
Re: The Invalidity of Godel's Incompleteness Work.
Posted:
Oct 24, 2013 1:00 AM


On 20/10/2013 7:45 PM, fom wrote: > On 10/20/2013 8:09 PM, Nam Nguyen wrote: >> 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". >> > > I have additions to be made. I am constructing a representation > for the usual notion as associated with Peano arithmetic as a > system of relations within the theory expressed by those axioms. > > But, yes, that is the groundwork. > > It his, however, mathematics. How it is arrived at by me > has not yet been pursued. > > So, whereas I have a good idea of how I understand its formal > character, perhaps you should share your notion of formality.
Sure. Please see below.
> This will give me some sense of whether or not I am jeopardy > with respect to your notions.
First, a caveat: let me emphasize that in this thread I'm talking about FOL(=) formal system, when it comes to talking about "system" of formulas about which we'd talk provability or structuretheoretical truth value.
If one talks about something else, or intends so, then one is _not_ talking about the same thing I'm presenting in this thread.
Secondly, when I attribute the word "formal"/"formality" to reasoning in FOL(=), I mean to say that only the usage of finite string manipulation via rules of inference is mentioned, referred to, used, or not used: _NO_ concept or "natural numbers", recursion, language structure, interpretation, or the like would be used or allowed.
I'm OK if you (or anyone) has a different thread and would use the words "formal" or "formality" differently that my usage here.
But my presentation here presupposes such usage, such sense, of the words "formal" or "formality" and so if you don't stay with me on that sense then obviously you wouldn't understand my presentation about the invalidity of Godel's work.
It's like you take a test from, say, the NSA and where, _from purely_ _symbol manipulation_ , you're supposed to produce the string S0=S0 from certain other strings. Of course you could "intuit" or "interpret" S0=S0 as true in the natural numbers or some modulo arithmetic, but the NSA would give you an failing F if you do so, since the rule inside the test room is again: _purely symbol manipulation_ .
Hope that I've explained my position of the word "formal" and the like. Hope also that you are with me now, in order to move further in the thread.
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI

