We should always look to nature, yes. A lot of aerodynamic designs seem to look a lot like the world’s fastest birds. Trees really do seem to optimize for capturing solar energy in an easily encoded blueprint.

But also there are a few areas where we should recognize the limits of scope of the solutions nature has provided, or recognize the path dependency in how evolution might optimize for a particular pathway that no longer should continue to pose a restriction (the giraffe’s recurrent laryngeal nerve, for example).

We’re allowed to mix and match. Just gotta be careful and recognize just how powerful billions of years of evolution is, as an optimization method.

They are clearly mathematical.

Sure. But they’re also philosophical. The categories aren’t mutually exclusive. Basic set theory (which is both mathematics and philosophy).

I see philosophy as a place to make nonrigorous arguments.

Wait do you think Bertrand Russell and Alan Turing and Kurt Gödel weren’t making philosophical arguments?

Exactly.

HERE’S A THEOREM: IF IT’S PROVEN, IT’S TRUE EVERYWHERE, FOREVER

But at the same time, even if it’s true everywhere forever, it might still not be provable, because Gödel.

Doesn’t look like anything to me.