Re: The simple essence of Proof Theoretic Semantics

On 7/2/2026 6:35 PM, olcott wrote:
> 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?

Assuming that X & ~X has been proven from the axioms of a formal system, 
further truth preserving operations leads to the principle of explosion.

That it appears counterintuitive does not mean it is incorrect.  You 
were challenged to find a step that was not truth preserving and you 
were unable to do so.