Re: The simple essence of Proof Theoretic Semantics

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.