TH E
To motivate the claim that the comparison range, WR, should be taken as the EI range, we shall consider a more mundane case of a very large dartboard with only some small, fi nite region around the bull’s eye that is illuminated, with the bulk of the dartboard in darkness. In this case, we know neither how far the dartboard extends nor whether there are other bull’s eyes on it. If we saw a dart hit the bull’s eye in the illuminated (IL) region, and the bull’s eye was very, very small compared with the IL region, we would take that as evidence that the dart was aimed, even though we cannot say anything about the density of bull’s eyes on other regions of the board.
One way of providing a likelihood reconstruction of the confi rmation of the aiming hypothesis is to include the fact that the dart fell into the IL region as part of the information being conditioned on: that is, include it in the background information k′. We could then use the Likelihood Principle to argue as follows: given that we know that the dart has fallen into the IL region, it is very unlikely for it to have hit the bull’s eye by chance but not unlikely if it was aimed; hence, its falling in the bull’s eye confi rms the aiming hypothesis over the chance hypothesis. Similarly, for the case of fi ne-tuning, we should include the fact that the value of a constant is within the EI region as part of our background information k′.
Is including in k′ the fact that C falls into the EI range an adequate procedure? The case of the dartboard, I believe, shows that it is not only a natural procedure to adopt, but also arguably the only way of providing a Likelihood Principle reconstruction of the inference in this sort of mundane case. First, it is clearly the ratio of the area taken up by the bull’s eye to the IL region around the bull’s eye that leads us to conclude that it was aimed.
Second, one must restrict the comparison range to the IL range (i.e. include IL in k′) since one does not know how many bull’s eyes are in the unilluminated portion of the dartboard.
Thus, if one expanded the comparison range outside the IL range, one could make no estimate as to the ratio of the area of the bull’s eye regions to the non-bull’s eye regions, and thus could not provide a likelihood reconstruction. Yet it seems intuitively clear that 27. This is a different approach than in one of my earlier papers on the issue (Collins 2005b), where the range was constrained by what values are consistent with a universe’s existing – for example, too high of a value for the gravitational constant would reduce the whole universe to a singularity and so forms a natural bound of the range. The “universe existing constraint” is still valid (since NSU & k′ presuppose the existence of a universe), but it is typically trumped by the EI region constraint, since the latter is more stringent.
T E L E O LO G I C A L
A RG U M E N T 245
the dart’s hitting the bull’s eye in this case does confi rm the aimed hypothesis over the chance hypothesis.
Another way of seeing why the comparison range should be equal to the EI range is in terms of the rational degrees of credence in Lpc of the fi ctional unembodied alien observer introduced at the end of Section 3.2. In accordance with the method of dealing with old evidence, we imagine our alien observer holding background information k′, in which the knowledge of the value of C is subtracted out. Then we imagine that our alien observer learns that C falls into the EI range. Call this new information Q. Even assuming that it makes sense to speak of C as possibly having any value between minus infi nity and infi nity, the alien observer would not know whether the sum of the widths of all the life-permitting regions outside of the EI region are fi nite or infi nite. Hence, it would not know the value of P(Q|T & k′), since to say anything about the chance of God’s creating C in the EI region, it would have to know if there are other life-permitting regions besides the ones in EI. Hence, P(Q|NSU & k′)/P(Q|T & k′) would be indeterminate. This means that knowledge of Q neither confi rms nor disconfi rms T relative to NSU.
Suppose our alien observer learns the additional information, Lpc, that C falls into the life-permitting region of EI. Since our observer knows Q, assessing whether this additional information confi rms T with respect to NSU will depend on the ratio P(Lpc|k′
& Q & T)/P(Lpc|k′ & Q & NSU). Now, since k′ & Q & NSU implies nothing about where C falls in the EI region, it would leave our alien observer indifferent as to where it fell in this region. Hence, assuming the validity of the restricted Principle of Indifference (see Section 3.3.2), P(Lpc|k′ & Q & NSU) = Wr/WR, where WR is equal to width of the EI region. Thus, including the information Q that C falls into the EI region in our background information k′ is equivalent to choosing our comparison range as the EI range.
At this point, one might question the legitimacy of including Q in our background information k′: that is, choosing k′ such that k′ → k′ & Q. Besides appealing to examples such as the previously discussed dartboard case, in general when comparing hypotheses, we can place into the background information any evidence that we have good reason to believe neither confi rms nor disconfi rms the hypothesis in question. In some cases this is obvious: for example, when assessing the ratio of the probabilities of the defendant’s fi ngerprints’ matching those on the gun under the guilt and innocence hypothesis, respectively, the fact that Jupiter has over 62 moons would be irrelevant information. Thus, jurors would be free to include it as part of their background information.
Another way of thinking about this issue is to note that k′ determines the reference class of possible law structures to be used for purposes of estimating the epistemic probability of Lpc under NSU: the probability of Lpc given k′ & NSU is the relative proportion of law structures that are life-permitting in the class of all law structures that are consistent with k′ & NSU. (The measure over this reference class is then given by the restricted Principle of Indifference.) Thinking in terms of reference classes, the justifi cation for restricting our reference class to the EI region is similar to that used in science: when testing a hypothesis, we always restrict our reference classes to those for which we can make the observations and calculations of the frequencies or proportions of interest – what in statistics is called the sample class. This is legitimate as long as we have no reason to think that such a restriction produces a relevantly biased reference class. Tests of the long-term effi cacy of certain vitamins, for instance, are often restricted to a reference class of randomly selected doctors and nurses in certain participating hospitals, since these are the only individuals that one
can reliably trace for extended periods of time. The assumption of such tests is that we have no reason to think that the doctors and nurses are relevantly different than people who are neither doctors nor nurses, and thus that the reference class is not biased. As discussed in Section 4.2, the justifi cation for varying a constant instead of varying the mathematical form of a law in the fi ne-tuning argument is that, in the reference class of law structures picked out by varying a constant, we can make some estimate of the proportion of life-permitting law structures. This is something we probably could not do if our reference class involved variations of mathematical form. The same sort of justifi cation underlies restricting the class to the EI range.
It is also important to keep things in perspective by noting that there are really two separate issues here. First is the issue of the existence of a meaningful probability for P(Lpc|Q & k′ & NSU). That question reduces to whether there is an epistemic probability measure over the EI region; this will uncontroversially be the case if the EI region is fi nite and the restricted Principle of Indifference is true and applies. The second question is whether Q & k′ is the appropriate background information. If one allowed for prior probabilities and the full use of Bayes’s Theorem, then any choice is appropriate as long as one also has meaningful prior probabilities for P(NSU|Q & k′), P(T|Q & k′), and P(Lpc|Q & k′
& T).28 Since I have attempted to avoid the use of prior probabilities, it became important to have some procedure of determining the appropriate background information k′. So this issue arises only for the likelihood version of the argument that avoids prior probabilities. It does not arise for other versions, including the secondary method of probabilistic tension, since, as we saw earlier, that does not depend on the particular choice of appropriate background information.
Including Q in k′ provides a Likelihood Principle reconstruction of John Leslie’s “fl y on the wall” analogy, which he offers in response to the claim that there could be other unknown values for the constants of physics, or unknown laws, that allow for life: If a tiny group of fl ies is surrounded by a largish fl y-free wall area then whether a bullet hits a fl y in the group will be very sensitive to the direction in which the fi rer’s rifl e points, even if other very different areas of the wall are thick with fl ies. So it is suffi cient to consider a local area of possible universes, e.g., those produced by slight changes in gravity’s strength. . . . It certainly needn’t be claimed that Life and Intelligence could exist only if certain force strengths, particle masses, etc. fell within certain narrow ranges. . . . All that need be claimed is that a lifeless universe would have resulted from fairly minor changes in the forces etc. with which we are familiar. (1989, pp. 138–9).
Finally, notice how our methodology deals with a common major misunderstanding of the fi ne-tuning argument based on the constants of physics. On this misunderstanding, advocates of the fi ne-tuning argument are accused of implicitly assuming the laws somehow existed temporally or logically prior to the constants, and then afterwards the values of the constants were determined. Then one imagines that if NSU is true, the values occur by 28. According to the odds form of Bayes’s Theorem, P(NSU|Lpc & k)/P(T|Lpc & k) = P(NSU|Lpc & Q & k′)/
P(T|Lpc & Q & k′) = P(NSU|Q & k′)/P(T|Q & k′) × P(Lpc|Q & k′ & NSU)/P(Lpc|Q & k′ & T). [Lpc & Q & k′ = Lpc & k, since (i) Lpc & k′ = k and (ii) the life-permitting range is part of the EI range, and hence Lpc entails Q, which means Lpc & k′ = Lpc & k′ & Q. I am assuming none of the probabilities in the denominators are zero.]
T E L E O LO G I C A L
A RG U M E N T 247
“chance,” and hence it is very, very unlikely for them to fall into the life-permitting range. Thus, critics of the fi ne-tuning argument, such as Ian Hacking (1987, pp. 129–30) and John Earman (2006), have claimed that it begs the question, since it already presupposes the existence of a creator. According to Earman, talk of the existence of a fi ne-tuned universe’s being improbable “seems to presuppose a creation account of actuality: in the beginning there is an ensemble of physically possible universes – all satisfying the laws of our universe but with different values of the constants – awaiting to be anointed with the property of actuality by the great Actualizer . . .” (2006). It should be clear that the way in which I spell out the argument makes no such metaphysical assumption. We simply consider the ratio of epistemic probabilities P(Lpc|T & k′)/P(Lpc|NSU & k′), where Lpc denotes the claim that a constant fell into the life-permitting range; this does not presuppose a creation account of the laws any more than does a likelihood reconstruction of the confi rmation that old evidence e provides a scientifi c theory, in which a similar procedure of subtracting old evidence is involved.29
4.5. Examples of the EI region
In this section, we shall consider how to estimate the EI region for the force strengths and some other constants. In doing this, we fi rst note that, as argued in Section 4.2, we must make our estimates of epistemic probability relative to the best calculation-permitting models we have, as long as those models are reasonable approximations of the best current overall models. Consider, for instance, the strong nuclear force, which is only defi ned in a specifi c model. We know that this model has only limited applicability since the strong nuclear force is ultimately the byproduct (or residue) of the “color force” between the quarks of which neutrons and protons are composed. Further, the physical model, quantum chromodynamics, describing the color force is thought to have only limited range of applicability to relatively low energies. Thus, the EI region will be fi nite, since we can only do valid calculations for those values of the strong nuclear force or color force that stay within a relatively low-energy regime.
This limitation of energy regime does not apply just to the theory of strong interactions, but to all of the fundamental quantum theories of nature. In the past, we have found that physical theories are limited in their range of applicability – for example, Newtonian mechanics was limited to medium-sized objects moving at slow speeds relative to the speed of light. For fast-moving objects, we require special relativity; for massive objects, General Relativity; for very small objects, quantum theory. When the Newtonian limits are violated, these theories predict completely unexpected and seemingly bizarre effects, such as time dilation in special relativity or tunneling in quantum mechanics.
There are good reasons to believe that current physics is limited in its domain of applicability. The most discussed of these limits is energy scale. The current orthodoxy in high-29. Those, such as McGrew, McGrew, and Vestrup (Section 4.6), who claim that the entire possible range of constants is the only nonarbitrary comparison range, also appear to be in the grip of the mistaken idea that the relevant probabilities are determined by a model of “universe creation” in which fi rst the laws come into existence, and then the constants are “chosen” from the range of possible values that they could have. Since within such a conceptualization, the constants could have had any value, one is erroneously led to think that the only adequate comparison range is minus infi nity to plus infi nity.
energy physics and cosmology is that our current physics is either only a low-energy approximation to the true physics that applies at all energies or only the low-energy end of a hierarchy of physics, with each member of the hierarchy operating at its own range of energies.30 The energy at which any particular current theory can no longer to be considered approximately accurate is called the cutoff energy, although (despite its name) we should typically expect a continuous decrease in applicability, not simply a sudden change from applicability to nonapplicability. In contemporary terminology, our current physical theories are to be considered effective fi eld theories. The limitation of our current physics directly affects thought experiments involving changing the force strengths. Although in everyday life we conceive of forces anthropomorphically as pushes or pulls, in current physics forces are conceived of as interactions involving exchanges of quanta of energy and momentum.31 The strength of a particular force, therefore, can be thought of as proportional to the rate of exchange of energy-momentum, expressed quantum mechanically in terms of probability cross sections. Drastically increasing the force strengths, therefore, would drastically increase the energy-momentum being exchanged in any given interaction. Put another way, increasing the strength of a force will involve increasing the energy at which the relevant physics takes place. So, for instance, if one were to increase the strength of electromagnetism, the binding energy of electrons in the atom would increase; similarly, an increase in the strength of the strong nuclear force would correspond to an increase in the binding energy in the nucleus.32
The limits of the applicability our current physical theories to below a certain energy scales, therefore, translates to a limit on our ability to determine the effects of drastically increasing a value of a given force strength – for example, our physics does not tell us what would happen if we increased the strong nuclear force by a factor of 101,000. If we naively applied current physics to that situation, we should conclude that no complex life would be possible because atomic nuclei would be crushed. If a new physics applies, however, entirely new and almost inconceivable effects could occur that make complex life possible, much as quantum effects make the existence of stable atomic orbits possible, whereas such orbits were inconceivable under classical mechanics. Further, we have no guarantee that the concept of a force strength itself remains applicable from within the perspective of the new physics at such energy scales, just as the concept of a particle’s having a defi nite position and momentum, lost applicability in quantum mechanics; or the notion of absolute time lost validity in special relativity; or gravitational “force” (versus curvature of space-30. See, for instance, Zee (2003, pp. 437–8), Cao (1997, pp. 349–53), and Teller (1988, p. 87). For example, Zee says that he espouses “the philosophy that a quantum fi eld theory provides an effective description of physics up to a certain energy scale Λ, a threshold of ignorance beyond which physics not included in the theory comes into play” (p. 438).
