God, Design, and Fine-Tuning
Robin Collins[1]
This is an updated version of a
paper originally published in: God
Matters: Readings in the Philosophy of Religion, Raymond Martin and
Christopher Bernard (eds),
I. INTRODUCTION
The Evidence of Fine-tuning
Suppose we went on a mission to Mars, and found a domed structure in which everything was set up just right for life to exist. The temperature, for example, was set around 70o F and the humidity was at 50%; moreover, there was an oxygen recycling system, an energy gathering system, and a whole system for the production of food. Put simply, the domed structure appeared to be a fully functioning biosphere. What conclusion would we draw from finding this structure? Would we draw the conclusion that it just happened to form by chance? Certainly not. Instead, we would unanimously conclude that it was designed by some intelligent being. Why would we draw this conclusion? Because an intelligent designer appears to be the only plausible explanation for the existence of the structure. That is, the only alternative explanation we can think of--that the structure was formed by some natural process--seems extremely unlikely. Of course, it is possible that, for example, through some volcanic eruption various metals and other compounds could have formed, and then separated out in just the right way to produce the “biosphere,” but such a scenario strikes us as extraordinarily unlikely, thus making this alternative explanation unbelievable.
The
universe is analogous to such a “biosphere,” according to recent findings in
physics. Almost everything about the
basic structure of the universe--for
example, the fundamental laws and parameters of physics and the initial
distribution of matter and energy--is balanced on a razor’s edge for life to
occur. As eminent
Scientists and others call this extraordinary balancing of the fundamental physical structure of the universe for life the "fine-tuning of the cosmos." It has been extensively discussed by philosophers, theologians, and scientists, especially since the early 1970s, with many articles and books written on the topic. Today, many consider it as providing the most persuasive current argument for the existence of God For example, theoretical physicist and popular science writer Paul Davies claims that with regard to basic structure of the universe, “the impression of design is overwhelming” (Davies, 1988, p. 203).[3]
The fine-tuning for life falls into four distinct types, each of which we will briefly discuss below:
(i) The fine-tuning of the laws of physics.
(ii) The fine-tuning of the constants of physics.
(iii) The fine-tuning of the initial conditions of the universe.
(iv) The fine-tuning of certain higher-level features of the universe, such as various properties of the chemical elements.
To say that the laws are fine-tuned means that if we did not have just the right combination of laws, complex intelligent life would probably be impossible. For example, according to current physics, there are four forces in nature – gravity, the weak force, electromagnetism, and the strong nuclear force that binds protons and neutrons together in an atom. The existence of each of these forces is necessary for complex life. If gravity did not exist, masses would not clump together to form stars or planets, and hence the existence of complex, intelligent life would be seriously inhibited, if not rendered impossible; if the electromagnetic force didn’t exist, there would be no chemistry; if the strong force didn’t exist, protons and neutrons could not bind together and hence no atoms with atomic number greater than hydrogen would exist; and if the strong force were a long-range force (like gravity and electromagnetism) instead of a short range force that only acts between protons and neutrons in the nucleus, all matter would either almost instantaneously undergo nuclear fusion and explode or be sucked together forming a black hole.[4] It follows, therefore, that if any of these force laws did not exist, complex, intelligent life would be much less likely, if not impossible.
Similarly, other laws and principles are necessary for complex life: as physicist Freeman Dyson points out (1979, p. 251), if the Pauli-exclusion principle did not exist, which dictates that no two fermions can occupy the same quantum state, all electrons would occupy the lowest atomic orbit, eliminating complex chemistry; and if there were no quantization principle, which dictates that particles can only occupy certain discrete allowed quantum states, there would be no atomic orbits and hence no chemistry since all electrons would be sucked into the nucleus.
