Re: William T. Parry gets rid of Disjunction introduction

On 7/7/2026 6:17 PM, André G. Isaak wrote:
> On 2026-07-07 18:05, olcott wrote:
>> On 7/7/2026 6:06 PM, André G. Isaak wrote:
>>> On 2026-07-07 15:30, olcott wrote:
>>>> On 7/7/2026 4:24 PM, André G. Isaak wrote:
>>>>> On 2026-07-07 15:13, olcott wrote:
>>>>>> On 7/7/2026 3:08 PM, André G. Isaak wrote:
>>>>>>> On 2026-07-07 13:53, olcott wrote:
>>>>>>>> On 7/7/2026 2:29 PM, André G. Isaak wrote:
>>>>>>>>> On 2026-07-07 13:19, olcott wrote:
>>>>>>>
>>>>>>>>>> To do with with minimal simplicity the axioms of
>>>>>>>>>> PA are construed as semantic entailment thus when
>>>>>>>>>> there is no sequence of inference steps between G
>>>>>>>>>> and PA then G is Kripke undefined in PA.
>>>>>>>>>
>>>>>>>>> So why don't you illustrate this with an actual proof?
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> The principle is simply whenever X cannot be proven
>>>>>>>> in F then X is ungrounded in the atomic base F. Even
>>>>>>>> diagonalization makes to attempt at actual proof.
>>>>>>>
>>>>>>> I can't make heads or tails of that.
>>>>>>>
>>>>>>
>>>>>> The actual proof in meta-math that G cannot be
>>>>>> proved in PA is itself not any sequence of inference
>>>>>> steps. It simply uses a version of the proof that
>>>>>> Cantor use to show that reals are not countable.
>>>>>
>>>>> ???
>>>>>
>>>>> Cantor's proof absolutely contained inference steps, as did Gödels. 
>>>>> I don't think you actually know what you're talking about.
>>>>>
>>>>>>> If you can't illustrate your alleged system with a simple proof, 
>>>>>>> then I have no choice but to conclude that it is as ill-defined 
>>>>>>> to you as it is to me.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> 2 + 3 = 4 in PA cannot be proven because
>>>>>> s(s(0)) + s(s(s(0))) != s(s(s(s(0))))
>>>>>
>>>>> I asked you to provide an example of a proof which illustrates what 
>>>>> you mean by "semantic entailments encoded syntactically in the 
>>>>> language". I didn't ask for an example of something which cannot be 
>>>>> proven.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> PTS simply declares by fiat that syntactic inference steps
>>>> are semantic steps. I actually mean natural language semantic
>>>> inference in the CycL programming language. This is the place
>>>> where nothing follows form a contradiction is most easily seen.
>>>
>>> So basically you're saying that you are incapable of constructing 
>>> even a simple mathematical proof. Gödel is about theories of 
>>> arithmetic. CycL is not. If you can't construct proofs in an 
>>> arithmetic framework you really have no business talking about Gödel.
>>>
>>> André
>>>
>>
>> So basically you are totally not interested in understanding me.
>> As far as proofs go I always think in terms of syllogisms and
>> their extensions. Every other proof is utterly irrelevant to my
>> work.
> 
> If your interest is limited to syllogisms then both Gödel and the 
> halting problem are utterly irrelevant to your work, so you probably 
> should stop making claims about them.

Olcott thinks he is God, there is that... ;^o