
Re: The Invalidity of Godel's Incompleteness Work.
Posted:
Oct 20, 2013 9:09 PM


On 20/10/2013 5:29 PM, fom wrote: > On 10/20/2013 6:06 PM, Nam Nguyen wrote: >> On 20/10/2013 5:01 PM, fom wrote: >>> On 10/20/2013 5:52 PM, Nam Nguyen wrote: >>>> On 20/10/2013 1:40 PM, fom wrote: >>>> >>>>> >>>>> Start reading more and using your mouth less. >>>> >>>> You're a fucking hypocrite. >>>> >>> >>> What did I do when asked to provide my formal system? >>> >>> https://groups.google.com/forum/#!original/sci.math/ZmeoaTpI28A/VuyUSrWOt0J >>> >>> >>> >>> >>> I provided it. >>> >>> Do you see how that works? >>> >>> By the way, I read quite a bit. >> >> What did you constructively provide with your "Start reading more and >> using your mouth less", prior to which I had been very polite and >> technical in responding to you? >> > > A suggestion which might improve your understanding > of the issues here. > > Outside of your readings dedicated to firstorder > logic with identity, can you answer the question: > > "What is logic?" > > Perhaps that is too vague. Here is another small > batch of questions: > > Apparently, Alonzo Church described Bertrand Russell's > logic as "intensional". Can you explain that term? > Is mathematical logic "intensional"? If so, why? > If not, then what kind of logic is it, and, why is > it classified as it is? > > I am guessing that you cannot answer these questions > without some research. > > Historically, I have focused very little attention > to arithmetic. I might even give credence to the > statements in your "metaproofs". But, this is only > because my sense of logical priority tells me it is > a mistake to use numbers from within a theory to > skeptically discount the statements of a theory. > > Nevertheless, metamathematics has done precisely that. > As a consequence, one may only ask if a metamathematical > result such as Goedel's incompleteness theorem is faithful > to the task toward which it had been directed. There is > simply no reason to think otherwise. To the contrary, > it an unparalleled success. > > So, do you understand Hilbert's program of metamathematics > toward which Goedel's efforts had been directed? > > If not, how do you know that your assumptions are not > in error concerning the meaning of the theorem?
So, now we seem to have reversed the roles: you play the "nasty" Nam Nguyen keep asking questions in the middle of explanation and I play the role of "nice" fom who wouldn't ask questions in his explaining issues.
Any rate, this conversation started from your:
> Well, one interpretation of the problem is > that anything based upon "what is prior" and > "what is posterior" with a first step is > interpretable relative to the ordinal sequence > of natural numbers.
to which you I responded:
>> Kindly let me and the fora know what your _FORMAL definition_ >> of the "natural numbers". I don't know what your definition >> is so I don't see any relevance between your paragraph above and my >> thesis here. (For the record, my definition of the concept of natural >> numbers is such that it could be only of _informal knowledge_ ).
The issue is I would like to examine the state of _formality_ of your "naturalnumbers" definition, since according to my definition the concept would be _informal_ .
Now you did give a link defining _your_ definition of "naturalnumbers". I'm always critical of any idea to claim the definition of "natural numbers" be formal.
But before I open my criticism to your claimed "formal" definition there, kindly confirm that the link is indeed about _your_ _formal_ system (rivaling PA) describing the concept of the "natural numbers".
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI

