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severely dimmed in 1970, however, by Roger Penrose and Stephen Hawking’s formulation of the Singularity Theorems which bear their names. The theorems disclosed that under very generalized conditions an initial cosmological singularity is inevitable, even for inhomogeneous universes. Reflecting on the impact of this discovery, Hawking notes that the Hawking-Penrose Singularity Theorems “led to the abandonment of attempts (mainly by the Russians) to argue that there was a previous contracting phase and a non-singular bounce into expansion. Instead almost everyone now believes that the universe, and time itself, had a beginning at the big bang.”65
Despite the fact that no spacetime trajectory can be extended through a singularity, the Oscillating Model exhibited a stubborn persistence. Two further strikes were lodged against it. First, there are no known physics which would cause a collapsing universe to bounce back to a new expansion. If, in defiance of the Hawking-Penrose Singularity Theorems, the universe rebounds, this is predicated upon a physics which is as yet unknown. Second, attempts by observational astronomers to discover the mass density sufficient to generate the gravitational attraction required to halt and reverse the expansion continually came up short. In January of 1998 astronomical teams from Princeton, Yale, the Lawrence Berkeley National Laboratory, and the Harvard-Smithsonian Astrophysics Institute reported at the American Astronomical Society meeting that their various tests all showed that
“the universe will expand forever.”66 A spokesman for the Harvard-Smithsonian team stated that they were now at least 95 percent certain that “the density of matter is insufficient to halt the expansion of the universe.”67
At the same time, observations of the red-shifts of supernovae yielded unexpected results that have thrown the discussion of the universe’s fate into a wholly new arena and served to render questions of its density irrelevant. The red-shift data gathered from the distant supernovae indicate that, far from decelerating, the cosmic expansion is actually accelerating! There is some sort of mysterious
“dark energy” in the form of either a variable energy field (called “quintessence”) or, more probably, a positive cosmological constant or vacuum energy which at a certain point in the evolution of the cosmos kicks the expansion into a higher gear, causing the expansion to proceed more rapidly. Consequently, even high density universes may expand forever; a potentially infinite future is no longer the privileged prerogative of low density universes. Highly accurate recent measurements of the cosmic microwave background radiation by the Wilkinson Microwave An-isotropy Probe (WMAP) indicate, “For the theory that fits our data, the Universe will expand forever.”68
65. Stephen Hawking and Roger Penrose, The Nature of Space and Time, The Isaac Newton Institute Series of Lectures (Princeton, N. J.: Princeton University Press, 1996), 20.
66. Associated Press News Release, January 9, 1998.
67. Ibid.
68. See http://map.gsfc.nasa.gov/m_mm/mr_limits.html.
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Vacuum Fluctuation Models
Physicists realized that a physical description of the universe prior to the Planck time (10-43 second after the Big Bang singularity) would require the introduction of quantum physics in addition to GR. On the sub-atomic level so-called virtual particles are thought to arise due to fluctuations in the energy locked up in the vacuum, particles which the Heisenberg Indeterminacy Principle allows to exist for a fleeting moment before dissolving back into the vacuum. In 1973 Edward Tryon speculated whether the universe might not be a long-lived virtual particle, whose total energy is zero, born out of the primordial vacuum. This seemingly bizarre speculation gave rise to a new generation of cosmogonic theories which we may call Vacuum Fluctuation Models. These models were closely related to an adjustment to the Standard Model known as Inflation. In an attempt to explain the astonishing large-scale smoothness of the universe, certain theorists proposed that between 10-35 and 10-33 second after the Big Bang singularity, the universe underwent a phase of super-rapid, or inflationary, expansion which served to push the inhomogeneities out beyond our event horizon. Prior to the inflationary era the universe was merely empty space, or a vacuum, and the material universe was born when the vacuum energy was converted into matter via a quantum mechanical phase transition. In most inflationary models, as one extrapolates backward in time, beyond the Planck time, the universe continues to shrink down to the initial singularity. But in Vacuum Fluctuation Models, it was hypothesized that prior to inflation the Universe-as-a-whole was not expanding. This Universe-as-a-whole is a primordial vacuum which exists eternally in a steady state. Throughout this vacuum sub-atomic energy fluctuations constantly occur, by means of which matter is created and mini-universes are born (Fig. 3.5).
Time
Space
Fig. 3.5: Vacuum Fluctuation Models. Within the vacuum of the wider Universe, fluctuations occur which grow into mini-universes. Ours is but one of these, and its relative beginning does not imply a beginning for the Universe-as-a-whole.
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Our expanding universe is but one of an indefinite number of mini-universes conceived within the womb of the greater Universe-as-a-whole. Thus, the beginning of our universe does not represent an absolute beginning, but merely a change in the eternal, uncaused Universe-as-a-whole.
Vacuum Fluctuation Models did not outlive the decade of the 1980s. Not only were there theoretical problems with the production mechanisms of matter, but these models faced a deep internal incoherence. According to such models, it is impossible to specify precisely when and where a fluctuation will occur in the primordial vacuum which will then grow into a universe. Within any finite interval of time there is a positive probability of such a fluctuation’s occurring at any point in space. Thus, given infinite past time, universes will eventually be spawned at every point in the primordial vacuum, and, as they expand, they will begin to collide and coalesce with one another. Thus, given infinite past time, we should by now be observing an infinitely old universe, not a relatively young one.
One theorist tried to avoid this problem by stipulating that fluctuations in the primordial vacuum only occur infinitely far apart, so that each mini-universe has infinite room in which to expand.69 Not only is such a scenario unacceptably ad hoc, but it doesn’t even solve the problem. For given infinite past time, each of the infinite regions of the vacuum will have spawned an open universe which by now will have entirely filled that region, with the result that all of the individual mini-universes would have coalesced.
About the only way to avert the problem would be to postulate an expansion of the primordial vacuum itself; but then we’re right back to the absolute origin implied by the Standard Model. According to quantum cosmologist Christopher Isham these models were therefore jettisoned long ago and “nothing much” has been done with them since.70
Chaotic Inflationary Model
Inflation also forms the context for the next alternative: the Chaotic Inflationary Model. Inflationary theory, though criticized by some as unduly “metaphysical,” has been widely accepted among cosmologists. One of the most fertile of the inflation theorists has been the Russian cosmologist Andrei Linde, who has championed his Chaotic Inflationary Model.71 In Linde’s model inflation never ends: each inflating domain of the universe when it reaches a certain volume gives rise via inflation to another domain, and so on, ad infinitum (Fig. 3.6).
69. J. R. Gott III, “Creation of Open Universes from de Sitter Space,” Nature 295 (1982): 304–7. One might also try to avoid the difficulty of coalescing universes by holding that the mini-universes break off from the mother universe to become separate worlds. But see pp. 145–46.
70. Christopher Isham, “Quantum Cosmology and the Origin of the Universe,” lecture presented at the conference “Cosmos and Creation,” Cambridge University, July 14, 1994.
71. See, e.g., A. D. Linde, “The Inflationary Universe,” Reports on Progress in Physics 47 (1984): 925–86; idem, “Chaotic Inflation,” Physics Letters 1298 (1983): 177–81. For a critical review of inflationary scenarios, including Linde’s, see John Earman and Jesus Mosterin, “A Critical Look at Inflationary Cosmology,”
Philosophy of Science 66 (1999): 1–49.
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Fig. 3.6: Chaotic Inflationary Model. The wider universe produces via inflation separate domains which continue to recede from one another as the wider space expands.
Linde’s model thus has an infinite future. But Linde is troubled at the prospect of an absolute beginning. He writes, “The most difficult aspect of this problem is not the existence of the singularity itself, but the question of what was before the singularity. . . . This problem lies somewhere at the boundary between physics and metaphysics.”72 Linde therefore proposed that chaotic inflation is not only endless, but beginningless. Every domain in the universe is the product of inflation in another domain, so that the singularity is averted and with it as well the question of what came before (or, more accurately, what caused it). Our observable universe turns out to be but one bubble in a wider, eternal multiverse of worlds.
In 1994, however, Arvind Borde and Alexander Vilenkin showed that any spacetime eternally inflating toward the future cannot be “geodesically complete” in the past, that is to say, there must have existed at some point in the indefinite past an initial singularity. Hence, the multiverse scenario cannot be past eternal. They write: A model in which the inflationary phase has no end . . . naturally leads to this question: Can this model also be extended to the infinite past, avoiding in this way the problem of the initial singularity? . . . This is in fact not possible in future-eternal inflationary spacetimes as long as they obey some reasonable physical conditions: such models must necessarily possess initial singularities. . . . The fact that inflationary spacetimes are past incomplete forces one to address the question of what, if anything, came before.73
72. Linde, “Inflationary Universe,” 976.
73. A. Borde and A. Vilenkin, “Eternal Inflation and the Initial Singularity,” Physical Review Letters 72 (1994): 3305, 3307.
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In response, Linde concurred with the conclusion of Borde and Vilenkin: there must have been a Big Bang singularity at some point in the past.74
In 2003 Borde and Vilenkin in cooperation with Alan Guth were able to strengthen their conclusion by crafting a new theorem independent of the assumption of the so-called “weak energy condition,” which partisans of past-eternal inflation might have denied in an effort to save their theory.75 The new theorem, in Vilenkin’s words,
“appears to close that door completely.”76 Inflationary models, like their predecessors, thus failed to avert the beginning predicted by the Standard Model.
Quantum Gravity Models
At the close of their analysis of Linde’s Chaotic Inflationary Model, Borde and Vilenkin say with respect to Linde’s metaphysical question, “The most promising way to deal with this problem is probably to treat the Universe quantum mechanically and describe it by a wave function rather than by a classical spacetime.”77
For “it follows from the theorem that the inflating region has a boundary in the past, and some new physics (other than inflation) is necessary to determine the conditions of that boundary. Quantum cosmology is the prime candidate for this role.”78 They thereby bring us to the next class of models which we shall consider, namely, Quantum Gravity Models.
Vilenkin and, more famously, James Hartle and Stephen Hawking have proposed models of the universe which Vilenkin candidly calls exercises in “metaphysical cosmology.”79 Both the Hartle-Hawking and the Vilenkin models eliminate the initial singularity by transforming the conical geometry of classical spacetime into a smooth, curved geometry having no edge (Fig. 3.7). This is accomplished by the introduction of imaginary numbers for the time variable in Einstein’s gravitational equations, which effectively eliminates the singularity.
By positing a finite (imaginary) time on a closed surface prior to the Planck time rather than an infinite time on an open surface, such models actually seem to support, rather than undercut, the fact that time and the universe had a beginning. Such theories, if successful, would enable us to model the beginning of the universe without an initial singularity involving infinite density, temperature, 74. Andrei Linde, Dmitri Linde, and Arthur Mezhlumian, “From the Big Bang Theory to the Theory of a Stationary Universe,” Physical Review D 49 (1994): 1783–1826. Linde has since tried to suggest a way to escape the conclusion of a beginning (“Inflation and String Cosmology,” http://arXiv:hep-th/0503195v1
(March 24, 2005), 13. But he does not succeed in extending past spacetime paths to infinity, which is a necessary condition of the universe’s having no beginning.
75. Arvind Borde, Alan Guth, and Alexander Vilenkin, “Inflation Is Not Past-Eternal,” http://arXiv: gr-qc/0110012v1 (Oct. 1, 2001): 4. The article was updated in January 2003.
76. Alexander Vilenkin, “Quantum Cosmology and Eternal Inflation,” http://arXiv:gr-qc/0204061v1
(April 18, 2002): 10.
77. Borde and Vilenkin, “Eternal Inflation,” 3307.
78. Vilenkin, “Quantum Cosmology and Eternal Inflation,” 11.
79. A. Vilenkin, “Birth of Inflationary Universes,” Physical Review D 27 (1983): 2854. See J. Hartle and S. Hawking, “Wave Function of the Universe,” Physical Review D 28 (1983): 2960–75; A. Vilenkin,
“Creation of the Universe from Nothing,” Physical Letters 117B (1982): 25–8.
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Time
10–43 sec
Space
Fig. 3.7: Quantum Gravity Model. In the Hartle-Hawking version, spacetime is “rounded off” prior to the Planck time, so that although the past is finite, there is no edge or beginning point.
pressure, and so on. As Barrow points out, “This type of quantum universe has not always existed; it comes into being just as the classical cosmologies could, but it does not start at a Big Bang where physical quantities are infinite.”80 Barrow points out that such models are “often described as giving a picture of ‘creation out of nothing,’” the only caveat being that in this case “there is no definite . . . point of creation.”81 Having a beginning does not entail having a beginning point. Even in the Standard Model, theorists sometimes “cut out” the initial singular point without thinking that therefore spacetime no longer begins to exist and the problem of the origin of the universe is thereby resolved. Time begins to exist just in case for any finite temporal interval, there are only a finite number of equal temporal intervals earlier than it. That condition is fulfilled for Quantum Gravity Models as well as for the Standard Model. According to Vilenkin, “The picture presented by quantum cosmology is that the universe starts as a small, closed 3-geometry and immediately enters the regime of eternal inflation, with new thermalized regions being constantly formed. In this picture, the universe has a beginning but no end.”82 Thus, Quantum Gravity models, like the Standard Model, imply the beginning of the universe.
