Re: The simple essence of Proof Theoretic Semantics

On 7/1/2026 10:40 AM, olcott wrote:
> On 7/1/2026 6:55 AM, dbush wrote:
>> 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) 
>>
> 
> You already mangled it.
> The truth value of (∀ x, S(x) ≠ x) does not exist in Q.

In your own words, what does it mean for the truth value of statement to 
not exist in a formal system?

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