If you're a scientist who wants to show that science and faith are compatible and that the deep mysteries of physics or biology point to the existence of a creator in order to be adequately explained, then getting the endorsement of Richard Dawkins is basically a rhetorical homerun. And, apparently, Francis Collins has done just that. He claims, and we have no real reason to doubt him, that Richard Dawkins admitted in a private conversation that the argument for the existence of God based on the "fine tuning" of the universe is "the most troubling argument for nonbelievers to counter."
And why wouldn't it be?
By all scientific accounts the argument is based on a sound premise: any slight change to the values of the fundamental physical constants (the force of gravity, the nuclear forces, etc.) would have ensured that the universe never would have unfolded in such a way as to allow for life to have developed, and perhaps would not have allowed for a universe that resembles anything like ours. Given that the parameters of each of the individual constants seems arbitrary on its own, the confluence of just the right values can't simply be a coincidence, can it? It's a one in a billion chance (or worse). The universe must have been designed by a creator so as to allow for the emergence of his most prized creation, the only ones who can appreciate his greatness in so elegantly setting the stage for our arrival. This conclusion seems natural, almost unavoidable.
Except that it trades on a very subtle fallacy, which is to assume without proof that the mere fact of something being objectively unlikely is somehow evidence that it is the result of design or contrivance. It simply isn't so.
Let's say you flip a coin 20 times and get this result:
H T T H H H T H T H H T T H T H T H T H
That's 11 heads, and 9 tails. Strict probability would lead us to predict 10 and 10, but this is certainly within the margin of error for what we'd expect out of such a small sample size. And if we executed this series of coin tosses and got this result we'd simply record the data, unsurprised, and move on.
But let's say this is the result we get:
H H H H H H H H H H H H H H H H H H H H
Our first impulse would be to check the coin to determine if it was a double-headed coin, or to feel as if we were having a prank played on us. We feel that pure chance simply couldn't give us such an ordered outcome. In reality, though, the second series of coin tosses is no less objectively probable than the first. If you wanted to recreate either series, there is just one possible "correct" outcome of each toss that will yield the series you want to recreate. And with each toss, you have a 50/50 chance of getting the outcome required for the series to occur. Either series has the probability 9.53674316 x 10-7.
Applying this to the fine tuning argument, it's easy to see that even though the exact values of the fundamental physical constants are objectively a one-in-a-billion (or more) chance, we have no reason to consider this to be evidence that some agency or contrivance is responsible unless it can be shown that there is some other particular set of values that is significantly more likely than the one that is actual. If the set of constants that led to our coming to be via natural processes is simply one of a billion equally likely arrangements, then there is no cause for alarm, and no need to invoke design.
Further research may yield that the constants are not quite so free as it appears now, and that the range of possible values for them is much more constrained than we think now. Or it may yield the outcome that the objective unlikelihood of the set of values we have truly is so much less likely than other possible sets of values that it cries out for explanation.
For now, however, the fine tuning argument is simply a logical fallacy made plausible by the human tendency to look for agency when we perceive order.