Another particularly important category of fine-tuning is that of the constants of physics.[5]
The constants of physics are a set of fundamental numbers that, when plugged in
to the laws of physics, determine the basic structure
of the universe. An example of such a
constant is the gravitational constant G that is part of
Various calculations show that the strength of each of the forces of nature must fall into a relatively small region for intelligent life to exist. (See Collins, 2003). As one example, consider gravity. If, for instance, we increased the strength of gravity on earth a billionfold the force of gravity would be so great that any land-based organism anywhere near the size of human beings would be crushed. (The strength of materials depends on the electromagnetic force via the fine-structure constant, which would not be affected by a change in gravity.) As astrophysicist Martin Rees notes, "In an imaginary strong gravity world, even insects would need thick legs to support them, and no animals could get much larger." (Rees, 2000, p. 30). Now, the above argument assumes that the size of the planet on which life formed would be an earth-sized planet. Could life forms of comparable intelligence to ourselves develop on a much smaller planet in such a strong-gravity world? The answer appears to be no. A planet with a gravitational pull of a thousand times that of earth -- which would make the existence of organisms of our size very improbable-- would have a diameter of about 40 feet or 12 meters, once again not large enough to sustain the sort of large-scale ecosystem necessary for organisms like us to evolve. Of course, a billion-fold increase in the strength of gravity is large in absolute terms, but compared to the total range of strengths of the forces in nature (which span a range of 1040 as we saw above), this still amounts to a fine-tuning of one part in 1031. Indeed, other calculations show that stars with life-times of more than a billion years, as compared to our sun’s life-time of ten billion years, could not exist if gravity were increased by more than a factor of three thousand.[6] This would have significant intelligent life-inhibiting consequences.
There are other cases of the fine-tuning of the constants of physics besides the strength of the forces, however. Probably the most widely discussed among physicists and cosmologists – and esoteric-- is the fine-tuning of what is known as the cosmological constant. [7] The cosmological constant was a term that Einstein included in his central equation of his theory of gravity – that is, general relativity -- which today is thought to correspond to the energy density of empty space. A positive cosmological constant acts as a sort of anti-gravity, a repulsive force causing space itself to expand. If the cosmological constant had a significant positive value, space would expand so rapidly that all matter would quickly disperse, and thus galaxies, stars, and even small aggregates of matter could never form. The conclusion is that it must fall exceedingly close to zero, relative to its natural range of values, for complex life to be possible in our universe.
Now, the fundamental theories of particle physics set a natural range of values for the cosmological constant. This natural range of values, however, is at least 1053 – that is, one followed by fifty three zeros – times the range of life-permitting values. That is, if 0 to L represent the range of life-permitting values, the theoretically possible range of values is at least 0 to 1053L. To intuitively see what this means, consider a dartboard analogy: suppose that we had a dart board that extended across the entire visible galazy, with a target on the dart board of less than an inch in diameter. The amount of fine-tuning of the cosmological constant could be compared to randomly throwing a dart at the board and landing exactly in the target!
Further examples of the fine-tuning of the fundamental constants of physics can also be given, such as that of mass difference between the neutron and the proton. If, for example, the mass of the neutron were slightly increased by about one part in seven hundred, stable hydrogen burning stars would cease to exist. (Leslie, 1989, pp. 39 - 40, Collins, 2003.)
The third type of fine-tuning is
that of the initial conditions of the universe, which refers to the fact that
the initial distribution of mass-energy must fall within an exceedingly narrow
range for (intelligent) life to occur.
One aspect of this fine-tuning is the exceedingly low entropy at the
beginning of the universe, which requires an extraordinarily precise
arrangement of mass and energy. As Roger
Penrose, one of
As the above examples indicate, the evidence for fine-tuning is extensive, involving four different types of fine-tuning: that of the laws of nature, the constants of physics, the initial conditions of the universe, and various higher-level features of the world. As philosopher John Leslie has pointed out, “clues heaped upon clues can constitute weighty evidence despite doubts about each element in the pile” ( 1988, p. 300). Imaginatively, one could think of each instance of fine-tuning mentioned above as a radio dial: unless all the dials are set exactly right, complex, intelligent life would be impossible Or, one could think of the values of the initial conditions of the universe and the constants of physics as coordinates on a dart board that fills the whole
class=Section2>galaxy, and the conditions necessary for life to exist as an extremely small target, say less than a trillionth of an inch: unless the dart hits the target, complex life would be impossible. The fact that the dials are perfectly set, or the dart has hit the target, strongly suggests that some intelligent being set the dials or aimed the dart, for it seems enormously improbable that such a coincidence could have happened by chance. Below we will develop this argument more rigorously instead of relying on these sorts of analogies.
A Preliminary Distinction
Many people take the evidence mentioned above, along with the dart-board analogy, as sufficient reason to infer to theism as the best explanation of the fine-tuning. In this paper, however, I will attempt to make the argument more rigorous. To rigorously develop the fine-tuning argument, we will find it useful to distinguish between what I shall call the atheistic single-universe hypothesis and the many-universes hypothesis.[8] According to the atheistic single-universe hypothesis, there is only one universe, and it is ultimately an inexplicable, “brute” fact that the universe exists and is fine-tuned. Many atheists, however, advocate another hypothesis, what I call the many-universes hypothesis. According to the most popular version of this hypothesis, there exists some physical process that could be imaginatively thought of as a “universe generator” that produces a very large or infinite number of universes, with each universe having a randomly selected set of initial conditions and values for the constants of physics. Because this generator produces so many universes, just by chance it will eventually produce one that is fine-tuned for intelligent life to occur.
