Re: The simple essence of Proof Theoretic Semantics

On 7/3/2026 1:53 PM, dbush wrote:
> On 7/3/2026 2:45 PM, 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, 
>> int Not_A_Mapping(int X)
>> {
>>    return 0;
>> }
> 
> The above algorithm does in fact compute this mathematical mapping:
> 
> input     | output
> ------------------
> (any int) | 0
> 
>>
>> By construing that as a mapping is one of the screw-ups
>> that prevents true expressed in language from being computable.
>>
>> My HHH applies the operational semantics of
>> C to its finite string input DD to correctly
>> determine that the DD input to HHH has no PTS
>> well-founded justification tree within these
>> operational semantics.
>>
>> With your screwed up notion of a halt decider this
>> would be correct.
>>
>> int HHH(ptr DD)
>> {
>>    if (5 > 3)
>>     return 0;
>> }
> 

Because it ignores the input it is not any halt
function at all.

-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).