Re: The simple essence of Proof Theoretic Semantics

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.