Re: The simple essence of Proof Theoretic Semantics

On 6/30/2026 11:10 PM, olcott wrote:
> On 6/30/2026 10:02 PM, dbush wrote:
>> On 6/30/2026 10:57 PM, olcott wrote:
>>> On 6/30/2026 9:34 PM, dbush wrote:
>>>> On 6/30/2026 6:04 PM, olcott wrote:
>>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote:
>>>>>> On 2026-06-30 15:45, 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.
>>>>>>>>
>>>>>>>
>>>>>>> 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.
>>>>>>
>>>>>> None of the above answers my question:
>>>>>>
>>>>>> Would you agree that there is a difference between a statement 
>>>>>> being false and a statement being meaningless?
>>>>>>
>>>>>
>>>>> I don't answer dumb questions.
>>>>
>>>> Translation:
>>>>
>>>> "I don't answer questions that can prove me wrong"
>>>>
>>>>> That is why I am not responding to any posts
>>>>> besides yours. dbush has become a troll again.
>>>>
>>>>
>>>> Reminding people that you admitted that disjunction intruduction is 
>>>> truth-preserving by your repeated dishonest dodging of how P can be 
>>>> true and P ∨ Q can be false is not trolling.
>>>>
>>>
>>> In Robinson Arithmetic (often denoted as Q),
>>> the statement "no number is equal to its
>>> successor" is not provable. While this statement
>>> is true for the standard natural numbers, Robinson
>>> Arithmetic is too weak to prove it universally
>>> (∀ x, S(x) ≠ x).
>>>
>>> That you brought this up was a brilliant simplification
>>> of the point that I was making proving that you can
>>> understand the key ideas.
>>
>> What is was is a way to show more easily how you're wrong.  That you 
>> claim that "no number is equal to its successor" is semantically 
>> invalid shows everyone that your ideas are worthless.
>>
> 
> This is more accurate:
> The truth value of (∀ x, S(x) ≠ x) 

So you admit that the above statement which exists in Q must be either 
true or false.

> does not exist in Q.
> 

You just contradicted yourself.