William Lane Craig versus Rosenberg (part 3)

My series on the February 2013 debate between William Lane Craig and Alex Rosenberg:

1. The Leibnizian Cosmological Argument
2. The Kalam Cosmological Argument
3. The Applicability of Mathematics to the Physical World
4. The Fine-Tuning of the Universe for Intelligent Life
5. Intentional States of Consciousness in the World
6. Objective Moral Values and Duties in the World
7. The Historical Facts about Jesus of Nazareth
8. God can be Personally Known and Experienced
9. Arguments Against Naturalism
10. The Argument from Evil
11. Wrap-Up

Introduction

In February 2013 atheist philosopher Alex Rosenberg debated Christian philosopher William Lane Craig over whether faith in God is reasonable (debate begins at around 17:14). I’ve mentioned before the reason why William Lane Craig wins debates, and since this debate is a good example of how not to debate William Lane Craig, I have been going through some of what Rosenberg did wrong and how he could have done a lot better. One happy benefit from this is that in so doing I’ll also be refuting William Lane Craig’s arguments. In this entry I’ll address Craig’s argument from the applicability of mathematics to the physical world.

The Applicability of Mathematics to the Physical World

Craig’s argument in the debate goes like this:

1. If God did not exist, the applicability of mathematics to the physical world would be a happy coincidence.
2. The applicability of mathematics is not a happy coincidence.
3. Therefore, God exists.

What Rosenberg did

He talks about this at 1:18:26 and seems to dispute premise 1, noting that there are indefinitely many mathematical objects and indefinitely many mathematical functions relating these objects. He says it’s an argument from ignorance that this range of functions and objects that is so small so as to require divine authority to make it come out that way. I think what he was saying here is that the range of mathematics is so vast and the objects and functions that usefully apply to our world is so small, that it’s not really much of a coincidence that mathematics would apply to our world (though I think he could have made this point more clearly).

What Rosenberg should have done

One way to respond is to attack is premise 2. Why on earth should we believe that it is not a happy coincidence? Happy coincidences happen all the time! It was only though chance events that brought about my own existence, for example. Am I to assume that every alleged happy coincidence is really a product of God or some other designing intelligence? Why can’t fortunate events of chance happen? At least, why think that isn’t the case here given how often happy coincidences occur?

Craig says that in Rosenberg’s book, Rosenberg says that naturalism does not tolerate cosmic coincidences. He doesn’t really have much of an argument beyond this for premise 2. This is a very bad argument, in part because there doesn’t seem to be any reason to believe Rosenberg is right here (assuming Craig did not quote him out of context). Rosenberg should have retracted or qualified his statement and said something like, “Happy coincidences happen all the time, and Craig has given us no reason to believe a happy coincidence isn’t what happened here.” Another reason Craig’s argument is a poor one is because this isn’t a theism versus naturalism debate but a theism versus atheism one. Atheism and naturalism aren’t the same thing. Rosenberg should have pointed this out too.

Craig also asserts that on naturalism there is no explanation for the “uncanny” applicability of mathematics to the physical world. Again, naturalism isn’t the same thing as atheism, but another question needs to be raised: why think it is that “uncanny” in the first place? It seems that having a physical reality describable by some sort of mathematics would apply for any consistently operating physical reality. We could think of such a universe like a computer program that has a set of rules for how the universe consistently operates and to predict what would happen. Programs of course rely on binary code in conjunction with certain mathematical operations on said binary code, and so any consistently operating physical reality would inevitably be describable by some sort of mathematics. So the applicability of math to physical reality isn’t nearly as remarkable as Craig seems to think. This is another point Rosenberg could have made but didn’t.

In fairness, Rosenberg did seem to try to mitigate the “happy coincidences” claim (in the way that I described), but the point could have been argued more clearly and much more effectively, e.g. noting that some sort of mathematics would apply for any consistently operating physical reality.