Re: The simple essence of Proof Theoretic Semantics

On 7/4/2026 2:37 AM, Mikko wrote:
> On 2026-07-02 dbush wrote:
> 
>> The halting problem doesn't actually have self reference, as
>  > algorithms can be copied as in the below example of algorithm D:
>>
>> void D(ptr *I)
>> {
>>      // algorithm D; input: I
>>      ptr *X = D;
>>      ptr *Y = I;
>>      int result;
>>      {
>>          // algorithm H; inputs: X,Y
>>          result = 0;
>>      }
>>      if (result == 1) {
>>          while (1);
>>      }
>> }
>>
>> Which is the counter example input to algorithm H:
>>
>> int H(ptr *X, ptr *Y)
>> {
>>      int result;
>>      {
>>          // algorithm H; inputs: X,Y
>>          result = 0;
>>      }
>>      return result;
>> }
> 
> On 03/07/2026 18:36, 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.
> 
> For every possible input his H halts and returns either 0 for false
> or 1 for true. Therefore his H is a decider. It return 0 for D
> although D halts so the decider H is not a halt decider.
> 

counter-factual H always returns 0.

>> His input merely halted and did not call
>> this halt decider. He used {} in a way that
>> made no sense in C.
> 
> His use of {} is perfectly correct by C rules and as meaningful ans
> usually. Your false claim (not shown above) is false.
> 


-- 
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).