Re: William T. Parry gets rid of Disjunction introduction

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.

> 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))))

-- 
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).