Re: The simple essence of Proof Theoretic Semantics

On 02/07/2026 17:51, olcott wrote:
> On 7/2/2026 1:57 AM, Mikko wrote:
>> On 02/07/2026 07:03, olcott wrote:
>>> On 7/1/2026 11:01 PM, dbush wrote:
>>>> On 7/1/2026 11:59 PM, olcott wrote:
>>>>> On 7/1/2026 10:43 PM, dbush wrote:
>>>>>> On 7/1/2026 11:37 PM, olcott wrote:
>>>>>>> On 7/1/2026 10:18 PM, dbush wrote:
>>>>>>>> On 7/1/2026 11:17 PM, olcott wrote:
>>>>>>>>> On 7/1/2026 10:00 PM, dbush wrote:
>>>>>>>>>> On 7/1/2026 10:53 PM, olcott wrote:
>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote:
>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote:
>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote:
>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote:
>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote:
>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote:
>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> I'm actually not convinced that Olcott 
>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've 
>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he 
>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an 
>>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He 
>>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the place 
>>>>>>>>>>>>>>>>>>>>>>>> of definitions. Examples can be useful for 
>>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't 
>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> André
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> You want a definition look-it-up.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Until someone publishes an Olcott to Standard 
>>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> André
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright 
>>>>>>>>>>>>>>>>>>>>> Olcott 2018
>>>>>>>>>>>>>>>>>>>>> has been updated to this
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> That claims what it means to have the truth value 
>>>>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined 
>>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any 
>>>>>>>>>>>>>>>>>>>> way clarify what you think it means for something to 
>>>>>>>>>>>>>>>>>>>> not have a truth value.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> André
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> When I define a term hundreds of times and you did
>>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake
>>>>>>>>>>>>>>>>>>> and your fault.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You gave no such definition of what it means for the 
>>>>>>>>>>>>>>>>>> truth value of a statement to not exist in a formal 
>>>>>>>>>>>>>>>>>> system.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> A valid answer would look something like this:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> "The truth value of a statement does not exist in a 
>>>>>>>>>>>>>>>>>> formal system when ..."
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Now complete the sentence.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> It is neither provable nor refutable in F.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Good.  So when you say "The truth value of (∀ x, S(x) ≠ 
>>>>>>>>>>>>>>>> x) does not exist in Q", you mean "(∀ x, S(x) ≠ x) is 
>>>>>>>>>>>>>>>> unprovable in Q", which is commonly known.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So once again, you're saying the same thing as everyone 
>>>>>>>>>>>>>>>> else but using different words.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Not really. It is normally thought of as undecidable
>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> False.  It means that there are statements in the language 
>>>>>>>>>>>>>> of Q that have *only* an infinite connection to the axioms 
>>>>>>>>>>>>>> of the system.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> OK, I verified that.
>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The Halting Problem counter-example input 
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Which starts with the assumption that an algorithm H 
>>>>>>>>>>>>>> exists that meets the following requirements:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>>>>>>>>>>>> instructions) X described as <X> with input Y:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A solution to the halting problem is an algorithm H that 
>>>>>>>>>>>>>> computes the following mapping:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed 
>>>>>>>>>>>>>> directly
>>>>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when 
>>>>>>>>>>>>>> executed directly
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Sure and we could equally start with the requirement
>>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I really don't see how everyone did not immediately see
>>>>>>>>>>>>> that the requirement for H to correctly report the halt
>>>>>>>>>>>>> status of input D that does the opposite of whatever H
>>>>>>>>>>>>> reports is a moronically stupid requirement within the
>>>>>>>>>>>>> first five minutes that this requirement was made.
>>>>>>>>>>>>
>>>>>>>>>>>> In other words, you don't understand that if this was 
>>>>>>>>>>>> algorithm H:
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I spent 10,000 hours on it over 22 years.
>>>>>>>>>>
>>>>>>>>>> And still don't understand that this algorithm:
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> void D(ptr *I)
>>>>>>>>>> {
>>>>>>>>>>      ptr *X = D;
>>>>>>>>>>      ptr *Y = I;
>>>>>>>>>>      int result;
>>>>>>>>>>      {
>>>>>>>>>>          result = 0;
>>>>>>>>>>      }
>>>>>>>>>>      if (result == 1) {
>>>>>>>>>>          while (1);
>>>>>>>>>>      }
>>>>>>>>>> }
>>>>>>>>>>
>>>>>>>>>> Is the counter example input to this algorithm:
>>>>>>>>>>
>>>>>>>>>> int H(ptr *X, ptr *Y)
>>>>>>>>>> {
>>>>>>>>>>      int result;
>>>>>>>>>>      {
>>>>>>>>>>          result = 0;
>>>>>>>>>>      }
>>>>>>>>>>      return result;
>>>>>>>>>> }
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> That is just nonsense.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Thereby proving that you've misunderstood the halting problem 
>>>>>>>> for the last 22 years.
>>>>>>>
>>>>>>> D(D);   // merely halts
>>>>>>> H(D,D); // merely returns 0 and never looks at D(D)
>>>>>>
>>>>>> And algorithm H is wrong about algorithm D because algorithm D 
>>>>>> contains a copy of algorithm H and does the opposite.
>>>>>
>>>>> You just don't know jack shit dufus.
>>>>> I have been a professional C programmer since 1986.
>>>>>
>>>>
>>>> Says the person that just demonstrated that they don't know the 
>>>> difference between an algorithm and a C function.
>>>>
>>>
>>> Back to being ignored for trolling again.
>>
>> Maybe by someone but you are still far from being ignored by everone.
> 
> Do you know enough about C to understand that
> dbush example was foolish nonsense when proposed
> to show the halting problem counter-example?

It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.

-- 
Mikko