Introduction
Robin Collins and James Fodor recently debated the fine-tuning argument for the existence of God. The discussion largely revolved around what we should make of Collins’s dart analogy, which goes like this. There’s a gigantic dartboard with a spotlight on some portion of it, and you have no idea how far the dartboard extends beyond the illuminated area. You can see an incredibly small bullseye at the center of the illuminated portion. A dart comes into view and hits the bullseye.
According to Collins, in this scenario you may reasonably infer the dart was thrown by an astonishingly skilled dart thrower, even though you cannot see how many bullseyes there are outside the illuminated region of the dartboard. For there are only two possibilities. Either the illuminated region is a typical region of that size—such that, were the spotlight to shine elsewhere on the dartboard, you’d most likely see a large blank space with no more than a few miniscule dots on it—or it is an atypical region. In the former case, it is highly improbable that the dart would hit any bullseye by chance—no likelier than that it would hit the bullseye at the center of the illuminated region, assuming it was guaranteed to land at some point or other in that region. So we can conclude that someone aimed the dart at the bullseye. If, on the other hand, the illuminated region is atypical, the dartboard is mostly (or half) covered in bullseyes. So it is not unlikely that the dart would hit a bullseye by chance. But it is nonetheless improbable that it would hit the bullseye at the center of a region so sparsely populated with bullseyes. Few sizable regions of the dartboard are like that. So we can conclude that someone was trying to throw the dart at some atypical region or other like the illuminated one, if not at that particular region or the bullseye at its center.
Here’s how the dart scenario relates to fine-tuning. The whole dartboard, including both the illuminated and the dark regions, represents the totality of parameter space (i.e., the space of possible configurations of physical parameters, including fundamental constants, initial conditions, and perhaps laws). The dart’s landing at a certain point on the dartboard is analogous to the creation of a universe with a complete, determinate set of parameters. The illuminated region of the dartboard is like what Collins calls the epistemically illuminated region (EIR)—the set of points in parameter space for which we can determine whether those parameters permit life as we know it. Each bullseye corresponds to a complete, determinate set of parameters that allows for life—specifically embodied conscious agency (ECA), not necessarily carbon-based life constructed by sticking together protons, neutrons, and electrons to form molecules such as DNA.
Sets of parameters that prohibit our form of life—the form we observe in the actual universe—dominate the EIR, just as non-bullseye points dominate the illuminated part of the dartboard. Recall that Collins claims we may infer the dart was expertly aimed whether or not the dark region of the dartboard is jam-packed with bullseyes. Likewise, argues Collins, we may infer the universe was expertly designed whether or not parameter sets that permit ECA dominate the portions of parameter space we’re in the dark about. For if they do, then if our universe arose by chance, we would expect its parameters to lie outside the EIR, as it is an atypical region of parameter space. On the other hand, if parameter sets that permit ECA are rare outside the EIR, we should be surprised that, through sheer chance, our universe’s parameters permit ECA.
A Dilemma for Collins’s Dilemma
This argument from analogy stands or falls on what we mean by “blank space.” Suppose we mean a region devoid of bullseyes. Then the analogy breaks down. For we are in no position to compare the life-prohibiting portion of the EIR to the huge blank portion of the illuminated region of the dartboard. We do not know which sets of parameters, even within the EIR, prohibit every possible form of ECA. We only know that the vast majority of them prohibit the form we are familiar with.
That is James’s point, if I understand it. He’s not just saying we don’t know whether ECA can exist outside the EIR. He’s pointing out that we don’t know whether it can exist in subregions of the illuminated region other than the central bullseye, or the known life-permitting range. Collins would disagree here, since he thinks that there can be no ECA of any sort unless “matter sticks together,” and that we can determine matter only sticks together in a tiny segment of the EIR. But James demurs, as evidenced by his response to Collins’s saying, “I’m doing something very general, just the general notion of embodied conscious agents, and very minimal condition that matter stick together. That’s a pretty minimal condition.” To this James replies, “I agree, but we don’t know the conditions under which that will be fulfilled. All we know is the conditions under which we won’t have the type of matter that we currently have.” James rightly emphasizes that we don’t know matter would not stick together at all across the majority of the EIR; we only know, at most, that we wouldn’t get all the same kinds of particles sticking together as they do to form life as we know it—with up and down quarks making up protons and neutrons, which make up atomic nuclei, which together with electrons make up atoms, which make up molecules, cells, and ultimately organisms. So Collins would be begging the question against James were he to bake into his analogy the presupposition that matter’s sticking together, and so ECA, is possible only in a small portion of the EIR.
