And you don't see any problem with trying to prove a logical point using empirical natural laws?
How about this logical point? An immovable object would have to be at rest (otherwise it's moving) and it would have to have infinite mass. The force attempting to move it would have to be greater than infinite mass to create that infinite-mass-overcoming-force; if there's no mass, there's no force.
So the proposition that there can be both an immovable object and an irresistable force rests on the assumption that there can be two objects of infinite mass. That's a logically absurdity, since if A is of infinite mass, then there cannot exist B, another object, because that would require A's mass to be limited in that there exists something apart from A. It's also logically absurd because the object behind the force would have to be of greater infinite mass than the infinitely massive immovable object.
Here's another logical absurdity. Since the irresistible force comes from an object of infinite mass, where did the energy come from that set that mass into motion? In other words, where did the A come from in F=MA? You can not give an answer that doesn't require another object of infinite mass setting it into motion.
F=MA. Once you make M infinite, you need F to be infinite on the other side and all kinds of logical absurdities arise when you start playing with infinities.
In any case, this is wandering a little far afield of the main point, since most of us don't deal with infinite masses every day. But we do deal with apparent paradoxes every day, and recognizing that they are only
apparent paradoxes is a useful tool in getting at the truth. If a line of argument requires the conclusion that I am a woman and it also requires the conclusion that I am a man, that is a paradox, and there is a faulty premise in the argument somewhere. Homeopathy is full of apparent paradoxes, which enables us to conclude that it's nonsense without our having to have degrees in medicine or pharmacology.