Much of the human body, including neural tissue, is powered by diffusion (hi, Keifus!) which depends upon the random movement of molecules from one place to another. Neural tissue is capable of actual thought.

Also, if you don't think that quantum mechanics could have an effect on biological entities, you're suffering from a lack of imagination. I mean, a proton decays here, it sends a particle over yonder, where it busts up a DNA molecule, and, voila, your pet iguana turns to Godzilla.

Again, you're building a false dichotomy, where everything has to be set in stone or decided by Zeus.