Re: The simple essence of Proof Theoretic Semantics

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):

On 6/28/2026 11:56 PM, dbush wrote:
 > On 6/27/2026 11:34 PM, dbush wrote:
 >> On 6/27/2026 11:23 PM, olcott wrote:
 >>> On 6/27/2026 9:02 PM, dbush wrote:
 >>>> On 6/27/2026 9:53 PM, dbush wrote:
 >>>>> On 6/27/2026 9:49 PM, olcott wrote:
 >>>>>> On 6/27/2026 8:42 PM, dbush wrote:
 >>>>>>> On 6/27/2026 9:40 PM, olcott wrote:
 >>>>>>>> On 6/27/2026 8:29 PM, dbush wrote:
 >>>>>>>>> Given that the following natural language statement is true:
 >>>>>>>>>
 >>>>>>>>> --------------------------------------
 >>>>>>>>> Earth is the third planet from the sun.
 >>>>>>>>> --------------------------------------
 >>>>>>>>>
 >>>>>>>>> In the following natural language statement:
 >>>>>>>>>
 >>>>>>>>> --------------------------------------
 >>>>>>>>> At least one of the following statements is true:
 >>>>>>>>> - Earth is the third planet from the sun.
 >>>>>>>>> - <X>
 >>>>>>>>> --------------------------------------
 >>>>
 >>>> Given that <X> is any *truth bearing* natural language statement,
 >>>> does there exist a statement X such that the condition "At least one
 >>>> of the following statements is true" is false?
 >>>>
 >>>
 >>> Head games will be ignored.
 >>>
 >>
 >> Explain in detail how this is a head game.
 >>
 >> Failure to either answer the above question or explain how it is a
 >> head game in your next reply or within one hour of you next post in
 >> this newsgroup will be taken as your official, on-the-record admission
 >> that Disjunction introduction is in fact truth preserving and valid,
 >> and therefore so is the Principle of Explosion.
 >>
 >
 > Let the record show that Peter Olcott made the following post in this
 > newsgroup:
 >
 > On 6/28/2026 10:52 PM, olcott wrote:
 >  > Q also can't bake a birthday cake, this does not make
 >  > Q in any way "incomplete" relative to what it was
 >  > defined to do.
 >  > ...
 >
 > And more that one hour has passed with no attempt to answer the above
 > question or explain why it is a head game.  Therefore, as per the above
 > criteria:
 >
 > Let The Record Show
 >
 > That Peter Olcott
 >
 > Has *Officially* Admitted:
 >
 > That Disjunction introduction is in fact truth preserving and valid, and
 > therefore so is the Principle of Explosion.