31. Speaking of gravitational force as involving energy exchange is highly problematic, although speaking of gravitational binding energy is not nearly as problematic. One problem is that in General Relativity, gravity is not conceived of as a force but as curvature of space-time. Another problem is that there is no theoretically adequate defi nition for the local energy of a gravitational fi eld or wave. (See, for instance, Wald, 1984, p. 70, n. 6; p. 286.) Finally, although physicists often speak of gravitons as the carriers as the carrier of the gravitational force, the quantum theory of gravity out of which gravitons arise is notoriously non-renormalizable, meaning that infi nities arise that cannot be eliminated. Nonetheless, since gravitational waves cause changes in the energy of material objects at a certain rate, we can still meaningfully speak of energy scales at which a particular gravitational “force”
is operating, which is all that is needed for this argument.
32. The weak force does not involve binding energies but is an interaction governing the transmutation of particles from one form to another, and so this last argument would not apply to it.
T E L E O LO G I C A L
A RG U M E N T 249
time) in General Relativity.33 Thus, by inductive reasoning from the past, we should expect not only entirely unforeseen phenomena at energies far exceeding the cutoff, but we even should expect the loss of the applicability of many of our ordinary concepts, such as that of force strength.
The so-called Plank scale is often assumed to be the cutoff for the applicability of the strong, weak, and electromagnetic forces. This is the scale at which unknown quantum gravity effects are suspected to take place thus invalidating certain foundational assumptions on which current quantum fi eld theories are based, such a continuous space-time (see e.g. Peacock 1999, p. 275; Sahni & Starobinsky 1999, p. 44). The Plank scale occurs at the energy of 1019 GeV (billion electron volts), which is roughly 1021 higher than the binding energies of protons and neutrons in a nucleus. This means that we could expect a new physics to begin to come into play if the strength of the strong force were increased by more than a factor of ~1021. Another commonly considered cutoff is the grand unifi ed theory (GUT) scale, which occurs around 1015 GeV (Peacock 1999, pp. 249, 267). The GUT scale is the scale at which physicists expect the strong, weak, and electromagnetic forces to be united. From the perspective of the currently proposed GUT, these forces are seen as a result of symmetry-breaking of the united force that is unbroken above 1015 GeV, where a new physics would then come into play. Effective fi eld theory approaches to gravity also involve General Relativity’s being a low-energy approximation to the true theory. One common proposed cutoff is the Plank scale, although this is not the only one (see e.g.
Burgess 2004, p. 6).
Where these cutoffs lie and what is the fundamental justifi cation for them are controversial issues. The point of the previous discussion is that the limits of our current theories are most likely fi nite but very large, since we know that our physics does work for an enormously wide range of energies. Accordingly, if the life-permitting range for a constant is very small in comparison, then Wr/WR << 1, which means that there will be fi ne-tuning.
Rigorously determining Wr/WR is beyond the scope of this chapter. Almost all other purportedly fi ne-tuned constants also involve energy considerations: for example, because of Einstein’s E = mc2, the rest masses of the fundamental particles (which are fundamental constants) are typically given in terms of their rest energies – for example, the mass of the proton is 938 MeV (million electron volts). Further, the cosmological constant is now thought of as corresponding to the energy density of empty space. Thus, the considerations of energy cutoff mentioned will play a fundamental role in defi ning the EI region, and hence WR, for many constants of physics.
4.6. Purported problem of infi nite ranges
Finally, let us suppose that the comparison range is infi nite, either because of some new theory that applies at all energy scales or because the reasoning in the last two subsections is incorrect. Timothy McGrew, Lydia McGrew, and Eric Vestrup (2001) and, independently, Mark Colyvan, Jay Garfi eld, and Graham Priest (2005) have argued that if the comparison range is infi nite, no meaningful probability can be assigned to a constant’s landing in 33. More generally, since constants are only defi ned with respect to the theories of physics in which they occur, their range of applicability, and thus the EI range, is restricted to the range of applicability of those theories.
the life-permitting region. (They also mistakenly assume that the only nonarbitrary comparison range for the constants of nature consists of all possible values (−∞ to ∞).) These authors fi rst assert that (i) the total probability of a constant’s being somewhere in the infi nite range of possible values has to be 1 (since it must have some value), and (ii) if we assume an equiprobability distribution over the possible values – which they claim is the only nonarbitrary choice – the probability of its being in any fi nite region must be zero or undefi ned. Finally, (iii) they consider any arbitrary way of dividing up the entire range into a countably infi nite set of fi nite, nonoverlapping regions, and assert that the total probability of its being in the entire region must the sum of the probabilities of its being in each member of the set. For example, the probability of its being in the entire region is the sum of the probabilities of its being between 0 and 1, of its being between 1 and 2, of its being between 2 and 3, ad infi nitum, plus the sum of the probabilities of its being between 0 and −1, between −1 and −2, ad infi nitum. But since no matter how many times one adds zero together, one gets zero, this sum turns out to be zero. Hence, if we assume that each probability is zero, we get a contradiction since the probability of the constant having a value somewhere in the entire region is 1. Therefore, it must be undefi ned.
The problem with this argument is the assumption that the epistemic probability for the entire region is the sum of the individual probabilities of each fi nite disjoint region. In cases where the number of alternatives is fi nite, this is true: the sum of the probabilities of a die landing on each of its sides is equal to the probability of the die landing on some side. This is a fundamental principle of the probability calculus called fi nite additivity.
When fi nite additivity is extended to a countably infi nite number of alternatives, it is called countable additivity, which is the principle that McGrew and Vestrup implicitly invoke.
This latter principle, however, has been very controversial for almost every type of probability, with many purported counterexamples to it. Consider, for example, the following situation. Suppose that what you fi rmly believe to be an angel of God tells you that the universe is infi nite in extent and that there are a countably infi nite number of other planets with civilizations on each planet. Finally, the “angel” tells you that within a billion miles of one and only one of those planets is a golden ball 1 mile in diameter and that it has delivered the identical message to one person on each of those planets. Finally, you decide on the following arbitrary numbering system to identify the planets: you label Earth 1, the planet that is closest to Earth 2, the planet that is next farther out 3, and so forth. Since within current Big Bang cosmology an infi nite universe would have no center, there is nothing special about Earth’s location that could fi gure into one’s probability calculation. Accordingly, it seems obvious that, given that you fully believe the “angel”, for every planet k your confi dence that the golden ball is within a billion miles of k should be zero. Yet this probability distribution violates countable additivity. One cannot argue that the scenario I proposed is in any way self-contradictory, unless one wants to argue that an infi nite universe is self-contradictory. This, however, ends up involving substantive metaphysical claims and is arguably irrelevant, since the issue is the degree to which the propositions delivered by the “angel” justifi es, or warrants, the belief that the ball is within a billion miles of our planet, not whether these propositions ultimately could be true.
McGrew and McGrew (2005) have responded to these sorts of arguments by claiming that when the only nonarbitrary distribution of degrees of belief violates the axiom of countable additivity, the most rational alternative is to remain agnostic. They point out
T E L E O LO G I C A L
A RG U M E N T 251
that one need not assign epistemic probabilities to all propositions. I do not believe this is an adequate response, since I think in some cases it would be irrational to remain agnostic.
For example, it would be irrational for a billionaire who received the aforementioned message to spend millions, or even hundreds, of dollars in search of the golden planet, even if it were entirely rational for him to believe what the “angel” told him; it would even be irrational for him to hope to discover the planet. This is radically different than cases where people are legitimately agnostic, such as perhaps about the existence of extraterrestrials or the existence of God; for example, it seems rationally permitted at least to hope for and seek evidence for the existence of extraterrestrials or God.
The implausibility of being agnostic in the “golden planet case” is further brought out when one considers that if the billionaire were told that the universe was fi nite with exactly 1010,000 planets with civilizations, clearly he should be near certain that the golden planet is not near Earth. But, clearly, if the billionaire is told that there are even more planets – infi -
nitely many – the billionaire should be at least as confi dent that the planet is not near Earth; and, certainly, it should not become more rational for him to search for it than in the 1010,000
planets case, as it would if he should switch to being agnostic.
So the McGrews and others are wrong in claiming that there would be no epistemic probability if the range is infi nite. However, they are correct in claiming that this would turn the fi ne-tuning argument into what McGrew, McGrew, and Vestrup (2001) have called the course-tuning argument (CTA). As they correctly point out, if the comparison range is infi nite, then no matter how large the life-permitting range is, as long as it is fi nite the ratio Wr/WR will be zero. This means that the narrowness of the range becomes irrelevant to our assessment of degree of fi ne-tuning. The McGrews and Vestrup, reiterating a point made by Paul Davies (1992, pp. 204–5), claim that it is obvious that CTA is not a good argument since CTA would have the same force no matter how “un-fi ne-tuned” a constant is, as long as the life-permitting range is fi nite. Thus, they argue, this would render the appeal to physics, and the narrowness of the life-permitting range, completely superfl uous.
In response, an appeal to physics would still be necessary: we still should have to have good physical reasons to think the life-permitting range to be fi nite, which itself would involve having a model that we had good reasons to believe was accurate for all values of the parameter in question. This would involve a substantial appeal to physics. Of course, if it turned out that the comparison range were infi nite, the restrictiveness of the life-permitting range would no longer play a role, and thus the popular presentation of the argument would have to be modifi ed. Nonetheless, the formal presentation of the argument, based on the claim that Wr/WR << 1 and the restricted Principle of Indifference, would remain. As is, I suggest that the reason we are impressed with the smallness is that we actually do have some vague fi nite comparison range to which we are comparing the life-permitting range, namely the EI range.
Finally, rejecting CTA for the reasons the McGrews and Vestrup give is counterintuitive.
Assume that the fi ne-tuning argument would have probative force if the comparison range were fi nite. Although they might not agree with this assumption, making it will allow us to consider whether having an infi nite instead of fi nite comparison range is relevant to the cogency of the fi ne-tuning argument. Now imagine increasing the width of this comparison range while keeping it fi nite. Clearly, the more WR increases, the stronger the fi ne-tuning argument gets. Indeed, if we accept the restricted Principle of Indifference (Section 3.32), as WR approaches infi nity, P(Lpc|NSU & k′) will converge to zero, and thus P(Lpc|NSU
& k′) = 0 in the limit as WR approaches infi nity. Accordingly, if we deny that CTA has probative force because WR is purportedly infi nite, we must draw the counterintuitive consequence that although the fi ne-tuning argument gets stronger and stronger as WR
grows, magically when WR becomes actually infi nite, the fi ne-tuning argument loses all probative force.34
5. Justifying Premises (1) and (2)
5.1. Justifying premise (1)
The justifi cation of Premise (1) of our main argument in Section 1.3 will depend on which fi ne-tuned feature of the universe is being considered. For the fi ne-tuning of the laws of nature, Premise (1) would be justifi ed by an appeal to widely shared intuitions, as explained in Section 3.3.1. For the fi ne-tuning of the initial conditions of the universe, we have two choices. First, we could appeal to the standard measure of statistical mechanics (as is typically done). Second, if we have qualms about the applicability of the standard measure discussed in Section 2.4, we could appeal to the compelling reasons given in that section for thinking that the universe started in an extraordinarily special state; hence, in some real sense it is still epistemically enormously improbable, even if we cannot provide a rigorous mathematical grounding for that probability.
Finally, for the fi ne-tuning of the constants of physics, we shall appeal to the restricted Principle of Indifference (Section 3.3.2). This is the case we shall elaborate in detail. We shall begin by justifying Premise (1) for the case of individual constants that are fi ne-tuned and then consider the case in which the constants are combined. The argument has two steps:
(i) Let C be a constant that is fi ne-tuned, with C occurring in the simplest current formulation of the laws of physics. Then, by the defi nition of fi ne-tuning, Wr/WR << 1, where Wr is the width of the life-permitting range of C, and WR is the width of the comparison range, which we argued was equal to the width of the EI range.
(ii) Since NSU and k′ give us no reason to think that the constant will be in one part of the EI range instead of any other of equal width, and k′ contains the information that it is somewhere in the EI range, it follows from the restricted Principle of Indifference that P(Lpc|NSU & k′) = Wr/WR, which implies that P(Lpc|NSU & k′) << 1.
5.1.1. Combining constants
Some have faulted the fi ne-tuning arguments for only varying one constant at a time, while keeping the values of the rest fi xed. For example, Victor Stenger claims that, “One of the many major fl aws with most studies of the anthropic coincidences is that the investigators vary a single parameter while assuming all the others remain fi xed!” (2007, p. 148).
34. For an argument showing that various inferences in contemporary cosmological speculation use infi nite ranges, and for some mathematical justifi cation of these, see Koperski (2005).
T E L E O LO G I C A L
A RG U M E N T 253
This issue can be easily addressed for a case in which the life-permitting range of one constant, C1, does not signifi cantly depend on the value that another constant, C2, takes within its comparison range, R2. In that case, the joint probability of both C1 and C2 falling into their life-permitting ranges is simply the product of the two probabilities. To see why, note that by the method explicated in Sections 4.3 and 4.4, the appropriate background information, k′12, for the joint conditional probability of Lpc1 & Lpc2 on NSU is k′12 = k − Lpc1 & Q1 − Lpc2 & Q2 = k′1 & k′2. Here, −Lpc1 and the −Lpc2 represent the subtraction of the information that C1 and C2 have life-permitting values, respectively; Q1 and Q2 represent, respectively, the knowledge that they each fell into their respective EI regions (which is added back in, as explained in Section 4.4); and k′1 = k − Lpc1 & Q1 and k′2 = k − Lpc2 & Q2 represent the appropriate background information for C1 and C2, respectively, when they are considered separately.
By the defi nition of conditional probability, P(Lpc
|
|
1 & Lpc2 NSU & k′12) = P(Lpc1 NSU
& k′
|
12 & Lpc2) × P(Lpc2 NSU & k′12). Now, Q2 & Lpc2 = Lpc2 since the claim that C2 fell into its (known) life-permitting region entails that it fell into its EI region: that is, Lpc2 → Q2.
