Hi John,
A couple
of things:
1) You
seem to be equating the successful commutation of an MR with instances of
'mechanism', and failure to commute with complexity. This is not necessarily
the case - the MR is more general than that. If the model involved in the
MR is itself adequately complex, it may successfully commute with the specified
complex object system.
It is far
more typical that we deal only with simple (computable) models, and hence,
they commute fully only in cases of mechanism, but the totality of simple
models are only a subset of all possible models.
I am indeed under the impression that Rosen's definition of a mechanism is
a system that can be fully described by a model, i.e., commutes with a simple
description of it, therefore, a "largest system model." Fairly sure about
that, but the case you refer to may be the case where two natural systems
model each other. In that case they can both be complex. It seems like an
ambiguity in the theory, but I think it can be resolved by distinguishing
natural system from model, as Rosen does. How I think it works is that a
purely formal representation is simple, by virtue of being formal. The purely
structural/material part of a natural system is also simple. It is only their
combination that is complex. This criterion can then be applied hierarchically
and laterally between many systems.