Re: The simple essence of Proof Theoretic Semantics

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.