Re: The simple essence of Proof Theoretic Semantics

On 09/07/2026 06:28, olcott wrote:
> On 7/8/2026 3:09 AM, Mikko wrote:
>> On 06/07/2026 18:38, olcott wrote:
>>> On 7/6/2026 3:55 AM, Mikko wrote:
>>>> On 04/07/2026 20:03, olcott wrote:
>>>>> On 7/4/2026 3:00 AM, Mikko wrote:
>>>>>> On 03/07/2026 22:08, olcott wrote:
>>>>>>> On 7/3/2026 1:27 PM, dbush wrote:
>>>>>>>> On 7/3/2026 2:10 PM, olcott wrote:
>>>>>>>>> On 7/3/2026 12:10 PM, dbush wrote:
>>>>>>>>>> On 7/3/2026 12:52 PM, olcott wrote:
>>>>>>>>>>> On 7/3/2026 10:50 AM, dbush wrote:
>>>>>>>>>>>> On 7/3/2026 11:36 AM, olcott wrote:
>>>>>>>>>>>>> On 7/3/2026 4:22 AM, Mikko wrote:
>>>>>>>>>>>>>> On 02/07/2026 17:51, olcott wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Do you know enough about C to understand that
>>>>>>>>>>>>>>> dbush example was foolish nonsense when proposed
>>>>>>>>>>>>>>> to show the halting problem counter-example?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It is a valid example of a C program. It was present as a 
>>>>>>>>>>>>>> part of a
>>>>>>>>>>>>>> claim about you, and your response was the false claim 
>>>>>>>>>>>>>> that "That
>>>>>>>>>>>>>> is just nonsense". Later in the discussion you offer more 
>>>>>>>>>>>>>> evidence
>>>>>>>>>>>>>> to support his claim.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> His halt decider did not look at its input.
>>>>>>>>>>>>
>>>>>>>>>>>> Nor is it required to.  All it needs to do is map inputs to 
>>>>>>>>>>>> outputs.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> So a piece of metal sitting on the ground is an automobile.
>>>>>>>>>>
>>>>>>>>>> Does algorithm H map machine description X and machine input Y 
>>>>>>>>>> to an output of either 0 or 1?
>>>>>>>>>>
>>>>>>>>> Ignoring the input IS NOT A MAPPING
>>>>>>>>>
>>>>>>>>
>>>>>>>> A mapping is nothing more than an association of inputs to 
>>>>>>>> outputs, so there is nothing to ignore.  What an algorithm might 
>>>>>>>> do to *compute* the mapping has nothing to do with the mapping.
>>>>>>>
>>>>>>> It is conventionally construed as a mapping.
>>>>>>
>>>>>> More importantly, it satisfies the definition of "mapping".
>>>>>>
>>>>>>> It is not even conventionally construed as a halt
>>>>>>> function, not even a halt function that gets the
>>>>>>> wrong answer.
>>>>>>
>>>>>> Irrelevant, as the claim was that H does not implement the halt
>>>>>> function.
>>>>>
>>>>> If it ignores input it is no function of this input.
>>>>
>>>> Everything that is required to be in the argument list of a function
>>>> is an argument to that function, even when the function "ignores" it.
>>
>>> You are entirely right on the linguistic front. If we look strictly 
>>> at the compositional meaning of the words in everyday language, 
>>> calling something a "function of an input" when it ignores that input 
>>> is, at best, a paradox and, at worst, a semantic lie.
>>
>> The word "function" is has many meanings in everday language anyway.
> 
> A function of its inputs cannot fucking ignore these
> fucking inputs and not be a damned liar.

By the mathematical meaning of "function" there is nothing wrong
in ignoring any part of the input. In particular, the zero function
which has the value zero for every argument value is the basis of
certain formualtions of the theory of recursive functions, which has
a central role in the theory of computation.

-- 
Mikko