When I wrote my post last week about the existence of mathematical objects, I had not yet noticed that Massimo Pigliucci was writing about similar topics. More specifically, he is discussing cosmologist Max Tegmark’s idea that ultimate reality just is mathematics. Here’s Pigliuccia describing Tegmark’s ideas:
The basic idea is that the ultimate structure of reality is, well, a mathematical one. Please understand this well, because it is the crux of the discussion: Tegmark isn’t saying anything as mundane as that the world is best described by mathematics; he is saying that the ultimate nature of reality is mathematics.
This is actually not at all a new thesis, though Max is advancing it in new form and based on different reasoning then before. Indeed, the idea has a long philosophical history, and can fruitfully be thought of as based on two distinct philosophical positions: Pythagoreanism, or mathematical Platonism; and Mathematical monism.
Mathematical Platonism is the idea that mathematical structures are real in a mind-independent fashion. They are not “real” in the same sense as, say, chairs and electrons, but they do have an ontological status independent of the human (or any other) mind. As readers of this blog know, I’m actually sympathetic to (though not necessarily completely on board with) mathematical Platonism. The best point in its favor is the so-called “no miracles” argument, the idea that mathematics is too unreasonably effective (at predicting things about the world) for it to be just a human invention, rather than somehow part of the inherent fabric of the world. (Interestingly, this argument is equivalent to one by the same name advanced by scientific realists to claim that science really does describe — approximately — how the world is, as opposed to the antirealist position that the only thing we can say about science is that it is empirically adequate.)
Mathematical monism is the stronger doctrine that not only are mathematical structures real, but they are the only real thing out there (or, more precisely, everywhere).
The combination of Platonism and monism yields a class of theories about the ultimate nature of reality, of which Tegmark’s MUH is one example. We have seen another one several times in the past, in the form of Ladyman and Ross’ ontic structural realism, the notion that there are no “objects” or “things” at the bottom, just (mathematical) relations.
I’ve liked Tegmark’s writing about multiverses, so I’ll look forward to reading his book when it becomes available. I’m sure it will be very clever and cogently argued.
But my knee-jerk reaction to this idea is just to throw up my hands and say I give up. As I indicated in my post from last week, I have enough trouble just understanding what it could possibly mean to say that mathematical objects exist in a mind-independent fashion. Now I’m supposed to believe not only that they exist, but also that ultimately they are the only things that do? That the physical stuff of our daily reality is somehow made of mathematics? Words are being used in ways I don’t understand.
Frankly, this is the sort of thing that makes me see the appeal of anti-realism as a philosophy of science. Science works really well for ordering our daily experiences and for rendering natural processes predictable and controllable. If you go beyond that, say by discoursing about “ultimate reality” or whatnot, then there’s real danger you’re just babbling.
Tegmark’s going to need a mighty good argument to persuade me of his view. But who knows? Maybe he has one. I’ll reserve judgment until I’ve had a chance to read his book.