Hans-Cees wrote:
> So what is the use of making the set-theory statement?
This use of set theory is only instrumental in order to illuminate the
differences of these similar but distinct concepts. For instance, it's important
to know that a dissipative structure isn't automatically a living system
although
all living beings are dissipative structures.
Jeff writes:
> The circle
>on the left representing systems that can make a copy of themselves
>(systems that can replicate).
I'm not sure this is my definition of replication. Replication is simply the act
of copying something. It does not specify who or what is doing it.
Self-reproduction specifies who the replicating agent is, namely the replicated
system.
>I do admit that a very importnat consideration in this discussion is the
>degree to which we can separate "what something is" from "how it
>got there".
Extremely important point. Once you start talking about ultimate origins then
everything becomes very complicated. This may actually be when the ordinary set
distinction between the different classes of organization breaks down.
Autopoiesis theory is full of juicy paradoxes on this point as are all
self-referential systems. This paradox is related to both the incompleteness
theorem of Godel and the flaw in Causality theory. A linguistic system can by
definition never be complete for there will always be some aspect of the system
which is not part of the language. Similarly, the theory of causality states
that "all events have a cause". But what about emergence? the origin of the
universe? the origin of life? All are exemples of a first "causeless cause".
Emergence is by definition order from NOWHERE. Even the very universe suffers
from this problem. All the mass we see around us arose from NOTHING. Quantum
mechanics assumes the continuous emergence and destriction of matter out of
nothing. It's all very weird when we start thinking in terms of ultimate
origins.
Onar.