Re: The simple essence of Proof Theoretic Semantics

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.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.

// Greater_Than_Five function
int Transform(int X)
{
   if (X > 5)
     return 1;
   return 0;
}

int Do_Not_Transform(int X)
{
   return 0;
}

-- 
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).