A contradiction in thought is implied, not actual. No one can think something is and that it is not in one thought. It's impossible to actually think about a triangular circle. However, there can be inconsistent thoughts that imply a contradiction: he can be asserting something in one instance, and then denying it in the next. And then we say, "That can't be right, because there are no contradictions: what is, is what it is, not what it isn't. So at least one of your statements has to be wrong."
Edit: Yes, math cognoscenti, I'm aware that triangular circles can exist in certain topologies. I don't really think that's relevant, and you can stop pointing it out.