Given this distinction, we will next attempt to rigorously develop the argument from fine-tuning against the atheistic single universe hypothesis, and then consider four major objections to it. Finally, in section IV we will consider the many-universes hypothesis and some theistic responses to it.
II. Argument Against Atheistic Single-Universe Hypothesis
In this section, we will attempt to rigorously develop the argument for preferring theism over the atheistic single-universe hypothesis, an argument I refer to as the core version of the fine-tuning argument. It should be stressed, however, that the soundness of the inference to design based on the fine-tuning does not crucially depend on the ability to make this argument rigorous. We accept many inferences in science, even though philosophers have yet to produce a philosophically rigorous account of these inferences.[9] Of course, the skeptic might object that scientific theories are testable, whereas the theistic explanation of the fine-tuning is not. But why should testability be epistemically relevant? After all, testability is about being able to find evidence against a theory in the future. What matters for the likelihood of an hypothesis’s truth (or empirical adequacy), however, is the current evidence in its favor, not whether it is possible to find evidence against it in the future.
In order to show inference to design based on the fine-tuning is flawed, skeptics must show that it is based on a manifestly problematic form of reasoning. Indeed, a typical atheist objection against the design argument, going back to the famous Scottish philosopher David Hume, is to cast it as an argument from analogy, and then to argue that arguments from analogy in this context are fatally flawed. As we will show below, however, the argument from fine-tuning can be cast into a form that is very different from the argument from analogy, a form that is difficult to refute. This should go a long way both toward making the argument rigorous and toward answering the criticism of some skeptics that the fine-tuning argument relies on a manifestly flawed form of reasoning.
Although the fine-tuning argument against the atheistic single-universe hypothesis can be cast in several different forms – such as inference to the best explanation – I believe the most rigorous way of formulating the argument is in terms of what I will call the prime principle of confirmation (PPC), and which Rudolph Carnap has called the “increase in firmness” principle, and others have simply called the likelihood principle.[10] The prime principle of confirmation is a general principle of reasoning which tells us when some observation counts as evidence in favor of one hypothesis over another. Simply put, the principle says that whenever we are considering two competing hypotheses, an observation counts as evidence in favor of the hypothesis under which the observation has the highest probability (or is the least improbable). (Or, put slightly differently, the principle says that whenever we are considering two competing hypotheses, H1 and H2, an observation, O, counts as evidence in favor of H1 over H2 if O is more probable under H1 than it is under H2.)[11] Moreover, the degree to which the evidence counts in favor of one hypothesis over another is proportional to the degree to which the observation is more probable under the one hypothesis than the other.[12] For example, I will argue that the fine-tuning is much more probable under the theism than under the atheistic single-universe hypothesis , so it counts as strong evidence for theism over this atheistic hypothesis. In the next major subsection, we will present a more formal and elaborated rendition of the fine-tuning argument in terms of the prime principle. First, however, let’s look at a couple of illustrations of the principle and then present some support for it.
For our first illustration, suppose that I went hiking in the mountains, and found underneath a certain cliff a group of rocks arranged in a formation that clearly formed the pattern "Welcome to the mountains Robin Collins." One hypothesis is that, by chance, the rocks just happened to be arranged in that pattern--ultimately, perhaps, because of certain initial conditions of the universe. Suppose the only viable alternative hypothesis is that my brother, who was in the mountains before me, arranged the rocks in this way. Most of us would immediately take the arrangements of rocks to be strong evidence in favor of the “brother” hypothesis over the “chance” hypothesis. Why? Because it strikes us as extremely improbable that the rocks would be arranged that way by chance, but not improbable at all that my brother would place them in that configuration. Thus, by the prime principle of confirmation we would conclude that the arrangement of rocks strongly supports the "brother" hypothesis over the chance hypothesis.
Or consider another case, that of finding the defendant’s fingerprints on the murder weapon. Normally, we would take such a finding as strong evidence that the defendant was guilty. Why? Because we judge that it would be unlikely for these fingerprints to be on the murder weapon if the defendant was innocent, but not unlikely if the defendant was guilty. That is, we would go through the same sort of reasoning as in the above case.
