the fact that finding a treadmill that can act in a manner as suggested by the problem is impossible is another issue completely. Fine, but the reader's accept

the fact that finding a treadmill that can act in a manner as suggested by the problem is impossible is another issue completely. Fine, but the reader's acceptance or non-acceptance of the existence of such a magical treadmill pretty much exclusively determines how they decide the issue, so you can't claim that it's irrelevant. Nobody that accepts that such a treadmill exists (in the problem) says the plane will take off, and nobody that thinks it doesn't exist says it won't. Which makes it a brilliant problem from a psychological standpoint - everybody gets to feel like they're smarter than the other side, but really they're all just being asses and arguing about different problems. Any time you can prove both P and !P in a system, you can prove literally any statement. The airplane on a treadmill problem asks us to assume "normal physics," but then postulates some magical treadmill, vitally important to the "paradox," that violates everything we know about physics. It's no wonder the arguments degenerate into foolishness quite rapidly. Think people: They have breaks on aircraft wheels do they not? (They do) You can sit on a runway with the engine revved equal to your break ability and not move. If the engine in the problem can outperform the treadmill, you've solved a different problem. The brakes on the airplane are not supposedly engaged during the treadmill experiment; if the problem specified that there was some specific amount of residual friction from the wheel joint, then we might have a problem to discuss, but it doesn't. So the best we can do is suppose that we're talking about a normal plane, and for a normal plane with normal wheels the treadmill would have to be moving so rapidly as to rip the wheels right off the plane before it could overcome the force of the engine. At that point, the plane would fall on its belly onto the treadmill, and the backwards force the treadmill could exert on the plane would be dominated by the coefficient of friction between the fuselage and the treadmill. But that becomes far less fun to discuss, because it's now a standard physics problem and we actually have to find the parameters involved.