Perhaps it will be said that such an interpretation of Quantum Gravity models fails to take seriously the notion of “imaginary time.” Introducing imaginary numbers for the time variable in Einstein’s equation has the peculiar effect of making the time dimension indistinguishable from space. But in that case, the imaginary time regime prior to the Planck time is not a spacetime at all, but a Euclidean four-dimensional space. Construed realistically, such a four-space would be evacuated of all temporal becoming and would simply exist timelessly. Hawking describes it as “completely self-contained and not affected by anything outside itself. It would be neither created nor destroyed. It would just BE.”83
80. John D. Barrow, Theories of Everything (Oxford: Clarendon, 1991), 68.
81. Ibid., 67–68.
82. Alexander Vilenkin, “Quantum Cosmology and Eternal Inflation,” 11.
83. Stephen Hawking, A Brief History of Time (New York: Bantam, 1988), 136.
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The question which arises for this construal of the model is whether such an imaginary time regime should be interpreted realistically or instrumentally. On this score, there can be little doubt that the use of imaginary quantities for time is a mere mathematical device without ontological significance. For, first, there is no intelligible physical interpretation of imaginary time on offer. What, for example, would it mean to speak of the lapse of an imaginary second or of a physical object’s enduring through two imaginary minutes? Second, time is metaphysically distinct from space, its moments being ordered by an earlier than relation which does not similarly order points in space. But this essential difference is obscured by imaginary time. Thus, “imaginary time” is most plausibly construed as a mathematical contrivance. Barrow observes, physicists have often carried out this “change time into space” procedure as a useful trick for doing certain problems in ordinary quantum mechanics, although they did not imagine that time was really like space. At the end of the calculation, they just swop back into the usual interpretation of there being one dimension of time and three . . . dimensions of . . . space. 84
Hawking simply declines to reconvert to real numbers. If we do, then the singularity reappears. Hawking admits, “Only if we could picture the universe in terms of imaginary time would there be no singularities. . . . When one goes back to the real time in which we live, however, there will still appear to be singularities.”85
Hawking’s model is thus a way of redescribing a universe with a singular beginning point in such a way that that singularity is transformed away; but such a redescription is not realist in character.
Vilenkin recognizes the use of imaginary time as a mere “computational convenience” without ontological significance.86 Remarkably, so does Hawking in other contexts.87 This precludes their models’ being construed realistically as accounts of the origin of the spacetime universe in a timelessly existing four-space. Rather their theories are ways of modeling the real beginning of the universe ex nihilo in such a way as to not involve a singularity. What brought the universe into being remains unexplained on such accounts.
String Scenarios
We come finally to the extreme edge of cosmological speculation: string cosmology. These scenarios are based on an alternative to the standard quark model of 84. Barrow, Theories of Everything, 66–67.
85. Hawking, Brief History of Time, 138–39.
86. Vilenkin, Many Worlds in One, 182.
87. The clearest example of Hawking’s instrumentalism is his description in The Nature of Space and Time of particle pair creation in terms of an electron’s quantum tunneling in Euclidean space (with time being imaginary) and an electron/positron pair’s accelerating away from each other in Minkowski spacetime.
This description is directly analogous to the Hartle-Hawking cosmological model; and yet no one would construe particle pair creation as literally the result of an electron’s transitioning out of a timelessly existing four-space into our classical spacetime.
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elementary particle physics. So-called string theory (or M-theory) conceives of the fundamental building blocks of matter to be, not particles like quarks, but tiny, vibrating, one-dimensional strings of energy. String theory is so complicated and embryonic in its development that all its equations have not yet even been stated, much less solved. But that has not deterred some cosmologists from trying to envision cosmological scenarios based on concepts of string theory to try to avert the beginning predicted by customary Big Bang cosmology.
Two sorts of scenarios have been proposed. The first of these is the Pre-Big Bang Scenario championed by the Italian physicists Gabriele Veneziano and Maurizio Gasperini.88 They conceive of the Big Bang as the transitional event between a contraction phase chronologically prior to the Big Bang and the observed expansion phase after it.
Such a rebound is postulated on the basis of limits which the size and symmetries of strings set to the increase in quantities like spacetime curvature, density, temperature, and so forth. Prior to the Big Bang a black hole formed in the eternally preexisting, static vacuum space and collapsed to the maximum allowed values of such quantities before rebounding in the current expansion observed today (Fig. 3.8).
Observable universe
Time
“Expanding” Region
“Contracting” Region
Space
Fig. 3.8: Pre-Big Bang Scenario. Our observable universe results from the rebound of the collapse of a black hole in a wider preexisting vacuum space.
The scenario differs from the old oscillating models in that the prior contraction is conceived to take place within a wider, static space and to proceed from infinity.
If the expansion will go on forever, then the contraction has gone on forever. The further one regresses into the infinite past, the less dense the universe becomes, as one approaches a limit in the infinite past of a nearly empty universe consisting of an ultra-thin gas of radiation and matter. As one moves forward in time, the material contents of various regions of space begin to collapse into black holes.
But rather than collapsing to singularities, these black holes reach a maximum of 88. Gabriele Veneziano, “A Simple/Short Introduction to Pre-Big Bang Physics/Cosmology,” http://
arXiv:hep-th/9802057v2 (March 2, 1998); M. Gasperini, “Looking Back in Time beyond the Big Bang,”
Modern Physics Letters A 14/16 (1999): 1059–66; M. Gasperini, “Inflation and Initial Conditions in the Pre-Big Bang Scenario,” Physics Review D 61 (2000): 87301–305; M. Gasperini and G. Veneziano, “The Pre-Big Bang Scenario in String Cosmology,” http://arXiv:hep-th/0207130v1 ( July 12, 2002).
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spacetime curvature, density, and so on, before rebounding into expansion phases.
Our universe is just one of these collapsing and rebounding regions within the wider universe. Thus, an absolute beginning of the universe is averted.
Although the Pre-Big Bang Scenario is based on a non-existent theory and is dogged with problems concerning how to join the pre- and post-Big Bang phases together, these purely physical problems pale in comparison to the deep conceptual difficulties attending such a scenario. Like the old Vacuum Fluctuation Models, the Pre-Big Bang Scenario postulates an eternal, static space in which our observable universe originates via a Big Bang event a finite time ago. But since there is a positive probability of a black hole’s forming in any patch of pre-existing space, such an event, given infinite past time, would have happened infinitely long ago, which is inconsistent with the finite age of our observable universe. Moreover, all the pre-Big Bang black holes should in infinite time have coalesced into one massive black hole coextensive with the universe, so that the post-Big Bang universe ought to be observed as infinitely old. Similarly, such a static wider universe, if it is a closed system, should, given infinite past time, have already arrived at a state of thermodynamic equilibrium, in contradiction to the observed disequilibrium (more on this in the sequel). In their efforts to explain the origin of the observable universe from a pre-Big Bang condition, Gasperini and Veneziano have been singularly inattentive to the problematic issues arising from their supposition of a wider, eternally pre-existing space. What they have done, in effect, is to treat the past as a potentially infinite process approaching an infinitely distant limit, rather than as an actually infinite sequence of events having no beginning but an end in the present.
The more celebrated of the string scenarios has been the so-called Ekpyrotic Scenario championed by Paul Steinhardt.89 In the most recent revision, the Cyclic Ekpyrotic Scenario, we are asked to envision two three-dimensional membranes (or “branes” for short) existing in a five-dimensional spacetime (Fig. 3.9). One of these branes is our universe. These two branes are said to be in an eternal cycle in which they approach each other, collide, and retreat again from each other.
It is the collision of the other brane with ours that causes the expansion of our universe. With each collision, the expansion is renewed. Ripples in the branes are said to account for the large-scale structure of our three-dimensional universe.
Thus, even though our universe is expanding, it never had a beginning.
Again, wholly apart from its speculative nature, the Ekpyrotic Scenario has been plagued with problems.90 But let that pass. Perhaps all these problems can somehow be solved. The more important point is that it turns out that, like the Chaotic Inflationary Model, the Cyclic Ekpyrotic Scenario cannot be eternal in the past. With the formulation of their stronger theorem Borde, Guth, and 89. See http://feynman.princeton.edu/~steinh/.
90. For typical criticisms see especially Gary Felder, Andret Frolov, Lev Kaufman, and Andrei Linde,
“Cosmology with Negative Potentials,” http://arXiv:hep-th/0202017v2 (February 16, 2002) and the therein cited literature, particularly the studies by David Lyth.
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Fig. 3.9: Cyclic Ekpyrotic Scenario. Two three-dimensional membranes in an eternal cycle of approach, collision, and retreat. With each collision the expansion of our universe is re-invigorated.
Vilenkin were able to generalize their earlier results on inflationary models in such a way to extend their conclusion to other models. Indeed, the new theorem implies that any universe which has on average been globally expanding at a positive rate is geodesically incomplete in the past and therefore has a past boundary.
Specifically, they note, “Our argument can be straightforwardly extended to cosmology in higher dimensions,” specifically brane-cosmology like Steinhardt’s.91
According to Vilenkin, “It follows from our theorem that the cyclic universe is past-incomplete,”92 that is to say, the need for an initial singularity has not been eliminated. Therefore, such a universe cannot be past-eternal. Steinhardt has himself come to recognize this implication of the theorem for Ekpyrotic Scenarios and so now acknowledges that on his scenario the universe has a past boundary at some point in the metrically finite past.93
Summary
The history of twentieth-century cosmogony has, in one sense, been a series of failed attempts to craft acceptable non-standard models of the expanding universe in such a way as to avert the absolute beginning predicted by the Standard Model.
This parade of failures can be confusing to the layman, leading him mistakenly to 91. Borde, Guth, and Vilenkin, “Inflation Is Not Past-Eternal,” 4. See also Alexander Vilenkin, “Quantum Cosmology and Eternal Inflation,” 11.
92. Alexander Vilenkin, personal communication.
93. See www.phy.princeton.edu/~steinh/ under “Answers to Frequently Asked Questions: Has the cyclic model been cycling forever?” Steinhardt seeks to mollify the impact of the Borde-Guth-Vilenkin theorem by maintaining that clocks run progressively faster as one approaches the past boundary, so that elapsed time becomes what he calls “semi-infinite.” This trick does nothing to abrogate the finitude of the past or the beginning of the universe.
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infer that the field of cosmology is in constant flux, as new theories of the universe’s origin continually come and go, with no assured results. In fact, the Standard Model’s prediction of an absolute beginning has persisted through a century of astonishing progress in theoretical and observational cosmology and survived an onslaught of alternative theories. With each successive failure of alternative cosmogonic theories to avoid the absolute beginning of the universe predicted by the Standard Model, that prediction has been corroborated. It can be confidently said that no cosmogonic model has been as repeatedly verified in its predictions and as corroborated by attempts at its falsification, or as concordant with empirical discoveries and as philosophically coherent, as the Standard Big Bang Model.
A watershed of sorts appears to have been reached in 2003 with Borde, Guth, and Vilenkin’s formulation of their theorem establishing that any universe which has on average over its past history been in a state of cosmic expansion cannot be eternal in the past but must have a spacetime boundary. Theorists intent on avoiding the absolute beginning of the universe could previously always take refuge in the period prior to the Planck time, an era so poorly understood that one commentator has compared it with the regions on the maps of ancient cartographers marked “Here there be dragons!”—it can be filled with all sorts of chimeras. But the Borde-Guth-Vilenkin theorem does not depend upon any particular physical description of the universe prior to the Planck time, being based instead on deceptively simple physical reasoning which will hold regardless of our uncertainty concerning that era. It single-handedly sweeps away the most important attempts to avoid the absolute beginning of the universe, especially the darling of current cosmologists, the eternal inflationary multiverse. Vilenkin pulls no punches: “It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape, they have to face the problem of a cosmic beginning.”94
Of course, in view of the metaphysical issues raised by the prospect of a beginning of the universe, we may be confident that the quest to avert the absolute beginning predicted by the Standard Model will continue unabated. Such efforts are to be encouraged, and we have no reason to think that such attempts at falsification of the prediction of the Standard Model will result in anything other than further corroboration of its prediction of a beginning. While scientific evidence is always provisional, there can be little doubt in this case where the evidence points.
Scientific Arguments:
(4) The Thermodynamic Properties of the Universe
As if this were not enough, there is a second scientific confirmation for the beginning of the universe, the evidence from thermodynamics. According to the second law of thermodynamics, processes taking place in a closed system always tend 94. Vilenkin, Many Worlds in One, 176.
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toward a state of equilibrium. In other words, unless energy is constantly being fed into a system, the processes in the system will tend to run down and quit. For example, if I had a bottle that was a sealed vacuum inside, and I introduced into it some molecules of gas, the gas would spread itself out evenly inside the bottle.
It is virtually impossible for the molecules to retreat, for example, into one corner of the bottle. This is why when you walk into a room, the air in the room never separates suddenly into oxygen at one end and nitrogen at the other. It’s also why when you step into your bath you may be confident that it will be an even temperature instead of frozen solid at one end and boiling at the other. It’s clear that life would not be possible in a world in which the second law of thermodynamics did not hold.
Cosmological Implications of the Second Law
Now our interest in the law is what happens when it is applied to the universe as a whole. For the universe is, on the atheistic view, a gigantic closed system, since it is everything there is and there is nothing outside it. Already in the nineteenth century, scientists realized that the application of the second law to the universe as a whole implied a grim eschatological conclusion: given sufficient time, the universe will eventually come to a state of equilibrium and suffer “heat death.” Once the universe reaches this state, no further change is possible. The universe is dead.
But this apparently firm projection raised an even deeper question: if, given sufficient time, the universe will suffer heat death, then why, if it has existed forever, is it not now in a state of heat death? If in a finite amount of time the universe will inevitably come to equilibrium, from which no significant further change is physically possible, then it should already be at equilibrium by now, if it has existed for infinite time. Like a ticking clock, it should by now have run down. Since it has not yet run down, this implies, in the words of Richard Schlegel, that “in some way the universe must have been wound up.”95
The nineteenth-century German physicist Ludwig Boltzmann offered a daring hypothesis in order to explain why we do not find the universe in a state of heat death or thermodynamic equilibrium.96 Boltzmann hypothesized that the universe as a whole does, in fact, exist in an equilibrium state, but that over time fluctuations in the energy level occur here and there throughout the universe, so that by chance alone there will be isolated regions where disequilibrium exists. Boltzmann referred to these isolated regions as “worlds.” We should not be surprised to see our world in a highly improbable disequilibrium state, he maintained, since in the ensemble of all worlds there must exist by chance certain worlds in disequilibrium, and ours just happens to be one of these.
95. Richard Schlegel, “Time and Thermodynamics,” in The Voices of Time, ed. J. T. Fraser (London: Penguin, 1968), 511.
96. Ludwig Boltzmann, Lectures on Gas Theory, trans. Stephen G. Brush (Berkeley: University of California Press, 1964), §90, pp. 446–48.
