> You could build a brain out of any of them, unless the brain computes something that is not computable.

Could you? That's sort of begging the question. We do not know if something "Turing complete" can be used to build a brain like the human brain. That's precisely the point.

> If the brain does something that is not computable, that's a direct challenge to some of our most established science.

A challenge for computational neuroscience maybe. Otherwise I don't see the challenge for neither neuroscience nor computer science. If someone wants to make the claim you can build a human brain out of something Turin-machine-like, that's an extraordinary claim, not established science.

The argument I'm responding to is one that says people are wrong about brains being computers because people always believe they can make brains out of technology of the day. My point is that all of these things are the same theory, and it is one that has not been disproven.

If a brain cannot be produced in a turing machine, it must perform some non-computable activity. That would mean physics cannot be accurately simulated in a computer, which I believe would be earth-shaking in that world. That brains can be reproduced in a simulation is a default assumption, that something composed of molecules can produce outcomes that cannot be computed is an extraordinary claim, for which, I believe, there is no evidence.