Re: The simple essence of Proof Theoretic Semantics

On 04/07/2026 19:58, 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.

That is insufficient to make the expression "incorrect requirements"
meaningful in Common Language or well known.

-- 
Mikko