In Western logic, a fundamental principle is that a thing can be either true or false, but not both.

Basic principles like: If A = B and B = C then A = C fall apart if this principle is false because then A could equal C, but also not equal C (If A = B and B = C then A may or may not = C).

In more concrete terms, If 6+4=10 and 15-5=10 then 6+4=15-5 becomes If 6+4=10 and 15-5=10 then 6+4 may or may not = 15-5.

Here's a video describing the problem:

So - is it possible for a thing to be both true and false at the same time?

(I realize that this seems to be a highly abstract problem, but it has huge aplications in real-world thinking. Instead of being forced to say "yes" or "no" in responding to a simple question it becomes intellectually valid - i.e. Not a copout or mealy-mouthed - to say "yes and no.")