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The problem with Boltzmann’s hypothesis was that if our world were merely a fluctuation in a sea of diffuse energy, then it is overwhelmingly more probable that we should be observing a much tinier region of disequilibrium than we do. In order for us to exist, a smaller fluctuation would have sufficed and is much more probable than one so large as the observable universe. Moreover, even a colossal fluctuation that produced our world instantaneously by an enormous accident is inestimably more probable than a progressive decline in entropy over billions of years to fashion the world we see. In fact, Boltzmann’s hypothesis, if adopted, would force us to regard the past as illusory, everything having the mere appearance of age, and the stars and planets as illusory, mere “pictures” as it were, since that sort of world is vastly more probable given a state of overall equilibrium than a world with genuine, temporally and spatially distant events. Therefore, Boltzmann’s hypothesis has been universally rejected by the scientific community, and the present disequilibrium is usually taken to be just a result of the initial low entropy condition mysteriously obtaining at the beginning of the universe.
Eschatological Scenarios
The advent of relativity theory and its application to cosmology altered the shape of the eschatological scenario predicted on the basis of the second law of thermodynamics but did not materially affect the fundamental question. Assuming that there is no positive cosmological constant fueling the expansion of the universe, that expansion will decelerate over time. Two radically different eschatological scenarios then present themselves. If the density of the universe exceeds a certain critical value, then the internal pull of the universe’s own gravity will eventually overcome the force of the expansion and the universe will collapse in upon itself in a fiery Big Crunch. Beatrice Tinsley described such a scenario: If the average density of matter in the universe is great enough, the mutual gravitational attraction between bodies will eventually slow the expansion to a halt. The universe will then contract and collapse into a hot fireball. There is no known physical mechanism that could reverse a catastrophic big crunch. Apparently, if the universe becomes dense enough, it is in for a hot death.97
If the universe is fated to re-contraction, then as it contracts the stars gain energy, causing them to burn more rapidly so that they finally explode or evaporate. As everything in the universe grows closer together, the black holes begin to gobble up everything around them and eventually begin themselves to coalesce. In time,
“all the black holes finally coalesce into one large black hole that is coextensive with the universe,” from which the universe will never reemerge. 98 There is no known physics that would permit the universe to bounce back to a new expansion prior to a final singularity or to pass through the singularity into a subsequent state.
97. Beatrice Tinsley, “From Big Bang to Eternity?” Natural History Magazine (October 1975), 103.
98. Duane Dicus, et al., “The Future of the Universe,” Scientific American, March 1983, 99.
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On the other hand, if the density of the universe is equal to or less than the critical value, then gravity will not overcome the force of the expansion and the universe will expand forever at a progressively slower rate. Tinsley described the fate of this universe:
If the universe has a low density, its death will be cold. It will expand forever at a slower and slower rate. Galaxies will turn all of their gas into stars, and the stars will burn out. Our own sun will become a cold, dead remnant, floating among the corpses of other stars in an increasingly isolated Milky Way.99
At 1030 years the universe will consist of 90 percent dead stars, 9 percent supermas-sive black holes formed by the collapse of galaxies, and 1 percent atomic matter, mainly hydrogen. Elementary particle physics suggests that thereafter protons will decay into electrons and positrons, so that space will be filled with a rarefied gas so thin that the distance between an electron and a positron will be about the size of the present galaxy. At 10100 years, the commencement of the so-called Dark Era, some scientists believe that the black holes themselves will dissipate by a strange effect predicted by quantum mechanics. The mass and energy associated with a black hole so warp space that they are said to create a “tunnel” or “worm-hole”
through which the mass and energy are ejected in another region of space. As the mass of a black hole decreases, its energy loss accelerates, so that it is eventually dissipated into radiation and elementary particles. Eventually all black holes will completely evaporate and all the matter in the ever-expanding universe will be reduced to a thin gas of elementary particles and radiation. Because the volume of space constantly increases, the universe will never actually arrive at equilibrium, since there is always more room for entropy production. Nonetheless, the universe will become increasingly cold, dark, dilute, and dead.
Very recent discoveries provide strong evidence that there is effectively a positive cosmological constant which causes the cosmic expansion to accelerate rather than decelerate. Paradoxically, since the volume of space increases exponentially, allowing greater room for further entropy production, the universe actually grows farther and farther from an equilibrium state as time proceeds. But the acceleration only hastens the cosmos’s disintegration into increasingly isolated material patches no longer causally connected with similarly marooned remnants of the expanding universe. Each of these patches faces, in turn, thermodynamic extinction. Therefore, the grim future predicted on the basis of the second law remains fundamentally unaltered.
Thus, the same pointed question raised by classical physics persists: why, if the universe has existed forever, is it not now in a cold, dark, dilute, and lifeless state? In contrast to their nineteenth-century forbears, contemporary physicists have come to question the implicit assumption that the universe is past eternal. Davies reports, 99. Tinsley, “Big Bang,” 105.
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Today, few cosmologists doubt that the universe, at least as we know it, did have an origin at a finite moment in the past. The alternative—that the universe has always existed in one form or another—runs into a rather basic paradox. The sun and stars cannot keep burning forever: sooner or later they will run out of fuel and die.
The same is true of all irreversible physical processes; the stock of energy available in the universe to drive them is finite, and cannot last for eternity. This is an example of the so-called second law of thermodynamics, which, applied to the entire cosmos, predicts that it is stuck on a one-way slide of degeneration and decay towards a final state of maximum entropy, or disorder. As this final state has not yet been reached, it follows that the universe cannot have existed for an infinite time.100
Davies concludes, “The universe can’t have existed forever. We know there must have been an absolute beginning a finite time ago.”101
Oscillating Models
During the 1960s and 1970s some scientists tried to escape this conclusion by arguing that the universe oscillates in and out from eternity, and so never reaches a final state of equilibrium (Fig. 3.4). But wholly apart from the difficulties mentioned earlier, the fact is that the thermodynamic properties of oscillating models imply the very beginning of the universe that their proponents sought to avoid. For entropy is conserved from cycle to cycle in such models, which has the effect of generating larger and longer oscillations with each successive cycle (Fig. 3.10).
Radius of the universe
Time
Fig. 3.10: Oscillating Model with entropy increase. Due to the conservation of entropy each successive oscillation has a larger radius and longer expansion time.
Therefore, if one traced the expansions back in time they would get smaller and smaller and smaller. One scientific team explains, “The effect of entropy production will be to enlarge the cosmic scale, from cycle to cycle. . . . Thus, looking back in time, each cycle generated less entropy, had a smaller cycle time, and had a smaller cycle expansion factor then [ sic] the cycle that followed it.”102 Therefore, in the words of another scientific team, “the multicycle model has an infinite future, but 100. Paul Davies, “The Big Bang—and Before,” The Thomas Aquinas College Lecture Series, Thomas Aquinas College, Santa Paula, Calif., March 2002.
101. Paul Davies, “The Big Questions: In the Beginning,” ABC Science Online, interview with Phillip Adams, http://aca.mq.edu.au/pdavieshtml.
102. Dicus, “Cosmological Future,” 1, 8.
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only a finite past.”103 Indeed, astronomer Joseph Silk estimates on the basis of the current level of entropy in the universe that it could not have gone through more than 100 previous oscillations.104
Even if this difficulty were avoided, a universe oscillating from eternity past would require an infinitely precise tuning of initial conditions in order to persist through an infinite number of successive bounces. A universe rebounding from a single, infinitely long contraction is, if entropy increases during the contracting phase, incompatible with the initial low entropy condition of our expanding phase. Postulating an entropy decrease during the contracting phase in order to escape this problem would violate the second law. In either case such a universe involves a radical fine-tuning of a very special sort, since the initial conditions have to be set at -∞ in the past.105
Baby Universes
Is there some other plausible way of holding onto the eternality of the past in the face of the universe’s disequilibrium state? Speculations have been floated in eschatological discussions about our universe’s begetting future “baby universes.”
It has been conjectured that black holes may be portals of wormholes through which bubbles of false vacuum energy can tunnel to spawn new expanding baby universes, whose umbilical cords to our universe may eventually snap as the wormholes close up, leaving the baby universe an independently existing spacetime (Fig. 3.11). Perhaps we might imagine that our observable universe is just one of the newly birthed offspring of an infinitely old, preexisting universe.
The conjecture of our universe’s spawning future offspring by such a mechanism was the subject of a bet between Stephen Hawking and James Preskill, which Hawking in 2004 finally admitted, in an event much publicized in the press, that he had lost.106 The conjecture would require that information locked up in a black hole could be utterly lost forever by escaping to another universe. One of the last holdouts, Hawking finally came to agree that quantum theory requires that information is preserved in black hole formation and evaporation. The implica-103. I.D. Novikov and Ya. B. Zeldovich, “Physical Processes Near Cosmological Singularities,” Annual Review of Astronomy and Astrophysics 11 (1973): 401–2.
104. Joseph Silk, The Big Bang, 2nd ed. (San Francisco: W. H. Freeman, 1989), 311–12.
105. Cosmologist George Ellis remarks: “The problems are related: first, initial conditions have to be set in an extremely special way at the start of the collapse phase in order that it is a Robertson-Walker universe collapsing; and these conditions have to be set in an acausal way (in the infinite past). It is possible, but a great deal of inexplicable fine tuning is taking place: how does the matter in widely separated causally disconnected places at the start of the universe know how to correlate its motions (and densities) so that they will come together correctly in a spatially homogeneous way in the future? Secondly, if one gets that right, the collapse phase is unstable, with perturbations increasing rapidly, so only a very fine-tuned collapse phase remains close to Robertson-Walker even if it started off so, and will be able to turn around as a whole (in general many black holes will form locally and collapse to a singularity). G. F. R. Ellis to James Sinclair, January 25, 2006.
Ellis then pointedly asks, “Who focused the collapse so well that it turns around nicely?”
106. For a firsthand account see James Preskill’s website www.theory.caltech.edu/~preskill/jp-24jul04.
html.
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tions? “There is no baby universe branching off, as I once thought. The information remains firmly in our universe. I’m sorry to disappoint science fiction fans, but if information is preserved, there is no possibility of using black holes to travel to other universes.”107 Even if Hawking had won the bet, could such an eschatological scenario be in any case successfully extrapolated into the past, such that our universe is one of the baby universes spawned by the mother universe or by an infinite series of ancestors? It seems not, for while such baby universes appear as black holes to observers in the mother universe, an observer in the baby universe itself will see the Big Bang as a white hole spewing out energy. But this is in sharp contrast to our observation of the Big Bang as a low-entropy event with a highly constrained geometrical structure.
Inflationary Multiverse
Inflationary theory has been exploited by some theorists in an attempt to revive Boltzmann’s explanation of why we find ourselves in a universe thermodynamically capable of sustaining observers. The question here, in the words of Dyson, Kleban, and Susskind, is “whether the universe can be a naturally occurring fluctuation, or must it be due to an external agent which starts the system out in a specific low entropy state?”108 According to generic inflationary theory, our universe exists in a 107. S. W. Hawking, “Information Loss in Black Holes,” http://arXiv:hep-th/0507171v2 (15 September 2005): 4.
108. Lin Dyson, Matthew Kleban, and Leonard Susskind, “Disturbing Implications of a Cosmological Constant,” http://arXiv.org/abs/hep-th/0208013v3 (November 14, 2002), 4. Their point of departure is Henri Poincaré’s argument that in a closed box of randomly moving particles every configuration of particles, no matter how improbable, will eventually recur, given enough time; given infinite time, every configuration will recur infinitely many times. Eschewing a global perspective in favor of a restriction to our causally connected patch of the universe, they argue for the inevitability of cosmological Poincaré recurrences, allowing the process of cosmogony to begin anew. N.B. that even if bubble universes decay before the Poincaré recurrences could happen, there is still enough time for the invasion of Boltzmann brains, discussed below.
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true vacuum state with an energy density that is nearly zero; but earlier it existed in a false vacuum state with a very high energy density. If we hypothesize that the conditions determining the energy density and evolution of the false vacuum state were just right, then the false vacuum will expand so rapidly that, as it decays into bubbles of true vacuum, the “bubble universes” formed in this sea of false vacuum, though themselves expanding at enormous rates, will not be able to keep up with the expansion of the false vacuum and so will find themselves increasingly separated with time (Fig. 3.12).
Fig. 3.12. Bubbles of true vacuum in a sea of false vacuum. As the inflating false vacuum decays, bubbles of true vacuum form in the false vacuum, each constituting an expanding universe. Though rapidly expanding, the bubbles will not coalesce because the false vacuum continues to expand at an even more rapid rate.
Moreover, each bubble is subdivided into domains bounded by event horizons, each domain constituting an observable universe. Observers internal to such a universe will observe it to be open and infinite, even though externally the bubble universe is finite and geometrically closed. Despite the fact that the multiverse is itself finite and geometrically closed, the false vacuum will, according to the theory, go on expanding forever. New bubbles of true vacuum will continue to form in the gaps between the bubble universes and become themselves isolated worlds.
The proposed solution to the problem, then, is essentially the same as Boltzmann’s.
Among the infinity of worlds generated by inflation there will be some worlds that are in a state of thermodynamic disequilibrium, and only such worlds can support observers. It is therefore not surprising that we find the world in a state of disequilibrium, since that is the only kind of world that we could observe.
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But then the proposed solution is plagued by the same failing as Boltzmann’s hypothesis. In a multiverse of eternally inflating vacua most of the volume will be occupied by high entropy, disordered states incapable of supporting observers.
There are two ways in which observable states can exist: first, by being part of a relatively young, low entropy world, or, second, by being a thermal fluctuation in a high entropy world. Even though young universes are constantly nucleating out of the false vacuum, their volumes will be small in comparison with the older bubbles.
Disordered states will therefore be on average strongly predominant. That implies that observers are much more likely to be the result of thermal fluctuations than the result of young, low entropy conditions.
