Re: The simple essence of Proof Theoretic Semantics

On 7/1/2026 2:01 PM, olcott wrote:
> On 7/1/2026 12:33 PM, dbush wrote:
>> 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?
>>
> 
> The same thing as: "cats are animals" expressed in
> English has no English meaning in Chinese.

I didn't ask for an example.  I asked for a definition of what it mean 
for the truth value of a statement to not exist in a formal system.