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

On 7/3/2026 3:32 PM, André G. Isaak wrote:
> On 2026-07-03 14:13, olcott wrote:
>> 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.
> 
> That's *one* definition of incomplete. It's hardly *the* definition and 
> you have provided no reason to think that it is the 'base definition' 
> whatever that might mean to you.
> 

The parent node of an inheritance hierarchy.

>>>> 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.
> 
> No. It confuses *you*. The vast majority of people are not confused by 
> this. And stating that Q is incomplete has nothing to do with 
> computation. Computation is a separate field.
> 

It is a shade of a nuance of the same reasoning that
incorrectly determines that computation is limited.

Computation is in its most basic essence applying
finite string transformations to inputs to derive
outputs.

Anything that cannot be so computed is out-of-scope
of computation is the same way that a Turing machine
cannot bake a birthday cake.

> André
> 
>> 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).