Re: The simple essence of Proof Theoretic Semantics

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.

 From *there*, the principle of explosion is applied, demonstrating that 
the system that proved the contradiction is useless.