Causation, constructors and codes

Abstract

Relational biology relies heavily on the enriched understanding of causal entailment that Robert Rosen's formalisation of Aristotle's four causes has made possible, although to date efficient causes and the rehabilitation of final cause have been its main focus. Formal cause has been paid rather scant attention, but, as this paper demonstrates, is crucial to our understanding of many types of processes, not necessarily biological. The graph-theoretic relational diagram of a mapping has played a key role in relational biology, and the first part of the paper is devoted to developing an explicit representation of formal cause in the diagram and how it acts in combination with efficient cause to form a mapping. I then use these representations to show how Von Neumann's universal constructor can be cast into a relational diagram in a way that avoids the logical paradox that Rosen detected in his own representation of the constructor in terms of sets and mappings. One aspect that was absent from both Von Neumann's and Rosen's treatments was the necessity of a code to translate the description (the formal cause) of the automaton to be constructed into the construction process itself. A formal definition of codes in general, and organic codes in particular, allows the relational diagram to be extended so as to capture this translation of formal cause into process. The extended relational diagram is used to exemplify causal entailment in a diverse range of processes, such as enzyme action, construction of automata, communication through the Morse code, and ribosomal polypeptide synthesis through the genetic code.