Do we (or can we) really understand God?
Are "God-talks" meaningful?
What is the difference between understanding and knowing?
What is consciousness?
What do you think about the Sleeping Beauty Problem (SBP) or the Newcomb's paradox?
Here is a link to the Sean Carroll's post on SBP and how it is connected to quantum mechanics (it has a very nice diagram of the problem):
http://www.preposterousuniverse.com/blog/2014/07/28/quantum-sleeping-beauty-and-the-multiverse/
The Monty Hall Problem (the issue is pretty much settled today [you should change your door]), but do you agree with the solution?
Here is the wikipedia link for those who are not familiar with the problem:
http://en.wikipedia.org/wiki/Monty_Hall_problem