Re: The simple essence of Proof Theoretic Semantics

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.
> 

Yes. That is why I need to carefully find the exact
text that backs me up. Because PTS has their own
private author by author language it must be a
work written for a general audience like this work.
https://plato.stanford.edu/entries/proof-theoretic-semantics/


> Would you agree that there is a difference between a statement being 
> false and a statement being meaningless?
> 

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.

PTS counts a finite sequence of inference steps between
an expression and a set of axioms as the definition of
this expression. These are the two papers that establish
this Definitional View.

The Definitional View of Atomic Systems in Proof-Theoretic Semantics
Thomas Piecha and Peter Schroeder-Heister

Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister

>> The biggest mistake that humanity makes that is killing
>> the whole planet is treating unbelievable as exactly
>> one-and-the-same-thing as untrue.
> 
> I have no idea what you're getting at here.
> 

Climate change is killing the planet and too many people
do not believe this because of the well funded hired liars.

> 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).