Nam Nguyen wrote: > On 19/10/2013 2:58 PM, Peter Percival wrote: >> Nam Nguyen wrote: >>> On 19/10/2013 2:44 PM, Peter Percival wrote: >>>> Nam Nguyen wrote: >>>> >>>>> [...], I'll have to work with you on your understanding >>>>> first, and we'll see if you'd still have the same protest. >>>> >>>> Surely that would be a "cruel and unusual punishment"? >>> >>> I don't know what you're talking about. >> >> It's a quotation from some amendment to the US constitution. Don't ask >> me, I know nothing. >> >>> Surely other posters (e.g., fom, Alan, ...) and I on the occasions >>> _when needed_ did clarify technical matters. Why can't you? >> >> Is this clear enough? > > No: it's not clear enough that you do - or do not - understand the > definition. >> >> From your definition: >> >> > _A meta truth_ is said to be impossible to know if it's not in the >> > collection of meta truths, resulting from all available definitions, >> > permissible reasoning methods, within the underlying logic framework >> > [FOL(=) in this case]. > > Right. That's my definition of the phrase here. >> >> this follows: > > No. _It does NOT follow from my definition_ .
Why not? Where does the following (quite brilliant, in my opinion) reasoning fail?
>> >> We don't yet know if PA|-cGC or PA|-~cGC, so we don't know if "PA|-cGC" >> or "PA|-~cGC" is in the collection of meta truths. So we don't know if >> it's impossible to know cGC (or ~cGC). Why, then, do you claim that >> it's impossible to know cGC (or ~cGC)? >> >> Do you know that both cGC and ~cGC are not in the collection of meta >> truths? If so you must know that neither PA|-cGC nor PA|-~cGC. You >> should publish your proof. And stop claiming that Gödel's >> incompleteness theorem is invalid, because if neither PA|-cGC nor >> PA|-~cGC, then that is an example of incompleteness. >> >> Also if you know that neither PA|-cGC nor PA|-~cGC, then you've proved >> PA consistent. So you should stop claiming that its consistency is >> unprovable. >> > >
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