Re: The simple essence of Proof Theoretic Semantics

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.

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.