A Christian apologist with a new argument is like a kid with a new toy. William Lane Craig is excited to show us the Argument from Mathematics (part 1 of the discussion here). He marvels at what he calls “the uncanny effectiveness of mathematics” in describing the world around us. Unsurprisingly, he’s quick to push forward his favorite deity as the explanation.

Limits on math

So how effective is math? It’s fundamental in physics, but it doesn’t do much for other fields like literature. Or art. Or history, geology, sociology, politics, human relations, or lots of other fields. Impressive attempts have been made to find mathematics to model human behavior—catastrophe theory, for example—with little success. Compared to the scope of human endeavors, math is actually quite limited.

Consider where math does its impressive work, the intersection of Math and the Physical World.

There’s a lot of the physical world that benefits little from math (on the left of this diagram), and there’s a lot of math that has little direct applicability to the real world (on the right). In addition, math in the real world isn’t always tidy and simple.

• The orbits of planets aren’t simple circles but rather ellipses.
• Fundamental particles are composed of three quarks, not one or two.
• The n-body problem has no simple solution.
• Chaos theory shows that some systems are deterministic but not predictable.
• NP-complete problems like the traveling salesman problem are computationally difficult.
• Important numbers like pi or e are transcendental (nonrepeating and nonterminating).
• Quantum mechanical events are describable only with statistics and may have no individual cause.
• There is no simple rule for enumerating primes.

Math gives neat, simple answers where it does, and it doesn’t where it doesn’t. Our awe at math’s effectiveness may be due to confirmation bias, in which we count the hits and ignore the misses. We marvel at the places where math provides a neat solution and ignore those where it doesn’t.

Another bump in the road to math’s “uncanny effectiveness” are Gödel’s incompleteness theorems, which argue that finding a complete and consistent set of axioms for all mathematics is impossible.

And consider whether God or reality calls the shots. Take just one primitive truth in our reality, 2 + 2 = 4. Could God have made it anything different? If so, we await the evidence. If not, what role is left for God if reality defines the fundamentals from which the rest of math follows? God is sidelined without much to do.

Craig’s antagonist in this discussion, Dr. Daniel Came, raised many of the points I’ve mentioned here. About math’s applicability, he said,

If you think of the number of possible questions that human beings can ask, the number that are actually tractable with science and mathematics is a vanishingly small percentage.

Craig’s weak explanation

Craig claims that “God did it” is an inference to the best explanation. He wants the teacher to declare that time is up because he has an answer. Problem is, it’s not much of an answer.

He doesn’t care that the consequences of his explanation are either untestable (such as the existence of an afterlife) or have been tested and failed (such as answered prayer).

He doesn’t care that his claim isn’t even falsifiable.

He doesn’t care that “God did it” raises more questions than it answers—questions about who or what God is, his motivations, how and why he created the universe, and so on. “God did it” is no explanation at all.

He doesn’t care that whenever science has found an explanation, it’s always natural. Science has accepted zero supernatural explanations.

He doesn’t care that, when you look around at God’s project with its natural disasters, parasites, childhood illnesses, and so on, it looks more like an experiment of the kid who burned ants with a magnifying glass, inexplicably given omnipotence, than the design of an all-loving deity.

He doesn’t provide evidence that his god even exists.

No, Craig says, his answer has great explanatory power, “unless you’re closed to theism.” (Did you see that clever role reversal coming? If there’s a problem with embracing Craig’s position, it must be that the atheist is simply closed-minded!)

We see cracks begin to form, however, when he admits that his isn’t an empirical explanation but rather a metaphysical one. But then what good is it—I mean, besides advancing Craig’s pet theory?

Craig retreats

Craig says that simple math would always apply to the physical world in any universe. That sounds plausible to me, but Craig is overconfident as usual as he tosses out claims about which he couldn’t possibly have definite knowledge. And if Craig admits that God isn’t needed for simple math, how can you exclude the rest when complex math is built on simple math? As an example of “simple math,” Craig includes the Bridges of Königsberg problem, which was the beginning of graph theory.

Craig demands an explanation because that’s where he imagines his advantage lies. He’s got an explanation, pathetic though it is, which is more than the other side has.

The problem, of course, is that “we don’t have an answer” is a perfectly reasonable response from the side of reason and science. The last ten thousand puzzles that science resolved started from that position of honest ignorance. Every Christian explanation of “God did it!” for these puzzles was wrong, and yet here Craig pops up again like a Weeble with the same childish and simple-minded proposition. “Well, how about now? Is God an explanation now?”

Christianity assures its flock that it’s doing important work as it pretends to answer science’s unresolved questions with the same mindless, one-size-fits-all answer, but this is just god-of-the-gaps reasoning. (In my list of 25 stupid arguments Christians should avoid, this is #20a: Science can’t explain everything; therefore, God.)

As his antagonist chipped away at Craig’s ice floe, Craig’s argument essentially dribbled from “math’s effectiveness is uncanny” down to “math’s effectiveness is kind of uncanny.” All he could do was whine that what was left was still extraordinary and needs an explanation. Sure, let’s work on an explanation, but in the meantime, don’t imagine that you have one.

William Lane Craig and Barbie—separated at birth?

Craig reminds me of Teen Talk Barbie, a doll from 1992 that could say a number of phrases, including one that has been paraphrased as “Math is hard!” Craig seems to confuse difficult math (and there’s plenty of that) with math that depends on God, and his argument seems to devolve into little more than Barbie’s observation.

Yes, math is hard, but both Barbie and Craig have yet to show that mathematical explanations of the real world would fail in a godless universe. They seem to even be unaware of the problem.

Related posts:

• “A Universe That’s Understandable Points to God,” but How Understandable Is the Universe?
• Stupid argument #36: Nature is intelligible.

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(This is an update of a post that originally appeared 2/9/15.)

Image from stuartpilbrow, CC license

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