Re: The simple essence of Proof Theoretic Semantics

On 7/1/2026 4:23 PM, olcott wrote:
> On 7/1/2026 2:52 PM, dbush wrote:
>> 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.
> 
> True in the formal language of formal system L for expression X means
> that there exists a subset of the axioms of L such that a finite
> sequence of inference steps in L reach this subset of axioms of L.
> 

I didn't ask what you think true in a formal system means.  I asked what 
you think it means for the truth value of a statement to not exist in a 
formal system.