🚀 go-pugleaf

On May 20, 1:16 am, MoeBlee <jazzm...@hotmail.com> wrote:
> On May 17, 8:08 am, "R. Srinivasan" <sradh...@in.ibm.com> wrote:
>
> > The basic philosophical ideas behind NAFL can be understood without
> > delving into details.
>
> That's not adequate when NAFL is being used in a technical sense to
> comment on details in other systems.
>
But you have given no indication whatsoever that you have even
attempted to understand the philosophical origins of NAFL or how it
differs fundamentally from classical/intuitionistic logics.
>
> > a NAFL theory cannot
> > be defined as a mathematical object.
>
> Then I'm not very interested in NAFL.
>
Suit yourself. You prefer the circular "formalizations" that exist for
classical theories. A NAFL theory cannot be formalized as a
mathematical object within NAFL theories for deep reasons that you
cannot begin to appreciate. Note that even though classical PA
contains infinitely many axioms, each theorem of PA will only appeal
to finitely many axioms. As long as it is clear where these axioms are
coming from, there is no *need* to formulate a theory as a
mathematical object. The definitions need only be precise enough so
that we may work unambigously *within* a theory. Notions of
incompleteness and consistency appeal to *all* the axioms/theorems/
proofs/sentences of a theory and cannot be formulated as sentences
within NAFL theories. You are too deeply into the present mess, to be
able to make the effort to understand NAFL.
>
> > You can only make the definition
> > precise enough to be able to work within NAFL theories. There are
> > solid reasons for this requirement. One of these is that Godel's
> > incompleteness theorems cannot go through in NAFL,
>
> NAFL or NAFL theories are not even not just a formal theories, not a
> theories even as ones not formally axiomatized; not theories, as you
> say, as mathematical objects. Saying that incompleteness doesn't go
> through for NAFL is like saying incompleteness doesn't go through for
> my grandmother's diary.
>
False. A NAFL theory is a metamathematical object and incompleteness
and consistency, provability, etc. are valid phenomena that cannot be
formalized within NAFL theories. What *you* have in classical logic is
worse than your grandmother's diary. It is meaningless infinitary
reasoning that leads nowhere.
>
> > Pathetic that nobody in IBM Research is
> > even willing to discuss NAFL with me.
>
> Have you ever considered looking at that fact from outside your own
> urgent emotional agenda?
>
Unwillingness to *discuss* a new logic amongst logicians.
Unwillingness to *dscuss* a new philosophy amongst philosophers. Etc.
etc. I am supposed to nod and tell myself that I must have done
something really stupid, that these brilliant geniuses have been
stunned into silence by the sheer stupidity of it all. And IBM US is
the place from where loud noises emanate from time to time about
ethics, honesty, integrity, and about how great the achievements of
IBM Research has been in the past. So *I* must be the unethical guy
here (apart from being stupid) for even daring to question such
geniuses; e.g. Gregory Chaitin, whose reasoning is flatly rejected in
NAFL as infinitary.

Regards, RS