For the sake of completeness, I must mention that William Lane Craig has a second way to argue that the universe must have a beginning. It goes as follows.
2.21 A collection formed by successive addition cannot be actually infinite.I am not afraid to concede a few points to William Lane Craig, and that is what I am going to do here.
2.22 The temporal series of past events is a collection formed by successive addition.
2.23 Therefore, the temporal series of past events cannot be actually infinite.
The first premise (2.21) is correct, though perhaps imprecisely phrased. By successive addition, I believe WLC means adding a finite sequence of finite numbers together. So if you add 1 minute and 1 minute and 1 minute together, you will only get a finite interval of time. You can add finite intervals, one by one, all you want, and you will never get an infinite interval of time.
As for the second premise (2.22), that could be correct too. If you believe that time works such that any moment must be "formed" by successive addition from some sort of beginning moment, then you would accept WLC's argument. It sounds like a reasonable enough philosophy of time to me.
The problem is that if I had some evidence suggesting that the universe did not have a beginning, then I would simply have to find a different philosophy of time. As a scientist, I just can't let little philosophical hangups get in the way of determining what's really true, am I right? I gotta be practical about it, that's my attitude.
As it is, I think physics already uses a different philosophy of time. Not because it is the metaphysically correct philosophy of time, but because it's a convenient model. Time... is just a variable. A coordinate. The state of any physical system is a function of time. The entire function of time can be determined from the state at any particular time, just as a unique solution to a differential equation is specified by a single point. Physics doesn't say anything about the future being "formed" from the past. It doesn't say anything about adding finite sequences of finite intervals together.
But I'm not saying WLC is wrong. For all I know, all moments really are formed from the past by successive addition. We may never know, since there aren't any obvious ways to put the claim to the test.
WLC does not address other ways of viewing time, but instead refers to G. J. Whitrow's The Natural Philosophy of Time, 2nd ed. Supposedly, Whitrow defends a form of WLC's argument without presupposing WLC's view of time.
Funny story, I could only find the 1st edition, which appears to contain no such defense. Instead, I found Whitrow discussing one of Kant's antinomies. Kant argues that the universe must have begun for the same reason WLC suggests. He also argues that the universe couldn't have begun, because the idea of beginning makes no sense without time being there in the first place. From these contradicting arguments, Kant concludes that time is not applicable to the world, but rather a way for us to visualize the world. Immanuel Kant, ladies and gentlemen.
Other research revealed that Whitrow wrote an article called "On the Impossibility of an Infinite Past" for The British Journal for the Philosophy of Science. Whitrow uses the Tristram Shandy paradox, which involves a person who writes a complete autobiography, but who takes a whole year to commit the events of one day to paper. There was also a reply, which I judge to be a devastating critique. I feel like my work's already been done.
Does anyone want me to summarize the two papers on the Tristram Shandy paradox, and add it as an appendix? Otherwise, I will skip it.
"A few things wrong about the cosmological argument"
1. Actual and potential infinities
2. Actual infinities in physics
3. What is real?
4. The "absurdity" of Hilbert's Hotel
5. Interlude: God is infinite
6. Forming Infinity, one by one
7. Uncertain beginnings
8. Entropy: The unsolved problem
9. Kalam as an inductive argument
10. Getting from First Cause to God