MaoShan comments on Mixed Reference: The Great Reductionist Project - Less Wrong
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It does indeed seem possible that in the long run we'll end up with one kind of stuff, either from the reduction of logic to physics, or the reduction of physics to math. It's also worth noting that my present model does have magical-reality-fluid in it, and it's conceivable that this will end up not being reduced. But the actual argument is something along the lines of, "We got it down to two crisp things, and all the proposals for three don't have the crisp nature of the two."
That seems to me more like an irreducible string of methods of interpretation. You have physics, whether you like it or not. If you want to understand the physics, you need math. And to use the math, you need logic. Physics itself does not require math or logic. We do, if we want to do anything useful with it. So it's not so much "reducible" as it is "interpretable"--physics is such that turning it into a bunch of numbers and wacky symbols actually makes it more understandable. But to draw from your example, you can't have a physical table with physically infinite apples sitting on it. Yet you can do math with infinities, but all the math in the world won't put more apples on that table.
...and since when is two apples sitting next to each other a pile??