From: pcollac@pyrnova.mis.pyramid.com (Paul Collacchi)
Newsgroups: sci.philosophy.meta
Subject: More On Mysticism
Date: 12 Jan 93 01:41:37 GMT
Reply-To: pcollac@pyrnova.mis.pyramid.com (Paul Collacchi)
Distribution: usa
Organization: Pyramid Technologies, Mt. View, California.


Keywords: >>>  & > (Randall Holmes) writes:
>>       (Leo Smith)

>> 
>>> The Buddhist logicians were not sufficiently technically competent to
>>> get anywhere near Godel's results, although they were not bad for the
>>> time.  If you can give actual quotes which resemble Godel's results,
>>  I'll reconsider.
>> 
>> Well - you are presumably a technically competent mathematician, so I 
>> will forgive you what appears to be a bias in favor of mathematical 
>> formulations. For me, the paradox of recursion - which is what I 
>> understand to be the underlying aspect of Godel, is very clearly 
>> expressed in a 13th century Taoist text "Seek not to probe behind 
>> consciousness with consciousness - that cannot be done" (Wilhelm 
>> translation 'Secret of the Golden Flower')
>
>Recursion _per se_ is not paradoxical; show me diagonalization (the
>paradox of the Cretan is the only ancient version which really shows
>insight of this kind that I know of).
>

Its unfortunate that the origional point was digressed upon....to which
the stuff about the seeming paradox of recursion is irrelevant.  
Godel's result was basically a result of "incompleteness", not paradox.
His theorem tells us that there are truths which are not theorems.

The analytical method, which Godel applied to symbolic logic, is to build
the domain or space of elements which can be created by the fundamental
building blocks of the particular space in question.  For example we can
build a "space" of functions which are generated by certain building
blocks.  Depending on which building blocks we choose, we can get
polynomials, or continuous functions, or Lebesgue measurable functions,
etc.  Each of these particular classes is "larger" in the sense of set
inclusion -- LP spaces (set) include continous functions which (set)
include polynomials.

Godel attempted to generate the space of theorems by numbering up his
formal system, and iteratively applying the rules of deduction as a simple
arithmetic operater.  Had it worked, it would have cranked out the entire
space of theorems -- logical Truth. It was an ambitious undertaking, and 
brilliant.  Two results he cranked out are results of limitation.  They are:

1.) Not all truths are theorems
2.) His method of "cranking out" theorems would not crank out all of them.


If we are able to imagine anecdotally that "REASON" -- perception, thought,
logic, Science, observation, measurement, etc. -- is a "system" which can 
output its own theorems, then "mysticism", as I know it, starts as the 
Godel's theorem of Reason.  It understands that 

1.) Not all Truths are (Reason) theorems, or Reason is "incomplete." 

Mysticism, as I know it, is a rigorous, objective effort to pursue Truth 
beyond the Domain of what Reason is capable of producing.  In Math-ese, 
it attempts to "complete" the theorem-space of Reason.  In order to do so,
the mystic must transform himself, his own consciousness, and attain a
state unimpeded by the limitations of Reason.  One term coined to describe
this mental state is "no-mind."

But the point is, Randall, that the incompleteness of Reason -- a direct
anecdote of Godel's theorem -- is the seminal inspiration underlying
*all* mystical endeavor.  You see, "good" mystics really *got* the limitations
of Reason and so they took another course -- why travel on a road that
can't get you to where you want to go?

To assert therefore, that certain mystics, Buddhists, are unaware of
results such as Godel's theorem is kind of like asserting that scuba-divers 
are unaware of water.  

I think you really should reconsider.

Paul Collacchi
Newsgroups: sci.philosophy.meta