Finally, several things can be said in favor of the prime principle of confirmation. First, many philosophers think that this principle can be derived from what is known as the probability calculus, the set of mathematical rules that are typically assumed to govern probability. Second, there does not appear to be any case of recognizably good reasoning that violates this principle. Finally, the principle appears to have a wide range of applicability, undergirding much of our reasoning in science and everyday life, as the examples above illustrate. Indeed, some have even claimed that a slightly more general version of this principle undergirds all scientific reasoning. (See Howson and Urbach, 1989 and Earman, 1992).
Further Development of Argument
To further develop the core version of the fine-tuning argument, we will summarize the argument by explicitly listing its two premises and its conclusion:
Premise 1. The existence of the fine-tuning is not improbable under theism.
Premise 2. The existence of the fine-tuning is very improbable under the atheistic single-universe hypothesis.[13]
Conclusion: From premises (1) and (2) and the prime principle of confirmation, it follows that the fine-tuning data provides strong evidence in favor of the design hypothesis over the atheistic single-universe hypothesis.
At this point, we should pause to note two features of this argument. First, the argument does not say that the fine-tuning evidence proves that the universe was designed, or even that it is likely that the universe was designed. Indeed, of itself it does not even show that we are epistemically warranted in believing in theism over the atheistic single-universe hypothesis. In order to justify these sorts of claims, we would have to look at the full range of evidence both for and against the design or theistic hypothesis, something we are not doing in this paper. Rather, the argument merely concludes that the fine-tuning strongly supports theism over the atheistic single-universe hypothesis.
In this way, the evidence of fine-tuning is much like fingerprints found on a gun: although they can provide strong evidence that the defendant committed the murder, one could not conclude merely from them alone that the defendant is guilty; one would also have to look at all the other evidence offered. Perhaps, for instance, ten reliable witnesses claimed to see the defendant at a party at the time of the shooting. In this case, the fingerprints would still count as significant evidence of guilt, but this evidence would be counterbalanced by the testimony of the witnesses. Similarly the evidence of fine-tuning strongly supports theism over the atheistic single-universe hypothesis, though it does not itself show that everything considered theism is the most plausible explanation of the world.
The second feature of the argument we should note is that, given the truth of the prime principle of confirmation, the conclusion of the argument follows from the premises. Specifically, if the premises of the argument are true, then we are guaranteed that the conclusion is true: that is, the argument is what philosophers call valid. Thus, insofar as we can show that the premises of the argument are true, we will have shown that the conclusion is true. Our next task, therefore, is to attempt to show that the premises are true, or at least that we have strong reasons to believe them.
Support for the Premises
Support for Premise (1).
The argument in support of premise (1) can be simply stated as follows: since God is an all good being, and it is good for intelligent, conscious beings to exist, it not surprising or improbable that God would create a world that could support intelligent life. Thus, the fine-tuning is not improbable under theism, as premise (1) asserts.
Support for Premise (2).
Upon looking at the data, many people find it very obvious that the fine-tuning is highly improbable under the atheistic single-universe hypothesis. And it is easy to see why when we think of the fine-tuning in terms of the analogies offered earlier. In the dart-board analogy, for example, the initial conditions of the universe and the fundamental constants of physics are thought of as a dart board that fills the whole galaxy, and the conditions necessary for life to exist as a small one-foot wide target. Accordingly, from this analogy it seems obvious that it would be highly improbable for the fine-tuning to occur under the atheistic single-universe hypothesis--that is, for the dart to hit the board by chance.
Often advocates of the fine-tuning argument are satisfied with resting the justification of premise (2), or something like it, on this sort of analogy. Many atheists and theists, however, question the legitimacy of this sort of analogy, and thus find the argument unconvincing. Although a full scale, rigorous justification of premise (2) is beyond the scope of this paper, we will briefly sketch how such a further justification could be given in section III below, under objection (5).
III. SOME OBJECTIONS TO CORE VERSION
As powerful as the fine-tuning argument for theism against the atheistic single-universe hypothesis is, several major objections have been raised to it by both atheists and theists. In this section, we will consider these objections in turn.
Objection 1: More Fundamental Law Objection
One criticism of the fine-tuning argument is that, as far as we know, there could be a more fundamental law under which the constants of physics must have the values they do. Thus, given such a law, it is not improbable that the known constants of physics fall within the life-permitting range.
Besides being entirely speculative, the problem with postulating such a law is that it simply moves the improbability of the fine-tuning up one level, to that of the postulated physical law itself. As astrophysicists Bernard Carr and Martin Rees note “even if all apparently anthropic coincidences could be explained [in terms of some grand unified theory], it would still be remarkable that the relationships dictated by physical theory happened also to be those propitious for life” (1979, p. 612).
