Re: The simple essence of Proof Theoretic Semantics

On 7/2/2026 2:52 PM, dbush wrote:
> On 7/2/2026 3:33 PM, olcott wrote:
>> On 7/2/2026 1:22 PM, dbush wrote:
>>> On 7/2/2026 2:13 PM, olcott wrote:
>>>> On 7/2/2026 11:55 AM, dbush wrote:
>>>>> 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.
>>>>>
> 
> Still no reply to this, so I have to assume you agree it's correct.
> 
>>>>
>>>> I am trying to keep liars from killing the
>>>> whole fucking planet by making truth computable
>>>
>>> Which can't be done as proved by Turing / Godel / Tarksi and others.
>>>
>>
>> By proving the errors in logic I can make
>> logic into correct reasoning. That most
>> logic people are a herd of sheep that would
>> gladly leap off the POE cliff when that is
>> what their herd accepts makes correcting this
>> error too fucking difficult.
> 
> There is no error.  The POE follows from a series of truth preserving 
> operations 

To say this objectively classical logic is objectively incorrect
when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.

(P ∧ ¬P) ⊢ Q  is ridiculously stupid when we plug English
sentences in for P and Q and use semantic entailment in English
as the measure of correct reasoning.


-- 
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).