[Part 7 is here. Probably it's worth reviewing before reading this.]
I’ll begin with the Peculiar, or let’s say, Unsettling, or Cautionary. Cantor allowed that “sets” could be defined by any well-formed logical statement. As it happened, this was not precise enough. And by that I mean, you can describe collections of things by well-formed logical statements which are somehow, too large or strange. A first sign of trouble came from British mathematician and philosopher Bertrand Russell, in the form of a paradox. This is not one of those namby-pamby literary/political/economic/theological/legal things where it seems some assumption or other leads to an outlandish or uncomfortable conclusion. No. This is a genuine fault in the system, FULL STOP.
Trouble in paradise.