Re: The simple essence of Proof Theoretic Semantics

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:

int H(ptr *X, ptr *Y)
{
     int result;
     {
         result = 0;
     }
     return result;
}

The counter-example algorithm D is this:

void D(ptr *I)
{
     ptr *X = D;
     ptr *Y = I;
     int result;
     {
         result = 0;
     }
     if (result == 1) {
         while (1);
     }
}

> 
>>
>>> is more like
>>> the Liar Paradox. For HHH(DD) 
>>
> If it is true that makes it false.
> If it is false that make is true.
> Therefore is has always been fucking nonsense.
> 
> That it took humans more than five minutes to
> see this conclusively proves how stupid they are.
>