Re: The simple essence of Proof Theoretic Semantics

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 mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.

typedef int (*ptr)();
int HHH(ptr P);

01 int DD()
02 {
03   int Halt_Status = HHH(DD);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 void main()
10 {
11   DD();
12   HHH(DD);
13 }

The HP requires HHH to report on the DD() invoked
in main(). This is impossible because HHH has no
idea who its caller is.

-- 
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).