XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 6/23/2025 2:37 AM, Mikko wrote:   
   > On 2025-06-22 14:38:56 +0000, olcott said:   
   >   
   >> On 6/21/2025 11:01 PM, Alan Mackenzie wrote:   
   >>> In comp.theory olcott  wrote:   
   >>>> int DD()   
   >>>> {   
   >>>> int Halt_Status = HHH(DD);   
   >>>> if (Halt_Status)   
   >>>> HERE: goto HERE;   
   >>>> return Halt_Status;   
   >>>> }   
   >>>   
   >>>> https://chatgpt.com/s/t_6857335b37a08191a077d57039fa4a76   
   >>>> ChatGPT agrees that I have correctly refuted every   
   >>>> halting problem proof technique that relies on the above   
   >>>> pattern.   
   >>>   
   >>> That's neither here nor there.  The plain fact is you have NOT refuted   
   >>> any proof technique.  How could you, you don't even understand what is   
   >>> meant by proof?   
   >>   
   >> A proof is any sequence of steps such that its conclusion   
   >> can be correctly determined to be necessarily true.   
   >   
   > False. There are other requirements. Every sentence of the sequence,   
   > not just the last one, must either be a premise or follow from   
   > earlier ones with an acceptable inference rule.   
      
   There is a subset of proofs that have this requirement.   
   They typically are of the form that a conclusion is   
   proved definitely true within a set of assumptions.   
      
   Another form of this same proof only has expressions   
   of language known to be true as its premises.   
      
   *This is the kind of proof that ChatGPT outputs*   
   A more generic proof of this form is any set of expressions   
   of language that proves that an expression of language is   
   definitely true. This more generic proof can be much more   
   powerful because it can fully integrate natural language   
   semantics into its inference steps.   
      
   > Most commonly   
   > accepted rules are modus ponens and substitution of equals. Modus   
   > tollens and reduction are often accepted, too.   
   >   
   > The usual purpose of a proof is to convince. Therefore, what is not   
   > convincing is not a proof or at least not a useful proof.   
   >   
      
      
   --   
   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)