Limitative results in formal modelling and their philosophical implications: the example of undecidability in the spatialized prisoner´s dilemmas

Summary form only given. The iterated prisoner´s dilemma has become the standard model of evolution in a community of egoistic agents, often cited for implications in biology and aspects of sociology. The technical core of this paper is presentation of a formal undecidability result for an instantiation of the prisoner´s dilemma in the spatial form of cellular automata. The proof has some features of interest in its own right: it proceeds: 1) by outlining a species of abstract machines closely related to both Turing machines and Minsky register machines, 2) by embedding these machines in fairly complex cellular automata which mimic wires and standard gates, and 3) by showing that there are strategies of the prisoner´s dilemma which behave in spatial arrays in precisely the manner of the basic elements of these automata. The purpose of this paper is to use the case of undecidability within the spatialized prisoner´s dilemma as an example of philosophical implications of limitative results within formal modelling more generally