Pedro Domingos

All mathematics is produced by physical objects (brains, computers). Therefore the laws of physics determine what theorems are possible, and mathematics has no existence independent of our universe.

Just as offensive and questionable as: “All physical objects result from information processing in human brains, and therefore human brains determine what physical objects are possible, and physics has no existence independent of our psychology,” no?

No. All the mathematics we know is produced by our brains and computers. That's a fact. As for physical objects, we don't know what they're produced by.

The limits of mathematical structure are not given by physics, but by mathematical structure itself. The Church Turing thesis is a physical law, but one that also applies to a-physical universes (if you arrange *anything* into a computer you can do constructive math on it).

I don't think you got my point. The Church-Turing thesis is a product of Church's and Turing's minds, and therefore it's a physical entity, whatever universes it might apply to or not. (And its universes can be realized in computers or in our imagination, i.e., physically.)