Hence, k′12 & Lpc2 = k − Lpc1 & Q1 − Lpc2 & Q2 & Lpc2 = k − Lpc1 & Q1 − Lpc2 & (Q2 & Lpc2) = k − Lpc1 & Q1 − Lpc2 & Lpc2 = k − Lpc1 & Q1 = k′1. It follows, therefore, that P(Lpc |
|
1 NSU & k′12 & Lpc2) = P(Lpc1 NSU & k′1), which was merely the probability we calculated for Lpc1 on the background information in which we held all the other constants fi xed. So, our next question is, what is the value of P(Lpc |2NSU & k′12)? Now, k′12 includes the values of all the other constants besides C1 and C2. For C1 and C2 it only includes the information that they are in their respective EI regions. Thus, if the width, Wr2, of the life-permitting range of C2 is not signifi cantly dependent on the value of C1 in C1’s EI region, then by the restricted Principle of Indifference, P(Lpc |
|
2 NSU & k′12) ~ Wr2/WR2 = P(Lpc2 NSU
& k′2 ), where WR2 is the width of EI region for C2 when all other constants are held fi xed.35
This means that P(Lpc
|
|
|
1 & Lpc2 NSU & k′12) ~ P(Lpc1 NSU & k′1) × P(Lpc2 NSU & k′2).
Thus, we can treat the two probabilities as effectively independent.
When will two constants be independent in this way? Those will be cases in which the factors responsible for C1’s being life-permitting are effectively independent of the factors responsible for C2’s being life-permitting. For example, consider the case of the fi ne-tuning of the cosmological constant (C1) and the fi ne-tuning of the strength of gravity (C2) relative to the strength of materials – that is, the fi rst case of the fi ne-tuning of gravity discussed in Section 2.3.2. The life-permitting range of gravity as it relates to the strength of materials does not depend on the value of the cosmological constant, and hence P(Lpc |
|
2 k′12 & NSU) = P(Lpc2 k′2 & NSU). This means that the joint probability of both gravity and the cosmological constant’s falling into their life-permitting ranges is the product of these two probabilities: Wr/WR for gravity times Wr/WR for the cosmological constant. This same analysis will hold for any set of fi ne-tuned constants in which the life-permitting range for each constant is independent of the values the other constants take in their respective EI ranges: e.g., the set consisting of the fi ne-tuning of the strong nuclear force needed for stable nuclei and the previously discussed example of the fi ne-tuning of gravity.
35. If Wr2 is dependent on the value C1 takes in its EI region, then one would have to take the average value of Wr2 over C1’s EI region. This would cover those cases for which the two constants are not independent, although we are not considering those cases here. We are also assuming that WR2 is not signifi cantly dependent on the value C1 takes in its EI region; otherwise, we would also have to take the average of WR2.
5.2. Justifying premise (2)
In order to justify Premise (2) of our main argument in Section 1.3, we shall need to argue that God has some reason to bring about LPU.36 For defi niteness, we shall fi rst consider the case of the fi ne-tuning of the constants under the assumption that T is true and that there is only one universe. That is, we shall attempt to justify the claim that for any constant C that is fi ne-tuned, ~P(Lpc|TSU & k′) << 1, where TSU is the theistic single-universe hypothesis and k′ is the background information defi ned in Sections 4.3 and 4.4. It should then be clear how this case generalizes to cases in which the constants are combined, and for the two other fundamental types of fi ne-tuning discussed in Section 2. Finally, we shall indicate how this argument generalizes for the theistic multiverse hypothesis (TMU).
To determine P(Lpc|TSU & k′), let us invoke our imaginative device (Section 3.2) of an unembodied, alien observer with cognitive faculties relevantly similar to our own and who believes TSU and k′. This observer would designate our universe as “the universe that is actual” – which we shall abbreviate as U – and would know that U has the laws that our universe has and the values of all the other constants, except that it only would know that constant C had a value in the EI region. Now if this unembodied being could perceive no reason for God to create the universe with C in the life-permitting region instead of any other part of the EI region, then P(Lpc|TSU & k′) = Wr/WR << 1. So the claim that
~P(Lpc|TSU & k′) << 1 hinges on this unembodied being’s (and hence our) perceiving some reason why God would create a life-permitting universe over other possibilities.
As Richard Swinburne has argued (2004, pp. 99–106), since God is perfectly good, omniscient, omnipotent, and perfectly free, the only motivation God has for bringing about one state of affairs instead of another is its relative (probable) contribution to the overall moral and aesthetic value of reality.37 Simple forms of life, such as bacteria, do not seem in and of themselves to contribute to the overall moral value of reality, although it is possible that they might contribute to its overall aesthetic value. On the other hand, embodied moral agents seem to allow for the realization of unique types of value. Hence, it is this form of life that is most relevant for arguing that ~P(Lpc|k′ & T) << 1, and thus the most relevant for the fi ne-tuning argument.
Now let EMA represent the claim that the universe contains embodied moral agents, and let Wh represent whatever else God must do over and above creating the universe with the right laws, constants, and initial conditions to ensure that it contains such agents, such as God’s intervening in the unfolding of the universe. Now P(EMA|TSU & k′) = P(Lpc & Wh|TSU & k′) = P(Wh|Lpc & k′ & TSU) × P (Lpc|TSU & k′), given that these probabilities have well-defi ned values or ranges of value. Since P(Wh|Lpc & k′ & TSU) ≤ 1, it follows that P(Lpc|TSU & k′) ≥ P(EMA|TSU & k′), once again assuming that these probabilities have well-defi ned values or ranges of value. Thus, if we can establish that ~P(EMA|TSU & k′) << 1, we shall have established that ~P(Lpc|TSU & k′) << 1 (which will automatically 36. For the specifi c case of the fi ne-tuning argument, this section will answer a major objection that is often raised more generally against the design argument (e.g. by Sober 2005): namely, that for the features F that these arguments appeal to, we have no way of determining the probability of God’s creating a world with those features, since we have no way of determining God’s desires.
37. “Probable” is parenthetically inserted before “value” here and elsewhere to allow for open theism, in which God cannot predict with certainty human free choices and hence the overall value of reality.
T E L E O LO G I C A L
A RG U M E N T 255
be true if the probabilities are not well defi ned). In order for ~P(EMA|TSU & k′) << 1, it must be plausible to suppose that on balance, God has more reason to make U in such a way that EMA is true than to make it in such a way that EMA is false. We must be very careful about what is required here. Since we are dealing with epistemic probabilities, which are relative to human cognitive faculties and limitations, to establish that ~P(EMA|TSU & k′) << 1 does not require that we show that God actually has more reason, only that it is plausible to suppose that God does.
This will require fi rst that we perceive, however dimly, that it is plausible to think that the existence of embodied creatures like us – that is, fi nite, vulnerable, embodied moral agents –has a (probable) overall positive value, thus giving God a reason to create a world in which such beings could come about. One cannot merely argue for the value of personal agents in general. The reason is that God’s fi ne-tuning universe U to make EMA true will result in various forms of moral and natural evil, unless God constantly intervenes to prevent it, which clearly does not happen in our world.38 Thus, in order for God to have a reason to adjust C so that U contains our type of embodied moral agents, there must be certain compensatory goods that could not be realized, or at least optimally realized, without our type of embodiment. This brings us directly to the problem of evil.
If we have an adequate theodicy, then we could plausibly argue that our unembodied alien observer would have positive grounds for thinking that God had more reason to create the universe so that EMA is true, since it would have good reason to think that the existence of such beings would add to the overall value of reality. In that case, we could argue that P(Lpc|TSU & k′) > 0.5.39 On the other hand, if we have no adequate theodicy, but only a good defense – that is, a good argument showing that we lack suffi cient reasons to think that a world such as ours would result in more evil than good – then our unembodied being would both lack suffi cient reason to expect that God would make U so that EMA would be true and lack suffi cient reason to expect God to create U so that EMA would be false. Hence, there would be no conditional epistemic probability of EMA on TSU & k′ and therefore no conditional epistemic probability for P(Lpc|TSU & k′). It would still follow, however, that Lpc is not epistemically improbable under TSU: that is, ~P(Lpc|TSU & k′) << 1. Hence, Lpc would still give us good reason to believe TSU
over NSU.40
38. I would like to thank Paul Draper for making me aware of the need to address the problem of evil as part of the fi ne-tuning argument. (See Draper 2008.)
39. One such theodicy (Collins, unpublished manuscript) that I believe explains much of the evil in the world is what I call the “connection building theodicy,” in which the greater goods are certain sorts of deep eternal, ongoing relations of appreciation and intimacy created by one person’s helping another – for example, out of moral and spiritual darkness, in times of suffering, and so on.
40. One might challenge this conclusion by claiming that both the restricted Likelihood Principle and the method of probabilistic tension require that a positive, known probability exist for Lpc on T & k′. This seems incorrect, as can be seen by considering cases of disconfi rmation in science. For example, suppose some hypothesis h conjoined with suitable auxiliary hypotheses, A, predict e, but e is found not to obtain. Let ~E be the claim that the experimental results were ~e. Now, P(~E|h & A & k) << 1, yet P(~E|h & A & k) ≠ 0 because of the small likelihood of experimental error. Further, often P(~E|~(h & A) & k) will be unknown or indeterminate, since we do not know all the alternatives to h nor what they predict about e. Yet, typically we would take ~E to disconfi rm h
& A in this case because P(~E|h & A & k) << 1 and ~P(~E|~(h & A) & k) << 1.
Thus, unless the atheist can show that it is highly improbable that God would create a world which contained as much evil as ours, it will still be the case that, given the evidence of the fi ne-tuning of the constants, the conjunction of the existence of evil and the fact that the constants have life-permitting values strongly confi rms TSU over NSU. This means that theism is still confi rmed when the strongest evidence that atheists typically offer for their position (i.e. the existence of evil) is combined with the evidence of the fi ne-tuning of the constants. Specifi cally, if we let Ev denote the existence of the kinds and degrees of evil we fi nd in the world, then, for all fi ne-tuned constants C, Lpc & Ev gives us good reason to believe in TSU over NSU.41
What about the case of TMU – that is, the hypothesis that God exists and created many universes. One possibility is to consider the evidence, Lpc*, where Lpc* = “the value of the constant C of this universe falls into the life-permitting range,” where “this universe”
refers to our universe by some means other than “the one and only actual universe”: for example, by means of some sort of indexical, such as “the universe that contains this electron,” where the unembodied being has some way of referring to “this electron” other than by a defi nite description that uses only purely qualitative properties. Now, some might worry here that given the existence of multiple universes, God would have no reason to make this universe life-permitting, and thus that P(Lpc*|TMU & k′) << 1. For example, Roger White claims that, “It is only the assumption that there are no other options that we should expect the designer to fi ne-tune this universe for life” (2000, p. 243). I disagree.
Given that the existence of our type of embodied moral agents is a (probable) overall good, it would contribute to the overall value of reality even if there were such beings in other universes. Thus, God would still have a reason for fi ne-tuning this universe, and hence
~P(Lpc*|TMU & k′) << 1. Yet, P(Lpc*/NSU & k′) = P(Lpc/NSU & k′) << 1, and hence Lpc*
would confi rm TMU over NSU.
Even if White is correct, however, our unembodied alien would still have the same reason as offered earlier for thinking that God would create some life-permitting universe. Thus,
~P(LPU*|TMU & k′) << 1, where LPU* is the claim that “some life-permitting universe exists.” Nonetheless, since for every constant C, NSU & k′ & LPU* entails Lpc & NSU & k′, P(LPU*|NSU & k′) ≤ P(Lpc|NSU & k′) << 1. Thus, by the restricted version of the Likelihood Principle, LPU* confi rms TMU over NSU. If White is right, therefore, the relevant confi rmatory evidence for TMU versus NSU would become “some life-permitting universe exists” instead of “this universe has life-permitting values for its constants.”
6. The Multiverse Hypothesis
6.1. Introduction
The multiverse hypothesis is the hypothesis that there exist many regions of space-time –
that is, “universes” – with different initial conditions, constants of physics, and even laws of nature. It is commonly considered the major alternative to the competing hypotheses 41. Finally, in a worst-case scenario in which an atheist offered good reason to believe that Ev is unlikely under T, it would still probably be the case that Lpc & Ev would disconfi rm NSU over TSU, not only because the improbability of Lpc is so great under NSU that it would be less than P(Ev|TSU & k′) but also because P(Lpc|NSU & k′) << 1 receives a principled justifi cation – via the restricted Principle of Indifference – whereas the arguments offered for P(Ev|T & k) << 1 are typically based on highly controversial intuitions.
T E L E O LO G I C A L
A RG U M E N T 257
of T and NSU. Just as in a lottery in which all the tickets are sold, one is bound to be the winning number, so given a varied enough set of universes with regard to some life-permitting feature F, it is no longer surprising that there exists a universe somewhere that has F.
Multiverse hypotheses differ both in the features that vary from universe to universe – for example, the initial conditions, the constants of physics, and so on – and what physical process, if any, produced them.
The multiverse objection can be interpreted as either claiming that the multiverse provides an alternative explanation of the fi ne-tuning of the cosmos, or that it simply eliminates the epistemic improbability of the fi ne-tuning. We shall focus primarily on the latter objection, since such an objection would undermine any argument based on the Likelihood Principle that the fi ne-tuning provides evidence for T over a naturalistic version of the multiverse hypothesis. Put precisely, this version of the multiverse objection is that
~P(LPU|NMU & k′) << 1, where k′ is some appropriately chosen background information and NMU is the relevant naturalistic multiverse hypothesis. Thus, it is claimed, LPU does not provide evidence via the Likelihood Principle for T over an appropriately chosen multiverse hypothesis.
