Closure to efficient causation, computability and artificial life

The major insight in Robert Rosenʹs view of a living organism as an (M,R)-system was the realization that an organism must be “closed to efficient causation”, which means that the catalysts needed for its operation must be generated internally. This aspect is not controversial, but there has been confusion and misunderstanding about the logic Rosen used to achieve this closure. In addition, his corollary that an organism is not a mechanism and cannot have simulable models has led to much argument, most of it mathematical in nature and difficult to appreciate. Here we examine some of the mathematical arguments and clarify the conditions for closure.