I agree that the degree of self-production rests upon the perspective taken on
the formal system. 0-3 may indeed be seen as primitives, but this is true both
for the Heuristic and Reflexive perspective. The very word 'perspective' implies
that there is some primitive beyond the formal system. This primitive is the
observer and his emergent experience of the world. As such these are just new
primitives, not a grounding of the existing primitives. From this perspective
hypersets are just as axiomatic as ordinary sets in their formalism. All it does
is to note that hypersets and sets have an identical structure when viewed upon
from different angles.
On the other hand, can we really exclude the primitives? Has the formal system
any meaning without the conscious symbolic observer and interpreter? Does the
formal system exist at all beyond its embedding in a conscious agent? If the
answer to these questions are NO then indeed we have not only shown that
hyperset formalism is self-defining (when incorporating the conscious agent and
his perspectives) but also that the conscious agent is a very real and active
part of the formal system, though it is never explicitly stated in the
formalism. In fact we may generally see formal systems as a special kind of
reflexive system where the conscious agent is a hidden assumption.
But if we take on this view we find that hyperset theory is not only natural, it
may be even more natural than ordinary sets. By hiding the conscious agent in
the formal system we are also hiding the reciprocal relations and interactions
which are so typical for hypersets. In other words, the formal system appears
neat and simple *as long as we hide the conscious agent*. If, however, we
include him we may be forced to accept that hyper relations are more primitive
than ordinary relations.
I think I've shown that this subject is far from exhausted.
Onar.