Re: William T. Parry gets rid of Disjunction introduction

On 7/7/2026 8:17 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.
> 
> André
> 

My interest is in defining automated reasoning
that approximates infallibility and knows all
the general knowledge known to man. A system such
as this would make the best funded disinformation
teams look like ridiculous fools even to themselves.

Being able to show all the steps of how PA
derives 2 + 3 = 5 is totally unrelated to this.

-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).