I wonder if this is what a discussion of math was like, before the concept of zero was invented.

A paradox is a product of flawed perception. It's impossible to draw a triangle with three right angles, unless you do it in three dimensions -- why shouldn't time be any different? It's 'impossible,' incomprehensible, whatever -- to travel back in time and kill yourself..... so what? Is that supposed to stop you from doing it? Change the paradigm and anything becomes possible.