Re: The simple essence of Proof Theoretic Semantics

On 6/29/2026 8:54 PM, André G. Isaak wrote:
> On 2026-06-29 19:19, olcott wrote:
>> On 6/29/2026 8:01 PM, André G. Isaak wrote:
>>> On 2026-06-29 18:37, olcott wrote:
>>>> On 6/29/2026 6:45 PM, André G. Isaak wrote:
>>>>> On 2026-06-29 17:36, olcott wrote:
>>>
>>>>>> It does seem that they do agree that no proof
>>>>>> of G can possibly exist in PA does means that
>>>>>> G has no semantic meaning in PA.
>>>>>
>>>>> I've not seen anyone operating in PTS who says anything remotely 
>>>>> like that. They do not agree with this; rather, you are projecting 
>>>>> your own peculiar views onto their theory.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> Because they beat around the bush about that using
>>>> terminology that varies across every author.
>>>
>>> It's not that they are beating around the bush; it's that they aren't 
>>> actually saying what you want them to say. Face it, you really don't 
>>> understand the PTS literature as it is above your head.
>>>
>>> André
>>>
>>
>> PTS is the way that meaning actually works.
>> We can make a simpler analogy in that English
>> words are meaningless until they are defined.
>>
>> The PTS connection of an expression in Q to
>> its axioms Q is analogous to the connection
>> of an English word to its definition.
>>
>> A proof merely looks to see if a definition
>> exists and if it does not then the English
>> Word / Expression of Q remains meaningless.
> 
> That's not what PTS says; that's simply you.
> 

That <is> the essence of what PTS says.

-- 
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).