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

On 2026-06-29 13:08, olcott wrote:
> On 6/29/2026 1:29 PM, André G. Isaak wrote:

>> Is "has a box of clowns" in the language of Q? No. I didn't think so, 
>> so your example is completely irrelevant.
>>
> 
> It is an idiom stipulated to mean:
> sentences in the language of Q which can neither
> be proven nor disproven by Q

Q doesn't have idioms. That's a natural language concept alien to 
theories of arithmetic.

>>> So we can say that the halting problem "has a box
>>> of clowns" instead of saying that computation is
>>> in any way limited.
>>>
>>>> When mathematicians talk about rings, do you object based on the 
>>>> fact that you can't put them on your finger?
>>
>> No answer?
>>
> 
> Off topic, irrelevant.
> 
>>>> When mathematicians talk about fields, do you object based on the 
>>>> fact that nothing can graze on them?
>>
>> No answer?

These questions are relevant because they get to whether your objection 
to the term 'incomplete' extends to other terms as well. If Gödel had 
used the term 'fnord' instead of incomplete, I suspect you wouldn't have 
the same objection to it. Your objection seems to be entirely based on 
the fact that you are reading things into the term 'incomplete' which 
aren't actually there based on your own interpretation of the colloquial 
term 'incomplete'. But the mathematical term and the colloquial term are 
different, just as the mathematical term 'ring' differs from the 
colloquial term. Technical terms often diverge significantly from 
colloquial ones. For example, to an astronomer, oxygen is classified as 
a metal despite the fact that this doesn't correspond to everyday usage. 
This doesn't cause problems for astronomers.

André

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