Re: The simple essence of Proof Theoretic Semantics

On 7/4/2026 12:58 PM, olcott wrote:
> On 7/4/2026 2:48 AM, Mikko wrote:
>> On 04/07/2026 05:37, olcott wrote:
>>> On 7/3/2026 9:19 PM, dbush wrote:
>>>> On 7/3/2026 10:05 PM, olcott wrote:
>>>>> On 7/3/2026 8:58 PM, dbush wrote:
>>>>>> On 7/3/2026 9:52 PM, olcott wrote:
>>>>>>> On 7/3/2026 5:51 PM, André G. Isaak wrote:
>>>>>>>> On 2026-07-03 16:37, olcott wrote:
>>>>>>>>> On 7/3/2026 1:47 PM, André G. Isaak wrote:
>>>>>>>>>> On 2026-07-03 12:36, olcott wrote:
>>>>>>>>>>> On 7/3/2026 1:18 PM, dbush wrote:
>>>>>>>>>>
>>>>>>>>>>>> If an algorithm takes an input and produces an output, that 
>>>>>>>>>>>> is by definition a mapping. 
>>>>>>>>>>> That only proves that the definition is incoherent.
>>>>>>>>>>> The coherent way that it actually works is that
>>>>>>>>>>> inputs are transformed into outputs by applying
>>>>>>>>>>> finite string transformation rules to inputs to
>>>>>>>>>>> derive outputs.
>>>>>>>>>>
>>>>>>>>>> Apparently you don't understand the difference between a 
>>>>>>>>>> mapping and an algorithm. They are two different things.
>>>>>>>>>>
>>>>>>>>>> André
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> A function that ignores its input and only returns 0
>>>>>>>>> is not any sort of halt function.
>>>>>>>>
>>>>>>>> He was defining 'mapping', not 'halt function'.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> A actual halt function must compute 
>>>>>> The mathematical halting function:
>>>>>>
>>>>>
>>>>> When you actually implement this concretely 
>>>>
>>>> We find that it is not possible, as Linz and others have proved.
>>>
>>> Impossible requirements are incorrect requirements.
>>
>> There is no well known meaning of "incorrect requirements".
>>
> 
> I just established the meaning of incorrect requirements
> as any requirement that requires the logically impossible.
> 
> The halting problem requires a decider that correctly
> reports the halt status of an input that does the opposite
> of whatever it reports. 

For example, algorithm H1 and algorithm D1 below:

void D(ptr *I)
{
      // algorithm D1; input: I
      ptr *X = D;
      ptr *Y = I;
      int result;
      {
          // algorithm H1; inputs: X,Y
          result = 0 + (X-X) + (Y-Y);
      }
      if (result == 1) {
          while (1);
      }
}

int H(ptr *X, ptr *Y)
{
      int result;
      {
          // algorithm H1; inputs: X,Y
          result = 0 + (X-X) + (Y-Y);
      }
      return result;
}

> 
> I already established that an incorrect polar question
> is any yes/no question lacking a correct yes/no answer.
> 

And the question "does algorithm X with input Y halt when executed 
directly for any algorithm X and input Y" is not such a question, as it 
does have a correct yes/no question in all cases.