Re: The simple essence of Proof Theoretic Semantics

On 6/30/2026 11:49 PM, olcott wrote:
> On 6/30/2026 10:17 PM, dbush wrote:
>> 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.
>>

Your lack of reply confirms your above admission.

>>> does not exist in Q.
>>>
>>
> 
> Unlike PA it cannot possibly have any finite sequence
> of inference steps in Q that resolve to a truth value in Q.

Which means, by definition, you agree that Q is incomplete.

> 
>> You just contradicted yourself.
>>
>>
> 
>