To address this objection, we fi rst need to get clear on exactly how multiverse hypotheses are supposed to explain, or take away the seeming improbability of, the fi ne-tuning. To begin, we need to distinguish between three facts with regard to the fi ne-tuning that are candidates for explanation: (1) what I call the observer-relative life-permitting (LP) fact that we, or I, observe a life-permitting universe instead of a non-life-permitting universe; (2) what I call the indexical LP fact that this universe is life-permitting – or has some life-permitting feature F, where “this” is an indexical that picks out the universe we inhabit; and (3) what I call the existential LP fact that a life-permitting universe exists, a fact that is equivalent to what we have been referring to by “LPU”. The so-called Weak Anthropic Principle, which states that the universe we inhabit must have a life-permitting structure, appears to be enough to make the observer-relative LP fact unsurprising. With regard to the indexical LP fact, some philosophers claim that we cannot make a purely indexical reference to our universe but can only refer to our universe via an implicit description.
Thus, for instance, one could claim that “this universe” is reducible to “the universe we inhabit,” where the “we” is in turn reducible to some other description such as “conscious observers with characteristics X,” where X refers to some set of purely qualitative properties.
If this analysis is correct, then the claim that “this universe is life-permitting” would be a tautology, and hence have an epistemic probability of one. Even if one rejected this analysis, one could still claim that the life-permitting character of our universe is a defi ning, or at least an essential, feature of it, so the indexical LP fact is a necessary truth and thus not surprising. Consequently, it is questionable whether this indexical fact is in any way improbable. In any case, it is clear that the multiverse hypothesis does not itself explain or render probable this indexical LP fact, since whether or not other universes exist is irrelevant to the features our universe might have.
So the only place where the multiverse hypothesis could help in explaining the fi ne-tuning or undercutting its improbability is by explaining or undercutting the apparent improbability of LPU – that is, of the existential LP fact expressed by (3). A hypothesis postulating a suffi ciently varied multiverse will entail LPU; hence, purportedly it will not only explain why some such universe exists but will also undercut any claim that the existence of such a universe is improbable. It is here, and only here, that the multiverse could do any work in undercutting the fi ne-tuning argument for T. The so-called observer-selection effect,
often considered an essential part of the multiverse explanation, does not itself contribute at all; this effect only explains the observer-relative LP fact given by (1) and is already taken into account by the Weak Anthropic Principle.
Now it is important to distinguish between two categories of multiverse hypotheses: the unrestricted version (which I shall label UMU) and various types of restricted versions. The unrestricted version is the hypothesis that all possible worlds exist, a version famously advocated by philosopher David Lewis as an account of modal claims. According to Lewis, every possible world actually exists (as a region of space-time) parallel to our own. Thus, for instance, there exists a reality parallel to our own in which objects can travel faster than the speed of light. Dream up a possible scenario, and it exists in some parallel reality, according to Lewis. These worlds, however, are completely isolated from ours, and there are no spatiotemporal or causal relations between the worlds – for example, things in one world do not happen before, at the same time, or after things in our world. Further, they do not overlap in any way, except for the possibility of sharing immanent universals. (1986, p. 2).
Lewis advocates his hypothesis as an account of modal statements – that is, statements that make claims about possibility and impossibility, such as “it is possible that Al Gore won the US presidential election in 2004,” and “it is impossible for an object to be a perfect cube and a perfect sphere at the same time.” Thus, Lewis calls his view modal realism, with the term “realism” indicating that every possible world exists in as real a way as our own.
This term, however, is a misnomer, since it implies that other accounts of modal claims are antirealist, which they are not. The other major advocate of a similar view is Massachusetts Institute of Technology astrophysicist Max Tegmark (1998, 2003). According to Tegmark,
“everything that exists mathematically exists physically” (1998, p. 1), by which he means that every self-consistent mathematical structure is in one-to-one correspondence with some physical reality (1998, pp. 1–3). Unlike Lewis, Tegmark’s primary argument for his view is to explain LPU. Further, it is unclear whether Tegmark is claiming that every possible universe exists, or only that every possible universe that can be described purely mathematically; in the latter case it would not be a completely unrestricted multiverse hypothesis.
In contrast to Lewis’s and perhaps Tegmark’s hypothesis, restricted multiverse hypotheses postulate some restriction on the possible universes (or worlds) that actually exist. The most widely discussed versions are those that claim that a multitude of varied universes are generated by some physical process (what I will call a “multiverse generator”). We shall discuss these in Section 6.3. The important point here is that such a restriction will run the danger of reinstantiating the problem of fi ne-tuning at the level of the restrictions placed on the set of existing universes. In Section 6.3, I shall argue in detail that this is what happens in the case of the most widely discussed multiverse-generator hypothesis, the infl ationary-superstring multiverse hypothesis.
Unlike the restricted versions of the multiverse hypothesis, the unrestricted version does not run any danger of reinstantiating the problem of fi ne-tuning. As I shall argue in the next subsection, however, it faces the following devastating dilemma as an alternative to a theistic explanation of the fi ne-tuning: it either undercuts almost all scientifi c reasoning and ordinary claims of improbability, or it completely fails to undercut the fi ne-tuning argument for T. 42
42. Here, I am simply making rigorous an argument suggested by others, such as William Lane Craig (2003, p. 173) and cosmologist Robert Mann (2005, pp. 308–9).
T E L E O LO G I C A L
A RG U M E N T 259
6.2. Critique of the unrestricted multiverse
To begin our argument, consider a particular event for which we would normally demand an explanation, say, that of Jane’s rolling a six-sided die 100 times in a row and its coming up on six each time. Call the type of sequence “coming up 100 times on six” type Tx.
Further, let “D” denote the particular die that Jane rolled and DTx the state of affairs of D’s falling under type Tx for the particular sequence of die rolls: that is, DTx is the state of affairs of D’s coming up 100 times in a row on six for that particular sequence of die rolls. Normally, we should not accept that DTx simply happened by chance; we should look for an explanation. The reason is that DTx is both very improbable, having a one in 6100
chance of occurring, and in some way “special.” The quality of being “special” is necessary for our seeking an explanation since all 100 sequences of rolls are equally improbable, but they are not all in need of an explanation. In general, what makes an improbable occurrence special, and thus a coincidence in need of explanation, is diffi cult to explicate precisely.
John Leslie, for example, has proposed that this specialness consists of our being able to glimpse a simple, unifi ed explanation of the occurrence (Leslie, 1988, p. 302). In whatever way one explicates being “special,” however, certainly, a six-sided die coming up 100 times in a row on six qualifi es.
Now, for any possible state of affairs S – such as DTx – UMU entails that this state of affairs S is actual. Thus, with regard to explanation, for all possible states of affairs S, advocates of UMU must claim that the fact that UMU entails S either (i.a) undercuts all need for explanation, or (i.b) it does not. Further, with regard to some state of affairs S (such as DTx) that we normally and uncontroversially regard as improbable, they must claim that the fact that UMU entails S either (ii.a) undercuts the improbability of S (since it entails S), or (ii.b) it does not. Both (i.a) and (ii.a) would constitute a reductio of UMU, since it would undercut both all justifi cations in science based on explanatory merits of an hypothesis and ordinary claims of probability, such as in our die example. If advocates of UMU adopt (i.b) and (ii.b), however, then the mere fact that UMU entails LPU undercuts neither the need to explain LPU nor its apparent improbability.43
Part of what gives rise to the temptation to think that UMU can explain, or render unsurprising, LPU (without doing the same for every other occurrence) is the existence of other “many-trials” scenarios that appear to be analogous but which are really crucially disanalogous. The way in which they are disanalogous is that they only entail the occurrence of a very limited number of states of affairs that we fi nd highly surprising, without entailing the existence of all such states of affairs. What drives inferences of epistemic probability in these cases is what I call the Entailment Principle. This principle states that if h & k′ is known to entail S, or known to render the statistical probability of S near 1, then the conditional epistemic probability of S on h & k′ is near 1: that is, P(S|h & k′) ~ 1.44
For limited multiple-trial hypotheses the Entailment Principle can render epistemically 43. Lewis (1986, pp. 131–2) explicitly adopts (i.b).
44. In standard presentations of the logical and subjective accounts of conditional probability, the fact that h & k′ entails S is suffi cient to render P(S|h & k′) = 1, whether or not we know that h & k′ entails S. The account of epistemic probability that I developed in Section 3.2, however, assumes that epistemic probability is relative to human cognitive limitations. Thus, the fact that h & k′ entails S would only make P(S|h & k′) = 1 if we knew that fact.
probable the actuality of some state of affairs whose actuality would otherwise be considered highly improbable, without at the same time rendering the actuality of other states of affairs probable that we normally consider improbable. Consider, for example, what could be called the multiple-die-roll hypothesis (MDR), according to which an enormous number of dice are being rolled at every moment throughout the galaxy, in fact so many that the statistical probability that some sequence of 100 die rolls will come up all sixes is almost one. By the Entailment Principle, it follows that it is highly epistemically probable under MDR that some 100-member sequence of die rolls will come up all sixes. The conjunction of MDR and the Entailment Principle, however, does not change the probability of other states of affairs whose improbability is critical for everyday inferences, such as that of some particular sequence of die rolls coming up all sixes.
Now, advocates of UMU could affi rm the Entailment Principle and still retain the claim that for some states of affairs S, the actuality of S is epistemically improbable under UMU. As we saw earlier, if S is a possible state of affairs, then UMU entails that S is actual.
If we can know that S is possible without knowing that S is actual, then the claim that S is possible would be part of our background information k′, and hence P(S|UMU & k′) = 1. Suppose that for some cases, however, we cannot know whether S is possible apart from S’s actually occurring. In those cases, the Entailment Principle could be true and yet for some S, P(S|UMU & k′) < 1, even though UMU entails S. In the case of the die D in our earlier example, the particular die D exists only as part of the world W it occupies, and thus the only possible sequence of rolls of D are those that it has in W.45
Consequently, unless we know the sequences of rolls of D that have actually occurred in W, we cannot know whether it is possible for D to fall in sequence type Tx without knowing whether D has actually fallen in type Tx. This means that even though UMU
might entail that D lands in type Tx, we could not deduce this from UMU, and, hence, the conditional epistemic probability of D’s falling in Tx could be less than 1. The epistemic probability of P(DTx|k′ & UMU) would then be given by the degree to which k′ & UMU
of itself rationally justifi es the proposition, DTx, that die D came up in sequence type Tx.
Call this the nondeducibility loophole, since it arises from the fact that even though UMU
entails the actuality of all actual states of affairs S, we cannot always derive S’s actuality from UMU.
Now the nondeducibility loophole will work only if we can refer to D in W in a way that is not equivalent or reducible to providing some qualitative description that uniquely picks it out from among all dice that exist across worlds, since such a qualitative description would have to include everything about D that distinguishes it from its counterparts in other worlds, including DTx, or ~DTx. Put differently, it will work only if we can make statements about the die that essentially involve the use of indexicals – that is, involve the use of indexicals, such as “this die,”
in a way that cannot be translated in terms of statements that only use qualitative descriptions such as “the die with properties P,” where the properties P are purely qualitative properties.46
45. Of course, Lewis would want to affi rm the ordinary claim that it possible for D to land in a different sequence than it actually does in world W. He would interpret that ordinary claim, however, as really saying that there are certain relevantly similar counterparts to D in other worlds that landed in a different sequence, not that it was possible for the particular die D to have landed differently.
46. It is hard to see how such essentially indexical claims are possible under UMU, since such claims seem to imply unrealized alternative possibilities, which would contradict UMU. For example, if die D is not defi ned by the conjunction of all its qualitative properties, then it seems that it could have had different qualitative properties, such as landing on a different sequence of numbers.
T E L E O LO G I C A L
A RG U M E N T 261
If we allow such essentially indexical propositions about particular objects in the universe, such as the die, then it seems we can also make such essentially indexical statements about the universe we inhabit: we could simply specify that universe U (or “this universe”) refers to the universe that contains some particular object – for example, some particular electron
– that we are referring to in an essentially indexical manner. This will allow us to adopt the same loophole to the Entailment Principle as adopted by advocates of UMU. Put differently, what I called the indexical LP fact – that is, the fact that universe U is life-permitting – could no longer be simply dismissed as needing no explanation (or lacking improbability) because it is purportedly a defi ning or essential feature of this universe that it is life-permitting. The reason is that even though it would be an essential feature of this universe, we could not deduce it from UMU without already knowing that it is possible for universe U to be life-permitting, just as we could not deduce DTx from UMU without knowing that DTx is possible.
Finally, to exploit the nondeducibility loophole for the indexical LP fact, we simply apply our standard procedure for subtracting out old evidence – such as that the universe has life-permitting values for its constants – to obtain background information k′. Now, although k′ and UMU entail that universe U is life-permitting, a being with cognitive faculties relevantly similar to our own could not deduce that simply by knowing k′ and UMU: for example, if our unembodied being introduced at the end of Section 3.2 were given the information k′ and UMU, it would not know whether U was life-permitting or not.
Consequently, by the same argument used for the case of the NSU, P(Universe U is life-permitting|UMU & k′) << 1 and P(Lpc|UMU & k′) << 1.47 Of course, one might argue against this subtraction procedure, but this sort of argument is a direct challenge to my version of the fi ne-tuning argument itself, not a challenge arising from UMU. (See Section 4.3 for a defense of the subtraction procedure.)48
A general lesson to be gained from this analysis is that any multiverse hypothesis that purportedly undercuts the fi ne-tuning argument by entailing LPU will have to be restricted in the right way: specifi cally, it will have to be such that it does not entail states 47. Further, the probability, P(Lpc|TSU & k′), discussed in Section 5.2 would be unaffected, although now its interpretation would be different: Lpc in both P(Lpc|UMU & k′) and P(Lpc|TSU & k′) would refer to the fact that this universe U has a life-permitting value for its constant C instead of the fact that the “universe that is actual” has a life-permitting value, as it did in Sections 5, where Lpc* denoted the former use of Lpc. If we had strong independent reasons for believing in multiple universes (of some sort of restricted variety, not UMU), then we should have to consider whether ~P(Lpc*|TMU & k′) << 1 since TSU would no longer be a viable hypothesis. (TMU is the theistic multiverse hypothesis.) See the end of Section 5.2 for brief discussion of ~P(Lpc*|TMU & k′) << 1.
