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

On 06/07/2026 21:12, olcott wrote:
> On 7/6/2026 12:56 PM, André G. Isaak wrote:
>> On 2026-07-06 11:45, olcott wrote:
>>> On 7/6/2026 12:27 PM, André G. Isaak wrote:
>>>> On 2026-07-06 10:58, olcott wrote:
>>>>> 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.
>>>>
>>>> And you presumably have a reference to back that up?
>>>>
>>>
>>> It is common knowledge that was Robinson's purpose
>>>
>>> In mathematics, Robinson arithmetic is a finitely
>>> axiomatized fragment of first-order Peano arithmetic
>>> (PA), first set out by Raphael M. Robinson in 1950.
>>> It is usually denoted Q.
>>>
>>> https://en.wikipedia.org/wiki/Robinson_arithmetic
>>>
>>>> But it doesn't matter either way since the mathematical definition 
>>>> of incomplete makes no reference to the 'spec' of a system.
>>>>
>>>
>>> Within the natural preexisting order of the body
>>> of knowledge saying that incomplete(math) inherits
>>> part of its meaning from incomplete(base) semantic
>>> parent node is simply a lie.
>>
>> Yes, I agree that it is a lie.
>>
>> For starters, there's no such thing as the 'natural preexisting order 
>> of the body of knowlege'.
> 
> Sure there is. There is a minimal sized knowledge ontology.

The minimal size is of course the size of the empty ontology. But
there is no natural order of ontologies between the minimal size
and the useful sizes.

And any position of ontoloty in the body of knowledge is artificial.

-- 
Mikko