anything*

--
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

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Oct 22, 2023, 9:04:04 PM10/22/23
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On 10/22/23 5:57 PM, olcott wrote:
> This is the essence of an alternative proof related to
> the halting problem
>
> *It seems that everyone agrees with this*
> (a) When the halting problem is defined with a program
> specification that requires an H to report on the behavior
> of the direct execution of D(D) that does the opposite of
> whatever Boolean value that H returns then this is an
> unsatisfiable program specification.
>
> (b)  *An unsatisfiable program specification is merely*
> *the inability to do the logically impossible thus places*
> *no actual limit on anyone or anything*
>

But, since that isn't actually the program specification, your claim
means nothing.

Yes, we can show that it is impossible to write a program to compute if
a given program halts. If you want to define that question as "invalid",
then how do you determine if a specification is actually valid? Or do
you thiink "Validity" can change based on Knowledge, which yields a very
weak version of "Truth".

Now, does your claim of no actual limit mean that we can definitely
write a program to determine the truth or falsity of the twin primes
conjecture? (since there are no limits on what can be computed from a
valid question).

Or, are you saying that because we found one program to no be writable,
it doesn't affect what other programs are writable, since they never were.

In other words, a worthless statement.

Yes. the proof that the halting problem is not computable does not
change which other problems are computable or not, but does help see
which category some problems are in, and becomes a clear proof that some
problems are definitely not computable.

There are many other problem that might be found to be not computable,
and we know some of them.

Just as there are statements that might not be provable, and we know
that there exist statements that are not provable (but are still true).

So, none of this gets you to the point of showing you big claim, and in
fact, by admitting that Halting is not computable, we can prove a lot of
the limits to possible knowledge.

olcott

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Oct 22, 2023, 9:26:17 PM10/22/23
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On 10/22/2023 7:57 PM, olcott wrote:
> This is the essence of an alternative proof related to
> the halting problem
>
> *It seems that everyone agrees with this*
> (a) When the halting problem is defined with a program
> specification that requires an H to report on the behavior
> of the direct execution of D(D) that does the opposite of
> whatever Boolean value that H returns then this is an
> unsatisfiable program specification.
>
> (b)  *An unsatisfiable program specification is merely*
> *the inability to do the logically impossible thus places*
> *no actual limit on anyone or anything*
>

The halting problem proofs only show that no machine
can do the logically impossible.

Since 1936 no one ever noticed that the inability to
do the logically impossible is merely a fake ruse of
a limit and not any actual limit what-so-ever.

Richard Damon

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Oct 22, 2023, 9:40:27 PM10/22/23
to
On 10/22/23 6:26 PM, olcott wrote:
> On 10/22/2023 7:57 PM, olcott wrote:
>> This is the essence of an alternative proof related to
>> the halting problem
>>
>> *It seems that everyone agrees with this*
>> (a) When the halting problem is defined with a program
>> specification that requires an H to report on the behavior
>> of the direct execution of D(D) that does the opposite of
>> whatever Boolean value that H returns then this is an
>> unsatisfiable program specification.
>>
>> (b)  *An unsatisfiable program specification is merely*
>> *the inability to do the logically impossible thus places*
>> *no actual limit on anyone or anything*
>>
>
> The halting problem proofs only show that no machine
> can do the logically impossible.
>
> Since 1936 no one ever noticed that the inability to
> do the logically impossible is merely a fake ruse of
> a limit and not any actual limit what-so-ever.
>

No, it shows that writing a program to correctly determine the halting
status of any program given as input is impossible.

IF you think that knowledge is worthless, so be it, your loss.

So, how do you determine that a given problem is "invalid"?

Do you first need to determine if it is impossible?

And, do you accept that some logically correct problems, like the twins
prime conjecture, might not be possible to determine with a program?

Or does the problem suddenly become "logically impossible" if we find
out that it is impossible to program?

