Re: The simple essence of Proof Theoretic Semantics

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;
}