If they can’t see the inherent contradiction in saying that something exists simultaneously in two contradictory states, then no power on Earth can help them.
It is actually not a contradiction. Any object (be it an electron or you or a planet) is at once both a wave and a particle. It's just the way G-d set up the universe.
So if you test an electron for wave behavior, it will pass every wave test, perfectly. So an electron must be a wave.
But if you test an electron for particle behavior, it will pass every particle test, perfectly. So an electron must be a particle.
So what is an electron, a wave or a particle? It must be two entirely different things at once. How it shows itself to you just depends on how are are examining it!