Re: The simple essence of Proof Theoretic Semantics

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.

-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).