Re: The simple essence of Proof Theoretic Semantics

On 7/4/2026 9:38 AM, olcott wrote:
> On 7/4/2026 2:41 AM, Mikko wrote:
>> On 03/07/2026 21:10, 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
>>
>> No, but dbush's program H implements a mapping anyway. It just is
>> a different mapping from the one a halt decider is required to do.
>>
> 
> Making it complete nonsense.
> 
> A actual halt function must compute 
The mathematical halting function:


Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

A solution to the halting problem is an algorithm H that computes the 
following mapping:

(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly