Re: The simple essence of Proof Theoretic Semantics

On 7/2/2026 12:52 PM, olcott wrote:
> On 7/2/2026 11:04 AM, dbush wrote:
>> On 7/2/2026 10:51 AM, olcott wrote:
>>> On 7/2/2026 1:57 AM, Mikko wrote:
>>>> On 02/07/2026 07:03, olcott wrote:
>>>>> On 7/1/2026 11:01 PM, dbush wrote:
>>>>>> 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.
>>>>>>
>>>>>
>>>>> Back to being ignored for trolling again.
>>>>
>>>> Maybe by someone but you are still far from being ignored by everone.
>>>>
>>>
>>> Do you know enough about C to understand that
>>> dbush example was foolish nonsense when proposed
>>> to show the halting problem counter-example?
>>>
>>
>> It perfectly illustrates an algorithm that attempts to be a halt decider, 
> 
> Ridiculously stupid. Your H does not even look at its input.

Algorithm H doesn't need to read its inputs in order to map all inputs 
to non-halting.

> 
> Also your D simply stops running I ran it to verify.

Verifying that algorithm H doesn't correctly report what algorithm D 
does, as per the design of algorithm D.

> 
> I will not respond to any of your future posts that
> are very stupid. Say something smart or you will be
> ignored from now on.
> 
>> and another algorithm built by the template that the first one answers 
>> wrong.
>>
>> If you disagree, explain in detail why.
> 
>