But then the objection once again arises that it is incomprehensibly more probable that a much smaller region of disequilibrium should arise via a fluctuation than a region as large as our observable universe. Roger Penrose calculates that the odds of our universe’s initial low entropy condition’s coming into existence are on the order of one part in 1010(123).109 He comments, “I cannot even recall seeing anything else in physics whose accuracy is known to approach, even remotely, a figure like one part in 1010 (123).”110 By contrast, the odds of our solar system’s being formed instantly by random collisions of particles is about 1:1010(60), a vast number, but inconceivably smaller than 1010(123). (Penrose calls it “utter chicken feed” by comparison.111) Thus, in the multiverse of worlds, observable states involving such an initial low entropy condition will be an incomprehensibly tiny fraction of all the observable states there are. If we are just one random member of an ensemble of worlds, we should therefore be observing a smaller world.
Adopting the multiverse hypothesis to explain our ordered observations would thus result once more in a strange sort of illusionism. It would be overwhelmingly more probable that there really isn’t a vast, orderly universe out there, despite our observations; it’s all an illusion. Indeed, the most probable state which is adequate to support our ordered observations is an even smaller “universe” consisting of a single brain which appears out of the disorder via a thermal fluctuation. In all probability, then, you alone exist, and everything you observe around you, even your physical body, is illusory! Some cosmologists have, in melodramatic language reminiscent of grade-B horror movies of the 1950s, dubbed this problem “the invasion of the Boltzmann brains.”112 Boltzmann brains are much more plenteous in the ensemble of universes than ordinary observers, and, therefore, each of us ought to think that he is himself a Boltzmann brain if he believes that the universe is but 109. Roger Penrose, “Time-Asymmetry and Quantum Gravity,” in Quantum Gravity 2, ed. C. J. Isham, R. Penrose, and D. W. Sciama (Oxford: Clarendon, 1981), 249; cf. Hawking and Penrose, Nature of Space and Time, 34–5.
110. Penrose, “Time-Asymmetry,” 249.
111. Roger Penrose, The Road to Reality (New York: Alfred A. Knopf, 2005), 762–65.
112. For literature see Don N. Page, “Return of the Boltzmann Brains,” (November 15, 2006), http://
arXiv:hep-th/0611158. See especially Andrei Linde, “Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem,” http://arXiv:hep-th/0611043 and the articles by Dyson, et al., by Bousso and Freivogel, and by Banks cited below.
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one member of an ensemble of worlds. Since that seems crazy, that fact strongly disconfirms the hypothesis that there is a multiverse old enough and big enough to have evolved sufficient volume to account for our low entropy condition’s appearing by chance.
One might try to avoid the problem by holding that no bubble universe eternally inflates, so that what one theorist calls “respectable, ordinary observers like us” dominate on average. But as Bousso and Freivogel protest, “Such a conclusion would be shocking and is at odds with our current, admittedly crude, understanding of the string landscape.”113 They therefore advise that we avoid the problem by shunning the “global point of view” in favor of a purely local picture of our “causal diamond,” that is, the spacetime patch which an observer can causally influence and be influenced by. “In the local picture, the causal diamond is all there is. No-one can go and probe the exponentially large regions allegedly created by the cosmological expansion, so we do not consider them to be part of reality.”114 Taken as serious metaphysics, one can only regard this proposal as an outrageous example of Verificationism at work. Our inability to probe areas outside our causal diamond gives absolutely no warrant for thinking that these regions are unreal and therefore cosmically irrelevant.115 Moreover, regarding the wider universe as literally unreal would be to give up the multiverse hypothesis, so that we are right back where we started in trying to explain our observed disequilibrium!
By contrast, if we postulate the finitude of past time and space, such problems are avoided.116 The reason for the observed disequilibrium state is that spacetime 113. R. Bousso and B. Freivogel, “A paradox in the global description of the multiverse,” http://arXiv: hep-th/0610132, 6.
114. Ibid., 7.
115. Even on the local point of view we still face the problem of the Poincaré recurrences (n. 108). Dyson, Kleban, and Susskind recognize that the fatal weakness of the hypothesis that our observable universe is the result of such a chance recurrence is that there are “far more probable ways of creating livable (‘anthropically acceptable’) environments” than those that begin in a low entropy condition. Susskind thinks that the recurrence problems can be avoided because the bubble universes decay into terminal states in which life can never again arise before the recurrences have time to take place. But Banks points out that the problem of the Boltzmann Brains remains unresolved: “The real prediction is that the dominant form of intelligent life in the DKS universe is a form created spontaneously with knowledge of a spurious history, which lives just long enough to realize that its memories are faulty. . . . The DKS model . . . appears to founder on the bizarre phenomenon of Boltzmann’s brain” (T. Banks, “Entropy and Initial Conditions in Cosmology,”
http://arXiv-hep-th/0701146 v1 [ January 1, 2007], 16, 31).
116. Dyson, Kleban, and Susskind respond to such a suggestion as follows: “Another possibility is that an unknown agent intervened in the evolution and for reasons of its own restarted the universe in the state of low entropy characterizing inflation. However, even this does not rid the theory of the pesky recurrences.
Only the first occurrence would evolve in a way that would be consistent with usual expectations” (Dyson, Kleban, and Susskind, “Disturbing Implications of a Cosmological Constant,” 20–21). But so saying, they have misconstrued the hypothesis. The hypothesis was not of an external agent which “restarted” the universe but of “an external agent which starts the system out in a specific low entropy state” (ibid., 4). On such a hypothesis “some unknown agent initially started the inflation high up on its potential, and the rest is history” (Ibid., 2). On this hypothesis the recurrence problems do even not arise. By contrast, Dyson, Kleban, and Susskind are finally driven to suggest that “perhaps the only reasonable conclusion is that we
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had an absolute beginning in a low entropy condition a finite time ago and is on its way toward states of increasing disorder.
In any case it is now widely acknowledged that a future-eternal inflationary universe, which constitutes the sine qua non for the multiverse proposal, cannot be past-eternal. Linde, you’ll recall, once proposed that a model of the universe which is eternally inflating toward the future might also be extended infinitely into the past, but the Borde-Guth-Vilenkin Theorem closed the door on that possibility. The attempt to revive the Boltzmann hypothesis thus relies upon a mechanism which itself requires the finitude of the past and so a beginning of time and space.
Summary
Thermodynamics implies that the universe had a beginning. In a certain respect, the evidence of thermodynamics is even more impressive than the evidence afforded by the expansion of the universe. For while an accurate physical description of the universe prior to the Planck time remains and perhaps always will remain unknown, thereby affording room for speculations aimed at averting the origin of time and space implied by the expanding cosmos, no such uncertainty attends the laws of thermodynamics and their application. Indeed, thermodynamics is so well established that this field is virtually a closed science.117 Even though we may not like it, concludes Davies, we must say on the basis of the thermodynamic properties of the universe that the universe’s energy was somehow simply “put in” at the creation as an initial condition.118 Prior to the creation, says Davies, the universe simply did not exist.119
THE UNIVERSE HAS A CAUSE
On the basis of the four arguments for the finitude of the past, we have good grounds for affirming the second premise of the kalām cosmological argument, that the universe began to exist. From the first premise—that whatever begins to exist has a cause—and the second premise, it follows logically that the universe has a cause. This conclusion ought to stagger us, to fill us with awe, for it means that the universe was brought into existence by something which is greater than and beyond it.
do not live in a world with a true cosmological constant” (ibid., 21), a desperate hypothesis which flies in the face of the evidence and fails in any case to address the global problem.
117. One recalls Eddington’s remark: “The second law of thermodynamics holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but collapse in deepest humiliation.” Arthur S. Eddington, The Nature of the Physical World (New York: Macmillan), 74.
118. P. C. W. Davies, The Physics of Time Asymmetry (London: Surrey University Press, 1974), 104.
119. My thanks to James Sinclair for his comments on the section concerning scientific arguments for the universe’s beginning.
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Or does it? Dennett, as we have seen, agrees that the universe must have a cause of its beginning. But, he claims, the cause of the universe is itself; the universe brought itself into being! Dennett writes:
What does need its origin explained is the concrete Universe itself, and as Hume . . . long ago asked: Why not stop at the material world? It . . . does perform a version of the ultimate bootstrapping trick; it creates itself ex nihilo. Or at any rate out of something that is well-nigh indistinguishable from nothing at all.120
Here Dennett spoils his radical idea by waffling at the end: maybe the universe did not create itself out of nothing but at least out of something well-nigh indistinguishable from nothing. This caveat evinces a lack of appreciation of the metaphysical chasm between being and nothingness. There is no third thing between being and non-being; if anything at all exists, however ethereal, it is something and therefore not nothing. So what could this mysterious something be? Dennett does not tell us. In fact, he seems somewhat impatient with the question. He complains: This leads in various arcane directions, into the strange precincts of string theory and probability fluctuations and the like, at one extreme, and into ingenious nitpicking about the meaning of “cause” at the other. Unless you have a taste for mathematics and theoretical physics on the one hand, or the niceties of scholastic logic on the other, you are not apt to find any of this compelling, or even fathomable.121
How strange that Dennett, who fancies himself, unlike Christian dullards, to be among the “brights,” should indict an argument because it appeals only to the inquisitive and the intelligent! In any case, the appeal of the argument is irrelevant; if even Dennett’s complaint were correct, it constitutes at best a piece of friendly, atheistic advice to believers about the limited utility of the kalām cosmological argument in evangelism. We can thank Professor Dennett for his advice, while still demanding an account of the origin of the universe.
The best sense I can make of Dennett’s suggestion is to construe it as an endorsement of a model of quantum creation such as is offered by his Tufts University colleague Alexander Vilenkin. It will be recalled that Vilenkin equates the initial state of the universe explanatorily prior to quantum tunneling with nothingness.
Unfortunately, we saw that this equivalence is clearly mistaken (perhaps Dennett’s waffling betrays an understanding of this fact). Thus, on Vilenkin’s model we are still left wondering what caused the initial state of the universe to come into being.
Dennett’s answer is: the universe, in the ultimate boot-strapping trick, created itself! Dennett’s bold hypothesis would at least help to resolve the objection that if something can come into being out of nothing, then it becomes inexplicable why anything and everything does not come into being out of nothing. On Dennett’s 120. Dennett, Breaking the Spell, 244.
121. Ibid., 242.
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view the coming of the universe into being is causally constrained: it creates itself.
Of course, that still leaves us wondering why other things, say, bicycles and hot dogs and wombats, do not have the same capacity; but never mind. As Aquinas argued, self-creation is metaphysically absurd, since in order to cause itself to come into being, the universe would have to already exist. One is thus caught in a vicious circle. Aquinas made the point with respect to an eternally existing universe, but his argument is even more forceful with respect to a universe with a beginning.
For in the latter case the universe must be not only explanatorily prior to itself but even, it seems, chronologically prior to itself, which is incoherent. Thus, Dennett’s imaginative suggestion is wholly untenable.
The Nature of the First Cause
It therefore follows that the universe has an external cause. Conceptual analysis enables us to recover a number of striking properties which must be possessed by such an ultra-mundane being. For as the cause of space and time, this entity must transcend space and time and therefore exist atemporally and non-spatially (at least without the universe).122 This transcendent cause must therefore be changeless and immaterial, since timelessness entails changelessness, and changelessness implies immateriality. Such a cause must be beginningless and uncaused, at least in the sense of lacking any antecedent causal conditions, since there cannot be an infinite regress of causes. Ockham’s Razor (the principle which states that we should not multiply causes beyond necessity) will shave away further causes. This entity must be unimaginably powerful, since it created the universe without any material cause.
Finally, and most remarkably, such a transcendent cause is plausibly to be taken to be personal. Three reasons can be given for this conclusion. First, as Richard Swinburne points out, there are two types of causal explanation: scientific explanations in terms of laws and initial conditions and personal explanations in terms of agents and their volitions.123 For example, if I come into the kitchen and find the kettle boiling, and I ask Jan, “Why is the kettle boiling?” she might answer, “The heat of the flame is being conducted via the copper bottom of the kettle to the water, increasing the kinetic energy of the water molecules, such that they vibrate so violently that they break the surface tension of the water and are thrown off in the form of steam.” Or she might say, “I put it on to make a cup of tea. Would you like some?” The first provides a scientific explanation, the second a personal explanation. Each is a perfectly legitimate form of explanation; indeed, in certain contexts it would be wholly inappropriate to give one rather than the other. Now a first state of the universe cannot have a scientific explanation, since there is noth-122. Or, alternatively, the cause exists changelessly in an undifferentiated time in which temporal intervals cannot be distinguished. On this view God existed literally before creation but there was no moment, say, one hour or one million years before creation. For discussion of this alternative see my Time and Eternity, chap. 6.
123. Richard Swinburne, The Existence of God, rev. ed. (Oxford: Clarendon, 1991), 32–48.
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ing before it, and therefore it cannot be accounted for in terms of laws operating on initial conditions. It can only be accounted for in terms of an agent and his volitions, a personal explanation.
Second, the personhood of the cause of the universe is implied by its timelessness and immateriality. The only entities we know of which can possess such properties are either minds or abstract objects, like numbers. But abstract objects do not stand in causal relations. Indeed, their acausal nature is definitive for abstract objects; that is why we call them abstract.124 Numbers, for example, cannot cause anything. Therefore, the transcendent cause of the origin of the universe must be of the order of mind.
Third, this same conclusion is also implied by the fact that we have in this case the origin of a temporal effect from a timeless cause. We’ve concluded that the beginning of the universe was the effect of a first cause. By the nature of the case, that cause cannot have any beginning of its existence or any prior cause. Nor can there have been any changes in this cause, either in its nature or operations, prior to the beginning of the universe. It just exists changelessly without beginning, and a finite time ago it brought the universe into existence. Now this is exceedingly odd. The cause is in some sense eternal and yet the effect which it produced is not eternal but began to exist a finite time ago. How can this be? If the necessary and sufficient conditions for the production of the effect are eternal, then why isn’t the effect eternal? How can all the causal conditions sufficient for the production of the effect be changelessly existent and yet the effect not also be existent along with the cause? How can the cause exist without the effect?
