Those treacherous foemen were avoiding logic and using such unheard-of devices as surprise and sabotage, treason and trickery. They even had Alphaland's Deputy of Information believing Betastani propaganda without even realizing it. Of course he still thought he was being loyal to Alphaland, because he thought that one and one must logically add up to two.
And that kind of thinking could make him the biggest traitor of them all.