Re: The simple essence of Proof Theoretic Semantics

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.