48. Lewis could also attempt to appeal to statistical probability in defense of the improbability of DTx by claiming that D should be considered a part of a reference class of all relevantly similar dice in nearby worlds. This, however, opens the door to an advocate of the fi ne-tuning argument to make a similar claim about the improbability of the fi ne-tuning of our universe: namely, we should consider our universe part of a reference class of worlds with the same mathematical form for the laws of nature but with constants that are allowed to differ. Then, by the restricted Principle of Indifference, P(Lpc*|UMU & k′) = Wr/WR << 1. (See note 47 for defi nition of Lpc*.) Another major objection that can be raised against UMU is that the overwhelming majority of worlds are deceptive worlds and worlds in which induction fails. For example, Peter Forrest has argued that there are a vastly greater proportion of worlds in which observers exist with the same past and the same subjective experiences as ours, but in which the future does not in any way resemble the past. Purportedly, this raises an enormous skeptical problem for UMU. I tend to agree with Forrest, but I also agree with Lewis’s response to Forrest that without a measure over the class of other worlds, one cannot make this objection rigorous (Lewis, 1986, pp. 115–21). Thus, I have not pursued this objection here.
of affairs S that we normally take to be improbable. Consider, for example, a multiverse hypotheses M that attempts to explain the special initial conditions of our universe by hypothesizing that it is part of a vast array of universes all of which have the same laws L but in which every possible initial condition is realized. The standard infl ationary-superstring scenario discussed in the next section contains such a multiverse as a subset.
So do standard multiverse theories based on the existence of an infi nite universe with widely varying initial conditions. Assuming that universes lack haecceities – which in this case implies that they are distinguished only by their initial conditions – and assuming the laws are deterministic, then M will entail the existence of our universe along with all of its properties. For example, M will entail DTx. Hence, the mere fact that M entails the existence of our universe and its life-permitting structure cannot be taken as undercutting the claim that it is improbable without at the same time undercutting claims such as that DTx is improbable. Of course, an advocate of M could always use the nondeducibility loophole discussed earlier to save the improbability of the actuality of these states of affairs, but that will open the door to the advocate of the fi ne-tuning argument’s using the same loophole.49 If this analysis is correct, it will spell trouble for those who claim that the multiverses discussed in contemporary cosmology – such as the infl ationary multiverse –
can undercut the improbability of the extraordinarily special initial conditions of our universe by claiming that every possible initial condition is realized in some universe or another.
6.3. The infl ationary-superstring multiverse explained and criticized
As mentioned in Section 6.1, by far the most commonly advocated version of the restricted multiverse hypothesis is the “multiverse-generator” version that claims that our universe was generated by some physical process that produces an enormous number of universes with different initial conditions, values for the constants of nature, and even lower-level laws. Many scenarios have been proposed – such as the oscillating Big Bang model and Lee Smolin’s claim that many universes are generated via black holes (Smolin 1997).
Among these, the one based on infl ationary cosmology conjoined with superstring theory is by far the most widely discussed and advocated, since this is the only one that goes beyond mere speculation. According to infl ationary cosmology, our universe started from an exceedingly small region of space that underwent enormous expansion due to a hypothesized infl aton fi eld that both caused the expansion and imparted a constant, very large energy density to space as it expanded. The expansion caused the temperature of space to decrease, causing one or more so-called “bubble universes” to form. As each bubble 49. If universes have haecceities, then M would not necessarily entail the existence of our universe but only one qualitatively identical with it. In that case, M would not necessarily entail DTx, but only that a die qualitatively identical to D came up on six 100 times in a row. Allowing for haecceities, however, means that one must consider the improbability of purely indexical LP facts about our universe, since the essential features of our universe no longer must include all of its qualitative properties, such as its initial conditions. In that case, the fi ne-tuning argument could be relocated to the indexical fact regarding the improbability of our universe’s having life-permitting initial conditions, since M no longer entails that our universe U has the initial conditions it does. (The earlier argument was formulated on the assumption that the laws are deterministic; I believe that a similar argument also works if the laws are indeterministic, but I cannot pursue it here.)
T E L E O LO G I C A L
A RG U M E N T 263
universe is formed, the energy of the infl aton fi eld is converted into a burst of “normal”
mass-energy, thereby giving rise to a standard Big Bang expansion of the kind we see in our universe.
In chaotic infl ation models – widely considered the most plausible – space expands so rapidly that it becomes a never-ending source of bubble universes. Thus, an enormous number of universes naturally arise from this scenario. In order to get the parameters of physics to vary from universe to universe, however, there must be a further physical mechanism/law to cause the variation. Currently, many argue that this mechanism/law is given by superstring theory or its proposed successor, M-Theory, which are widely considered the only currently feasible candidates for a truly fundamental physical theory. It should be stressed, however, that both infl ationary cosmology and superstring/M-Theory are highly speculative. For example, Michio Kaku states in his recent textbook on superstring theory,
“Not a shred of experimental evidence has been found to confi rm . . . superstrings” (1999, p. 17). The same remains true today. The major attraction of superstring/M-Theory is its mathematical elegance and the fact that many physicists think that it is the only game in town that offers signifi cant hope of providing a truly unifi ed physical theory of gravitation with quantum mechanics (Greene 1999, p. 214).
6.3.1. Infl ationary-superstring multiverse requires right laws
One major possible theistic response to the multiverse generator scenario, whether of the infl ationary variety or some other type, is that the laws of the multiverse generator must be just right – fi ne-tuned – in order to produce life-sustaining universes. To give an analogy, even a mundane item such as a bread machine, which only produces loaves of bread instead of universes, must have the right structure, programs, and ingredients (fl our, water, yeast, and gluten) to produce decent loaves of bread. Thus, it seems, invoking some sort of multiverse generator as an explanation of the fi ne-tuning reinstates the fi ne-tuning up one level, to the laws governing the multiverse generator. So, at most, it could explain the fi ne-tuning of the constants and initial conditions. (Even the latter will be problematic, however, as we shall see in the next two sections.)
As a test case, consider the infl ationary type multiverse generator. In order for it to explain the fi ne-tuning of the constants, it must hypothesize one or more “mechanisms”
or laws that will do the following fi ve things: (i) cause the expansion of a small region of space into a very large region; (ii) generate the very large amount of mass-energy needed for that region to contain matter instead of merely empty space; (iii) convert the mass-energy of infl ated space to the sort of mass-energy we fi nd in our universe; and (iv) cause suffi cient variations among the constants of physics to explain their fi ne-tuning.
Glossing over the details, in infl ationary models, the fi rst two conditions are met via two factors. The fi rst factor is the postulated infl aton fi eld that gives the vacuum (that is, empty space), a positive energy density. The second factor is the peculiar nature of Einstein’s equation of General Relativity, which dictates that space expand at an enormous rate in the presence of a large near-homogenous positive energy density (see Section 2.3.3).
Finally, because the infl aton fi eld gives a constant positive energy density to empty space, as space expands the total vacuum energy within the space in question will increase enormously. This, in turn, generates the needed energy for the formation of matter in the universe. As one text in cosmology explains, “the vacuum acts as a reservoir of unlimited
energy, which can supply as much as is required to infl ate a given region to any required size at constant energy density” (Peacock 1999, p. 26).
So, to achieve (i)–(ii), we effectively have a sort of “conspiracy” between at least two different factors: the infl aton fi eld that gives empty space a positive energy density, and Einstein’s equation. Without either factor, there would neither be regions of space that infl ate nor would those regions have the mass-energy necessary for a universe to exist. If, for example, the universe obeyed Newton’s theory of gravity instead of Einstein’s, the vacuum energy of the infl aton fi eld would at best simply create a gravitational attraction causing space to contract, not to expand.
The conversion of the energy of the infl aton fi eld to the normal mass-energy of our universe (condition (iii)) is achieved by Einstein’s equivalence of mass and energy, E = mc2, along with the assumption that there is a coupling between the infl aton fi eld and the matter fi elds. Finally, the variation in the constants (and to some extent the laws) of nature is typically claimed to be achieved by combining infl ationary cosmology with superstring/
M-Theory, which purportedly allows for an enormous number (greater than 10500) possible combinations of values for the constants of physics. The important point here is that the laws underlying the infl ationary scenario must be just right in order to cause these variations in the constants of physics from one universe to another. If the underlying laws are those given by superstring/M-Theory, arguably there is enough variation; this is not the case, however, for the typical grand unifi ed theories that have been recently studied, which allow for only a very limited number of variations of the parameters of physics, about a dozen or so in the case of the simplest model (Linde 1990, p. 33). As Joseph Polchinski notes in his textbook on superstring theory (1998, vol. II, pp. 372–3), there is no reason to expect a generic fi eld to have an enormous number of stable local minima of energy, which would be required if there is to be a large number of variations in the constants of physics among universes in infl ationary cosmology.
In addition to the four factors listed, the fundamental physical laws underlying a multiverse generator – whether of the infl ationary type or some other – must be just right in order for it to produce life-permitting universes, instead of merely dead universes. Specifi -
cally, these fundamental laws must be such as to allow the conversion of the mass-energy into material forms that allow for the sort of stable complexity needed for complex intelligent life. For example, as elaborated in Section 2.2, without the Principle of Quantization, all electrons would be sucked into the atomic nuclei, and, hence atoms would be impossible; without the Pauli Exclusion Principle, electrons would occupy the lowest atomic orbit, and hence complex and varied atoms would be impossible; without a universally attractive force between all masses, such as gravity, matter would not be able to form suffi ciently large material bodies (such as planets) for life to develop or for long-lived stable energy sources such as stars to exist.
Although some of the laws of physics can vary from universe to universe in superstring/
M-Theory, these fundamental laws and principles underlie superstring/M-Theory and therefore cannot be explained as a multiverse selection effect. Further, since the variation among universes would consist of variation of the masses and types of particles, and the form of the forces between them, complex structures would almost certainly be atomlike and stable energy sources would almost certainly require aggregates of matter. Thus, the said fundamental laws seem necessary for there to be life in any of the many universes generated in this scenario, not merely in a universe with our specifi c types of particles and forces.
T E L E O LO G I C A L
A RG U M E N T 265
In sum, even if an infl ationary-superstring multiverse generator exists, it must have just the right combination of laws and fi elds for the production of life-permitting universes: if one of the components were missing or different, such as Einstein’s equation or the Pauli Exclusion Principle, it is unlikely that any life-permitting universes could be produced.
Consequently, at most, this highly speculative scenario would explain the fi ne-tuning of the constants of physics, but at the cost of postulating additional fi ne-tuning of the laws of nature.
6.3.2. Low-entropy problems for infl ationary cosmology
Infl ationary cosmology runs into a major problem in explaining the low entropy of the universe. This is a critical problem, since unless it can do this, arguably much, if not all, of the motivation for infl ationary cosmology vanishes. Further, this problem will cast severe doubt on the ability of an infl ationary multiverse to explain the fi ne-tuning. The problem is that, applied to the universe as a whole, the second law of thermodynamics demands that the entropy of the universe always increase. Indeed, even if one has doubts about the applicability of the second law to the universe as a whole, infl ation invokes a thermalization process, and thermalization is known to be a paradigmatic entropy-increasing process. As Oxford University physicist Roger Penrose states:
Indeed, it is fundamentally misconceived to explain why the universe is special in any particular respect by appealing to a thermalization process. For, if the thermalization is actually doing anything (such as making temperatures in different regions more equal than they were before), then it represents a defi nite increasing of entropy. Thus, the universe would have had to be more special before the thermalization than after. This only serves to increase whatever diffi -
culty we might have had previously in trying to come to terms with the initial extraordinarily special nature of the universe. . . . invoking arguments from thermalization, to address this particular problem [of the specialness of the universe], is worse than useless! (2004, p. 756) Based on this sort of argument, it is now widely accepted that the preinfl ationary patch of space-time that infl ated to form our universe must have had lower entropy than the universe right after infl ation. For example, Andreas Albrecht, a defender of infl ationary cosmology, admits that infl ationary cosmology must hypothesize a special initial low entropy state: “For infl ation, the infl aton fi eld is the out-of-equilibrium degree of freedom that drives other subsystems. The infl aton starts in a fairly homogeneous potential- dominated state which is certainly not a high-entropy state for that fi eld . . .” (2004, p. 382). Elsewhere, he says the preinfl ation patch must have been in a “very special state” (2004, p. 380).
6.3.3. Albrecht’s “dominant channel” response
So, how does infl ation explain the special initial conditions of the Big Bang, which is the primary aim of the theory? According to Albrecht, it explains the initial conditions by a two-stage process, via the “chaotic infl ation” models mentioned in Section 6.3. First, as Albrecht explains, “One typically imagines some sort of chaotic primordial state, where the infl aton fi eld is more or less randomly tossed about, until by sheer chance it winds up in a very rare fl uctuation that produces a potential-dominated state . . .” (Albrecht 2004, p. 384). Potential-dominated states are those in which the potential energy of the infl aton
fi eld is enormous compared to the rate of change of the infl aton fi eld with respect to time and space. That is, in order for infl ation to occur, the infl aton fi eld must be almost uniform both spatially and temporally relative to the total energy density of the fi eld (Peacock 1999, p. 329). Although macroscopic uniformity of matter is typically a state of very high entropy (such as perfume spread throughout a room), it is generally accepted that in the case of the gravitational fi eld and the infl aton fi eld, greater uniformity entails lower entropy. This is said to explain why the universe becomes more and more inhomogeneous as it expands (with matter clustering into galaxies and stars forming), and yet at the same time its entropy increases. Entropy increases because the gravitational fi eld becomes less uniform. Since the gravitational fi eld would play a signifi cant role in the space-time of the early universe, a near uniform infl aton fi eld would correspond to extremely low entropy.
Now a general requirement for infl ation is that the infl aton fi eld be nearly uniform, in the potential-dominated sense defi ned earlier, over some very small patch. Although these states will be extremely rare, given a large enough initial infl aton fi eld, or enough time, they are likely eventually to occur in some small patch of space simply as a result of thermal fl uctuations. Once they occur, infl ation sets in, enormously expanding the patch. Eventually, because of the postulated nature of the infl aton fi eld, in one or more regions of this expanded space, the fi eld decays, resulting in reheating that produces a bubble universe with ordinary matter. So, in effect, because infl ation can only occur in highly uniform states of the infl aton fi eld, any universe produced from an infl ated region will have initially low entropy.