One might say that the cause came to exist or changed in some way just prior to the first event. But then the cause’s beginning or changing would be the first event, and we must ask all over again for its cause. And this cannot go on forever, for we know that a beginningless series of events cannot exist. There must be an absolutely first event, before which there was no change, no previous event. We know that this first event must have been caused. The question is: How can a first event come to exist if the cause of that event exists changelessly and eternally?
Why isn’t the effect co-eternal with its cause?
To illustrate: Let’s say the cause of water’s freezing is subzero temperatures. If the temperature were eternally below zero degrees Centigrade, then any water around would be eternally frozen. If the cause exists eternally, the effect must also exist eternally. But this seems to imply that if the cause of the universe existed eternally, the universe would also have existed eternally. And this we know to be false.
One way to see the difficulty is by reflecting on the different types of causal relations. In event/event causation, one event causes another. For example, the brick’s striking the window pane causes the pane to shatter. This kind of causal relation clearly involves a beginning of the effect in time, since it is a relation between events which 124. See discussion in Paul Copan and William Lane Craig , Creation out of Nothing: A Biblical, Philosophical, and Scientific Exploration (Grand Rapids, Mich.: Baker, 2004), 168–70.
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occur at specific times. In state/state causation one state of affairs causes another state of affairs to exist. For example, the water’s having a certain surface tension is the cause of the wood’s floating on the water. In this sort of causal relation, the effect need not have a beginning: the wood could theoretically be floating eternally on the water. If the wood begins to float on the water, then this will be a case of event/event causation: the wood’s beginning to float is the result of its being thrown into the water. Now the difficulty that arises in the case of the cause of the beginning of the universe is that we seem to have a peculiar case of state/event causation: the cause is a timeless state but the effect is an event that occurred at a specific moment in the finite past. Such state/event causation doesn’t seem to make sense, since a state sufficient for the existence of its effect should have a state as its effect.
There seems to be only one way out of this dilemma, and that is to say that the cause of the universe’s beginning is a personal agent who freely chooses to create a universe in time. Philosophers call this type of causation “agent causation,” and because the agent is free, he can initiate new effects by freely bringing about conditions which were not previously present. For example, a man sitting changelessly from eternity could freely will to stand up; thus, a temporal effect arises from an eternally existing agent. Similarly, a finite time ago a Creator endowed with free will could have freely brought the world into being at that moment. In this way, the Creator could exist changelessly and eternally but choose to create the world in time. By “choose” one need not mean that the Creator changes his mind about the decision to create, but that he freely and eternally intends to create a world with a beginning. By exercising his causal power, he therefore brings it about that a world with a beginning comes to exist.125 So the cause is eternal, but the effect is not. In this way, then, it is possible for the temporal universe to have come to exist from an eternal cause: through the free will of a personal Creator.
On the basis of a conceptual analysis of the conclusion implied by the kalām cosmological argument, we may therefore infer that a personal Creator of the universe exists, who is uncaused, beginningless, changeless, immaterial, timeless, spaceless, and unimaginably powerful. This, as Thomas Aquinas was wont to remark, is what everybody means by “God.”
Objections
Now certain thinkers have objected to the intelligibility of this conclusion. For example, Adolf Grünbaum, a prominent philosopher of space and time and a vociferous critic of theism, has marshaled a whole troop of objections against inferring God as the Creator of the universe.126 As these are very typical, a brief review of his objections should be quite helpful.
125. Such an exercise of causal power plausibly brings God into time, if he was not temporal already.
For more on God’s relationship to time, see my response to Grünbaum’s final objection below.
126. Adolf Grünbaum, “The Pseudo-Problem of Creation in Physical Cosmology,” in Physical Cosmology and Philosophy, ed. John Leslie, Philosophical Topics (New York: Macmillan, 1990), 92–112.
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Grünbaum’s objections fall into three groups. Group I seeks to cast doubt upon the concept of “cause” in the argument: (1) When we say that everything has a cause, we use the word “cause” to mean something that transforms previously existing materials from one state to another. But when we infer that the universe has a cause, we must mean by “cause” something that creates its effect out of nothing.
Since these two meanings of “cause” are not the same, the argument is guilty of equivocation and is thus invalid. (2) It does not follow from the necessity of there being a cause that the cause of the universe is a conscious agent. (3) It is logically fallacious to infer that there is a single conscious agent who created the universe.
But these objections do not seem to present any insuperable difficulties: (1) The univocal concept of “cause” employed throughout the argument is the concept of something which brings about or produces its effects. Whether this production involves transformation of already existing materials or creation out of nothing is an incidental question. Thus, the charge of equivocation is groundless. (2) The personhood of the cause does not follow from the two premises of the cosmological argument proper, but rather from a conceptual analysis of the notion of a first cause of the beginning of the universe, as we have seen. (3) The inference to a single cause of the origin of the universe seems justified in light of the principle, commonly accepted in science, that one should not multiply causes beyond necessity. One is justified in inferring only causes such as are necessary to explain the effect in question; positing any more would be gratuitous. Since the universe is a single effect originating in the Big Bang event, we have no grounds for inferring a plurality of causes.
The objections of Group II relate the notion of causality to the temporal series of events: (1) Causality is logically compatible with an infinite, beginningless series of events. (2) If everything has a cause of its existence, then the cause of the universe must also have a cause of its existence.
Both of these objections, however, seem to be based on misunderstandings.
(1) It is not the concept of causality which is incompatible with an infinite series of past events. Rather the incompatibility, as we have seen, is between the notion of an actually infinite number of things and the series of past events. The fact that causality has nothing to do with it may be seen by reflecting on the fact that the philosophical arguments for the beginning of the universe would work even if the events were all spontaneous, causally unconnected events. (2) The argument does not presuppose that everything has a cause. Rather the operative causal principle is that whatever begins to exist has a cause. Something that exists eternally and, hence, without a beginning would not need to have a cause. This is not special pleading for God, since the atheist has always maintained the same thing about the universe: it is beginningless and uncaused. The difference between these two hypotheses is that the atheistic view has now been shown to be untenable.
Group III objections are aimed at the alleged claim that creation from nothing surpasses all understanding: (1) If creation out of nothing is incomprehensible,
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then it is irrational to believe in such a doctrine. (2) An incomprehensible doctrine cannot explain anything.
But with regard to (1), creation from nothing is not incomprehensible in Grünbaum’s sense. By “incomprehensible” Grünbaum appears to mean “unintelligible”
or “meaningless.” But the statement that a finite time ago a transcendent cause brought the universe into being out of nothing is clearly a meaningful statement, not mere gibberish, as is evident from the very fact that we are debating it. We may not understand how the cause brought the universe into being out of nothing; but then it is even more incomprehensible, in this sense, how the universe could have popped into being out of nothing without any cause, material or productive. One cannot avert the necessity of a cause by positing an absurdity. (2) The doctrine, being an intelligible statement, obviously does constitute a purported explanation of the origin of the universe. It may be a metaphysical rather than a scientific explanation, but it is no less an explanation for that.
Grünbaum has one final objection against inferring a cause of the origin of the universe: the cause of the Big Bang can be neither after the Big Bang (since backward causation is impossible) nor before the Big Bang (since time begins at or after the Big Bang). Therefore, the universe’s beginning to exist cannot have a cause.127 But this argument pretty clearly confronts us with a false dilemma. For why couldn’t God’s creating the universe be simultaneous (or coincident) with the Big Bang? On the view I’ve defended at length elsewhere, God may be conceived to exist timelessly (or in an undifferentiated time) without the universe and in time from the moment of creation. Perhaps an analogy from physical cosmology will be illuminating. The initial Big Bang singularity is not considered to be part of physical time, but to constitute a boundary to time. Nevertheless, it is causally connected to the universe. In an analogous way, we could say that God’s timeless eternity is, as it were, a boundary of time which is causally, but not temporally, prior to the origin of the universe. It seems to me, therefore, that it is not only coherent but also plausible in light of the kalām cosmological argument that God, insofar as he exists changelessly alone without creation, is timeless and that he enters time at the moment of creation in virtue of his causal relation to the temporal universe.
Given that time began to exist, the most plausible view of God’s relationship to time is that he is timeless without creation and temporal subsequent to creation.
None of Grünbaum’s objections, therefore, seems to undermine the credibility of the kalām cosmological argument for God as the Personal Creator of the universe.
We thus have so far two good arguments for the existence of God: the Leibnizian cosmological argument and the kalām cosmological argument. But there’s more to come!
127. Adolf Grünbaum, “Pseudo-Creation of the Big Bang,” Nature 344 (1990): 821–22.
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The Existence of God (2)
Teleological Argument
The teleological argument for God’s existence has come roaring back into prominence in recent years. The explanatory adequacy of the neo-Darwinian mechanisms of random mutation and natural selection with respect to observed biological complexity has been sharply challenged, as advances in microbiology have served to disclose the breathtaking complexity of the micro-machinery of a single cell, not to speak of higher level organisms. The field of origin of life studies is in turmoil, as all the old scenarios of the chemical origin of life in the primordial soup have collapsed, and no new, better theory is on the horizon. And the scientific community has been stunned by its discovery of how complex and sensitive a nexus of initial conditions must be given in order for the universe even to permit the origin and evolution of intelligent life.
Undoubtedly, it is this last discovery which has most served to reopen the books on the teleological argument. Due to sociological factors surrounding the neo-Darwinian theory of biological evolution, captured most poignantly in the public image of the Scopes trial, biologists have been for the most part extremely loath so much as even to contemplate a design hypothesis, lest they let a creationist foot in the door; but cosmologists, largely untainted by this controversy, have been much more open to entertain seriously the alternative of design. The discovery of cosmic fine-tuning for intelligent life has led many scientists to conclude that such a delicate balance of physical constants and quantities as is requisite for life cannot be dismissed as mere coincidence but cries out for some sort of explanation.
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Cosmic Fine-Tuning
What is meant by “fine-tuning”? The physical laws of nature, when given mathematical expression, contain various constants (such as the gravitational constant) whose values are not determined by the laws themselves; a universe governed by such laws might be characterized by any of a wide range of values for these constants. Take, for example, a simple law like Newton’s law of gravity F = Gm m /r2.
1
2
According to this law, the gravitational force F between two objects depends not just on their respective masses m and m and the distance between them r, but 1
2
also on a certain quantity G which is constant regardless of the masses and distance. The law doesn’t determine what value G actually has. In addition to these constants, moreover, there are certain arbitrary physical quantities, such as the entropy level, which are simply put into the universe as boundary conditions on which the laws of nature operate. They are therefore also independent of the laws.
By “fine-tuning” one means that small deviations from the actual values of the constants and quantities in question would render the universe life-prohibiting or, alternatively, that the range of life-permitting values is exquisitely narrow in comparison with the range of assumable values.
We can cite various examples of cosmic fine-tuning.1 The world is conditioned principally by the values of the fundamental constants α (the fine structure constant, or electromagnetic interaction), α (gravitation), α (the weak force), α (the G
w
s
strong force), and m /m (the ratio between the mass of a proton and the mass of n
e
an electron). When one assigns different values to these constants or forces, one discovers that the proportion of observable universes, that is to say, universes capable of supporting intelligent life, is shockingly small. Just a slight variation in some of these values would render life impossible. For example, according to the physicist P. C. W. Davies, changes in either α or α of only one part in 10100 would have G
w
prevented a life-permitting universe. In investigating the initial conditions of the Big Bang, one also confronts two arbitrary parameters governing the expansion of the universe: Ω , related to the density of the universe, and H , related to the speed 0
0
of the expansion. Observations indicate that at 10-43 second after the Big Bang the universe was expanding at a fantastically special rate of speed with a total density close to the critical value on the borderline between recollapse and everlasting expansion. Stephen Hawking estimates that a decrease in the expansion rate of even one part in a hundred thousand million million one second after the Big Bang would have resulted in the universe’s recollapse long ago; a similar increase would have precluded the galaxies’ condensing out of the expanding matter. At the Planck time, 10-43 second after the Big Bang, the density of the universe must have apparently been within about one part in 1060 of the critical density at which space 1. For discussion of examples of fine-tuning, see John D. Barrow and Frank J. Tipler, The Anthropic Cosmological Principle (Oxford: Clarendon, 1986); John Leslie, “The Prerequisites of Life in Our Universe,”
in Newton and the New Direction in Science, ed. G. V. Coyne, M. Heller, J. Zycinski (Vatican: Citta del Vaticano, 1988); Martin Rees, Just Six Numbers (New York: Basic, 2000); Robin Collins, The Well-Tempered Universe (forthcoming).
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is flat. Most theorists today think that this so-called flatness problem has been adequately explained by an early inflationary era in the history of the universe. As we have seen, according to inflationary theory, the energy density of the primordial false vacuum state overwhelmed even the intense gravitational attraction generated by the extremely high matter density of the early universe, causing a super-rapid, or inflationary, expansion, during which the universe grew from atomic proportions to a size larger than the observable universe in a fraction of a microsecond.
Because the universe has inflated to such enormous dimensions, space appears to be flat, just as the surface of the Earth appears flat to its tiny surface dwellers. But inflation only serves to raise a new problem: the fine-tuning of the cosmological constant Λ which drives inflation and is responsible for the recently discovered acceleration of the universe’s expansion. The cosmological constant is inexplicably fine-tuned to around one part in 10120. Classical cosmology serves to highlight another parameter, S, the entropy per baryon in the universe. The structure of the Big Bang must have been severely constrained in order that thermodynamics as we know it should have arisen. As we have seen, Oxford physicist Roger Penrose calculates that the odds of the special low entropy condition having arisen sheerly by chance in the absence any constraining principles is at least as small as about one part in 1010(123) in order for our universe to exist.
Laymen might think that if the constants and quantities had assumed different values, then other forms of life might well have evolved. But this is not the case.
By “life” scientists mean that property of organisms to take in food, extract energy from it, grow, adapt to their environment, and reproduce. The point is that in order for the universe to permit life so defined, whatever form organisms might take, the constants and quantities have to be incomprehensibly fine-tuned. In the absence of fine-tuning, not even atomic matter or chemistry would exist, not to speak of planets where life might evolve!
