there must be more to the definition of a machine than the Rosen quotes
you gave and your conclusions.
> "A natural system N is a machine if and only if it is a mechanism, such
> that at least one of its models is already a mathematical machine"
> Further: "A natural system N is a mechanism if and only if all of its
> models are simulable."
Not all the models of a car are simulable, which is why they become
unmaintainable after a while (seneseance). Of course *most* of the
relevant day-to-day models of its behaviour in its initial years are
simulable, which is why we can _use_it_as_ a machine.
However the definition above, if taken in an absolute sense, means that
there are no machines except formal systems. That means that the
machines I see around me are not really machines (according to this).
The trouble comes if you insist on a completely cut-and-dried definition
of machine which will categorize systems as machine and otherwise.
Regards.
--------------------------------------------------
Bruce Edmonds,
Centre for Policy Modelling,
Manchester Metropolitan University, Aytoun Bldg.,
Aytoun St., Manchester, M1 3GH. UK.
Tel: +44 161 247 6479 Fax: +44 161 247 6802
http://bruce.edmonds.name