
Re: The Invalidity of Godel's Incompleteness Work.
Posted:
Oct 19, 2013 4:33 PM


On 19/10/2013 2:21 PM, Peter Percival wrote: > Nam Nguyen wrote: >> On 19/10/2013 2:06 PM, Peter Percival wrote: >>> Nam Nguyen wrote: >>>> On 19/10/2013 1:24 PM, Nam Nguyen wrote: >>>>> On 19/10/2013 12:53 PM, Peter Percival wrote: >>>>>> 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 PAcGC or PA~cGC, so we don't know if >>>>>>>> "PAcGC" >>>>>>>> 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)? >>>>> >>>>> "Fom" asked me a very specific DEFINITIONquestion and I've given a >>>>> very >>>>> specific answer to his question. >>>>> >>>>> Until you and fom let me know if this definition is understood by >>>>> you both, I'm not answering further to your endless postings resulted >>>>> from _your not understanding my definition_ . >>>>> >>>>> So, here it is again: >>>>> >>>>> > _Do you first understand the definition itself_ ? >>>>> > >>>>> > Would you please confirm you now do or still don't? Thanks. >>>>> >>>>>>>> >>>>>>>> Do you know that both cGC and ~cGC are not in the collection of >>>>>>>> meta >>>>>>>> truths? If so you must know that neither PAcGC nor PA~cGC. >>>>>>>> You >>>>>>>> should publish your proof. And stop claiming that Gödel's >>>>>>>> incompleteness theorem is invalid, because if neither PAcGC nor >>>>>>>> PA~cGC, then that is an example of incompleteness. >>>>>>>> >>>>>>>> Also if you know that neither PAcGC 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, >>>>> >>>>> You forgot another possibility: >>>>> >>>>> You're too intellectually coward to admit my definition is sound, >>>>> which would lead to the fact you've been so stupid in this debate. >>>>> >>>>>> iii) you admit that your claims about cGC and Gödel are wrong? >>>>>> Not iii) I bet. >>>> >>>> I'll give you a breathing room: let me know if you understand my >>>> definition of "impossible to know" >>> >>> It is from your definition of "impossible to know" that I deduce that >>> you can prove that neither PAcGC nor PA~cGC. Hence you have proved >>> Gödel's incompleteness theorem and you have proved PA is consistent. >> >> >>> So >>> if I understood your definition then you are wrong about Gödel's >>> incompleteness theorem being invalid and you are wrong about PA not >>> being provably consistent. >> >> You see: it's your keep saying "if I understood your definition" that >> has raised a red flag to me. What happen if your understanding of my >> definition is incorrect? Should it be in that case we have to see eye >> to eye on the definition itself first, before you blaming me for the >> alleged being wrong about Gödel's work here? >> >> So please confirm if you indeed you understand my definition. > > Do you want me to understand it? If I do, then I deduce that you can > prove that neither PAcGC nor PA~cGC. Hence you have proved Gödel's > incompleteness theorem and you have proved PA is consistent. So if I > understood your definition then you are wrong about Gödel's > incompleteness theorem being invalid and you are wrong about PA not > being provably consistent. > > Perhaps for that reason you don't want me to understand it.
Of course a presenter would want the listeners to understand his _definitions_ .
But do you, Peter Percival, understand my definition of "impossible to know" here?
Your answering me here would shape my further responses to you: if you don't understand, I'll have to work with you on your understanding first, and we'll see if you'd still have the same protest.
If you do understand, I'll point out where you were incorrect in your blaming me about GIT.
If you don't let me know whether or not you understand my definition, a million posts between you and me would go by and we'd go nowhere, and I'd keep asking you the very same question about my definition. > >> (From what you've said I don't think you understand. But I'd >> rather hear it from you, than my own guessing!)
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI

