There are in fact certain paradoxes involved in the notion of a system that predicts its own behaviour. These are reminiscent of Russell's Paradox in set theory and of the paradoxes that arise when one allows a statement to talk about itself (e.g., consider the statement, "This statement is false").
Page-16 of the Anti Tech Revolution
I think so the second example noted by the author is about the Godel's incompleteness theorem but reading the paragraph led me to wonder, are there examples other than these two where there is an occurrence of a paradox due to the logical system making a statement about itself?