Sometimes people will object that in universes governed by different laws of nature, such disastrous consequences might not result from varying the values of the constants and quantities. We needn’t deny that possibility. Maybe in a universe governed by different equations, the gravitational constant G could have a greatly different value and yet life still exist. But such universes are irrelevant to the argument. All we need to show is that among possible universes governed by the same equations (but having different values of the constants and quantities) as the actual universe, life-permitting universes are extraordinarily improbable. John Leslie gives the following illustration: imagine a solitary fly resting on a large, blank area of the wall. A single shot is fired, and the bullet strikes the fly. Now, even if the rest of the wall outside the blank area is covered with flies, such that a randomly fired bullet would probably hit one, nevertheless it remains highly improbable that a single, randomly fired bullet would strike the solitary fly within the large, blank area. In the same way, we need only concern ourselves with universes governed by the same equations in order to determine the probability of the existence of a
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life-permitting universe. Thus, although sloppy formulations of the fine-tuning argument are sometimes framed in terms of nature’s laws’ being fine-tuned, thereby leading to speculations of what universes governed by different laws of nature would be like, the correct formulation concerns universes governed by the same laws of nature as ours, but with different values of the constants and quantities.
Because the equations remain the same, we can predict what the world would be like, if, say, the gravitational constant were doubled.
Explaining the Fine-Tuning
In a sense more easy to discern than to articulate this fine-tuning of the universe seems to manifest the presence of a designing intelligence. The inference to design is best thought of, not as an instance of reasoning by analogy (as it is often portrayed), but as a case of inference to the best explanation.2 Leslie speaks of the need for what he calls a “tidy explanation.” A tidy explanation is one that not only explains a certain situation but also reveals in doing so that there is something to be explained. Leslie provides a whole retinue of charming illustrations of tidy explanations at work. Suppose, for example, that Bob is given a new car for his birthday. There are millions of license plate numbers, and it is therefore highly unlikely that Bob would get, say, CHT 4271. Yet that plate on his birthday car would occasion no special interest. But suppose Bob, who was born on August 8, 1949, finds BOB 8849 on the license plate of his birthday car. He would be obtuse if he shrugged this off with the comment, “Well, it had to have some license plate number, and any number is equally improbable . . .” But what makes this case different than the other?
An answer has recently been offered by William Dembski in his The Design Inference.3 He furnishes a ten-step Generic Chance Elimination Argument, which delineates the common pattern of reasoning that he believes underlies chance-elimination arguments. Dembski’s analysis can be used to formalize what Leslie grasped in an intuitive way. What makes an explanation a tidy one is not simply the fact that the explanandum (the thing to be explained) is some improbable event, but the fact that the event also conforms to some independently given pattern, resulting in what Dembski calls “specified complexity.” It is this specified complexity (high improbability + an independent pattern) that tips us off to the need for an explanation in terms of more than mere chance.
Regardless of whether one adopts Dembski’s analysis of design inferences or some alternative approach,4 the key to detecting design is to eliminate the two 2. See Peter Lipton, Inference to the Best Explanation (London: Routledge, 1991).
3. William A. Dembski, The Design Inference: Eliminating Chance through Small Probabilities, Cambridge Studies in Probability, Induction, and Decision Theory (Cambridge: Cambridge University Press, 1998).
4. An alternative approach is offered by Robin Collins. He employs Bayes’ Theorem to argue that the cosmic fine-tuning is much more probable on the hypothesis of theism than on the hypothesis of a single, atheistic universe and that therefore the evidence of fine-tuning strongly confirms theism over its rival hypothesis.
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competing alternatives of physical necessity and chance. Accordingly, a teleological argument appealing to cosmic fine-tuning might be formulated as follows: 1) The fine-tuning of the universe is due to either physical necessity, chance, or design.
2) It is not due to physical necessity or chance.
3) Therefore, it is due to design.
Three Alternative Accounts of Fine-Tuning
Premise (1), properly understood, should not be controversial. Recall that by “fine-tuning” cosmologists do not mean “designed” or “deliberately adjusted to high specification” or some such intentional expression; that would make the argument question-begging. Rather “fine-tuning” is a neutral expression that has to do with the constants and quantities’ being just right for the existence of intelligent life.
There is little doubt that the universe is fine-tuned in this neutral sense. Even if some of the evidence of fine-tuning should prove to be mistaken, the multiplicity of lines of evidence for the fine-tuning of certain constants and quantities as well as the number and variety of the constants and quantities that exhibit fine-tuning give ample grounds for thinking that fine-tuning is here to stay and cannot be just written off as a colossal blunder on the part of the scientific community.5
Moreover, premise (1) seems to exhaust the alternatives. If someone can think of another alternative, then he is free to suggest it. In the absence of a specific suggestion, however, we are justified in thinking that (1) includes all the alternatives, since necessity and chance seem to exhaust the alternatives to design.
The soundness of the argument will therefore depend on the plausibility of premise (2).
Physical Necessity
Can the cosmic fine-tuning be plausibly attributed to physical necessity? According to this alternative, the constants and quantities must have the values they do, and there was really no chance or little chance of the universe’s not being life-permitting.
Now, on the face of it, this alternative seems extraordinarily implausible. It requires us to believe that a life-prohibiting universe is virtually physically impossible. But surely it does seem possible. If the primordial matter and anti-matter had been differently proportioned, if the universe had expanded just a little more slowly, if the entropy of the universe were marginally greater, any of these adjustments and 5. Ernan McMullin concludes, “It seems safe to say that later theory, no matter how different it may be, will turn up approximately the same . . . numbers. And the numerous constraints that have to be imposed on these numbers . . . seem both too specific and too numerous to evaporate entirely. . . . A dozen or more constraints have been pointed out. . . . Might they all be replaced? . . . It surely seems a very long shot.” Ernan McMullin, “Anthropic Explanation in Cosmology,” paper delivered at the conference “God and Physical Cosmology,” University of Notre Dame, January 30–February 1, 2003.
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more would have prevented a life-permitting universe, yet all seem perfectly possible physically. The person who maintains that the universe must be life-permitting is taking a radical line which requires strong proof. But there is none; this alternative is simply put forward as a bare possibility.
Sometimes physicists do speak of a yet to be discovered Theory of Everything (T.O.E.), but such nomenclature is, like so many of the colorful names given to scientific theories, quite misleading. A T.O.E. actually has the limited goal of providing a unified theory of the four fundamental forces of nature, to reduce gravity, electromagnetism, the strong force, and the weak force to one fundamental force carried by one fundamental particle. Such a theory will, we hope, explain why these four forces take the values they do, but it will not even attempt to explain literally everything.
For example, in the most promising candidate for a T.O.E. to date, super-string theory or M-Theory, the physical universe must be 11-dimensional, but why the universe should possess just that number of dimensions is not addressed by the theory. Moreover, M-Theory fails to predict uniquely our universe. Stephen Hawking recently addressed this question at a cosmology conference at the University of California, Davis. Notice the alternative answers which he identifies to the question he poses:
Does string theory, or M theory, predict the distinctive features of our universe, like a spatially flat four dimensional expanding universe with small fluctuations, and the standard model of particle physics? Most physicists would rather believe string theory uniquely predicts the universe, than the alternatives. These are that the initial state of the universe, is prescribed by an outside agency, code named God. Or that there are many universes, and our universe is picked out by the anthropic principle.6
These represent precisely the three alternatives laid out in premise (1). Hawking argues that the first alternative, physical necessity, is a vain hope: “M theory cannot predict the parameters of the standard model. Obviously, the values of the parameters we measure must be compatible with the development of life. . . . But within the anthropically allowed range, the parameters can have any values. So much for string theory predicting the fine structure constant.” He wrapped up by saying,
Even when we understand the ultimate theory, it won’t tell us much about how the universe began. It cannot predict the dimensions of spacetime, the gauge group, or other parameters of the low energy effective theory. . . . It won’t determine how this energy is divided between conventional matter, and a cosmological constant, or quintessence. . . . So to come back to the question. . . . Does string theory predict 6. S. W. Hawking, “Cosmology from the Top Down,” paper presented at the Davis Cosmic Inflation Meeting, U. C. Davis, May 29, 2003.
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the state of the universe? The answer is that it does not. It allows a vast landscape of possible universes, in which we occupy an anthropically permitted location.
In fact, this idea of a “cosmic landscape” predicted by string theory has become something of a phenom in its own right.7 It turns out that string theory allows around 10500 different possible universes governed by the present laws of nature, so that the theory does not at all render the observed values of the constants and quantities physically necessary. Moreover, even though there may be a huge number of possible universes lying within the life-permitting region of the cosmic landscape, nevertheless that life-permitting region will be unfathomably tiny compared to the entire landscape, so that the existence of a life-permitting universe is fantastically improbable.8 Indeed, given the multiplicity of constants that require fine-tuning, it is far from clear that 10500 possible universes is enough to guarantee that even one life-permitting world will appear by chance in the landscape!9
All this has been said with respect to the constants alone; there is still nothing to explain the arbitrary quantities put in as boundary conditions. Davies comments,
Even if the laws of physics were unique, it doesn’t follow that the physical universe itself is unique. . . . the laws of physics must be augmented by cosmic initial conditions. . . . There is nothing in present ideas about “laws of initial conditions” remotely to suggest that their consistency with the laws of physics would imply uniqueness.
Far from it. . . . It seems, then, that the physical universe does not have to be the way it is: it could have been otherwise.10
7. See Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design (New York: Little, Brown, & Co., 2006). Susskind apparently believes that the discovery of the cosmic landscape undercuts the argument for design, when in fact precisely the opposite is true. Susskind doesn’t seem to appreciate that the 10500 worlds in the cosmic landscape are not real but merely possible universes consistent with M-Theory. To find purchase for the anthropic principle mentioned by Hawking as the third alternative, one needs a plurality of real universes, which string theory alone does not provide.
8. If only one universe out of 10120 has the life-permitting value of the cosmological constant, then, given 10500 possible universes, the number of universes with the life-permitting value will be only 10500 ÷
10120 = 10380. To the novice this may sound as if most of the worlds are then life-permitting, when in fact 10380 is an inconceivably small fraction of 10500, so that almost all of the possible universes will be life-prohibiting. To see the point, imagine that we have a million possible universes and the odds of a life-permitting universe are one out of a hundred. So the total number of life-permitting universes will be 1,000,000
÷ 100 = 10,000. So the total number of life-permitting universes is 106 ÷ 102 = 104. One sees that 104 is a tiny fraction of 106, for only 10,000 out of the one million worlds are life-permitting, while a whopping 990,000 are life-prohibiting.
9. For example, since the values of at least some of the constants are independent, we must multiply the individual probabilities of the constants to find the probability of two constants’ both being finely tuned together. So if the odds of the cosmological constant’s having the value it does is 1 out of 10120 and the odds of the gravitational constant’s having the value it does is 1 out of 10100, then their joint probability will be one chance out of 10120 + 100 = 10220. If we keep adding constants until we get a life-permitting universe, before too long we’ll have run out of possible universes and so will have exhausted all the probabilistic resources!
10. Paul Davies, The Mind of God (New York: Simon & Schuster, 1992), 169. I take Davies to mean by the laws of physics the laws with the actual values of the constants. Otherwise he is confusing there being different values of the constants with there being different laws.
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The extraordinarily low entropy condition of the early universe would be a good example of an arbitrary quantity which seems to have just been put in at the creation as an initial condition. There is no reason to think that showing every constant and quantity to be physically necessary is anything more than a pipedream.
Chance
Considerations of Probability
What, then, of the alternative of chance? One may seek to eliminate this hypothesis either by appealing to the specified complexity of cosmic fine-tuning or by arguing that the fine-tuning is significantly more probable on design (theism) than on the chance hypothesis (atheism). It is sometimes objected that it is meaningless to speak of the probability of our finely tuned universe’s existing because there is, after all, only one universe. But the following illustration from John Barrow clarifies the sense in which a life-permitting universe is improbable. Take a sheet of paper and place upon it a red dot. That dot represents our universe. Now alter slightly one or more of the finely tuned constants and physical quantities which have been the focus of our attention. As a result we have a description of another universe, which we may represent as a new dot in the proximity of the first. If that new set of constants and quantities describes a life-permitting universe, make it a red dot; if it describes a universe which is life-prohibiting, make it a blue dot. Now repeat the procedure arbitrarily many times until the sheet is filled with dots. What one winds up with is a sea of blue with only a few pin-points of red. That is the sense in which it is overwhelmingly improbable that the universe should be life-permitting.
There are simply a vastly greater proportion of more life-prohibiting universes in our local area of possible universes than there are life-permitting universes.
It might be objected that we do not know if all these possible universes are equally probable. This amounts, in effect, to the claim that the actual range of possible values for a certain constant or quantity may be very narrow. But even if that were the case, when one has many variables requiring fine-tuning, the probability of a life-permitting universe’s existing is still very small. Moreover, in the absence of any physical reason to think that the values are constrained, we are justified in assuming a principle of indifference to the effect that the probability of our universe’s existing will be the same as the probability of any other universe which is represented on our sheet.
Barrow’s illustration also helps to avoid a possible misunderstanding. Some people say that the existence of any universe is equally improbable and yet some universe must exist. The fine-tuning of the universe is said to be like a lottery in which any individual’s winning is fantastically and equally improbable but which some individual has to win. Just as the winner of such a lottery should not conclude that the lottery must be rigged just because he won, so we should not conclude that there is a cosmic designer just because our universe exists. The fallacy in this
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reasoning is that we are not trying to explain the existence of our universe; rather it is the existence of a life-permitting universe that demands explanation. We’re not asking why our dot exists but why a red dot exists. Thus, the proper lottery analogy to the fine-tuning of the universe is a lottery in which a single white ball is mixed into a billion billion billion black balls, and a ball is then selected randomly from the collection. True, any ball that rolls down the chute will be fantastically and equally improbable; nevertheless, it is overwhelmingly more probable that whichever ball rolls down the chute, it will be black rather than white. Similarly, the existence of any particular universe is equally improbable; but it is incomprehensibly more probable that whichever universe exists will be life-prohibiting rather than life-permitting. It is the enormous, specified improbability of a life-permitting universe that presents the hurdle for the chance hypothesis.
