Re: The simple essence of Proof Theoretic Semantics

On 7/3/2026 10:37 PM, 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.
> 

Nope.  Requirements are requirements for a reason.  If they can't be 
satisfied, then that's just the way it is.

I would like to have a single algorithm that can tell me whether any 
arbitrary algorithm with a given input will halt when executed directly, 
but unfortunately no such algorithm exists.