Re: The simple essence of Proof Theoretic Semantics

On 6/30/2026 5:51 PM, André G. Isaak wrote:
> On 2026-06-30 16:42, olcott wrote:
>> On 6/30/2026 5:06 PM, André G. Isaak wrote:
>>> On 2026-06-30 15:56, olcott wrote:
>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote:
>>>>> On 2026-06-29 21:06, olcott wrote:
>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote:
>>>>>>> On 2026-06-29 20:42, olcott wrote:
>>>>>
>>>>>>>> Those are specific concrete examples of how
>>>>>>>> Proof Theoretic Semantics rejects expressions
>>>>>>>> as Proof Theoretic Semantically incoherent.
>>>>>>>
>>>>>>> No, they are not. No author writing in the framework of proof- 
>>>>>>> theoretic semantics has ever offered those examples or comparable 
>>>>>>> examples or made any claims about 'rejecting expressions as proof 
>>>>>>> theoretic semantically incoherent'. And there's nothing 
>>>>>>> incoherent about the statement 'no number is equal to its 
>>>>>>> successor' which is the example under discussion.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> None-the-less what I have said remains completely true.
>>>>>> What I have spent 28 years reverse-engineering from first
>>>>>> principles is exactly that. That no one applied PTS
>>>>>> exactly that way before does not mean that it is not
>>>>>> exactly correct PTS.
>>>>>
>>>>> Unfortunately, your say so carries very little weight.
>>>>>
>>>>> Would you agree that there is a difference between a statement 
>>>>> being false and a statement being meaningless?
>>>>>
>>>>
>>>> Of course and that is such a dumb question that I
>>>> ignored it.
>>>
>>> But your interpretation of PTS claims that there is no difference. 
>>> You claim that unprovable statements are meaningless; but any false 
>>> statement will be unprovable in a consistent logic.
>>>
>>> PA can prove that 2 + 3 = 5
>>> PA can't prove that 2 + 3 ≠ 5
>>>
>>> But the latter isn't meaningless, it's simply false.
>>>
>>
>> If no connection exists between an expression E
>> (or its negation ~E) and the axioms of formal
>> system F then E is undefined in F.
> 
> So now you are adding 'or its negation' to your position (something not 
> present in your earlier presentations). Can you provide a reference to a 
> single author writing in PTS who makes such a claim?
> 

I did not put negation in there because I thought that
my words obviously included it. Clearly I was wrong
about this. The PTS people themselves mostly talk about
canonical proof, normalization and harmony.

> And does 'undefined' differ from your earlier term 'meaningless'?
> 
> André
> 


-- 
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).