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

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.

>>> 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.

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.
> 

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