On 10/17/2023 11:10 PM, olcott wrote:
> On 10/16/2023 9:52 PM, olcott wrote:
>> On 10/16/2023 9:04 PM, olcott wrote:
>>> On 10/16/2023 6:38 PM, olcott wrote:
>>>> On 10/16/2023 9:18 AM, olcott wrote:
>>>>> On 10/15/2023 10:49 PM, olcott wrote:
>>>>>> On 10/15/2023 8:08 PM, olcott wrote:
>>>>>>> On 10/15/2023 7:26 PM, olcott wrote:
>>>>>>>> On 10/15/2023 5:34 PM, olcott wrote:
>>>>>>>>> On 10/15/2023 2:07 PM, olcott wrote:
>>>>>>>>>> On 10/15/2023 9:03 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.
>>>>>>>>>>>
>>>>>>>>>>> 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.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Can Jack correctly answer “no” to this [yes/no] question?
>>>>>>>>>> and that this is isomorphic to the HP decider/input pair
>>>>>>>>>> is the 100% complete essence of the whole proof.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> 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.
>>>>>>>>>
>>>>>>>>> Likewise no computer program H can say what another computer
>>>>>>>>> program D will do when D does the opposite of whatever H says.
>>>>>>>>>
>>>>>>>>> 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.
>>>>>>>>>
>>>>>>>>
>>>>>>>> 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.
>>>>>>>>
>>>>>>>
>>>>>>> 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.
>>>>>>>
>>>>>>
>>>>>> Each element of the infinite set of every possible encoding of H
>>>>>> is a program. I am sure that you already knew this.
>>>>>>
>>>>>
>>>>> 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.
>>>>>
>>>>
>>>> "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.
>>>
>>> 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.
>>>
>>
>> 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.
>>
>
> I told the computer science professor about
> the loophole you found in his work.
>

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

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