XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 01/01/2026 01:29, Richard Damon wrote:   
   > On 12/31/25 8:04 PM, olcott wrote:   
   >> On 12/31/2025 6:35 PM, Richard Damon wrote:   
   >>> On 12/31/25 7:23 PM, olcott wrote:   
   >>>> On 12/31/2025 5:27 PM, Richard Damon wrote:   
   >>>>> On 12/31/25 6:08 PM, olcott wrote:   
   >>>>>> On 12/31/2025 4:48 PM, Richard Damon wrote:   
   >>>>>>> On 12/31/25 5:42 PM, olcott wrote:   
   >>>>>>>> On 12/31/2025 4:09 PM, Richard Damon wrote:   
   >>>>>>>>> On 12/31/25 4:59 PM, olcott wrote:   
   >>>>>>>>>> On 12/31/2025 3:56 PM, Richard Damon wrote:   
   >>>>>>>>>>> On 12/31/25 4:52 PM, olcott wrote:   
   >>>>>>>>>>>> On 12/31/2025 3:16 PM, Pierre Asselin wrote:   
   >>>>>>>>>>>>> In sci.logic Tristan Wibberley   
   >>>>>>>>>>>>>  wrote:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>> [ ... ]   
   >>>>>>>>>>>>>> Then he defines a new system "P" which he uses to get even   
   >>>>>>>>>>>>>> more muddled,   
   >>>>>>>>>>>>>> leaves out the crucial elements of his proof because it's   
   >>>>>>>>>>>>>> too easy to   
   >>>>>>>>>>>>>> get wrong,   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Gödel, muddled? He was the most meticulous sonovabitch that   
   >>>>>>>>>>>>> ever   
   >>>>>>>>>>>>> lived!   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>> and Stephen Meyer says he does get it wrong; he seems to be   
   >>>>>>>>>>>>>> the only person in the world that ever checked.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> People have misunderstood Gödel and proved it by their   
   >>>>>>>>>>>>> comments.   
   >>>>>>>>>>>>> I don't know who Stephen Meyer is; my money is on Gödel.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Gödel proved that there cannot possibly exist any   
   >>>>>>>>>>>> sequence of inference steps in F prove that they   
   >>>>>>>>>>>> themselves do not exist.   
   >>>>>>>>>>>   
   >>>>>>>>>>> No *FINITE* sequence of inference steps.   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> Nothing can prove that itself does not   
   >>>>>>>>>> exist because that forms proof that it   
   >>>>>>>>>> does exist, dumbo.   
   >>>>>>>>>   
   >>>>>>>>> So you are just ignoring context because you are stupid.   
   >>>>>>>>>   
   >>>>>>>>> The statement, with the added information of the meta-system   
   >>>>>>>>> proves (by a proof in the meta system) that the statment is true.   
   >>>>>>>>>   
   >>>>>>>>   
   >>>>>>>> Something else can prove that X cannot prove that   
   >>>>>>>> X does not exist, AKA your meta-system.   
   >>>>>>>>   
   >>>>>>>> Nothing can directly prove that itself does not   
   >>>>>>>> exist because this forms proof that it does exist.   
   >>>>>>>>   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> Nope, got a source for that?   
   >>>>>>>   
   >>>>>>> Why does my explanation not work?   
   >>>>>>>   
   >>>>>>   
   >>>>>> It is not that your explanation doesn't work.   
   >>>>>> It is that it ignores the root cause of why   
   >>>>>> G is unprovable in F.   
   >>>>>   
   >>>>> So, how do you think you can prove it in F?   
   >>>>>   
   >>>>   
   >>>> Nothing can prove that itself does not exist.   
   >>>> Any such proof would be self-refuting.   
   >>>>   
   >>>   
   >>> But it isn't the PROOF that does the proving, it is the statement.   
   >>>   
   >>> THe statement G exist, and it is True.   
   >>>   
   >>   
   >> ...We are therefore confronted with a proposition which   
   >> asserts its own unprovability. 15 … (Gödel 1931:40-41)   
   >   
   > You keep on repeating that, but show you don't know what it means,   
   > proving your stupidity.   
   >   
   >>   
   >> When we name this proposition G then a proof of G   
   >> would be a sequence of inference steps that prove   
   >> that they themselves do not exist.   
   >   
   > Right, we name the proposition G.   
   >   
   > Then we form a set of steps in M, the Meta-system that proves that G is   
   > True.   
      
   But then all you've done is show that there exists a meta-system in   
   which a non-theorem of the base-system equal to "⊢ G" in the meta-system   
   is a theorem. Well, yes, there exist lots of them - one with "⊢ G" as   
   its sole axiom and the deduction rule that from "⊢ G" deduce the   
   non-theorem of the base-system, for example.   
      
   Is this just a case of "can't see the woods through the trees" ?   
      
      
   --   
   Tristan Wibberley   
      
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