Friday, September 07, 2018

The applicability of math argument

There's an argument out there for God that sorta kinda fits under the teleological umbrella. It's the argument that the universe can be explained by math. There's an equation for everything. Sometimes one can figure out realities in the physical world just by doing math. But math is an abstract thing, and the physical world is a concrete thing, so why the connection? It's an inexplicable coincidence unless God designed it and wrote the laws of nature in the language of math.

I have heard both atheists and theists marvel at this. But I have to say that it doesn't impress me, and I wonder if it's because there's something I'm not seeing. First of all, I can't conceive of a world where math would not be applicable to the physical world. Consider simple math, like addition. Is it conceivable that the principle of two plus two equals four wouldn't apply to the physical world? It seems to me that in any possible world you can dream of that has objects, two of those objects, plus two more of those objects, add up to four objects. Of course the laws of nature are more complicated than that, but they are just extensions of those same basic principles. So I don't see how it's possible for there to be a physical world that does not cohere with math or that cannot be described by math.

Also, not all math is applicable to the natural world. Math uses all kinds of tools and devices that serve as tricks to solve difficult problems but that don't actually map on to the real world. Two off the top of my head are the notions of imaginary numbers and infinity. I remember using imaginary numbers to solve difficult problems in my third calculus class in college, but by the time we reached the solution in the end, we were back to real numbers. The imaginary numbers were just sort of place holders that allowed us to use certain tricks in solving the problems. I wish I could give you an example, but I've forgotten just about everything I once knew in calculus. Infinities are always treated as limits or idealizations, and they allow us to solve certain problems, like Taylor polynomials. But that doesn't mean there can actually be an infinite number of anything in the physical world.

So there's math that doesn't apply to the physical world, but some does, and surely that is surprising? I don't see why. The fact that we can derive equations or discover subatomic particles purely by doing math is a matter of logical deduction. Math is a kind of logic, and it operates by necessity. Logic and math both work by symbols. If P, then Q; not Q; therefore, not P. If you include true propositions in place of the symbols, then you will get true conclusions. So if you start off with a handful of equations that are already known to apply to the physical world, it's a matter of deduction to manipulate those equations until you arrive at a piece of new information that either describes a new phenomenon or a new particle, and as long as we haven't made any mistakes along the way, we should expect to be able to find the new particle or phenomenon in nature. It can't be otherwise if we've deduced the conclusion from true premises using necessary inferences.

I'm not totally convinced that absolutely everything in the physical world can be described with an equation either. Most things can, of course, but things like what it's like cannot. That may be because sentience isn't a physical thing in the first place, but it's certainly part of the physical world in some sense because I'm a physical being, and I have mind that thinks about things like math, physics, and what it's like to think about them.

For further reading:

The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner

The Applicability of Mathematics by William Lane Craig


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