Now I’ll deal with Craig’s philosophical arguments for the claim the universe had a beginning. The first argument goes like this (*Reasonable Faith *pp. 116-120):

- An actually infinite number of things cannot exist.
- A beginningless series of events in time entails an actually infinite number of things.
- Therefore, a beginningless series of events in time cannot exist.

Craig’s argument for (2) is that if the universe never began to exist, the number of past events is infinite. This is problematic, especially given that Craig believes Christians will be rewarded with eternal bliss in heaven. Craig seems to need it to be true that past events are real in a sense which future events are not, a controversial philosophical point.

This is because if past events are not real in the relevant sense, Craig’s argument fails. However, if *future* events *are *real in the relevant sense, and Craig is also right about premise (1), he will have inadvertently proved the future must be finite, and therefore there will be no eternal reward or punishment in heaven. (One of philosopher Wes Morriston’s papers has more on this.)

But it’s pretty clear there are no good reasons to think Craig is right about (1). Craig tries to support this claim by citing advanced mathematics, and when I first encountered *Kalam, *I actually found that part of the argument convincing. Only later, when I took a graduate-level course in logic, which covered Cantorian set theory, did I realize what nonsense this is.

In his debates, Craig likes to say things like, “mathematicians recognize that the existence of an actually infinite number of things leads to self-contradictions.” I’ve never heard him explain which mathematicians these are. In fact, the mathematics of infinity is a well-developed and perfectly consistent branch of mathematics.

In particular, contrary to what Craig often claims, Cantorian set theory does not say that when you take infinity minus infinity, you get contradictory results. Set theory does not say infinity is a single thing that can be subtracted from itself. Instead, set theory deals with a great variety of possible infinite sets. In set theory, you can take “A set minus B” where A and B are both infinite sets, but the result depends on which infinite sets A and B are.

That was very abstract. So here’s a thought-experiment often used to explain set theory: Hilbert’s Hotel. Imagine a hotel with an infinite number of rooms, all of which have guests in them. Here are two things that might happen (if you ignore practical problems, including the laws of physics):

- All the guests leave. An infinite number of guests have left, and no guests remain.
- All the guests in the even-numbered rooms leave. An infinite number of guests have left, and an infinite number of guests remain.

Strange, isn’t it? And Craig frequently calls Hilbert’s Hotel “absurd” and claims it is therefore impossible. But contra Craig, it involves no contradictions. In one situation, the guests do one thing, leading to one result. In the other, the guests do another thing, leading to another result. Hilbert’s Hotel is perfectly consistent, as is Cantorian set theory.

I’m not the first critic of *Kalam *to see no impossibility in Hilbert’s Hotel. Craig cites a number of philosophers who accept that Hilbert’s Hotel is possible. His response to them? Complain they haven’t given a reason to think the hotel is possible (p. 119).

This is just an example of Craig’s annoying tendency to make unsupported claims and then demand his critics disprove them, and it’s an absurd way to argue. If Craig is going that way, why not just announce God exist, demand atheists prove otherwise, and be done with it?

Craig’s other philosophical argument that the universe had a beginning goes like this (pp. 120-124):

- The series of events in time is a collection formed by adding one member after another.
- A collection formed by adding one member after another cannot be actually infinite.
- Therefore, the series of events in time cannot be actually infinite.

The question here is what Craig means by this. If “a collection formed by adding one member after another” Craig means “a collection formed by starting with nothing and then adding one member after another,” then premise (1) begs the question, because if the past is infinite, it has always been infinite. It did not start from nothing.

On the other hand, if “a collection formed by adding one member after another” means “a collection that has been added to by adding one member after another,” then premise (2) is false, because if you add to an infinite collection by adding one member after another, it will still be infinite.

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