Re: The simple essence of Proof Theoretic Semantics

On 7/1/2026 3:44 PM, olcott wrote:
> On 7/1/2026 2:19 PM, dbush wrote:
>> On 7/1/2026 3:09 PM, olcott wrote:
>>> On 7/1/2026 1:59 PM, dbush wrote:
>>>> 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*.
>>>>
>>>
>>> True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
>>
>> So in other words, the truth value of a statement not existing in a 
>> formal system simply means that the statement is not provable in that 
>> system.
>>
> That is not what I said.
> 

Then translate the above symbols to English so we can examine that more 
carefully.