It seems, your idea of logic doesn't understand what it can ask about
until you actually know the answer to the question, which make it a very
weak system.

olcott

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Oct 24, 2023, 4:16:53 PM10/24/23
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On 10/24/2023 12:54 PM, olcott wrote:
> On 10/24/2023 12:25 PM, olcott wrote:
>> On 10/24/2023 11:56 AM, olcott wrote:
>>> On 10/23/2023 11:16 PM, olcott wrote:
>>>> On 10/23/2023 11:03 PM, Jeff Barnett wrote:
>>>>> On 10/23/2023 6:51 PM, Mike Terry wrote:
>>>>>> On 24/10/2023 01:31, olcott wrote:
>>>>>
>>>>> <major snip>
>>>>>
>>>>>>> It provides significant evidence that I am not simply
>>>>>>> a crackpot that can be correctly dismissed out of hand.
>>>>>>
>>>>>> It provides NO such evidence, because your "supporter" is not here
>>>>>> in the thread.  Also, you are not dismissed "out of hand" - you
>>>>>> are dismissed because your posts show you to not understand what
>>>>>> you're talking about, and have no ability to process logical
>>>>>> arguments or understand abstract concepts, regardless of how
>>>>>> they're presented to you.  Many people (myself included) have
>>>>>> carefully explained to you why you are incorrect, but it always
>>>>>> turns out to be a waste of time!  :)
>>>>> So why do you persist? I know it's really hard to not try to
>>>>> "crack" a crackpot but virtue is in resisting. I hardly ever read a
>>>>> post by Impotent Pete or Richard the Ernest since their posts are a
>>>>> mechanism to avoid bleak lives - repetition upon repetition.
>>>>>
>>>>> Consider, for example, the Schopenhauer quote "Talent hits a target
>>>>> no one else can hit; Genius hits a target no one else can see." as
>>>>> part of the Impotent's signature: one can comment as much as you
>>>>> want about the fact that he 1) mostly strikes out and 2) is blind.
>>>>> What's the point? He's too stupid and non self-aware to notice the
>>>>> irony involved - repetition upon repetition.
>>>>
>>>> My latest line-of-reasoning has a full PhD professor of
>>>> computer science totally agreeing with one of my alternate
>>>> proofs that I began in 2004. He has published several
>>>> times in the two most prestigious computer science journals
>>>> and has been a full professor for decades.
>>>>
>>>> Recently I have only been posting summarized versions
>>>> of our shared view.
>>>>
>>>
>>> *He agrees that the halting problem is WRONG*
>>>
>>
>> *He agrees that the halting problem is WRONG*
>> How can this be misunderstood?
>
> As always dishonest reviewers change the subject
> rather than acknowledging that I proved my point.
>
> Dishonest reviewers have no interest in any honest
> dialogue and intentionally thwart the slightest
> degree of closure on even one single point.

In all of the cases where a computational problem cannot
be solved because it <is> isomorphic to a self-contradictory
question we reject the problem itself as incorrect.

In those cases where a computational problem cannot be solved
in finite time because it requires testing every element of
an infinite set the problem definition might not be construed
as incorrect.

Richard Damon

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Oct 24, 2023, 4:43:23 PM10/24/23
to
Nope. Show the actual "isomorphism"

The problem is that the actual question has an actual correct answer, so
it can't be "contradictory" (self or otherwise).

You just don't know what the words you are using actually mean.

>
> In those cases where a computational problem cannot be solved
> in finite time because it requires testing every element of
> an infinite set the problem definition might not be construed
> as incorrect.
>

Maybe it would be helpful to know WHAT this is in reply to.

Note, by your admission, it seems you are admitting that if the problem
CAN be solved with infinite time, then it is ok,

But IF H is allowed to process of infinite (unbounded) time, then it
would be ok for it, after that infinite time, to answer non-halting, as
then the the "pathological" input IS non-halting, as it ran for
unbounded time, and thus IS "non-halting" by the definition.

It just means that H itself failed, as the requirement is to give the
answer in finite time, so your criteria just shows that it is solvable
in unbound time, just not bounded time, so the problem is correct, but
uncomputable.



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