I ran across an article called “The Peculiar Math that Could Underlie the Laws of Nature“. It’s an interesting article. It goes way beyond any math I ever took, but it’s still interesting. What really struck me was the title. The idea that math underlies the laws of nature. That seems to be a common a sentiment. People are always talking about the math behind different phenomena rather than saying that math describes phenomena. We hear that there’s math behind everything from music to rocket launches. It made me wonder if most people implicitly believe in mathematical Platonism.
I should state for the record that philosophy of mathematics is not my specialty. I topped out with calculus in college. I always found math interesting, though. And I was always good at it. If not for a series of atrocious math teachers in high school, who knows. But that’s a different topic. For our purposes, I’m just trying to say that I’m an interested lay person. Nothing more. If I get some of the details wrong, I apologize, but hopefully the main points will make sense.
For those new to the topic, mathematical Platonism is the idea that there are abstract mathematical objects that actually exist, independently of anyone thinking about them. So math is not a human invention that we use to describe the world, math actually exists. This has been one of the most hotly debated topics in philosophy over the past 30 years. The implications of mathematical Platonism are big if it’s true. It would mean that mathematical truths are literally discovered. And if there are intelligent aliens, there’s a good chance that they would have discovered the same math we did and we’d have a chance of communicating. It also means that mathematical statements are true or false based on correspondence. Just like the statement, “Grass is green,” is true or false based solely on whether or not actual grass is actually green, 1+3=4 is not true by definition, but in the same way, “Grass is green,” is true. It is true because the actual entity 1, when added to the actual entity 3, equals the actual entity 4.
Just to drive home the point, the common sense view of the world says that there are two types of things, independent and dependent. Independent things are things that exist regardless of us knowing about them. These are things like rocks and trees and water. Dependent things are things that only exist because we have created them. These are things like money and marriage and laws. For someone to believe in mathematical Platonism is for someone to believe that mathematical objects are independent, like rocks, trees and water. It’s like saying that Pythagoras didn’t invent the Pythagorean Theorem. The theorem has been out there since the beginning of time, and Pythagoras just happens to be the person who discovered it.
Explained this way, I think most people would take the common sense position that mathematical Platonism is not true. It just seems weird to think that 6 exists independently in the same way the sun exists. But if people really believed that, why is it so common for people to make statements about math underlying, supporting and making up real independent phenomena? There seems to be a disconnect.
My personal view is that mathematical Platonism is incorrect. I see math as a language that we created to describe the world around us. Saying that prime numbers are actual independent entities is as absurd as saying that gerunds are actual independent entities. I don’t think mathematical Platonism is necessary to explain the success of math or the sense of discovery. It’s successful because we only keep what works. And we can discover new things about baseball, chess or democracy without there being independent democracy objects that actually exist. Yet I find myself falling into the language of mathematical Platonism frequently.
My best guess is that the reason we talk as if mathematical Platonism is true is because it’s a powerful metaphor. Talking about abstract concepts is difficult. Treating abstract concepts like objects makes it easier. It’s similar to the way we personify things all the time. It’s just easier to talk about things as if they have a purpose or a desire, it makes them more relatable. Math is just easier to talk about if we assume it’s real.
Of course this is just skimming the surface of the debate. It’s where both my intuition and my more considered thoughts lead me. I could very well be wrong. I might even be happy if I am wrong. I like the idea of mathematical Platonism. I just can’t bring myself to buy it. I think it’s a tool we came up with to make things easier to talk about. It would please me if someone could convince me otherwise.