A similar sort of response can be given to the claim that the fine-tuning is not improbable because it might be logically necessary for the constants of physics to have life-permitting values. That is, according to this claim, the constants of physics must have life-permitting values in the same way 2 + 2 must equal 4, or the interior angles of a triangle must add up to 180 degrees in Euclidian geometry. Like the “more fundamental law” proposal above, however, this postulate simply transfers the improbability up one level: of all the laws and constants of physics that conceivably could have been logically necessary, it seems highly improbable that it would be those that are life-permitting.[14]
Objection 2: Other Forms of Life Objection
Another objection people commonly raise against the fine-tuning argument is that as far as we know, other forms of life could exist even if the constants of physics were different. So, it is claimed, the fine-tuning argument ends up presupposing that all forms of intelligent life must be like us. One answer to this objection is that many cases of fine-tuning do not make this presupposition. Consider, for instance, the cosmological constant. If the cosmological constant were much larger than it is, matter would disperse so rapidly that no planets, and indeed no stars could exist. Without stars, however, there would exist no stable energy sources for complex material systems of any sort to evolve. So, all the fine-tuning argument presupposes in this case is that the evolution of life forms of comparable intelligence to ourselves requires some stable energy source. This is certainly a very reasonable assumption.
Of course, if the laws and constants of nature were changed enough, other forms of embodied intelligent life might be able to exist of which we cannot even conceive. But this is irrelevant to the fine-tuning argument since the judgement of improbability of fine-tuning under the atheistic single-universe hypothesis only requires that, given our current laws of nature, the life-permitting range for the values of the constants of physics (such as gravity) is small compared to the surrounding range of non-life-permitting values. A dart board analogy might help illustrate the point. If we saw a dart hit a very small target surrounded by a much, much larger blank area, we would still count its hitting the target as evidence that the dart was aimed even if we did not know whether other areas of the dart board were covered with targets. Why? Because even if other parts of the dart board had targets on them, it would still be very surprising under the chance hypothesis, but not under the aiming hypothesis, for it to hit the target instead of somewhere else in the surrounding blank area.[15]
Objection 3. Anthropic Principle Objection:
According to the weak version of so-called anthropic principle, if the laws of nature were not fine-tuned, we would not be here to comment on the fact. Some have argued, therefore, that the fine-tuning is not really improbable or surprising at all under atheism, but simply follows from the fact that we exist. The response to this objection is simply to restate the argument in terms of our existence: our existence as embodied, intelligent beings is extremely unlikely under the atheistic single-universe hypothesis (since our existence requires fine-tuning), but not improbable under theism. Then, we simply apply the prime principle of confirmation to draw the conclusion that our existence strongly confirms theism over the atheistic single-universe hypothesis.
To further illustrate this response, consider the following “firing-squad” analogy. As John Leslie (1988, p. 304) points out, if fifty sharp shooters all miss me, the response “if they had not missed me I wouldn’t be here to consider the fact” is not adequate. Instead, I would naturally conclude that there was some reason why they all missed, such as that they never really intended to kill me. Why would I conclude this? Because my continued existence would be very improbable under the hypothesis that they missed me by chance, but not improbable under the hypothesis that there was some reason why they missed me. Thus, by the prime principle of confirmation, my continued existence strongly confirms the latter hypothesis.
Objection 4: The "Who Designed God?" Objection
Perhaps the most common objection that atheists raise to the argument from design, of which the fine-tuning argument is one instance, is that postulating the existence of God does not solve the problem of design, but merely transfers it up one level. Atheist George Smith, for example, claims that
If the universe is wonderfully designed, surely God is even more wonderfully designed. He must, therefore, have had a designer even more wonderful than He is. If God did not require a designer, then there is no reason why such a relatively less wonderful thing as the universe needed one. (1980, p. 56.)
Or, as philosopher J. J. C. Smart states the objection:
If we postulate God in addition to the created universe we increase the complexity of our hypothesis. We have all the complexity of the universe itself, and we have in addition the at least equal complexity of God. (The designer of an artifact must be at least as complex as the designed artifact) . . . .If the theist can show the atheist that postulating God actually reduces the complexity of one’s total world view, then the atheist should be a theist. (pp. 275-276; italics mine)
The first response to the above atheist objection is to point out that the atheist claim that the designer of an artifact must be as complex as the artifact designed is certainly not obvious. But I do believe that their claim has some plausibility: for example, in the world we experience, organized complexity seems only to be produced by systems that already possess it, such as the human brain/mind, a factory, or an organisms’ biological parent.
