On 4/25/24 10:15 AM, olcott wrote:
> On 4/25/2024 3:16 AM, Mikko wrote:
>> On 2024-04-25 00:17:57 +0000, olcott said:
>>
>>> On 4/24/2024 6:01 PM, Richard Damon wrote:
>>>> On 4/24/24 11:33 AM, olcott wrote:
>>>>> On 4/24/2024 3:35 AM, Mikko wrote:
>>>>>> On 2024-04-23 14:31:00 +0000, olcott said:
>>>>>>
>>>>>>> On 4/23/2024 3:21 AM, Mikko wrote:
>>>>>>>> On 2024-04-22 17:37:55 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 4/22/2024 10:27 AM, Mikko wrote:
>>>>>>>>>> On 2024-04-22 14:10:54 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> On 4/22/2024 4:35 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-04-21 14:44:37 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 4/21/2024 2:57 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-04-20 15:20:05 +0000, olcott said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 4/20/2024 2:54 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 2024-04-19 18:04:48 +0000, olcott said:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> When we create a three-valued logic system that has these
>>>>>>>>>>>>>>>>> three values: {True, False, Nonsense}
>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Three-valued_logic
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Such three valued logic has the problem that a tautology
>>>>>>>>>>>>>>>> of the
>>>>>>>>>>>>>>>> ordinary propositional logic cannot be trusted to be
>>>>>>>>>>>>>>>> true. For
>>>>>>>>>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This
>>>>>>>>>>>>>>>> means that
>>>>>>>>>>>>>>>> some ordinary proofs of ordinary theorems are no longer
>>>>>>>>>>>>>>>> valid and
>>>>>>>>>>>>>>>> you need to accept the possibility that a theory that is
>>>>>>>>>>>>>>>> complete
>>>>>>>>>>>>>>>> in ordinary logic is incomplete in your logic.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I only used three-valued logic as a teaching device.
>>>>>>>>>>>>>>> Whenever an
>>>>>>>>>>>>>>> expression of language has the value of {Nonsense} then
>>>>>>>>>>>>>>> it is
>>>>>>>>>>>>>>> rejected and not allowed to be used in any logical
>>>>>>>>>>>>>>> operations. It
>>>>>>>>>>>>>>> is basically invalid input.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You cannot teach because you lack necessary skills.
>>>>>>>>>>>>>> Therefore you
>>>>>>>>>>>>>> don't need any teaching device.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> That is too close to ad homimen.
>>>>>>>>>>>>> If you think my reasoning is incorrect then point to the error
>>>>>>>>>>>>> in my reasoning. Saying that in your opinion I am a bad
>>>>>>>>>>>>> teacher
>>>>>>>>>>>>> is too close to ad hominem because it refers to your
>>>>>>>>>>>>> opinion of
>>>>>>>>>>>>> me and utterly bypasses any of my reasoning.
>>>>>>>>>>>>
>>>>>>>>>>>> No, it isn't. You introduced youtself as a topic of
>>>>>>>>>>>> discussion so
>>>>>>>>>>>> you are a legitimate topic of discussion.
>>>>>>>>>>>>
>>>>>>>>>>>> I didn't claim that there be any reasoning, incorrect or
>>>>>>>>>>>> otherwise.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> If you claim I am a bad teacher you must point out what is
>>>>>>>>>>> wrong with
>>>>>>>>>>> the lesson otherwise your claim that I am a bad teacher is
>>>>>>>>>>> essentially
>>>>>>>>>>> an as hominem attack.
>>>>>>>>>>
>>>>>>>>>> You are not a teacher, bad or otherwise. That you lack skills
>>>>>>>>>> that
>>>>>>>>>> happen to be necessary for teaching is obvious from you postings
>>>>>>>>>> here. A teacher needs to understand human psychology but you
>>>>>>>>>> don't.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You may be correct that I am a terrible teacher.
>>>>>>>>> None-the-less Mathematicians might not have very much
>>>>>>>>> understanding
>>>>>>>>> of the link between proof theory and computability.
>>>>>>>>
>>>>>>>> Sume mathematicians do have very much understanding of that. But
>>>>>>>> that
>>>>>>>> link is not needed for understanding and solving problems
>>>>>>>> separately
>>>>>>>> in the two areas.
>>>>>>>>
>>>>>>>>> When I refer to rejecting an invalid input math would seem to
>>>>>>>>> construe
>>>>>>>>> this as nonsense, where as computability theory would totally
>>>>>>>>> understand.
>>>>>>>>
>>>>>>>> People working on computability theory do not understand
>>>>>>>> "invalid input"
>>>>>>>> as "impossible input".
>>>>>>>
>>>>>>> The proof then shows, for any program f that might determine whether
>>>>>>> programs halt, that a "pathological" program g, called with some
>>>>>>> input,
>>>>>>> can pass its own source and its input to f and then specifically
>>>>>>> do the
>>>>>>> opposite of what f predicts g will do. No f can exist that
>>>>>>> handles this
>>>>>>> case, thus showing undecidability.
>>>>>>> https://en.wikipedia.org/wiki/Halting_problem#
>>>>>>>
>>>>>>> So then they must believe that there exists an H that does correctly
>>>>>>> determine the halt status of every input, some inputs are simply
>>>>>>> more difficult than others, no inputs are impossible.
>>>>>>
>>>>>> That "must" is false as it does not follow from anything.
>>>>>>
>>>>>
>>>>> Sure it does. If there are no "impossible" inputs that entails
>>>>> that all inputs are possible. When all inputs are possible then
>>>>> the halting problem proof is wrong.
>>>>>
>>>>> *Termination Analyzer H is Not Fooled by Pathological Input D*
>>>>> https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
>>>>>
>>>>> Everyone that objects to the statement that H(D,D) correctly
>>>>> determines the halt status of its inputs say that believe that
>>>>> H(D,D) must report on the behavior of the D(D) that invokes H(D,D).
>>>>
>>>> Right, because that IS the definition of a Halt Decider.
>>>>
>>>
>>> Everyone here takes the definition of a halt decider to be
>>> required to determine the halt status of the program that
>>> invokes this halt decider, knowing full well that the program
>>> that invokes this halt decider IS NOT ITS INPUT.
>>>
>>> All these same people also know the computable functions only
>>> operate on their inputs and are not allowed to consider anything
>>> else.
>>>
>>> Computable functions are the formalized analogue of the intuitive notion
>>> of algorithms, in the sense that a function is computable if there
>>> exists an algorithm that can do the job of the function, i.e. given an
>>> input of the function domain it can return the corresponding output.
>>> https://en.wikipedia.org/wiki/Computable_function
>>>
>>> When the definition of a halt decider contradicts the definition of
>>> a computable function they can't both be right.
>>
>> When the definitions of a term contradicts the definition of another term
>> then both of them are wrong. A correct definition does not contradict
>> anything other than a different definition of the same term.
>>
>
> *Wrong*
> In logic, the law of non-contradiction (LNC) (also known as the law of
> contradiction, principle of non-contradiction (PNC), or the principle of
> contradiction) states that contradictory propositions cannot both be
> true in the same sense at the same time
> https://en.wikipedia.org/wiki/Law_of_noncontradiction
>
> Computable functions are the formalized analogue of the intuitive notion
> of algorithms, in the sense that a function is computable if there
> exists an algorithm that can do the job of the function, i.e. given an
> input of the function domain it can return the corresponding output.
> https://en.wikipedia.org/wiki/Computable_function
> *That one is correct*