In order for the analogy to work, we must understand the empty space on the dartboard as being empty merely in a relative sense—devoid of bullseyes of a certain kind, representing conditions permitting the type of ECA under consideration, not devoid of bullseyes simpliciter. And once we interpret “blank region” this way, we discover that we can pass between the horns of Collins’s dilemma. The illuminated region may be typical in that most every region is chiefly empty of bullseyes of any given kind (each kind representing conditions for a distinct kind of ECA). But at the same time the dartboard can be jam-packed with bullseyes.
To see this let’s add a few details to the analogy. Imagine that the bullseyes are color coded. Bullseyes of the same color represent parameters conducive to the same form of life, and those of different colors represent parameters conducive to distinct forms of life. Say the bullseye at the center of the illuminated region is black. There’s a large space surrounding the black bullseye which is empty of black bullseyes; of the sets of parameters whose conduciveness to life we have considered, only a teensy-weensy proportion are conducive to life as we know it. But for all we know the vast majority of them are conducive to some form or other of ECA. So, returning to our analogy, even the illuminated portion of the dartboard may be loaded with bullseyes of various colors. This may be hard to believe, since you’d expect to see any bullseye the spotlight shines on, regardless of the bullseye’s color. But that’s simply a disanalogy between the dart scenario and fine-tuning. To make the analogy more appropriate, let’s stipulate the colors of any non-black bullseyes are visible only under a black light. The black light represents a fuller investigation than we have yet done of the conditions needed for exotic life, and of where those conditions are met within the EIR.
Okay, so the illuminated portion of the dartboard is, for all we know, full of bullseyes. But even if that were so, how could the illuminated portion be a typical region? Here’s how. Nearly every bullseye on the dartboard could lie at the center of a large space empty of other bullseyes the same color as the central bullseye—but still full of bullseyes. In that case, it would be no wonder that the dart happened to hit some bullseye, and that it fell within some region like the illuminated one. (Note that the blank region surrounding a bullseye can overlap other blank regions and the corresponding bullseyes, on the relative conception of blankness. Bullseyes can also overlap each other.)
On the Inference from Atypicality to Design
So much for my argument that the EIR may be typical even if parameter space is jam-packed with ECA-permitting parameter sets. Let’s suppose that the EIR is atypical. Are we actually licensed to infer from this that the universe’s parameters were deliberately selected from an atypical region of parameter space? Well, only if it’s less likely for a universe to randomly fall within an atypical region like the EIR than for there to be a designer motivated to make the universe that way. But while we do have some reason to think God would be motivated to create a universe that permits ECA, we lack reason to suspect he would be motivated to select the universe’s parameters from an atypical region of parameter space. And this strongly indicates he would not be motivated to do so.
Let a total set of divine intentions be a set of intentions such that, possibly, God has all and only those intentions. Let a plausible total set of divine intentions be a total set of divine intentions such that 1) it includes, but needn’t be limited to, every intention the concept of God gives us any reason to expect he has, and 2) the concept of God in no way suggests he lacks any intention in the set, other than the members mentioned in (1). Call the intentions (1) refers to plausible intentions, and the remaining intentions in the set epistemically indifferent intentions. (Assume for simplicity that God can have all these intentions at once.) By a principle of indifference we can take all plausible total sets of divine intentions to be equally likely. This is because, for each set, we can ignore the subset of all and only plausible intentions. Every plausible total set has those same members, and those members’ individual and joint plausibilities do not vary from set to set. So their inclusion cannot make one plausible total set more or less likely than another. All that could make one set more or less likely than another are differences between the plausibilities of epistemically indifferent intentions. But there are no such differences; the mere concept of God in no way suggests he has or lacks any of the epistemically indifferent intentions. (I’m assuming, of course, that every set of epistemically indifferent intentions is as epistemically indifferent as its individual members. One may contest this, but I don’t have space to address that objection here. By which I mean I lack the patience to.) Since the vast majority of plausible total sets exclude any given epistemically indifferent intention, we can assign an extremely low probability to God’s intending to select parameters from an atypical region. And I can’t see why we should suppose that probability is any higher than that of the parameters’ falling within an atypical region without a designer.
There’s nothing wrong with thinking, “Wow, what are the odds that the parameters would fall within an atypical region by sheer chance?” But if you have that thought, you should also ask yourself, “Wow, what are the odds that God intends to select life-permitting parameters from an atypical region rather than a typical one? Why on Earth would he care, or aim, to do that? What would it accomplish?”