Nam Nguyen wrote: > On 19/10/2013 12:10 PM, Peter Percival wrote: >> Nam Nguyen wrote: >>> On 19/10/2013 11:32 AM, fom wrote: >> >>>> And, the meaning of "impossible to know"? >>> >>> Right there: right in front of you. >>> >>> _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]. >> >> 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. > > _Do you first understand the definition itself_ ? > > Would you please confirm you now do or still don't? Thanks.
If I've understood it (the definition of "impossible to know") then my argument above is valid. If it's valid then you're wrong about Gödel. So you should be careful about what you ask to be confirmed.
You have been caught out in a contradiction. Now, what's it to be: i) you are too dim to recognize it, ii) you are too dishonest to recognize it, iii) you admit that your claims about cGC and Gödel are wrong? Not iii) I bet.
-- The world will little note, nor long remember what we say here Lincoln at Gettysburg