Accordingly, Albrecht proposes that infl ation explains the low entropy of our universe by a two-stage process: (i) a low-entropy patch occurs as a result of a statistical fl uctuation, and then (ii) that patch infl ates into our universe. As John Barrow and Frank Tipler pointed out over 20 years ago (1986, p. 437), however, if the right special initial conditions must be stumbled upon by a statistical fl uctuation, why not simply hypothesize a very large, or infi nite, material fi eld that undergoes a random fl uctuation that produces a universe relevantly like ours? Why invoke the additional mechanism of infl ation?
The answer requires looking at the standard objection to “random fl uctuation models.”
The objection is that universes being produced by such a fl uctuation (without infl ation) would almost certainly lead to small islands of observers surrounded by chaos, not one with a low degree of entropy throughout. Even more ominously, a random observer most likely would be a so-called Boltzmann brain (BB). A BB is a small region of mass-energy with the same structure as our brains (including the same sort of apparent memory and sensory experiences), but with the surrounding regions of space and time in a chaotic, high-entropy state. Although the experiences of such brains would be highly ordered for a brief time, they would not in any way correspond to reality, and any sort of inductive reasoning would fail.
The BB concept was originally articulated as part of an objection raised against the proposed anthropic-selection-effect explanation of the low initial entropy offered by Ludwig Boltzmann, one of the principal founders of statistical mechanics. Boltzmann attempted to explain the relatively low entropy of the universe by claiming that it was the result a fl uctuation from the normal “chaotic,” equilibrium state, and that a fl uctuation with a high degree of order was necessary for the existence of observers. As theoretical physicist Paul Davies and many others have pointed out in response to Boltzmann’s anthropic explanation, a fl uctuation “the size of the solar system would be suffi cient to ensure the existence of life on Earth, and such a fl uctuation is far more probable than one
T E L E O LO G I C A L
A RG U M E N T 267
of cosmic proportions” (Davies 1974, p. 103). Indeed, fl uctuations of even smaller dimensions – ones in which matter has the same organization as the brain with all its apparent memories and sense experiences but in which the surrounding space-time was chaos –
would be even more likely. Consequently, insofar as a random fl uctuation world contained observers, any randomly selected observer would almost certainly be a BB.
To intuitively see why Davies’s statement is correct, consider an analogy of a very large scrabble board. If we were to shake the scrabble board at random, we would be much more likely to get an ordered, meaningful arrangement of letters in one small region, with the arrangement on the rest of the board essentially chaotic, than for all the letters on the entire board to form meaningful patterns. Or, as another analogy, consider a hundred coins lined up in a row, which are then shaken at random. Defi ne a local island of order to be any consecutive sequence of fi ve coins which all are on the same side – that is, either all heads or all tails. It is much more likely for the sequence of a hundred coin tosses to contain one or more subsequences of fi ve consecutive heads or tails than for it to be all heads or all tails. Indeed, it is likely that such a sequence of coins will have at least one such island of fi ve consecutive heads or tails; the probability of the coins coming up all heads or all tails, however, is around one in 1030, or one in a thousand, billion, billion, billion.
The same argument applies to the mass-energy confi gurations of our visible universe, with the argument being grounded in probability calculations based on the standard probability measure of statistical mechanics over phase space. Roger Penrose’s calculations show that among all possible confi gurations, it is enormously more likely (by a factor of around 1 in 10x, where x = 10123) for local islands of low entropy to form than the whole visible universe to be in a low-entropy state (see e.g. Penrose 2004, pp. 762–5). Indeed, if we consider the set of all confi gurations of mass-energy that would result in an observer –
for example, an organized structure with the same relevant order as our brain – the subset of such confi gurations that are dominated by BB observers would be far, far larger than those confi gurations that are dominated by non-BB observers.
Some people attempt to draw from these calculations the conclusion that if the random fl uctuation model is correct, we should then expect ourselves to be BBs. This assumption, however, is diffi cult to justify. We can, however, derive the more limited conclusion that under the random fl uctuation model it is epistemically very likely that we are BBs conditioned on only our purely subjective experiences: that is, P(BB|k′ & RF) ~ 1, where BB
represents the hypothesis that “I am a BB,” RF the claim that the random fl uctuation model is correct, and k′ includes all of one’s own “purely subjective” experiences but no claim that these experiences correspond to reality.
Many have argued, however, that we have noninferential knowledge of the existence of the external world – that is, knowledge of the external world that cannot be deduced from k′. If this is right, then P(BB|k & RF) = 0, where k* = there is an external world that generally corresponds to our subjective experiences, and k = k′ & k* is our relevantly complete background information. This is the reason we cannot derive the skeptical conclusion that if the random fl uctuation model is true, we should expect ourselves to be BBs. However, since P(~BB & k*|RF & k′) << 1, the elaborated RF hypothesis, k & RF = ~BB & k′ & k* & RF, suffers from a severe probabilistic tension that the elaborated ~RF hypothesis, k &
~RF = ~BB & k′ & k* & ~RF, does not. (Here, ~BB is the claim that we are not BBs, and
~RF is the denial of the RF model.) This probabilistic tension gives us strong reasons to accept ~RF over RF, given that that we are not BBs. Or, given that ~RF is not ad hoc in the sense defi ned in section 1.3, the restricted version of the Likelihood Principle implies that
~BB & k* strongly confi rms ~RF over RF, since P(~BB & k*|RF & k′) << 1 and ~P(~BB & k*|~RF & k′) << 1.50
A major question for a chaotic infl ationary multiverse model is whether it can circumvent the BB problem that plagues the random fl uctuation model. If not, such a model will encounter the same disconfi rmation as RF, thus giving us strong reasons to reject it. According to Albrecht, the infl ationary model can avoid the BB problem, and this is its key advantage. Says Albrecht:
Infl ation is best thought of as the “dominant channel” from random chaos into a big bang-like state. The exponentially large volume of the Big Bang-like regions produced via infl ation appear to completely swamp any other regions that might have fl uctuated into a Big Bang-like state via some other route. So, if you went looking around in the universe looking for a region like the one we see, it would be exponentially more likely to have arrived at that state via infl ation, than some other way, and is thus strongly predicted to have the whole package of infl ationary predictions. (Albrecht 2004, p. 385; italics added)51
The idea here is that infl ation takes small, low-entropy regions and expands them into enormously large regions with enough order so that they will be dominated by non-BB observers (if they have observers). The assumption is that the regions that undergo infl ation are so small that they are much more likely to occur than regions that generate observers by random fl uctuations; further, because of infl ation, these initially small regions become so large that they dominate over those regions that produce observers by means of random fl uctuations. Albrecht admits, however, that his argument that infl ation would be the dominant channel “rests on very heuristic arguments” and that
“the program of putting this sort of argument on fi rmer foundations is in its infancy”
(2004, p. 396).
Several articles have been written in recent years arguing that infl ation will generate universes in which BBs enormously dominate among observers in the far future (Bousso
& Freivogel 2006; Banks 2007).52 These arguments, however, might only present a problem if one adopts a block universe view, according to which future events have the same ontological status as present and past events. Although advocates of infl ation typically assume such a view, they need not. If one adopts a metaphysical view in which the future is not yet real, these arguments will not themselves show that infl ation leads to a present dominance of BB universes. Further, as cosmologist Don Page (2006) has pointed out, the same dominance of BBs occurs for long-lived single universes; further, the evidence at present strongly suggests that our universe will continue existing for an enormously long time, if not forever, if there is no supernatural intervention. In any case, I shall next present a powerful reason 50. The claim that P(~BB & k*|RF & k′) << 1 assumes that one can separate out a “purely subjective” element of experience (corresponding to k′) from other aspects of experience that essentially involve reference to the external world. Some deny this assumption, although it seems very plausible to me. I also should note that the aforementioned argument provides a more rigorous way of proceeding than invoking the so-called “typicality”
assumption – that we are in some ill-defi ned sense “typical observers” – so often invoked in discussions of the BB problem.
51. See Albrecht (2004) for a more detailed presentation of this argument, especially pages 385–87 and 390.
52. I would like to thank James Sinclair for pointing out some of these articles to me. For a recent review of the literature, see Banks (2007, ref. 4).
T E L E O LO G I C A L
A RG U M E N T 269
for thinking that Albrecht’s argument is fl awed and that without assuming highly special initial conditions, infl ationary cosmology leads to a dominance of BBs for any period of time in which observers exist. Since there are many versions of infl ationary cosmology, my argument will be very general.
6.3.4. A BB objection to the infl ationary multiverse
There is a simple argument that if the BB problem exists for the random fl uctuation multiverse, then the same problem exists for the infl ationary multiverse. Defi ne a megaverse as some very large fi nite, or even infi nite, region of space-time of a universe or multiverse that has some confi guration of mass-energy in it.53 The BB problem arises for a random fl uctuation multiverse because, when the standard measure M of statistical mechanics is applied to the phase space of an arbitrary megaverse, the measure of confi gurations dominated by non-BB observers is much, much smaller than that of those confi gurations dominated by BB observers. Further, if this is true for the entire megaverse, then it will have to be true for any arbitrarily chosen spacelike hypersurface, hp, of constant time t of the megaverse. Thus, if we let Mt(BB) designate the measure of volume, Vt(BB), of the phase space of hp corresponding to those confi gurations dominated by BB observers, and Mt(~BB) designate the measure of volume, Vt(~BB), of hp corresponding to confi gurations dominated by non-BB observers, then Mt(~BB)/Mt(BB) << 1.54 That is, the measure for the possible mass-energy-momentum confi gurations of hp that are non-BB dominated will be much, much smaller than the measure for those confi gurations that are BB dominated.
Assuming that the laws of physics are deterministic and time-reversal invariant, then the measure is time-invariant, as explained in Section 2.4. If we consider the mass-energy-momentum confi gurations of hp as evolving with time, this means that for any volume of phase space V(t0) of measure MV(t0) at time t0, V(t0) will evolve into a volume V(t) of the same measure at time t: that is, MV(t) = MV(t0).
Now, consider the initial conditions of the megaverse defi ned on some spacelike hypersurface of constant time t0. Let Vt (BB) and V (~BB) represent the volume of phase space of 0
t0
that hypersurface that evolves into confi gurations dominated by BB observers and by non-BB
observers, respectively, for some later hypersurface at time t. Since the statistical mechanics measure m is time-invariant, the ratio of the measure of Vt (~BB) to V (BB), that is, M (~BB)/
0
t0
t0
Mt (BB), will remain the same. Consequently, M (~BB)/M (BB) = M
0
t0
t0
t(~BB)/Mt(BB) << 1.
This means that the measure of initial states that give rise to a universe dominated by non-BB observers at some arbitrarily chosen later time t is much, much smaller than the measure of initial states that give rise to a universe dominated by BB observers at t. Consequently, unless the initial state of the megaverse is in a very special low-probability state –
that corresponding to volume Vt (~BB) – it will not give rise to a universe dominated by 0
~BBs. This is true for any megaverse in which the laws of physics are deterministic and time-reversal invariant. Infl ationary cosmology denies neither of these assumptions. Further, even 53. I use the idea of a megaverse to avoid problems arising from defi ning a measure if the multiverse is infi nite.
If the multiverse is infi nite, we could avoid such potential problems by making our megaverse fi nite but large enough to include many observers.
54. A universe is dominated by non-BB observers (~BBs) if and only if it contains at least one observer, and in some well-defi ned sense there is a greater proportion of non-BB observers than BB observers.
though the laws of physics are not strictly speaking time-reversal invariant – since time-reversal symmetry is broken in weak interactions, notably the decay of neutral kaons – the argument offered by Albrecht and others that was explicated in Section 6.3.3 does not, in any way, exploit this lack of invariance, nor does it exploit any sort of quantum indeterminacy. Thus, without assuming highly special initial conditions, infl ationary cosmology cannot do better with regard to the BB problem than the random fl uctuation multiverse.
To illustrate this argument, consider the following analogy. Let a highly ordered, low-entropy non-BB-dominated megaverse of fi nite volume containing observers be represented as a black-and-white TV screen with rows and rows of O’s throughout, and let a megaverse dominated by BBs be represented by occasional O’s with large patches of “snow”
– that is, “random” confi gurations of black-and-white pixels. We shall call the former arrangement the ordered, non-BB-pixel arrangement, and the latter the BB-pixel arrangement. For simplicity, suppose there are only a fi nite number of pixels on the TV screen. In that case, the number of ordered non-BB-pixel arrangements would be very small compared with BB-pixel arrangements. Further, suppose the image on the TV screen is being generated by some small magnetic patch on a videocassette recorder (VCR) tape that the VCR head is reading. Finally, suppose that there is a one-to-one correspondence between arrangements of magnetic particles on the patch and the possible confi gurations of black-and-white pixels on the screen.
Because of the one-to-one correspondence, the ratio of possible confi gurations of magnetic particles on the patch of tape that give rise to non-BB-pixel arrangements to those that give rise to BB arrangements will be the same as the ratio of non-BB-pixel arrangements to BB-pixel arrangements on the TV screen. Thus, if the latter ratio is enormously small, so will the former ratio. This is analogous to what happens in the infl ationary megaverse: because the laws of physics are deterministic and time-reversal invariant, every microstate m(t0) at time t0 evolves into one and only one microstate, m(t), at time t, and, hence, they can be put into a one-to-one correspondence. Consequently, just as the ratios of the number of non-BB-pixel confi gurations to the BB-pixel confi gurations is preserved from VCR patch to TV screen, the ratio of the measure of initial confi gurations that lead to non-BB-dominant universes to the measure of those that lead to BB-dominant universes is the same as the corresponding ratio at a later time t.55
55. The fundamental error in Albrecht’s reasoning can be illustrated by another analogy. Consider a balloon that is being unevenly infl ated. Suppose some patches of its two-dimensional surface are massively blown up – say by a trillionfold in each of its two dimensions (e.g. one-trillionth of a meter becomes a meter). This corresponds to the space out of which bubble universes form, some parts of which are infl ated and other parts of which are not.
