Take a look at my response to tim. Replace god with Euclidean Geometry, and forget the fluff about god being inconsistent, and you can see that Euclidean Geometry is still coherent, because our minds can represent it with consistent rules, so these rules exist as an abstraction in the universe. So my view doesn’t make Euclidean Geometry incoherent. I’m not sure what exactly you mean by validity, but the only thing that my view says is “invalid” about Euclidean Geometry is that it is not the same as the geometry of our universe.
Now it gets a bit difficult to write about clearly, I’m sorry if it’s not clear enough to be understandable. Things we figure out about numbers using Euclidean Geometry can still be valid, simply because when we abstract the details about Euclidean Geometry to be left with only numbers, we get the same thing as when we abstract apples to numbers, and the same thing is true about our mental representation of PA. So proofs from one can be “transferred” over to another. But “transfer” doesn’t really describe it well. What’s really happening is that from the abstract numbers, you can un-abstract them by filling them in with some details. So you can remember that the apples were in a bag, and that gravity was acting on them. If, when you add in the details, the abstract number behavior still holds, then the object follows the rules of numbers. So if the added details about apples don’t affect the conclusions you make using PA, by abstracting PA into numbers, and then filling in the details about apples, you have shown that things that are true about PA are true about apples too. And all this is done using physical processes.
So my view doesn’t entail anything about accepting or rejecting mathematical statements. What it says is that mathematical concepts are abstract concepts, which we obtain by ignoring details in things in this world, and thanks to our awesome simple and universal laws of physics, the same abstract concepts emerge again and again.
Because epiphenomenalist theories are common but incorrect, and the goal of LessWrong is at least partially what its name implies.