Towards a new Teleology

	
        [Its' an epiphenomenal clue:]

Even the coinage "epiphemomenon" itself, as a name for 
those functions previously referred to more vaguely as 
"meta-programs" or "meta-level" occurrences, is a very 
useful conceptual tool, it seems to me.

The paradox of recursive iteration is that it CAN define 
itself: however, internal, arbitrary constraints (positive 
feedback) are ultimately beyond the parameters of a self 
consistent system, resulting in a statement that defines 
and also negates itself:

        [Epimenides paradox, too]

One can neither prove nor disprove that "this statement is 
false" - it merely casts doubt on its own validity - 
indeed, on the validity of the basic terms of the 
definition of statements in general.

This, of course, applies similarly to number theory as to 
semantics - in fact, to the "grammar" or "metalanguage" of 
any "vocabulary" of expression as structured in conceptual 
sets. The demonstrations Hofstadter use, i.e. "quining" 
for semantics and "arithmoquining" for number theory, is 
both elegant and eloquent. The fact that his "TNT" system 
is congruent with mappable DNA "codons" or genes, is 
certainly a powerful confirmation of the "Meta-Meaning" 
concept as such. It neatly contains Godel's own 
"meta-formula".

        [this Godel equation - negates iteration]

Iteration is counting, numbering, defining, stating. The 
strength - and the limitation - of science.

We have, then, a paradoxical cascade - of nested 
paradoxes. The logical extension of any epistemology is 
the hole in itself - so we ultimately arrive at a sort of 
metaphysical singularity, like the inside of a Klein 
bottle. A Poisson effect in terms of self-consistent 
logical systems. (formal or hierarchical) - until "one 
man's Mead is another man's Poisson" (Farmer) becomes   
"one man's Mede is another man's Persian"(Deric). The 
paradox occurs when attempting to define the "meta-level" 
recursivity in terms of he basic level of system 
iteration. It just won't go into itself that way - you 
have to pop "up" to the next "meta" level.

          [and the statement is false, it is true...]

(As if we hadn't known.)

Concerning the overview phenomenon of "G,E,B" as a whole 
historical event, I feel that it is an example of an idea 
whose time has come. It is intriguing to think of its 
emergence where and when, in the context of ideas and 
information, it is in fact right on the money. The 
political and technological implications, while certainly 
glossed over in the text, are nonetheless quite 
thought-provoking.  [As I am finally typing this 1982 
essay in 1990 it occurs to me that the de-centralization 
of the economy of Russia and the democratization of 
eastern Europe are both side effects of some of the new 
theories in math and science being put into practice.   
Eldon New]

I'm glad the book (GEB) was done as and when it was, and 
likewise pleased to have encountered it. (Deric)






      {         It's an epiphenomenal clue          }
      {          (Epimenides Paradox, too)          }
      {             This Godel equation             }
      {              Negates Iteration              }
      {    And the statement is false, it is true!  }