Those who argue that the plane cannot take off point out that a stationary plane cannot fly because it needs wind to create lift. Those who argue that the plane can take off point out that it is the jets, not the wheels, which push an airplane forward, and the treadmill has no means of counteracting that force, therefore the plane would take off normally. Thus, both sides believe that the other side simply does not understand how airplanes work, when in fact both sides understand them just fine.

The real problem is that the question itself is self-contradictory. Indeed, as the plane-takes-off crowd argues, the treadmill cannot stop the plane from moving forward. However, if the plane does move forward, then the wheels must necessarily be rotating forward faster than the treadmill is moving backwards, contradicting the premise. The only conclusion we can draw is that it is impossible to create a treadmill which exactly matches the speed of the wheels -- even in a simplified physical model that ignores most practical limitations. The question is flawed.

But the question is not obviously flawed. It seems perfectly plausible, and even after this reasoning, it does not seem intuitively true that the setup contradicts itself. This raises questions about thought experiments in general. How can we tell if the imaginary situation presented in a thought experiment is not self-contradictory? It's common for thought experiments to use unrealistic and exaggerated setups in order to get away from practical concerns and tackle the core of an issue. But we cannot draw any real conclusions about anything from a self-contradicting experiment, so if we cannot easily identify experiments than have become self-contradicting, then using thought experiments in any argument is dangerous.

And now you know why I named this weblog "Metathought".