The Anthropic Principle
Some theorists have tried to support the chance hypothesis by appeal to the so-called Anthropic Principle. As formulated by Barrow and Tipler, the Anthropic Principle states that any observed properties of the universe which may at first appear astonishingly improbable can only be seen in their true perspective after we have accounted for the fact that certain properties could not be observed by us, since we can only observe properties which are compatible with our own existence.
The implication is that we ought not to be surprised at observing the universe to be as it is and therefore no explanation of its fine-tuning need be sought.
The argument is, however, based on confusion. Barrow and Tipler have confused the true claim
A. If observers who have evolved within a universe observe its constants and quantities, it is highly probable that they will observe them to be fine-tuned for their existence.
with the false claim
Aʹ. It is highly probable that a universe exist which is finely tuned for the evolution of observers within it.
An observer who has evolved within the universe should regard it as highly probable that he will find the constants and quantities of the universe fine-tuned for his existence; but he should not infer that it is therefore highly probable that such a fine-tuned universe exist. Leslie gives the illustration of your being dragged before a firing squad of one hundred trained marksmen to be executed. The command is given: “Ready! Aim! Fire!” You hear the deafening roar of the guns. And then you observe that you’re still alive, that all the one hundred trained marksmen missed!
Now what do you conclude? “I really shouldn’t be surprised at the improbability of their all missing because if they hadn’t all missed, then I wouldn’t be here to
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be surprised about it. Since I am here, there’s nothing to be explained!” Of course not! While it’s correct that you shouldn’t be surprised that you don’t observe that you are dead (since if you were dead, you could not observe the fact), nevertheless, it doesn’t follow that you shouldn’t be surprised that you do observe that you are alive. In view of the enormous improbability of the marksmen’s all missing, you ought to be very surprised that you observe that you are alive and so suspect that more than chance alone is involved, even though you’re not surprised that you don’t observe that you are dead.
The Many Worlds Hypothesis
Theorists now recognize that the Anthropic Principle can legitimately be employed only when it is conjoined to a Many Worlds Hypothesis, according to which a World Ensemble of concrete universes exists, actualizing a wide range of possibilities. The Many Worlds Hypothesis is essentially an effort on the part of partisans of the chance hypothesis to multiply their probabilistic resources in order to reduce the improbability of the occurrence of fine-tuning. The very fact that otherwise sober scientists must resort to such a remarkable hypothesis is a sort of backhanded compliment to the design hypothesis. It shows that the fine-tuning does cry out for explanation. But is the Many Worlds Hypothesis as plausible as the design hypothesis?
If the Many Worlds Hypothesis is to commend itself as a plausible hypothesis, then some plausible mechanism for generating the many worlds needs to be to be explained. The best shot at providing a plausible mechanism comes from inflationary cosmology, which is often employed to defend the view that our universe is but one domain (or “pocket universe”) within a vastly larger universe, or multiverse. Vilenkin is one who vigorously champions the idea that we live in a multiverse. At the heart of Vilenkin’s view is the theory of future-eternal, or everlasting, inflation. In order to ensure that inflation will go on forever, Vilenkin hypothesizes that the primordial scalar fields determining the energy density and evolution of the false vacuum are characterized by a certain slope which issues in a false vacuum expanding so rapidly that, as it decays into pockets of true vacuum, the “island universes” thereby generated in this sea of false vacuum, though themselves expanding at enormous rates, cannot keep up with the expansion of the false vacuum and so find themselves increasingly separated with time. Moreover, each island is subdivided into subdomains which Vilenkin calls O-regions, each constituting an observable universe bounded by an event horizon.
Despite the fact that the multiverse is finite and geometrically closed, the false vacuum will, according to the theory, go on expanding forever. New pockets of true vacuum will continue to form in the gaps between the island universes and become themselves isolated worlds.
Now at this point Vilenkin executes a nifty piece of legerdemain. As the island universes expand, their central regions eventually grow dark and barren,
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while stars are forming at their ever-expanding perimeters. We should think of the decay of false vacuum to true vacuum going on at the islands’ expanding boundaries as multiple Big Bangs. From the global perspective of the inflating multiverse, these Big Bangs occur successively, as the island boundaries grow with time (Fig. 4.1).
time
now
Big Bang
Inflation
before
Fig. 4.1: A global perspective on an island universe. As the island expands with time, its central region grows dark and cold in accordance with the second law of thermodynamics, while at its perimeter new star-producing regions are constantly being formed. These regions are causally unconnected and so constitute different O-regions, or observable universes, within the island universe, each traceable back to a Big Bang event.
In the global time of the multiverse, each island is at any time finite in size though constantly growing. Now comes the sleight of hand. When we consider the internal, cosmic time of each island universe, each observer will trace it back to an initial Big Bang event. We can then string together these various Big Bang events as occurring simultaneously (Fig. 4.2). Big Bangs which will occur in the global future are, from the internal point of view, to be regarded as present. As a result, the infinite, temporal series of successive Big Bangs is converted into an infinite, spatial array of simultaneous Big Bangs. Hence, from the internal point of view each island universe is infinite in extent. As Vilenkin puts it, “The infinity of time in one view is thus transformed into the infinity of space in the other.”11
Vilenkin’s deft transformation seems to presuppose a static or B-Theory of time12 or, as it is sometimes called, four-dimensionalism or spacetime realism.
For if temporal becoming is an objective feature of reality, then the global fu-11. Alex Vilenkin, Many Worlds in One: The Search for Other Universes (New York: Hill and Wang, 2006), 99.
12. Recall our distinguishing two views of time on 123.
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time
now
Big Bang
Inflation
before
Fig. 4.2: An internal perspective on an island universe. The Big Bangs in which the various O-regions originate will be regarded as occurring simultaneously. Thus, the infinity of time on the global perspective is converted into an infinity of space on the internal perspective. Though finite in size from a global perspective, each island will be regarded as infinite in size by its inhabitants.
ture is potentially infinite only, and future O-regions do not in any sense exist.
If there is a global tide of becoming, then there is no actually infinite collection of O-regions after all. Internal observers, unaware of the global perspective, are simply mistaken in their taking the successive Big Bang events to be occurring simultaneously. Once again, we see how issues in the philosophy of time impinge crucially on scientific debates.13
But if an infinite ensemble of simultaneous universes does not actually exist, Vilenkin’s attempt to explain away the fine-tuning of the universe for intelligent life collapses. For if, in fact, an infinite array of universes does not yet exist, if most of them lie in the potentially infinite future and are therefore unreal, then there actually exist only as many observable universes as can have formed since any island’s origin in the finite past. Moreover, since the Borde-Guth-Vilenkin theorem requires that the multiverse itself cannot be extended into the infinite past, there can be only as many island universes now in existence as have formed in the false vacuum since the multiverse’s inception at its boundary in the finite past. Given the incomprehensible improbability of the constants’ all falling randomly into the life-permitting range, it may well be highly improbable that a life-permitting island universe should have decayed this soon out of the false vacuum. In that case the sting of fine-tuning has not been removed.
13. In my Time and Eternity, I defend the privileged nature of the global perspective. There I was considering the universe alone, so that the preferred time is cosmic time. But if a multiverse exists, then the global time will not be the cosmic time of any island universe but the proper time of the multiverse as a whole.
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Vilenkin’s whole multiverse scenario depends in any case on the hypothesis of future-eternal inflation, which in turn, it will be recalled, is based upon the existence of certain primordial scalar fields which govern inflation. Although Vilenkin observes that “inflation is eternal in practically all models suggested so far,”14 he also admits, “Another important question is whether or not such scalar fields really exist in nature. Unfortunately, we don’t know. There is no direct evidence for their existence.”15 This lack of evidence ought to temper the confidence with which the Many Worlds Hypothesis is put forward.
Wholly apart from its speculative nature, however, the Many Worlds Hypothesis faces a potentially lethal problem. Simply stated, if our universe is but one member of an infinite World Ensemble of randomly varying universes, then it is overwhelmingly more probable that we should be observing a much different universe than that which we in fact observe. Recall our discussion of Ludwig Boltzmann’s Many Worlds Hypothesis for why we do not find the universe in a state of “heat death” or thermodynamic equilibrium.16 The problem with Boltzmann’s daring Many Worlds Hypothesis was that if our world were merely a fluctuation in a sea of diffuse energy, then it is overwhelmingly more probable that we should be observing a much tinier region of disequilibrium than we do.
Now a precisely parallel problem attends the Many Worlds Hypothesis as an explanation of fine-tuning. As we have seen, Roger Penrose calculates that the odds of our universe’s low entropy condition obtaining by chance alone are on the order of 1:1010(123), an inconceivable number. If our universe were but one member of a collection of randomly ordered worlds, then it is vastly more probable that we should be observing a much smaller universe.17 Adopting the Many Worlds Hypothesis to explain away fine-tuning would thus result in a bizarre illusionism: it is far more probable that all our astronomical, geological, and biological estimates of age are wrong and that the appearance of our large and old universe is a massive illusion (recall the dreaded Boltzmann brains). Or again, if our universe is but one member of a World Ensemble, then we ought to be observing highly extraordinary events, like horses popping into and out of existence by random collisions, or perpetual motion machines, since these are vastly more probable than all of nature’s constants and quantities falling by chance into the virtually infinitesimal life-permitting range. Observable universes like those are much more plenteous in the ensemble of universes than worlds like ours and, therefore, ought to be observed by us if the universe were but one member of an ensemble 14. Vilenkin, Many Worlds in One, 214.
15. Ibid., 61.
16. See 146–50.
17. Roger Penrose, The Road to Reality (New York: Alfred A. Knopf, 2005), 762–65. The odds of our solar system’s being formed instantly by random collisions of particles is, according to Penrose, about 1:1010(60), a vast number, but inconceivably smaller than 1010(123). Penrose concludes that anthropic explanations are so “impotent” that it is actually “misconceived” to appeal to them to explain the special features of the universe.
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of worlds. Since we do not have such observations, that fact strongly disconfirms the multiverse hypothesis. On atheism, at least, it is therefore highly probable that there is no World Ensemble.
For these reasons the Many Worlds Hypothesis is severely disabled as a candidate for the best explanation of the observed cosmic fine-tuning. Since the alternative of chance stands or falls with the Many Worlds Hypothesis, that explanation is seen to be very implausible.
It therefore seems that the fine-tuning of the universe is plausibly due neither to physical necessity nor to chance. It follows that the fine-tuning is therefore due to design, unless the design hypothesis can be shown to be even more implausible than its competitors.
The Design Hypothesis
The implication of the design hypothesis is that there exists a Cosmic Designer who fine-tuned the initial conditions of the universe for intelligent life. Such a hypothesis supplies a personal explanation of the fine-tuning of the universe. Is this explanation implausible? Detractors of design sometimes object that on this hypothesis the Cosmic Designer himself remains unexplained. This objection is what Richard Dawkins calls “the central argument of my book” The God Delusion.18
He summarizes his argument as follows:
1) One of the greatest challenges to the human intellect has been to explain how the complex, improbable appearance of design in the universe arises.
2) The natural temptation is to attribute the appearance of design to actual design itself.
3) The temptation is a false one because the designer hypothesis immediately raises the larger problem of who designed the designer.
4) The most ingenious and powerful explanation is Darwinian evolution by natural selection.
5) We don’t have an equivalent explanation for physics.
6) We should not give up the hope of a better explanation arising in physics, something as powerful as Darwinism is for biology.
Therefore, God almost certainly does not exist.
This argument is jarring because the atheistic conclusion “Therefore, God almost certainly does not exist” doesn’t follow from the six previous statements even if we concede that each of them is true and justified. At most, all that follows is that we should not infer God’s existence on the basis of the appearance of design in the universe. But that conclusion is quite compatible with God’s existence and 18. Richard Dawkins, The God Delusion (New York: Houghton Mifflin, 2006), 157–58.
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even with our justifiably believing in God’s existence. Maybe we should believe in God on the basis of the cosmological argument or the ontological argument or the moral argument. Maybe our belief in God isn’t based on arguments at all but is grounded in religious experience or in divine revelation. The point is that rejecting design arguments for God’s existence does nothing to prove that God does not exist or even that belief in God is unjustified.
In any case, several of the steps of Dawkins’ argument are plausibly false. Step (5) alludes to the cosmic fine-tuning which has been the focus of our discussion.
Dawkins has nothing by way of explanation for it, and therefore the hope expressed in step (6) represents nothing more than the faith of a naturalist. Moreover, consider step (3). Dawkins’ claim here is that one is not justified in inferring design as the best explanation of the complex order of the universe because then a new problem arises: who designed the Designer?
This rejoinder is flawed on at least two counts. First, in order to recognize an explanation as the best, one needn’t have an explanation of the explanation. This is an elementary point concerning inference to the best explanation as understood in the philosophy of science. If archaeologists digging in the earth were to discover things looking like arrowheads and hatchet heads and pottery shards, they would be justified in inferring that these artifacts are not the chance result of sedimenta-tion and metamorphosis, but products of some unknown group of people, even though they had no explanation of who these people were or where they came from. Similarly, if astronauts were to come upon a pile of machinery on the back side of the moon, they would be justified in inferring that it was the product of intelligent agents, even if they had no idea whatsoever who these agents were or how they got there. In order to recognize an explanation as the best, one needn’t be able to explain the explanation. In fact, so requiring would lead to an infinite regress of explanations, so that nothing could ever be explained and science would be destroyed! So in the case at hand, in order to recognize that intelligent design is the best explanation of the appearance of design in the universe, one needn’t be able to explain the Designer.
