Re: The simple essence of Proof Theoretic Semantics

On 7/2/2026 7:49 PM, olcott wrote:
> On 7/2/2026 5:59 PM, dbush wrote:
>> On 7/2/2026 6:53 PM, olcott wrote:
>>> On 7/2/2026 5:47 PM, dbush wrote:
>>>> 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:
>>>>>>>>>>> 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, 
>>>
>>> Stipulating the ordinary English meaning of contradiction
>>
>> Is not the stipulated meaning used in logic and is therefore irrelevant.
>>
>> If you want an example, naive set theory is an inconsistent system.  
>> It is able to prove both X = "set R contains itself" and ~X = "set R 
>> does not contain itself".  So X & ~X is proven TRUE in naive set 
>> theory.  The principle of explosion can then be used to show that 
>> naive set theory is useless.
> 
> Russell's Paradox is the exact same issue as the
> pathological self reference (PSR) of the Halting
> Problem. I have studied PSR as a primary focus
> for 28 years.

The halting problem doesn't actually have self reference, as algorithms 
can be copied as in the below example of algorithm D:

void D(ptr *I)
{
      // algorithm D; input: I
      ptr *X = D;
      ptr *Y = I;
      int result;
      {
          // algorithm H; inputs: X,Y
          result = 0;
      }
      if (result == 1) {
          while (1);
      }
}

Which is the counter example input to algorithm H:

int H(ptr *X, ptr *Y)
{
      int result;
      {
          // algorithm H; inputs: X,Y
          result = 0;
      }
      return result;
}