Infinity is Not a Number

InfinityAnswersInEddas has posted 3 videos criticizing William Lane Craig’s arguments for the existence of God. I’ve only watched the first, but it is very good and I plan to check out the others. I’m no fan of Craig. To be stupid is unfortunate; to be brilliant and use it to obfuscate is evil; William Lane Craig is evil.

The video quotes Craig making an argument against an eternal universe. As the author points out, this is a strange argument to make because no one argues for an eternal universe. But this is typical of Craig’s long history of setting up straw men and whacking them down. While this must feel good, it is intellectually dishonest and certainly doesn’t lead to new knowledge.

In this argument, Craig offers an example of how the universe could not always exist. It displays an astounding ignorance of mathematics. It is more what you would expect of a bunch of drunk college students debating the existence of God:

Take the plants Jupiter and Saturn. Suppose that for every orbit that Saturn completes, the planet Jupiter completes two. If Saturn has completed ten orbits, Jupiter completed twenty. If Saturn has completed a trillion, Jupiter has completed two trillion. The longer they orbit, the father Saturn falls behind. If they continue to orbit forever, they will approach a limit at which Saturn is infinitely far behind Jupiter. Suppose Jupiter and Saturn have been orbiting the sun from eternity past. Now which one will have completed the most orbits? Well, the correct mathematical answer is, the number of orbits is identical. But that seems absurd! For, the longer they orbit, the greater the disparity between them grows.


I understand that infinity is a tricky concept but this is a stunning lack of understanding. And to be used in this context is bizarre. I wasn’t being hyperbolic to compare this to the ravings of drunk college students.

Infinity is not a number. If you treat it like a number, you can come up with all kinds of paradoxes. This is why we don’t treat it as a number. We can, however, say a lot about it. One of the most basic ideas is that the set of integers is a countable infinity, while the set of real numbers is an uncountable infinity. And we know something else.

In William Lane Craig’s example, at infinity, Jupiter will have gone through twice as many orbits as Saturn. How do we know this? Because infinity is a limit. Craig got to this by looking at what happens to the system as it gets bigger and bigger (10 and then a trillion). But then he claims infinity is just some bigger value on the number line where reality has a discontinuity. Yikes!

I know that for people who don’t think about these things, infinity can be a tricky subject. But that’s not what’s going on with Craig here. I suspect that once he discovered this paradox, he never gave it another thought. That’s what William Lane Craig does. Arguments have one purpose: to prove the Bible is correct. As Robert Price has pointed out, Craig uses his considerable intellect and erudition in one giant clean-up operation. It’s a hell of a way to spend a life.

2 thoughts on “Infinity is Not a Number

  1. Uh….
    If there is no such thing as infinity, how can a soul spend eternity in heaven or hell?
    If the non-existence of infinity is proof of the existence of God, then proof of God is disproof of heaven and hell.

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