Something that occured to me:
What happens in a conversation between two post-intelligences? If they are both able to postulate the end of the conversation, would they even talk at all? Or perhaps it would result is a sort of pseudo-telepathy, if you will, where even though they can't read each others' minds, they are indeed able to determine the entire content of the conversation without a single exchange. A possible philosophical conversation regarding the morality and ultimate benefits and detriments of Machiavellian politics in third-world countries might go something like this:
Bill Posti: Yup.
Bob Posti: Indeed.