What is this book about? Well, as Godel's Incompleteness theorem
showed that Formalizations (syntax-only systems) are incomplete
within the formal world of mathemetics, Rosen shows that our
Newtonian-based science does exactly the same thing (as the syntax-
only formalizations) and therefor Rosen suggests that our
Newtonian-based-science is incomplete (as a way to understand the
material world). In both realms, formal and natural, semantics
plays a role that is lost with formalizations or simulations.
Rosen defines complex systems as those systems where this
incompleteness shows up. He claims that organisms are examples in
the material world of complex systems. It is also possible that
some social, political, and ecological systems may qualify as being
complex.
We can only recognize that the newtonian system is incomplete if we
step out of it. The analogy with Godel (briefly) is as follows:
Consider there is a "universal truth machine" that can
syntactically generate statements (or theorems). The system is
able to encode its statements in such a way as to be able to make
statements about itself. Godel showed that the "universal truth
machine" is unable to generate the following theorem (statement):
"This statement is not provable by the universal truth machine"
But never-the-less, from outside the system, we know that statement
to be true. Rosen claims the same kind of thing is going on within
our science of the real world. People aren't noticing the
incompleteness (in science) because we are living in a scientific
world view where semantics can always be replaced by syntax. We
are like the "unicersal truth machine"... plugging away, generating
lots and lots of information about the world... not realizing that
we are only tapping into a subset of what we could be
understanding.
Should you read this book? You should if you think Godel's theorem
says something important.
Jeff Prideaux