Now, suppose one of the blown-up patches is one square meter in volume and is completely covered by adjacent black Os that are one centimeter in diameter, with the space in between simply consisting of random mix of black-and-white dots. The scale of the order on this patch is one centimeter; at a level of less than one centimeter, there is a random mix of black-and-white dots. The crucial thing to note, however, is that scale of order of the pre-blown-up patch will be much, much smaller: one-trillionth of a centimeter.
Now it is true that for any two patches, larger patches of the same order and scale of order will be much less likely to occur at random than small patches with the same order and scale – for example, a patch covered with adjacent Os of 1 cm in diameter that has an area of one square meter is much more likely to occur at random than a patch covered with the same pattern of Os that has an area of a thousand square meters. This kind of consideration misleads Albrecht into thinking that very small patches of space-time that infl ate into large observer fi lled, non-BB dominated universes are vastly more likely to occur than large patches of space-time that form
T E L E O LO G I C A L
A RG U M E N T 271
Some might try to dispute one or more of the assumptions of this argument. The most vulnerable assumptions are the problems of nonarbitrarily dealing with the possible infi nities that might arise when one attempts to defi ne a measure for the entire megaverse, along with the additional problem of making rigorous the claim that in the entire phase space, the measure of non-BB-dominated hypersurfaces is much, much less than that of BB-dominated hypersurfaces. These problems, however, are as much a problem for making Albrecht’s argument rigorous. The whole point of Albrecht’s argument is that infl ation does better with regard to BBs than the random fl uctuation multiverse. In order for this claim to be true, there must be some “correct” measure M for the possible mass-energy states of the multiverse (or at least for arbitrarily chosen very large fi nite subsets of it) such that non-BB-observer-dominated states have a much, much smaller measure than those of BB-observer-dominated states for the random fl uctuation model.
In response, perhaps Albrecht could appeal to some notion of a “generic” initial state that is not dependent on the existence of a measure over phase space. Such an appeal, however, will immediately run afoul an objection Penrose has raised. Consider an enormously large universe that eventually collapses back on itself and assume that all the special laws that are required by infl ation hold in that universe. (We could even have an infi nite universe with a negative cosmological constant to ensure collapse.) Suppose that this universe had many domains, some of which are highly irregular. In fact, we can suppose that it is chock full of BBs. As Penrose points out, the collapse of such a universe will result in
“a generic space-time singularity, as we can reasonably infer from precise mathematical theorems” (2004, p. 756). Assuming that the laws of physics (including those of infl ation) are time-symmetric (as is typically assumed in these contexts), if we now reverse the direction of time in our model, we shall “obtain an evolution which starts from a general-looking singularity and then becomes whatever irregular type of universe we may care to choose”
(2004, p. 757). Since the laws governing infl ation will hold in this time-reversed situation, it follows that one cannot guarantee that a uniform or non-BB-dominant universe will arise from generic initial conditions. Thus, infl ationary cosmology can explain such a universe only by effectively presupposing those subsets of generic initial conditions that will lead this type of universe. As Penrose notes, “The point is that whether or not we actually have infl ation, the physical possibility of an infl ationary period is of no use whatever in attempts to ensure that evolution from a generic singularity will lead to a uniform (or spatially fl at) universe” (2004, p. 757).
a non-BB-observer-fi lled universe via a thermal fl uctuation. Consequently, Albrecht is misled into thinking that infl ation can help overcome the BB problem confronting the RF model by increasing the relative proportion of non-BB observers. The problem for Albrecht’s reasoning is that in order to produce a non-BB observer-dominant universe, the order of the patch that infl ates would have to be at a vastly smaller scale – for example, inversely proportional to the factor by which the patch infl ated– and hence contain a vastly higher degree of order per unit of volume than a corresponding non-BB-observer patch of the size of our universe that did not infl ate. The decrease in likelihood resulting from the higher degree of order compensates for the increase in probability resulting from the size of the patch, as can be seen by our more rigorous argument offered earlier based on the time-invariance of the standard measure. In terms of our balloon analogy, a square patch with sides one-trillionth of a meter in length fi lled with adjacent Os one-trillionth of a centimeter in diameter is no more likely to occur at random than a square patch with sides of 1 m in length fi lled with Os that are 1 cm in diameter.
6.3.5. Conclusion
The aforementioned arguments do not show that infl ationary cosmology is wrong or even that scientists are unjustifi ed in accepting it. What they do show is that the infl ationary multiverse offers no help in eliminating either the fi ne-tuning of the laws of nature or the special low-entropic initial conditions of the Big Bang. With regard to the special low-entropic initial conditions, it can explain the special conditions of the Big Bang only by hypothesizing some other, even more special, set of initial conditions. Although a chaotic infl ationary model might lead one to expect a universe like ours, unless highly special initial conditions are assumed across the entire multiverse, it will not lead to a multiverse dominated by ~BBs for later times and thus does no better than a random fl uctuation model.
It also runs into the generic problems faced by multiverse hypotheses discussed at the end of Section 6.2. If we fi nd the existence of a BB-dominated multiverse unacceptable, it follows that an infl ationary-superstring multiverse at best eliminates only the need to explain the life-permitting values of the constants of physics (and perhaps other nonen-tropic types of special initial conditions). Because of the highly speculative extra laws and conditions required to make an infl ationary multiverse work, one could not be blamed if one judged that such purported explanatory ability were far too costly.
7. Miscellaneous Objections
7.1. The “who designed God?” objection
Perhaps the most common objection that atheists raise to the argument from design is that postulating the existence of God does not solve the problem of design but merely transfers it up one level to the question, “Who or what designed God?” The eighteenth-century philosopher David Hume hinted at this objection:
For aught we can know a priori, matter may contain the source or spring of order originally within itself, as well as mind does; and there is no more diffi culty conceiving that the several elements, from an internal unknown cause, may fall into the most exquisite arrangement, than to conceive that their ideas, in the great universal mind, from a like unknown cause, fall into that arrangement. (Hume 1980, pp. 17–8)
A host of atheist philosophers and thinkers, such as J. L. Mackie (1982, p. 144), Graham Oppy (2006, pp. 183–4), J. J. C. Smart (1985, pp. 275–6), Richard Dawkins (1986, p. 316), and Colin McGinn (1999, p. 86) have also repeated this objection. For example, J. J. C.
Smart claims that:
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). (1985, pp. 275–6)
As an objection to our version of fi ne-tuning argument, it is fl awed on several grounds.
I have addressed this objection in detail elsewhere (Collins 2005a). Here I shall present a brief response. To begin, this objection would arise only if either T were constructed
T E L E O LO G I C A L
A RG U M E N T 273
solely to explain the fi ne-tuning, without any independent motivation for believing it, or one considered these other motivations as data and then justifi ed T by claiming that it is the best explanation of all the data. Our main argument, however, is not that T is the best explanation of all the data, but only that given the fi ne-tuning evidence, LPU strongly confi rms T over NSU.
Further, we have substantial reasons for not treating the other motivations for T like data, which we then combine with the fi ne-tuning evidence to infer to the best explanation.
To illustrate, let me focus on one such motivation. Many theists have claimed that for most people at least, belief in God is grounded in a fundamental intuition regarding the existence of God, an intuition relevantly similar to moral intuitions or the intuitions regarding epistemic norms. If this is right, then, as Keith Ward and others have noted, treating the existence of God like a scientifi c hypothesis that needs to be justifi ed by some form of inference to the best explanation is “like trying to justify moral belief by reference to the fi ndings of the natural sciences” (1987, p. 178). On this view, faith can be seen as itself “a response to one who claims my loyalty by showing the true nature of my present mode of being and the way of salvation” (Ward 1987, p. 178). It is “a basic and distinctive mode of human thought and activity” (Ward 1987, p. 180). Thus, in analogy to our ethical intuitions, faith should be considered a mode of knowing, not just a mere leap of belief under insuffi cient evidence. Plantinga (2000) has provided one way of carefully developing this view and shows it has been commonplace in the Christian tradition – for example, Thomas Aquinas and John Calvin (Plantinga 2000, chap. 6). From this point of view, the religious mode of knowing or justifi cation involved in faith, therefore, should not be treated as providing data for an inference to the best explanation but rather as analogous to our ethical intuitions, or even our intuitions regarding epistemic virtues – for example, that, everything else being equal, simpler theories are more likely to be true or empirically adequate than complex theories. Clearly, one cannot ground our belief in these epistemic virtues in an inference to the best explanation, since all such inferences presuppose the virtues.
Finally, William Alston (1993) and others have made similar claims with regard to our knowledge of God based on religious experience, claiming it is relevantly analogous to our knowledge of the material world, which they claim is not justifi ed by appeal to an inference to the best explanation.
If we do not treat these other motivations for T as part of a body of data for which we employ the strategy of inference to the best explanation, then the “who designed God?”
objection largely evaporates. The existence of God is not a hypothesis that is being offered as the best explanation of the structure of the universe, and hence it is not relevant whether or not God is an explanatorily better (e.g. simpler) terminus for ultimate explanation than the universe itself. Nonetheless, via the restricted version of the Likelihood Principle (Section 1.3), the various features of the universe can be seen as providing confi rming evidence for the existence of God. One advantage of this way of viewing the situation is that it largely reconciles the views of those who stress a need for faith in coming to believe in God and those who stress reason. They each play a complementary role.
To illustrate this point, consider the following analogy. Suppose that in the year 2050
extraterrestrials visit Earth, and we fi nd that they share the same fundamental ethical beliefs as we do – for example, that it is wrong to torture others for no compelling ethical reason. Further, suppose that we were able to show that it is very epistemically unlikely that such an agreement would occur under ethical antirealism – for example, because we have good reason to believe both that unguided naturalistic evolution would not produce
these beliefs and that ethical antirealism is not compatible with viable, alternative explanations of human beings based on design (such as T). Finally, suppose we could show that it is not unlikely for this agreement to occur under ethical realism.56 The discovery that these aliens shared the same ethical beliefs as we do would therefore confi rm ethical realism, even though we would not believe ethical realism because it provided the best explanation of some set of phenomena. In fact, I believe it would decisively tip the balance in favor of ethical realism. I suggest that the evidence of fi ne-tuning does the same for T.
Apart from rejecting the claim that the justifi cation for the existence of God is based on some sort of inference to the best explanation, however, one can also object to the atheist’s key assumption, articulated by J. J. C. Smart in the aforementioned quotation, that the “designer of an artifact must be at least as complex as the artifact itself.” This assumption is not even clearly true in the human case, since it is at least conceivable that one could produce a computer that is more complicated than oneself, which is a common theme of science fi ction. In the case of God, however, we have even less reason to believe it. If the theist were hypothesizing an anthropomorphic God, with a brain and a body, then this objection would be much stronger: one would then be tempted to ask, is that not God’s brain and body as much in need of an explanation as the universe itself? Thus, this objection might seem to have signifi cant bite against such a conception of God. Within traditional theism, however, God has always been claimed to lack any sort of signifi cant internal complexity. In fact, most of the Western medieval tradition claimed that God was absolutely simple in every way – God did not even have complexity with regard to God’s properties. Aquinas, for instance, claimed that all of God’s properties (such as God’s omnipotence and perfect goodness) were absolutely identical; these were, in turn, identical with God’s essence and existence. Although I do not think that this view of God as being absolutely simple is coherent, the point here is that the “who designed God?” objection begs the question against traditional theism, by assuming a type of God which traditional theists would all disavow. Even the heirs to traditional Western theism who deny absolute divine simplicity, such as Richard Swinburne (2004), claim that God’s overall being is extraordinarily simple. Thus, what these atheists really need to show is that the God of all varieties of traditional theism is logically incoherent insofar as those versions of theism hold on to some form of divine simplicity. This, however, is a very different objection – and a much harder task – than simply raising the “who designed God?” objection and then claiming that one has eliminated the theistic explanation in a single stroke.
7.2. The more fundamental law objection
One criticism of the fi ne-tuning argument is that, as far as we know, there could be a more fundamental law that entails both the current laws of physics and the values of the constants of physics. Thus, given such a law, it is not improbable that the laws and constants of physics fall within the life-permitting range. Besides being entirely speculative, three problems confront such an objection. First, although many physicists had hoped that superstring theory would entail all the current laws and constants of physics, that hope has 56. For example, we might argue that it is not unlikely under ethical realism because ethical realism entails some form of ethical Platonism and because Platonism requires that the mind has some sort of direct access to Platonic truths.
T E L E O LO G I C A L
A RG U M E N T 275
almost completely faded as string theorists have come to recognize that superstring theory (and its proposed successor, M-Theory) has many, many solutions, estimated at 10500 or more. Consequently, the prospects of discovering such a fundamental law are much dimmer than they once were. Second, such a fundamental law would not explain the fi ne-tuning of the initial conditions of the universe. Finally, hypothesizing such a law merely moves the epistemic improbability of the fi ne-tuning of the laws and constants up one level, to that of the postulated fundamental law itself. Even if such a law existed, it would still be a huge coincidence that the fundamental law implied just those lower-level laws and values of the constants of physics that are life-permitting, instead of some other laws or values.
As astrophysicists Bernard Carr and Martin Rees note “even if all apparently anthropic coincidences could be explained [in terms of some fundamental law], it would still be remarkable that the relationships dictated by physical theory happened also to be those propitious for life” (1979, p. 612). It is very unlikely, therefore, that the fi ne-tuning of the universe would lose its signifi cance even if such a law were verifi ed.
