Dear Marc,
If I were to deal with every (from my point of view) objectionable idea, it would simply take too long. Instead, I selected three sections from your essay that I think might be representative of our differences. After each quote, I have added my response to it.
After these three sections, I continue with a general discussion of the issue, and explain (necessarily without much detail) my own views of these things.
"Imagine there's only math -- physics is nothing more than mathematics, we are self-aware mathematical substructures, and our physical universe is nothing more than a mathematical structure "seen from the inside.""
But this starting assumption is just that - an assumption. I don't deny that if you start with this assumption, then your conclusions (and likely a few more) can be said to follow.
"According to the MUH, physical reality is a web of relationships between entities that are themselves purely abstract: it's "all structure, no stuff," a view that Jim Holt [4] calls cosmic structuralism."
Only "stuff" can have real-world structure. Abstract structures (represented by drawings, computer simulations, or mathematics) contain no "stuff," and therefore cannot give rise to the (material) universe.
"But if you accept that a living being can be thought of as nothing more than a complex arrangement of atoms obeying the laws of physics, is it really that hard to accept that a physical universe can be thought of as nothing more than a complex mathematical structure?"
I think the implied equivalency is extremely weak.
We are free to define words like "existence" any way we like, but it is most useful to stick with accepted dictionary (usage) definitions. Ambiguity in philosophy or physics is not desirable, so I define "existence" as follows. Only those things that we can detect with our senses (even in principle) or those that we can detect with an enhancement of our senses (with instruments etc., again, even in principle) should be said to exist. If we included abstractions in "existence," it would be mixing very different things. (Of course, without abstractions, we would be leading a very primitive life.) Mathematics, per se, does not exist under this definition (what you see on paper or a computer screen is just ink or "pixels," the rest is happening inside your head).
Let me try a real world analogy. Consider an ordinary pocket calculator. It has a certain organization of atoms arranged so that when you press certain keys, you get a "desired" display as a consequence. We "say" that it has an internal logic, but what we actually did (in building it) is to utilize how the universe behaves on its own (in this case how silicon and electricity, etc. behave) and then used those behaviors to get the functioning we wanted. We are "exploiting" already built-in behaviors of the universe, but we think that we imputed logic into the calculator (and in an abstract way this is how we speak) while in fact we are only riding on the universe's coattails (to borrow an idiom from another discipline). The calculator is not doing any "mathematics" (although we call it that, and it is useful) - it is simply streaming electricity along different paths, depending on the keys you press.
The MUH is essentially saying that the implicit rules guiding the various electron streams (we abstract those rules and call them "mathematics") is the "cause" of the calculator itself (or better yet, is the calculator itself). The rules (which don't have a physical existence) cannot create the calculator. And the calculator is not doing any more "math" than a bicycle chain interacting with the gear it is engaged in. The bicycle chain only needs to have the right dimensions to fit the gear, and the rest is done "via that very fact" (no calculations are performed as you ride the bicycle).
My view is diametrically opposed to the MUH. The universe does no calculations of any kind. It just behaves that way without any mathematics. To put it more colloquially: "the universe does not even know what mathematics is." Mathematics just helps physics to describe (and economically codify) how the universe behaves. Of course, math has applications everywhere, and is not "subservient" to any other discipline.
Marc, I will give you a high rating on your essay. I like it. I don't feel any need to convince anyone about my views, and I don't think that a belief in what you said in your essay is in any way detrimental to science. I am sure you can think of many counterarguments to what I said, and after all, you could be right.
En
