[AlexandrB]

I don't think that's entirely accurate. We've done plenty of tests on animals and found nothing that would contradict either known physics or chemistry.

Moreover, even if human brains were somehow special relative to animal brains, there's no reason to think they operate in a way that that's separate from all the other matter in the universe. And as the GP said - interactions between matter are either causal or random. There's no "free will" interaction. Such a thing would be - almost by definition - supernatural.

[mensetmanusman]

I agree. Belief in free will is, by definition, supernatural. That it can never be proven is comforting in a sense.