Re: The simple essence of Proof Theoretic Semantics

On 7/2/2026 5:32 PM, dbush wrote:
> On 7/2/2026 6:13 PM, olcott wrote:
>> On 7/2/2026 4:59 PM, dbush wrote:
>>> On 7/2/2026 5:40 PM, olcott wrote:
>>>> On 7/2/2026 4:23 PM, dbush wrote:
>>>>> On 7/2/2026 5:12 PM, olcott wrote:
>>>>>> On 7/2/2026 3:54 PM, dbush wrote:
>>>>>>> On 7/2/2026 4:53 PM, olcott wrote:
>>>>>>>> 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.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> We already did that and you got confused, calling it a mind game 
>>>>>>> (see below):
>>>>>>>
>>>>>> The confusing part is how an intelligent person can
>>>>>> accept POE as correct for more than sixty seconds.
>>>>>>
>>>>>> Every average third grader knows that a contradiction
>>>>> States that both a statement and its negation are true.  And if a 
>>>>> formal system can reach a contradiction through a series of truth 
>>>>> preserving operations from its axioms, that means both statements 
>>>>> are proven true.
>>>>>
>>>>
>>>> Every third grader knows that it must have fucked up somewhere.
>>>
>>> Your intuition fails you.  It just means that the axioms of the 
>>> system in question are inconsistent.  And the principle of explosion 
>>> can be used to show that an inconsistent system is useless.
>>>
>>
>> It makes more sense to use the ordinary meaning
>> of contradiction:
>>
>> When-so-ever two sentences contradict each other
>> at least one of them is false.
> 
> Whatever you call it, if the axioms of a formal system can prove both X 
> and ~X, then the principle of explosion can be used to show that system 
> is useless.
> 

X & ~X proves FALSE.
How can anyone that is not nuts possibly think otherwise?

-- 
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).