Re: The simple essence of Proof Theoretic Semantics

On 7/1/2026 12:20 AM, olcott wrote:
> On 6/30/2026 11:01 PM, dbush wrote:
>> 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.
>>
> 
> I make a very specific statement.
> You mangle it and ask if I agree.

There was no mangling.  That is the meaning of the words you used.

> 
> The truth value of (∀ x, S(x) ≠ x) 

In order for it to have a truth value, it must be either true or false. 
That you say it has a truth value is your admission that it is in fact 
either true or false.

Only a statement that is semantically valid / correct can be true or 
false, as it is it semantics (in this case the semantics of Q and the 
English language sentence it translates to) that determines truth values.

This therefore constitutes your admission that the above statement is 
semantically valid / correct, and that by extension PTS is incorrect 
about this and therefore useless.


> does not exist in Q.
> If you change that in any way you can assume that I do not agree.
> 



>>>>> 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.
>>>>
>>>>
>>>
>>>
>>
> 
>