31.7 The recursively nested hierarchy
It is also worthwhile to investigate formally the whole hierarchical structure
of degrees, subdegrees, etc that has been deduced from scientific theism, according
to the recursive principles described in Chapter 19.
Some questions might be, for example, is it reasonable to use this structure
at only a finite depth, by which I mean
,
when we talk about (sub)^{n}degrees? What is the limiting form of
this structure as
?
Does it form a continuous set on a line or in a square? Should we form ‘coarsegraining’
approximations for finite creatures if we cannot make restrictions to finite
n? Formal arguments may help us see how this structure induces qualitatively
new dispositions everywhere, at every depth of analysis. Do we, in the ‘finegrain’
regime, end up with a continuous spectrum of qualities, or do they forever remain
discrete degrees?
Perhaps there is generated some kind of fractal structure, even if it
is as simple as the Cantor fractal obtained when lines are divided and extended
in their central thirds. I certainly use many selfsimilarities between (sub)^{n}degree
triples and (sub)^{m}degrees triples for
:
these represent possible correspondences of function assumed to occur (in individual
ways) at all all levels and between all levels. But what is the full range of selfsimilarities
within the complete structure? What is the range of correspondences, mathematically
speaking?
Finally, we would like to know how the full generative structure of (sub)^{n}degrees
may be represented (in whole, or in parts) by means of physical structures such
as a biological body. Are there any formal guidelines for how this may be efficiently
accomplished? How is this related to the mapping assumed when I talked in Section
25.6 of how the human functional form is represented and
retained in the physical body according to correspondences of function?
