Re: Godel's comments about the "true reason" for incompleteness

On Mar 17, 10:34 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Mar 15, 10:18 am, "R. Srinivasan" <sradh...@xxxxxxxxxx> wrote:

After all,
there is no way for a powerless individual like me to change human
nature. But sooner or later, the farcical nature of this state of
affairs will become clear to everybody and hopefully some one of a
suitable stature and integrity will break away from the status quo and
seriously consider my contribution.

Yes, you are a great revolutionary thinker, and not until some other
great revolutionary thinker who also happens to have a research grant
comes along will mankind ever be free from the cave of ignorance.


Why don't you just answer the point I have made? Earlier your
objection was that you don't know what NAFL means. I will attempt to
address that soon. But this post makes a point that does not invoke
NAFL. Why can't I find a straightforward individual from amongst your
peers, someone who will engage me in a honest debate? What is the
point in denying credit to an individual for legitimate work that he
has done, even if one ignores the unethical and petty nature of such
an enterprise? I can understand and rationalize the existence of a few
individuals (e.g. closer to home) who are of this nature, but the
academic world seems to have mass-produced clones of this breed.

The "true reason" for incompleteness is that Godel overreached beyond
the boundaries of first-order logic. You might ask, what is the
objection to second-order logic, why not formally admit propositions
which quantify over "all" propositions? Take the assertion that "From
a contradiction, an arbitrary propostion follows", or , say,

P&~P --> Q, (*)

Let us take P to be fixed in (*), and consider this propositon for
arbitrary Q. Obviously there is an implied quantification over Q, if
we want to convey that "all" propositions follow from a contradiction.
If we admit (*) as a formal proposition in the same language which we
are considering the notion of "all" propositions (e.g. PA), then
clearly (*) is an impredicative construction, for the quantification
must include (*) as well in its domain. This is not permitted in NAFL,
which requires propositions like (*) to be metamathenmatical
constructions, outside the formal language. Then you can see that
there is no impredicativity.

In fact there is no such thing as a tautology in NAFL, and (*) is not
a meta-theorem of NAFL theories. I will elaborate this week-end, if I
manage to find some time (I am on leave Thursday-Sunday, so hopefully
I will be able to get started on the long-pending NAFL thread).

Regards, RS
.

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