Re: The simple essence of Proof Theoretic Semantics

On 7/4/2026 12:52 PM, olcott wrote:
> On 7/4/2026 2:43 AM, Mikko wrote:
>> On 03/07/2026 21:36, olcott wrote:
>>> On 7/3/2026 1:18 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
>>>>>
>>>>
>>>> If an algorithm takes an input and produces an output, that is by 
>>>> definition a mapping.
>>
>>> That only proves that the definition is incoherent.
>>
>> Your definitions often are. But the well known definition of "mapping"
>> is not.
>>
> 
> The output really should be based on the input
> because computing the mapping from an input to
> an output requires some kind of correspondence
> between the two.
> 

Given this correspondence:

input | output
--------------
0     | 4
1     | 4
2     | 4
3     | 4
...
253   | 4
254   | 4
255   | 4

i.e. for all inputs in the domain, output 4.

Requirement: an algorithm that computes the above mapping.

The following algorithm meets this requirement:

int foo(unsigned char x)
{
     return 4;
}