Fine-Tuning and the Search for an Archimedean Point

One of the benefits of working in the philosophy of religion today is the chance to engage with genuinely new empirical arguments. The fine-tuning argument, or FTA, ranks among the most intriguing of those arguments. Although it is in a broad sense a version of the design argument, which is not new, its structure and its empirical grounds are thoroughly modern and have attracted the attention of philosophers, physicists, and mathematicians alike.

I am, at the moment, a reluctant and somewhat tentative skeptic regarding the argument's force. But I am not immune to its intuitive appeal. In this paper I will sketch the argument as it is commonly discussed, explain where in my view some key difficulties lie, and then engage with a recent thoughtful attempt to circumvent those difficulties.

The Intuitive Picture and the Underlying Math

In your mind's eye, imagine a single speck of dust floating in the air in a vast cathedral. The mote is tiny, though not actually a mathematical point. Focus on that speck, and then zoom out. For practical purposes, the speck vanishes; it is lost in the immensity of the space around it. Once we lose sight of it, we have little hope of finding it again. If we were asked to specify its location with a random guess—say, while we were blindfolded—our task would be hopeless.

This mental picture, or something like it, is a fundamental intuition pump for the FTA; we need only change a few terms to exhibit the parallel. Instead of the physical space of the cathedral, we are speaking of an abstract space in which the values of certain physical constants can be specified. Instead of a physical mote, we are looking at the region of that abstract space in which the constants permit the existence of organic life in a recognizable form. And it turns out that, on physical grounds, the life-permitting region is small. The set of values picking out the constants in our own universe is in it, obviously, for here we are. And within a very limited region around those constants, life could theoretically flourish—say, in a universe like ours, but with a tiny increase in the gravitational constant. But the "ball" of such values, like the dust mote in our analogy, is dwarfed by the space of life-forbidding universes, as small variations in any of the constants (singly or jointly) prove fatal to the possibility of life. Zooming out, therefore, we find that the ball of life-friendly values is quickly lost to view in an immense space of hostile, sterile universes that consist (for example) of nothing but black holes or nothing but diffuse hydrogen. What are the odds, then, that the actual universe would have just those values that permit life, merely on chance?

To make the intuition behind the FTA more precise, we have to connect these intuitions to probabilities. The inside of the cathedral is the space of logically possible universes, and the entire interior volume corresponds to 100 percent. The volume of the speck of dust corresponds to the ball of life-permitting universes. The ratio of those two volumes—the speck divided by the space—will stand for the probability that a randomly selected (or generated) universe will be hospitable to life. This ratio is, so to speak, the Archimedean point of the argument. If we can define it carefully and defend a particular value (or even an approximate value) for it, then we have some hope of moving forward; if we cannot, the argument fails.

To complete the argument, we need one more piece of information—or two more pieces, depending on the conclusion we want to draw. First, we need to know how that first small probability compares to the probability that there would be a life-friendly universe, supposing that the physical constants are not selected at random. It is not necessary, in order to make a case against randomness, that we have an exact number for (say) the probability that a deity would create a life-friendly universe; it is sufficient...