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

On 7/3/2026 1:37 PM, André G. Isaak wrote:
> On 2026-07-03 12:20, olcott wrote:
>> On 7/3/2026 12:35 PM, André G. Isaak wrote:
> 
>>> And that differs from claiming that Q is incomplete exactly how...?
>>>
>>
>> The base definition of "incomplete" means that it is
>> not operating according to design spec.
> 
> And where exactly do you get this 'base definition' from? It certainly 
> does not correspond to any definition that I am aware of.
> 

An motor vehicle that is missing a motor is incomplete.
A bicycle that is missing a motor is NOT incomplete.

Incomplete is an adjective that describes something
missing essential parts, lacking necessary details,
or left unfinished.

>> terms of the art
>> are often misleading, thus deceptive.
> 
> Terms of the art are what they are. They are precisely defined so there 
> is no doubt about what they mean. So how can they therefore be 
> misleading. It's colloquial terms that have the potential to be 
> misleading since they are often not precisely defined.
> 

These TOTA that diverge from their base meanings confuse
people into thinking that computation is limited. The
inability to correctly compute the numerical square-root
of a dead chicken does not make computation incomplete
or limited.

>> When we start with an exhaustively complete list of
>> empirical "atomic facts" of general knowledge (combining
>> the analytic/synthetic distinction into one single system)
>> then any expression x that cannot be derived by semantic
>> entailment expressed syntactically in this system is
>> not an element of the body of general knowledge expressed
>> in language.
> 
> Q isn't concerned with general knowledge (expressed in language or 
> otherwise). It doesn't contain any notion of 'atomic fact'. So none of 
> this is relevant to the question of whether Q is complete.
> 
> André
> 

It has the "atomic facts" of Q.
Any expression that cannot reach these "atomic fact"
axioms is ungrounded in the atomic base of Q.

-- 
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).