The following PDF file contains a reply to a criticism of Rosen made by Ben Goertzel in his book Creating Internet Intelligence (2002, Kluwer Academic/Plenum Publishers, New York). The reply is made by Dr. Aloisius H. Louie, mathematical biologist and former student of Robert Rosen. It is posted on this site with his permission. Louie begins the paper as follows:
In this note I shall point out some errors in Ben Goertzel’s essay “Goertzel versus Rosen: Contrasting views on the autopoietic nature of life and mind”. Goertzel claimed that one could, using division algebras, construct computable systems fulfilling Rosen’s mathematical definition of a cell (i.e. an (M,R)-system). If such constructions were valid, they would of course provide counterexamples to one of Rosen’s central theorems, that “any material realization of the (M,R)- system must have noncomputable models” (and all the variations and corollaries). I shall show that Goertzel’s constructions place his mappings at the wrong levels in the categorical hierarchy, and therefore what he constructed were, in fact, not (M,R)-systems.