Re: The simple essence of Proof Theoretic Semantics

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.

As is well known, there are two truth values, usually called "true"
and "false". There are four functions that map a truth value to
truth value. Can you list them? There are 16 functions that map
a pair of truth values to a truth value. Can you list them?

For an analogy, note that

     int f1(int x) {
       return 4;
     }

is a valid C function. One way to use it is to pass it as a parameter
to another function. For example, if g is declared as

     double g(int (*f)(int));

and y as

     double y;

then

     y = g(f1);

is a valid statement in a C function.

-- 
Mikko