To illustrate the last response, consider the following analogy. Suppose that superdeterminism is true: that is, everything about the universe, including its initial conditions, is determined by some set of laws, although we do not know the details of those laws. Now consider a fl ip of a coin and let Lh and Lt denote the claims that the laws are such as to determine the coin to come up heads and tails, respectively. We would have equal reason to believe that Lh as that Lt. Hence, since Lh entails that the coin will come up heads, and Lt that the coin will come up tails, the epistemic probability of heads remains 50 percent, and likewise for tails. This would be true even though each of their physical probabilities would be one or zero. The fact that the laws of nature determine the initial conditions, instead of the initial conditions’ not being determined by any law, has no infl uence on the epistemic probability. This can be seen also by the fact that when Laplacian determinism was thought to be true, everyone nonetheless gave a fair coin a 50 percent chance of coming up heads.
A similar sort of response can be given to the claim that fi ne-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 mentioned, however, this postulate simply transfers the epistemic improbability up one level: of all the laws and constants of physics that conceivably could have been logically necessary, it seems highly epistemically improbable that it would be those that are life-permitting, at least apart from some sort of Axiarchic Principle discussed in Section 8.57
7.3. Other life-permitting laws objection
According to what I call the “other life-permitting laws objection,” there could be other life-permitting sets of laws that we know nothing about. This objection is directly answered by the way in which I have formulated the fi ne-tuning argument. As I formulated it, the fi ne-tuning argument does not assume that ours is the only possible set of life-permitting 57. As explained in Section 3.2, necessarily true propositions can still have an epistemic probability of less than one.
laws. Rather, it only assumes that the region of life-permitting laws (or constants or initial conditions) is very small compared with the region for which we can determine whether the laws, constants, or initial conditions are life-permitting – that is, what I called the EI region (see Section 4.5). In the case of the constants of physics, it assumed only that given our current laws of nature, the life-permitting range for the values of the constants (such as gravity) is small compared to the surrounding EI range for which we can determine whether or not a value is life-permitting.
7.4. Other forms of life objection
As raised against the fi ne-tuning argument based on the constants of physics, the “other forms of life objection” claims that as far as we know, other forms of non-carbon-based life could exist even if the constants of physics fell outside the purported life-permitting region. So, it is claimed, the fi ne-tuning argument ends up presupposing that all forms of embodied, conscious life must be based on carbon (e.g. Stenger 2004, pp. 177–8). Besides the extreme diffi culty of conceiving of how non-carbon-based material systems could achieve the sort of self-reproducing material complexity needed to support embodied moral agents, another problem with this objection is that many cases of fi ne-tuning do not presuppose that all life must be carbon based. Consider, for instance, the cosmological constant. If the cosmological constant were much larger than it is, matter would disperse so rapidly that no stars could exist. Without stars, however, there would be no stable energy sources for complex material systems of any sort to evolve. So, all the fi ne-tuning argument presupposes in this case is that the evolution of embodied moral agents in our universe require some stable energy source. This is certainly a very reasonable assumption.
7.5. Weak Anthropic Principle objection
According to the weak version of so-called Anthropic Principle, if the laws of nature were not fi ne-tuned, we should not be here to comment on the fact. Some have argued, therefore, that LPU is not really improbable or surprising at all under NSU, but simply follows from the fact that we exist. In response, we simply restate the argument in terms of our existence: our existence as embodied moral agents is extremely unlikely under NSU, but not improbable under T, and therefore our existence confi rms T over NSU. As explained in Section 4.3, this requires that we treat LPU and our existence as “old evidence,” which we subtract from our background information. This allows us to obtain an appropriate background information k′ that does not entail LPU. The other approach was to use the method of probabilistic tension, which avoided the issue entirely (see Sections 1.4, 4.3, and 4.4).
The methods used in Section 4 deal with this problem of old evidence, and our arguments in Section 3.2 for the existence of conditional epistemic probabilities for P(A|B & k′) for some cases in which our own existence entails A, provide the formal underpinnings in support of the intuitions underlying the “fi ring-squad” analogy offered by John Leslie (1988, p. 304) and others in response to this objection. As Leslie points out, if 50 sharpshooters all miss me, the response “if they had not missed me I would not be here to consider the fact” is inadequate. 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, conditioned on background information k′ that does not include my
T E L E O LO G I C A L
A RG U M E N T 277
continued existence – such as the background information of a third-party observer watching the execution – my continued existence would be very improbable under the hypothesis that they intended to kill me, but not improbable under the hypothesis that they did not intend to kill me.58
8. Conclusion: Putting the Argument in Perspective
As I developed in Sections 1.3 and 1.4, the fi ne-tuning argument concludes that, given the evidence of the fi ne-tuning of the cosmos, LPU signifi cantly confi rms T over NSU. In fact, as shown in Section 5.2, a good case can be made that LPU conjoined with the existence of evil signifi cantly confi rms T over NSU. This does not itself show that T is true, or even likely to be true; or even that one is justifi ed in believing in T. Despite this, I claimed that such confi rmation is highly signifi cant – as signifi cant as the confi rmation that would be received for moral realism if we discovered that extraterrestrials held the same fundamental moral beliefs that we do and that such an occurrence was very improbable under moral antirealism (see Section 7.1). This confi rmation would not itself show that moral realism is true, or even justifi ed. Nonetheless, when combined with other reasons we have for endorsing moral realism (e.g. those based on moral intuitions), arguably it tips the balance in its favor. Analogous things, I believe, could be said for T.
I also considered the challenge raised by the two most widely advocated versions of the multiverse hypothesis – what I called the unrestricted multiverse hypothesis, advocated by Lewis and Tegmark, according to which all possible universes exist, and the restricted multiverse hypothesis arising out of infl ationary cosmology. I argued that neither of these is able adequately to explain away the fi ne-tuning or undercut the fi ne-tuning argument.
Finally, one might wonder whether there are other viable alternative explanations of LPU to that offered by T, NSU, or the multiverse hypothesis. One such possibility is various nontheistic design hypotheses – either nontheistic supernatural beings or aliens in some meta-universe who can create bubble universes. The postulated designer, D, could 58. Sober rejects this sharpshooter analogy (2005, pp. 137–40). He admits, however, that for a bystander, the sharpshooters’ missing (evidence E) would strongly support the “fake-execution” hypothesis (FE) that the captors never really intended to shoot the prisoner. He then goes on to claim that for the prisoner, E does not support FE, claiming that “the bystander and prisoner are in different epistemic situations, even though their observation reports differ by a mere pronoun” (p. 138). To see the problem with Sober’s claim, suppose that: (i) the prisoner and bystander had exactly the same prior probabilities for the FE hypothesis (say, 0.01); (ii) they had relevantly the same cognitive faculties; and (iii) they both had all the same information that could be expressible in sentences, except the difference in the pronouns each would use. Finally, suppose they had to make a practical decision whether to risk their lives with a dangerous escape attempt or to bet that the captors did not intend to kill them.
How should the bystander advise the prisoner? Attempt to fl ee, because P(FE) < 0.5 from the prisoner’s perspective? Do not attempt to fl ee because P(FE) ~1 for the bystander? And, if they wanted to fl ee together, whose perspective do they go with? Surely, the bystander should not go with the prisoner’s perspective, since the bystander’s perspective involves nothing suspicious – there is no observational selection effect for the bystander. Furthermore, it seems clear that the prisoner cannot support his probability claim over that of the bystander’s by appeal to special insight based on experiencing the attempted execution, since both would agree that this does not give special insight. (This is one way this case differs from religious and other kinds of fundamental disagreement.) Thus, if there is any course of action which is rational regarding fl eeing together, it is that given by the bystander’s perspective. So, contrary to Sober, there cannot be two radically different rational degrees of belief in FE.
not be a merely “generic” designer but must be hypothesized to have some motivation to create a life-permitting universe; otherwise P(LPU|D & k′) = P(LPU|NSU & k′), as explained in Section 5.2. Unless these non-generic hypotheses were advocated prior to the fi ne-tuning evidence, or we had independent motivations for them, they would not pass the non- ad hocness test of the restricted version of the Likelihood Principle (Section 1.3). Furthermore, from the perspective of probabilistic tension, these alternative design hypotheses typically would generate a corresponding probabilistic tension between the claim that the postulated being had a motive to create a life-permitting world instead of some other type of world and the beings’ other attributes, something that does not arise for classical theism (see Section 5.2). Finally, for some of these postulated beings, one could claim that even if LPU
confi rms their existence, we lack suffi cient independent reasons to believe in their existence, whereas for T we have such reasons; or one could claim that they simply transfer the problem of design up one level (see Section 7.1).
The only one of these alternatives that I consider a serious contender is the axiarchic hypothesis, versions of which have been advanced in the last 30 years by John Leslie (1989, chap. 8) and recently by Hugh Rice (2000) and others, wherein goodness or ethical
“required-ness” has a direct power to bring about concrete reality. Whatever the merits of this hypothesis, it is likely to entail T. Since God is the greatest possible being, it is supremely good that God exists (Leslie 1989, pp. 168–9). Therefore, it is unclear that the axiarchic hypothesis actually confl icts with T.59 In any case, this chapter has shown that we have solid philosophical grounds for claiming that given the fi ne-tuning evidence, LPU provides signifi cant support for T over its nonaxiarchic contenders.
References
Albert, D. (2000) Time and Chance. Cambridge, MA: Harvard University Press.
Albrecht, A. (2004) Cosmic infl ation and the arrow of time. In J. D. Barrow, P. C. W. Davies, and C.
L. Harper (eds.), Science and Ultimate Reality: Quantum Theory, Cosmology and Complexity, 363–401. New York: Cambridge University Press.
Alston, W. (1993) Perceiving God: The Epistemology of Religious Experience. Ithaca, NY: Cornell University Press.
Banks, T. (2007). Entropy and initial conditions in cosmology. http://arxiv.org/PS_cache/hep-th/
pdf/0701/0701146v1.pdf (accessed May 1, 2008).
Barenboim, G. (2006) The dark(er) side of infl ation. http://arxiv.org/PS_cache/hep-ph/pdf/0605/
0605111v1.pdf (accessed May 1, 2008).
Barrow, J. and Tipler, F. (1986) The Anthropic Cosmological Principle. Oxford: Oxford University Press.
Bousso, R. and Freivogel, B. (2006) A paradox in the global description of the multiverse. http://arxiv.
org/PS_cache/hep-th/pdf/0610/0610132v2.pdf (accessed May 1, 2008).
Burgess, C. P. (2004). Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory. Living Rev. Relativity 7, 5. http://www.livingreviews.org/lrr-2004–5 (accessed March 15, 2005).
59. I would like to thank the John Templeton Foundation for a grant to support this work, William Lane Craig for comments on an earlier draft of this chapter and fi nal editorial comments, David Schenk for comments on the next-to-the-fi nal version, physicists Don Page and Robert Mann for comments on an earlier version of the section on infl ationary cosmology, and many other people, such as Alvin Plantinga, who have encouraged me in, raised objections to, and offered comments on my work on the fi ne-tuning argument over the years.
T E L E O LO G I C A L
A RG U M E N T 279
Caldwell, R. and Steinhardt, P. (2000) Quintessence. Physicsworld.com, November 1. http://
physicsworld.com/cws/article/print/402 (accessed May 1, 2008).
Cao, T. Y. (1997) Conceptual Developments of 20th Century Field Theories. Cambridge: Cambridge University Press.
Carr, B. J. and Rees, M. J. (1979) The anthropic cosmological principle and the structure of the physical world. Nature 278, 605–12.
Collins, R. (2002) God, design, and fi ne-tuning. In R. Martin and C. Bernard (eds.), God Matters: Readings in the Philosophy of Religion, 54–65. New York: Longman Press.
Collins, R. (2003) Evidence for fi ne-tuning. In N. Manson (ed.), God and Design: The Teleological Argument and Modern Science, 178–99. London: Routledge.
Collins, R. (2005a) Hume, fi ne-tuning and the “who designed God?” objection. In J. Sennett and D.
Groothius (eds.), In Defense of Natural Theology: A Post-Humean Assessment, 175–99. Downers Grove, IL: Inter Varsity Press.
Collins, R. (2005b) How to rigorously defi ne fi ne-tuning. Philosophia Christi 7, 382–407.
Collins, R. (2007) The teleological argument. In P. Copan and C. V. Meister (ed.), Philosophy of Religion: Contemporary Issues, 98–111. Oxford: Wiley-Blackwell.
Collins, R. (2008) The case for cosmic design. God or Blind Nature? Philosophers Debate the Evidence (2007–2008). Available at: http://www.infi dels.org/library/modern/debates/great-debate.html (accessed May 1, 2008).
Colyvan, M., Garfi eld, J., and Priest, G. (2005) Some problems with the “fi ne tuning argument.”
Synthese 145: 3, 325–38.
Craig, W. L. (2003) Fine-tuning of the universe. In Neil Manson (ed.), God and Design: The Teleological Argument and Modern Science, 155–77. London: Routledge.
Davies, P. (1974) The Physics of Time Asymmetry. Berkeley: University of California Press.
Davies, P. (1982) The Accidental Universe. Cambridge: Cambridge University Press.
Davies, P. (1992) The Mind of God: The Scientifi c Basis for a Rational World. New York: Simon and Schuster.
Dawkins, R. (1986) The Blind Watchmaker. Why the Evidence of Evolution Reveals a Universe without Design. New York: W. W. Norton.
Denton, M. (1998) Nature’s Destiny: How the Laws of Biology Reveal Purpose in the Universe. New York: The Free Press.
Dodson, E. (1984) The Phenomena of Man Revisited: A Biological Viewpoint on Teilhard de Chardin.
New York: Columbia University Press.
Donoghue, J. (2007) Fine-tuning problems of particle physics. In B. Carr (ed.), Universe or Multiverse? , 231–46. Cambridge: Cambridge University Press.
Draper, P. (2008) Collins’ case for cosmic design. God or Blind Nature? Philosophers Debate the Evidence (2007–2008). Available at: http://www.infi dels.org/library/modern/debates/great-debate.
html (accessed May 1, 2008).
Earman, J. (2006) The improbable universe. Talk delivered at the APA Central Division Symposium:
“Fine Tuning and the Improbable Universe,” April 26–9.
Edwards, A. W. F. (1992) Likelihood. Baltimore: Johns Hopkins University Press.