The second, and better, response is to point out that, at most, the atheist objection only works against a version of the design argument that claims that all organized complexity needs an explanation, and that God is the best explanation of the organized complexity found in the world. The version of the argument I presented against the atheistic single-universe hypothesis, however, only required that the fine-tuning be more probable under theism than under the atheistic single-universe hypothesis. But this requirement is still met even if God exhibits tremendous internal complexity, far exceeding that of the universe. Thus, even if we were to grant the atheist assumption that the designer of an artifact must be as complex as the artifact, the fine-tuning would still give us strong reasons to prefer theism over the atheistic single-universe hypothesis.
To illustrate, consider the example of the “biosphere” on Mars presented at the beginning of this paper. As mentioned, the existence of the biosphere would be much more probable under the hypothesis that intelligent life once visited Mars than under the chance hypothesis. Thus, by the prime principle of confirmation, the existence of such a “biosphere” would constitute strong evidence that intelligent, extraterrestrial life had once been on Mars, even though this alien life would most likely have to be much more complex than the “biosphere” itself.
The final, and I believe the best, response theists can give to this objection is to show that a “supermind” such as God’s would not require a high degree of unexplained organized complexity to create the universe. Although I have presented this response elsewhere (Collins, “Who Designed God Objection,” forthcoming), presenting it here is beyond the scope of this paper. Here I simply note that, for reasons entirely independent of the argument from design, God has been thought to have little, if any, internal complexity. Indeed, Medieval philosophers and theologians often went as far as advocating the doctrine of Divine Simplicity, according to which God is claimed to be absolutely simple, without any internal complexity. So, atheists who push this objection have a lot of arguing to do to make it stick.
Objection 5: No Probability Objection
Some philosophers object to claim that the fine-tuning is highly improbable under the atheistic single-universe hypothesis (that is, premise (2) above) by arguing that since we only have one universe, the notion of the fine-tuning of the universe being probable or improbable is meaningless. Further, they argue, even if it were meaningful, we would have no way of adequately justifying, besides appealing to intuition, that the fine-tuning is very improbable under the atheistic single-universe hypothesis. Typically, the claim behind the first part of this objection is that probability only makes sense in terms of relative frequency within some reference class. Thus, for instance, the assertion that the probability that a randomly selected male smoker will die of lung cancer is 30% means that the 30% of the members of the class of male smokers die of lung cancer. But, if there is only one universe, there is no reference class of universes to compare it to, and hence claims regarding the probability or improbability of fine-tuning in this context do not make sense.
The problem with this argument is that it completely ignores other prominent conceptions of probability. One of these is the epistemic notion of probability. Epistemic probability is a widely-recognized type of probability that applies to claims, statements, and hypotheses--that is,
class=Section3>what philosophers call propositions. [16] Roughly, the epistemic probability of a proposition can be thought of as the degree of credence--that is, degree of confidence or belief--we rationally should have in the proposition. Put differently, epistemic probability is a measure of our rational degree of belief under a condition of ignorance concerning whether a proposition is true or false. For example, when one says that the universe is probably older than fifteen billion years, one is making a statement of epistemic probability. After all, the universe is actually either older than fifteen billion years or it is not. But, we do not know for sure which one it is, so we use the word “probably” to indicate that we should put more confidence in its being older than fifteen billion years than its being younger.
Besides epistemic probability simpliciter, philosophers also speak of what is known as the conditional epistemic probability of one proposition on another. (A proposition is any claim, assertion, statement, or hypothesis about the world). The conditional epistemic probability of a proposition R on another proposition S--written as P(R/S)--can be defined as the degree to which the proposition S of itself should rationally lead us to expect that R is true. Under the epistemic conception of probability, therefore, the statement that the fine-tuning of the cosmos is very improbable under the atheistic single-universe hypothesis makes sense: it is to be understood as making a statement about the degree to which the atheistic single-universe hypothesis would or should, of itself, rationally lead us to expect cosmic fine-tuning. The claim that a state of affairs is epistemically very improbable, therefore, can be thought of as equivalent to the claim that it is very unexpected or surprising. Thus, for instance, one could reword premise (2) of our main argument to say that the fine-tuning is very surprising under the atheistic single-universe hypothesis. Rewording premises (1) and (2), and the prime principle of confirmation, in terms of degrees of surprise might be especially helpful for those trained in the sciences who associate probability primarily with some sort of relative frequency.
