Re: The simple essence of Proof Theoretic Semantics

On 7/1/2026 2:54 PM, olcott wrote:
> On 7/1/2026 1:35 PM, dbush wrote:
>> On 7/1/2026 2:21 PM, olcott wrote:
>>> On 7/1/2026 1:15 PM, dbush wrote:
>>>> 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.
>>>>
>>>
>>> Wittgenstein (1937)
>>> 'True in Russell's system' means, as was said:
>>> proved in Russell's system; and 'false in Russell's
>>> system' means: the opposite has been proved
>>> in Russell's system
>>
>> I specifically didn't ask for an external quote, as you have 
>> demonstrated on countless occasions that you can't understand what 
>> others have written.
> 
> Everything that I have said in the last five years
> sums up to the above quote.

Don't sum it up in someone else's words.  Sum it up *in your own words*.

> 
>>
>> Tell me, *in your own words*, what you think it means for the truth 
>> value of a statement to not exist in a formal system.
> 
> I have mean exactly what Wittgenstein (1937) means
> several years before I ever heard of him.

What you think he means and what others think he means may not be the same.

That's why I asked you what you think it means in your own words.