Re: The simple essence of Proof Theoretic Semantics

On 7/8/2026 2:48 AM, Mikko wrote:
> On 06/07/2026 18:27, olcott wrote:
>> On 7/6/2026 3:11 AM, Mikko wrote:
>>> On 04/07/2026 19:58, olcott wrote:
>>>> On 7/4/2026 2:48 AM, Mikko wrote:
>>>>> On 04/07/2026 05:37, olcott wrote:
>>>>>> On 7/3/2026 9:19 PM, dbush wrote:
>>>>>>> On 7/3/2026 10:05 PM, olcott wrote:
>>>>>>>> On 7/3/2026 8:58 PM, dbush wrote:
>>>>>>>>> On 7/3/2026 9:52 PM, olcott wrote:
>>>>>>>>>> On 7/3/2026 5:51 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2026-07-03 16:37, olcott wrote:
>>>>>>>>>>>> On 7/3/2026 1:47 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2026-07-03 12:36, olcott wrote:
>>>>>>>>>>>>>> On 7/3/2026 1:18 PM, dbush wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Apparently you don't understand the difference between a 
>>>>>>>>>>>>> mapping and an algorithm. They are two different things.
>>>>>>>>>>>>>
>>>>>>>>>>>>> André
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> A function that ignores its input and only returns 0
>>>>>>>>>>>> is not any sort of halt function.
>>>>>>>>>>>
>>>>>>>>>>> He was defining 'mapping', not 'halt function'.
>>>>>>>>>>>
>>>>>>>>>>> André
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> A actual halt function must compute 
>>>>>>>>> The mathematical halting function:
>>>>>>>>>
>>>>>>>>
>>>>>>>> When you actually implement this concretely 
>>>>>>>
>>>>>>> We find that it is not possible, as Linz and others have proved.
>>>>>>
>>>>>> Impossible requirements are incorrect requirements.
>>>>>
>>>>> There is no well known meaning of "incorrect requirements".
>>>>
>>>> I just established the meaning of incorrect requirements
>>>> as any requirement that requires the logically impossible.
>>>
>>> That is insufficient to make the expression "incorrect requirements"
>>> meaningful in Common Language or well known.
>>
>> In other words if the requirement is to compute the square
>> root of the actual dead flesh of a dead chicken you would
>> not reject this out-of hand?
> 
> Depends on what yuo count as rejection. I don't think I would
> try to meet that requirement.
> 

Incorrect decision problem requirements.

-- 
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).