Now that we know what it means to say that the fine-tuning of the constants of physics is very unlikely under the atheistic single-universe hypothesis, it is time to briefly outline how such a statement could be justified. Here I think we need to apply what is known as the principle of indifference. Applied to the case at hand, the principle of indifference could be roughly stated as follows: when we have no reason to prefer any one value of a parameter over any other, we should assign equal probabilities to equal ranges of the parameter, given that the parameter in question directly corresponds to a natural parameter. [17] Specifically, if the “theoretically possible” range (that is, the range allowed by the relevant background theories) of such a parameter is R and the life-permitting range is r, then the probability is r/R. Suppose, for instance, that the “theoretically possible” range, R, of values for the strength of gravity is zero to the strength of the strong nuclear force- – that is, 0 to 1040G0, where G0 represents the current value for the strength of gravity. As we saw above, the life-permitting range r for the strength of gravity is at most 0 to 109G0. Now, of itself (specifically, apart from the knowledge that we exist), the atheistic single-universe hypothesis gives us no reason to think that the strength of gravity would fall into the life-permitting region instead of any other part of the theoretically possible region. Thus, assuming the strength of the forces constitute a natural variable, the principle of indifference would state that equal ranges of this force should be given equal epistemic probabilities, and hence the epistemic probability of the strength of gravity falling into the life-permitting region would be at most r/R = 109 /1040 = 1/1031.[18] In sum, we should find it very surprising under the atheistic single-universe hypothesis for the strength of gravity to have fallen into the life-permitting range given the enormous range of force strengths in nature.
One major problem with this rough version of the principle of indifference is the well-known Bertrand Paradoxes (e.g., see Weatherford, 1982, p. 56), in which there are two equally good but conflicting parameters that directly correspond to a physical quantity. A famous example of the Bertrand paradox is that of a factory that produces cubes whose sides vary from zero to two inches, which is equivalent to saying that it produces cubes whose volumes vary from zero to eight cubic inches. Given that this is all we know about the factory, the naive form of the principle of indifference implies that we should assign both equal probabilities to equal ranges of lengths and equal probabilities to equal ranges of volumes, since both lengths and volumes correspond to actual physical magnitudes. It is easy to see, however, that this leads to conflicting probability assignments – e.g., using lengths, we get a probability of 0.5 of a cube being between zero and one inch in length, whereas using volumes we get a probability of 0.125.
Although many philosophers have taken the Bertrand Paradoxes as constituting a fatal objection to the principle of indifference, one can easily avoid this objection either by restricting the applicability of the principle of indifference to those cases in which Bertrand Pardoxes do not arise or by claiming that the probability should not be assigned an exact value but rather a range of values. This range would be the range spanning the values given by the various conflicting parameters. The problem of conflicting parameters, however, does not seem to arise for most cases of fine-tuning.
Another problem is the total theoretically possible range R of values a constant of physics could have. This is a difficult issue beyond the scope of this paper to address. Here we simply note that often one can make plausible estimates of a lower bound for the theoretically possible range – e.g., since the actual range of forces in nature span a range of 1040, the value of 1040 provides a natural lower bound for the theoretically possible range of force strengths.[19]
Finally, several powerful reasons
can be offered for its soundness of the principle of indifference if it is restricted in the
ways explained above. First, it has a
wide range of applicability. As philosopher Roy Weatherford notes in his book, Philosophical Foundations of Probability
Theory, "an astonishing number of extremely complex problems in
probability theory have been solved, and usefully so, by calculations based
entirely on the assumption of equiprobable
alternatives [that is, the principle of indifference]"(p. 35). Second, at least for the discrete case, the
principle can be given a significant theoretical grounding in information
theory, being derivable from
Although we have only had space to provide a brief account of how one could go about rigorously defending the claim that the fine-tuning is very improbable under the atheistic single-universe hypothesis, the above account does show, I believe, that there is an initially plausible method available of rigorously supporting our intuitive judgement of the improbability of fine-tuning under the atheistic single-universe hypothesis. Nonetheless, it should be stressed again that even if ultimately our method of support fails, this is not fatal to the fine-tuning argument. As with arguments in science, the fine-tuning argument has great initial intuitive plausibility. Accordingly, to defeat this initial plausibility, the burden is on the skeptic to show that the fine-tuning argument rests on a clearly faulty form of reasoning.
