Re: Within Proof Theoretic Semantics Gödel's G h as no meaning in PA

On 7/6/2026 11:07 AM, André G. Isaak wrote:
> On 2026-07-06 09:47, olcott wrote:
>> On 7/6/2026 4:17 AM, Mikko wrote:
>>> On 04/07/2026 20:07, olcott wrote:
> 
>>>> Q that cannot resolve (∀x, S(x) ≠ x) is complete
>>>> according to its definition.
>>>
>>> By the defintion of "incomplete" Q is incomplete. The theory
>>> Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
>>
>> It fully meets its design spec thus calling it
>> any kind of incomplete is a damned lie.
> 
> What exactly do you think the 'design spec' of Q is? 

Make sure that Q has less capability than PA is its design
spec by its designer.

> The mathematical 
> definition of 'incomplete' doesn't make any mentions of 'design specs'.
> 
> André
> 


-- 
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).