But the question is *IF* the Halting Function is computable, you can't
just assume it is.

We have a "Function", we can call HALTING, which maps input to the
output answer, and for this problem HALTING(M,d) maps to True if M(d)
will halt, and to False if M(d) will never halt.

For H to be a "Halt Decider, and show that HALTING is a computable
funciton, then H must be able to take in the representation of ANY
possible input the HALTING, and give the correct answer that the HALTING
mapping generates.

>
> 01 int D(ptr x)  // ptr is pointer to int function
> 02 {
> 03   int Halt_Status = H(x, x);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 void main()
> 10 {
> 11   D(D);
> 12 }
>
> That H(D,D) must report on the behavior of its caller is the
> one that is incorrect.
>

So, given that we have some actual program H defined, then D will be an
actual program and D can also be the description of an actual program so
HALTING(D,D) will map to the behavior of D(D).

For H to be an actual Halt Decider, it MUST be able to take that exact
same input, and give the right answer.

THere is *NO* ground for H to somehow say that the input isn't "valid",
as if H is program, then so is D, so it *IS* in the domain of the
mapping it is trying to compute.

The fact that for ANY H you might be able to create, the answer returned
by H(D,D) for the D built on it is wrong, shows that no H can exist that
works on EVERY input, and thus HALTING is a non-computable mapping.

Note, H is NOT being asked to answer about "the program that is calling
it", but about "the program described by its input", which IS a valid
question.

Your confusing those two questions, even though in THIS case reference
the exact same program, but the question themselves are different.

The fact that it is invalid to ask the question about deciding on "The
Program that is calling H" does not make asking about D(D) invalid, as
that is a perfectly valid input to give it, it only makes asking that
EXACT question invalid.

This shows your lack of ability to understand logic.