Complexity is the property of a real world system that is manifest in the inability of
any one formalism being adequate to capture all its properties. It requires that we find
distinctly different ways of interacting with systems. Distinctly different in the sense
that when we make successful models, the formal systems needed to describe each distinct
aspect are NOT derivable from each other.
This is the basic definition of complexity that I suggest everyone adopt. I will now
show that it either leads to or is consistent with all the following
attributes/properties/definitions of a complex system.
- It is non-fragmentable. If a complex system were fragmentable it would be a machine. We
require the distinction to be dichotomous. Therefore complex systems are not fragmentable.
That is not to say that they are incapable of being reduced to parts, but such
reduction destroys important system characteristics irreversibly.
- Consists of real components that are distinct from its parts. At least one set of these
components is defined by its functions. These functional components are not simply
collections of parts. If they were the system would be fragmentable in the above sense.
These functional components are therefore defined by the system and have their ontology
dependent on the context of the system. Outside the system they have no meaning. Further,
if they are "removed" from the system in any way the system looses its original
identity as a whole system.
- Real (complex) systems have models as in the modeling relation. These models may be
analytic or synthetic models. The analytic models differ from the synthetic. This must be
so for consistency with the requirement for non-fragmentability. When synthetic models can
replace analytic models, the system is fragmentable and is therefore a machine.
- There can be no "largest model". If there were a largest model, all other
models could be derived from it and fragmentability would result.
- The system falls outside the Newtonian paradigm in some important ways. If it could be
described by the Newtonian Paradigm it would have a largest model from which all others
could be derived.
- Causalities in the system are mixed when distributed over the parts. There is final
cause in the sense that functional components have their own ontology. These components
are defined by their function. For this reason, the system can be
"anticipatory". That is to say, it can have causal relations which arise out of
some future event if these future events are contained tentatively in a model the system
has of its environment (in the broadest sense, i.e., the system is included in its
environment.)
- The nature of causality and, especially the definition of functional components,
requires that there be closed loops of causality of a nature forbidden, or at least
excluded, by the Newtonian Paradigm.
- The result of these traits is that much of the system's important attributes are beyond
algorithmic definition or realization by algorithms and therefore non-computable in the
usual sense. In that sense they refute Church's thesis.
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On to Ontology of Complexity
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