Re: William T. Parry gets rid of Disjunction introduction

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.

André

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