IV. THE MANY-UNIVERSES HYPOTHESIS
The Many-Universes Hypothesis Explained
In response to this theistic or intelligent design explanation of the fine-tuning, many atheists have offered an alternative explanation, what I will call the many-universes hypothesis, but which in the literature goes under a variety of names, such as many-worlds hypothesis, the many-domains hypothesis, the world-ensemble hypothesis, the multi-universe hypothesis, and so on. According to this hypothesis, there are a very large--perhaps infinite --number of universes, with the constants of physics varying from universe to universe.[21] Of course, in the vast majority of these universes the constants of physics would not have life-permitting values. Nonetheless, in a small proportion of universes they would, and consequently it is no longer improbable that universes such as ours exist in which the constants of physics have just the right values for intelligent life.
Further, usually these universes are thought to be produced by some sort of physical mechanism, which I call a many-universes generator. The universe generator can be thought of as analogous to a lottery ticket generator: just as it would be no surprise that a winning number is eventually produced if enough tickets are generated, it would be no surprise that a universe fine-tuned for life would occur if enough universes are generated.[22]
The Inflationary Many-Universes Model
Most many-universes models are entirely speculative, having little basis in current physics. One many-universes model, however, does have a reasonable basis in current physics – namely, that based on inflationary cosmology. Inflationary cosmology is a currently widely discussed cosmological theory that attempts to explain the origin of the universe. Essentially, it claims that our universe was formed by a small area of pre-space being massively blown up by an hypothesized inflaton field, in much the same way as a soup bubble would form in an ocean full of soap. In chaotic inflation models--widely considered the most plausible– various points of the pre-space are randomly blown up, forming innumerable bubble universes. Further, because of the inflaton field, the pre-space expands so rapidly that it becomes a never ending source of bubble universes, much as a rapidly expanding ocean full of soap would become a never ending source of soap bubbles. Thus, inflationary cosmology can naturally give rise to many universes.[23]
In order to get the initial conditions and constants of physics to vary from universe to universe, as they must do if this scenario is going to explain the fine-tuning, there must be a further physical mechanism to cause the variation. Such a mechanism might be given by superstring theory, but it is too early to tell. Superstring theory is currently one of the most hotly discussed hypotheses about the fundamental structure of the physical universe (Greene, 1999, p. 214). According to superstring theory, the ultimate constituents of matter are strings of energy that undergo quantum vibrations in a 10 (or 11) dimensional space-time, six or seven dimensions of which are "compactified" to extremely small sizes and are hence unobservable. The shape of the compactified dimensions, however, determines the modes of vibration of the strings, and hence the types and masses of fundamental particles, along with many characteristics of the forces between them. Thus, universes in which compactified dimensions have different shapes will have different constants of physics and differrent lower-level laws governing the forces. It is presently controversial whether superstring theory allows for significant variation in the shape of the compactified dimensions, though the direction of current research indicates that it does. (See Susskind, forthcoming). If it does, however, it is then possible that an inflationary/superstring scenario could be constructed in which the shape of the compactified dimensions, and hence the constants of physics, underwent enough variation from universe to universe to explain the fine-tuning.[24]
Thus, it is in the realm of real physical plausibility that a viable inflationary/superstring many-universes scenario could be constructed that would account for the fine-tuning of the constants of physics. Nonetheless, it should be noted that despite the current popularity of both inflationary cosmology and superstring theory, both are highly speculative. For instance, as Michio Kaku states in his recent textbook on superstring theory, “Not a shred of experimental evidence has been found to confirm . . . superstrings” (1999, p. 17). The major attraction of string theory is its mathematical elegance and the fact that many physicists think that it currently offers the most plausible proposal for providing a truly unified physical theory that combines gravitation with quantum mechanics, the two cornerstones of modern physics (Greene, 1999, p. 214).
It should be stressed, however, that even if superstring theory or inflationary cosmology turn out to be false, they have opened the door to taking the many-universes explanation of the fine-tuning as a serious physical possibility since some other physical mechanisms could give rise to multiple universes with a sufficiently large number of variations in the constants of physics. The only way we could close this door is if we were to discover that the ultimate laws of physics do not allow either many universes or sufficient variation in the constants and laws of physics among universes.
Theistic Responses to Many-Universes Generator Scenario
One major theistic response to the many-universes generator scenario, whether of the inflationary variety or some other type, is that a “many-universes generator” would seem to need to be “well-designed” in order to produce life-sustaining universes. After all, even a mundane item like a bread machine, which only produces loaves of bread instead of universes, must be well designed to produce decent loaves of bread. If this is right, then invoking some sort of many-universes generator as an explanation of the fine-tuning only kicks the issue of design up one level, to the question of who designed the many-universes generator.
The inflationary scenario discussed above