A Note on Interaction and Incompleteness
The notion of interaction and interaction machines, developed by Peter Wegner, includes the comparison between incompleteness of interaction machines and Gödel incompleteness. However, this comparison is not adequate, because it combines different notions and different sources of incompleteness. In particular, it merges syntactic with two senses of semantic completeness, and results about truth (Tarski) with results about provability and their consequences (Gödel). The comparison also overlooks structural differences in the way diagonalization produces incompleteness. More generally, the comparison is unlikely because interaction incompleteness is supposed to come from a system’s involvement with its environment, whereas Gödel incompleteness comes from a system’s involvement with itself.