Second, Dawkins thinks that in the case of a divine Designer of the universe, the Designer is just as complex as the thing to be explained, so that no explanatory advance is made. This objection raises all sorts of questions about the role played by simplicity in assessing competing explanations; for example, how simplicity is to be weighed in comparison with other criteria like explanatory power, explanatory scope, and so forth. But leave those questions aside. Dawkins’s fundamental mistake lies in his assumption that a divine Designer is an entity comparable in complexity to the universe. As an unembodied mind, God is a remarkably simple entity. As a non-physical entity, a mind is not composed of parts, and its salient properties, like self-consciousness, rationality, and volition, are essential to it. In contrast to the contingent and variegated universe with all its inexplicable constants and quantities, a divine mind is startlingly simple. Certainly such a mind may have complex
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ideas—it may be thinking, for example, of the infinitesimal calculus—but the mind itself is a remarkably simple entity. Dawkins has evidently confused a mind’s ideas, which may, indeed, be complex, with a mind itself, which is an incredibly simple entity. Therefore, postulating a divine mind behind the universe most definitely does represent an advance in simplicity, for whatever that is worth.
It seems to me therefore that of the three proffered alternatives—physical necessity, chance, or design—the most plausible of the three is the hypothesis of design. Thus, the teleological argument based on the fine-tuning of the universe fares well as a sound and persuasive argument for a Designer of the cosmos.
MORAL ARGUMENT
Like the cosmological argument, the moral argument is a family of diverse arguments for the existence of God, but in this case springing from moral considerations. The version I find most convincing is the argument for God on the basis of the objectivity of moral values and duties. A very simple and straightforward formulation of this argument is as follows:
1) If God does not exist, objective moral values and duties do not exist.
2) Objective moral values and duties do exist.
3) Therefore, God exists.
Although the argument as such does not reach the conclusion that God is the basis of objective moral values and duties, such a claim tends to be implicit in premise (1) and emerges in the defense of that premise against objections.
God and Objective Morals
Every one of us guides his life, however inconsistently, by a certain set of values.
But are the values we hold dear and guide our lives by mere social conventions akin to driving on the left- versus right-hand side of the road or mere expressions of personal preference akin to having a taste for certain foods rather than others? Or are they valid independently of our apprehension of them, and if so, what is their foundation? Are there things which I ought not to do and other things which I ought to do? Or is this sense of obligation a mere illusion due to sociological and psychological conditioning? Many philosophers have argued that if God does not exist, then morality is ultimately subjective and non-binding. We might act in precisely the same ways that we do in fact act, but in the absence of God such actions would no longer count as good or evil, right or wrong, since in the absence of God, objective moral values and duties do not exist.
In order to unpack this point, it will be helpful to distinguish between moral values and moral duties. When we speak of moral values, we’re talking about whether something is good or bad; when we talk about moral duties we are concerned with whether something is right or wrong. Although we are apt to equate what is right with what is good and what is wrong with what is bad, a little reflection reveals this
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to be mistaken. Right and wrong have to do with moral obligation, what I ought or ought not to do. But obviously, I am not morally obligated to do something just because it would be good for me to do it. For example, it’s a good thing to become a chemist, but that doesn’t imply that it is therefore my duty to become a chemist.
For it is also good to become a firefighter or a diplomat or a doctor, and I can’t become all of them. Moreover, there are occasionally circumstances in which I am, tragically, confronted with nothing but bad choices (think of Sophie’s Choice), but it is not therefore wrong of me to choose one, since I must choose. So there is a conceptual difference between something’s being good (or bad) and something’s being right (or wrong). The former has to do with something’s worth, while the latter concerns something’s obligatoriness. In premise (1) we’re concerned with the question whether without God there would be an objective distinction between good and evil and between right and wrong.
Let me say something as well to clarify the distinction between something’s being objective and something’s being subjective. To say that something is objective is to say that it is independent of what people think or perceive. By contrast, to say that something is subjective is just to say that it is not objective; that is to say, it is dependent on what human persons think or perceive. So, for example, the distinction between being on Mars and not being on Mars is an objective distinction; a particular rock’s being on Mars is in no way dependent upon our beliefs.
By contrast, the distinction between “here” and “there” is not objective: whether a particular event at a certain spatial location occurs here or occurs there depends upon a person’s point of view.
To say that there are objective moral values is to say that something is good or evil independently of whether any human being believes it to be so. Similarly to say that we have objective moral duties is to say that certain actions are right or wrong for us independently of whether any human being believes them to be so.
For example, to say that the Holocaust was objectively wrong is to say that it was wrong even though the Nazis who carried it out thought that it was right, and it would still have been wrong even if the Nazis had won World War II and succeeded in exterminating or brainwashing everybody who disagreed with them so that it was universally believed that the Holocaust was right. The claim of premise (1) is that if there is no God, then moral values and duties are not objective in this sense.
Consider, then, moral values. If theism is false, why think that human beings have objective moral value? After all, on the naturalistic view, there’s nothing special about human beings. They’re just accidental byproducts of nature which have evolved relatively recently on an infinitesimal speck of dust called the planet Earth, lost somewhere in a hostile and mindless universe, and which are doomed to perish individually and collectively in a relatively short time. Richard Dawkins’
assessment of human worth may be depressing, but why, on atheism, is he mistaken when he says, “There is at bottom no design, no purpose, no evil, no good,
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nothing but pointless indifference. . . . We are machines for propagating DNA.
. . . It is every living object’s sole reason for being”?19
Atheist philosophers who are humanists do not seem to have faced squarely the consequences of their naturalism. For example, humanist philosopher Paul Kurtz insists that human flourishing is “the be-all and end-all” of human life,20 while affirming like Dawkins that “the discoveries of Copernicus and Darwin . . . have
[undermined] the belief that we are fundamentally different from all other species.”21 He muses that “many [people] still refuse to accept the full implications of these discoveries.”22 They “still seek to find a special place for the human species in the scheme of things.”23 Kurtz is doubtlessly thinking of theists. Ironically, however, it is precisely humanists themselves who seek to find a special place for the human species in the scheme of things, who refuse to accept the full implications of reducing human beings to just another animal species. For humanists continue to treat human beings as morally special in contrast to other species.
What justification is there for this differential treatment? On a naturalistic view moral values are just by-products of socio-biological evolution. Just as a troupe of baboons exhibit co-operative behavior and even altruistic, sacrificial behavior because evolution has determined it to be advantageous in the struggle for survival, so their primate cousins homo sapiens exhibit similar behavior for the same reason.
As philosopher of science Michael Ruse explains,
The position of the modern evolutionist . . . is that humans have an awareness of morality . . . because such an awareness is of biological worth. Morality is a biological adaptation no less than are hands and feet and teeth. . . . Considered as a rationally justifiable set of claims about an objective something, ethics is illusory. I appreciate that when somebody says “Love thy neighbor as thyself,” they think they are referring above and beyond themselves. . . . Nevertheless, . . . such reference is truly without foundation. Morality is just an aid to survival and reproduction, . . . and any deeper meaning is illusory.24
As a result of socio-biological pressures, there has evolved among homo sapiens a sort of “herd morality” which functions well in the perpetuation of our species in the struggle for survival. But on the atheistic view there doesn’t seem to be anything about homo sapiens that makes this morality objectively true. If the film of evolutionary history were rewound and shot anew, very different creatures with a very different set of values might well have evolved. By what right do we regard 19. Cited in Lewis Wolpert, Six Impossible Things before Breakfast (London: Faber and Faber, 2006), 215. But see n.19 of chap. 2 above.
20. Paul Kurtz, The Courage to Become (Westport, Conn.: Praeger, 1997), 125.
21. Ibid., 5–6.
22. Ibid., 6.
23. Ibid., 53.
24. Michael Ruse, “Evolutionary Theory and Christian Ethics,” in The Darwinian Paradigm (London: Routledge, 1989), 262, 268–89.
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our morality as objective rather than theirs? To think that human beings are special is to be guilty of specie-ism, an unjustified bias toward one’s own species.
Thus, if there is no God, then any basis for regarding the herd morality evolved by homo sapiens as objectively true seems to have been removed. So, if theism is false, it is hard to see what basis remains for the affirmation of objective moral values and in particular of the special value of human beings.
Second, if theism is false, then what is the basis for objective moral duties?
Crudely put, on the atheistic view human beings are just animals, and animals have no moral obligations to one another. The ethicist Richard Taylor powerfully illustrates the point. He invites us to imagine human beings living in a state of nature without any customs or laws. Suppose one of them kills another one and takes his goods. Taylor reflects:
Such actions, though injurious to their victims, are no more unjust or immoral than they would be if done by one animal to another. A hawk that seizes a fish from the sea kills it, but does not murder it; and another hawk that seizes the fish from the talons of the first takes it, but does not steal it—for none of these things is forbidden.
And exactly the same considerations apply to the people we are imagining.25
Why think that if God does not exist, we would have any moral obligations to do anything? Who or what imposes these moral duties upon us? As Taylor says,
“the concept of moral obligation [is] unintelligible apart from the idea of God.
The words remain, but their meaning is gone.”26
Thus, if atheism is true, it becomes impossible to condemn war, oppression, or crime as evil. Nor can one praise brotherhood, equality, or love as good. It doesn’t matter what you do—for there is no right and wrong; all things are permitted. To be sure, some actions—say rape or incest—may not be biologically or sociologically advantageous, and so, in the course of human development, have become taboo. But that does absolutely nothing to show that rape or incest is really wrong.
On the atheistic view, there’s nothing really wrong about raping someone. Such behavior goes on all the time in the animal kingdom. If, as Kurtz states, “the moral principles that govern our behavior are rooted in habit and custom, feeling and fashion,”27 then the rapist who chooses to flout the herd morality is doing nothing more serious than acting unfashionably. So if theism is false, it’s very hard to understand what basis remains for objective moral duties.
Now it’s important that we remain clear in understanding the issue before us.
The question is not: Must we believe in God in order to live moral lives? There’s no reason to think that atheists and theists alike may not live what we normally characterize as good and decent lives. Similarly, the question is not: Can we formulate a system of ethics without reference to God? If the non-theist grants that human 25. Richard Taylor, Ethics, Faith, and Reason (Englewood Cliffs, N.J.: Prentice-Hall, 1985), 14.
26. Ibid., 83–84.
27. Paul Kurtz, Forbidden Fruit (Buffalo, N.Y.: Prometheus, 1988), 73.
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beings do have objective value, then there’s no reason to think that he cannot work out a system of ethics with which the theist would also largely agree. Or again, the question is not: Can we recognize the existence of objective moral values without reference to God? The theist will typically maintain that a person need not believe in God in order to recognize, say, that we should love our children.
All of the above misunderstandings of the argument are based on confusing God’s existence with belief in God’s existence. The argument is not that belief in God’s existence is necessary for the objective reality of moral values and duties, but that God is necessary for the objective reality of moral values and duties. Nor is the argument that God is necessary for our knowledge of moral values and duties. I have been astonished at the confusion of moral ontology with moral epistemology on the part of prominent moral philosophers responding to premise (1).28 Moral ontology deals with the reality of moral values and properties; moral epistemology deals with our knowledge of moral truths. As far as moral epistemology is concerned, I can appeal to all the same mechanisms, such as moral intuition and reflection, by means of which humanist thinkers are confident that they accurately discern the good and the right. In fact, the Bible actually teaches that God’s moral law is
“written on the hearts” of all men, so that even those who do not know God’s law
“do naturally the things of the law” as “their conscience bears witness to them”
(Rom. 2.14–15 at). If that is the case, a theist’s moral epistemology need not differ broadly from the humanist’s own moral epistemology. Epistemological objections are thus red herrings which need not detain us. I’m contending that theism is necessary that there might be moral goods and duties, not that we might discern the moral goods and duties that there are. As Kurtz puts it, “The central question about moral and ethical principles concerns their ontological foundation. If they are neither derived from God nor anchored in some transcendent ground, are they purely ephemeral?”29
So what response can naturalistic thinkers make to premise (1)? Some philosophers, equally averse to anchoring moral values in some non-theistic transcendent ground as in God, try to maintain the existence of objective moral principles or moral properties in the context of a naturalistic worldview. But the advocates of such theories are typically at a loss to justify their starting point. If there is no God, then it’s hard to see any reason for thinking that the herd morality evolved by homo sapiens is objectively true or that the property of moral goodness supervenes on certain natural states of such creatures.
28. See the response by Walter Sinnott-Armstrong in our God? A Debate between a Christian and an Atheist (New York: Oxford University Press, 2003), and by Sinnott-Armstrong and Louise Antony in Paul Kurtz and my God and Ethics: A Contemporary Debate, ed. Nathan King and Robert Garcia (Lanham, Md.: Rowman & Littlefield, 2008). Ironically, the distinction between moral ontology and moral epistemology is drawn with wonderful clarity by Sinnott-Armstrong himself in his “Moral Skepticism and Justification,”
in Moral Knowledge? ed. Walter Sinnott-Armstrong and Mark Timmons (New York: Oxford University Press, 1996), 4–8.
29. Kurtz, Forbidden Fruit, 65.
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It seems that the atheistic humanist must simply insist, with the Dartmouth ethicist Walter Sinnott-Armstrong, that whatever contributes to human flourishing is morally good and whatever detracts from human flourishing is bad and take that as his explanatory stopping point.30 But the problem is that such an explanatory stopping point seems premature because of its arbitrariness and implausibility.
Why, given atheism, think that inflicting harm on other people would have any moral dimension at all? Why would it be wrong to hurt another member of our species? Sinnott-Armstrong answers, “It simply is. Objectively. Don’t you agree?”31
Of course, I agree that it is wrong, since I am a theist. But I can’t see any reason to think that it would be wrong if atheism were true. Sinnott-Armstrong thinks that rape is wrong, even though the physical activity that counts as rape among human beings goes on all the time in the animal kingdom—just as acts that count as murder and theft when done by one human to another occur constantly between members of other animal species—without any moral significance whatsoever. This is surely strange and cries out for explanation. As Michael Ruse has argued, we can well conceive of extra-terrestrial rational beings for whom rape would not be immoral.32 Were they to visit Earth, why should they respect the values that have evolved among homo sapiens? Had our own evolutionary history gone differently, creatures with a different set of moral values might have existed here. All this underlines the arbitrariness of Sinnott-Armstrong’s explanatory ultimate.
The naturalist might try to meet this objection by holding that moral properties supervene necessarily on certain natural states. But then the question as to the plausibility of this explanatory ultimate arises. The claim that moral properties necessarily supervene on certain physical states of affairs at best gives us reason to think that if moral properties do supervene on certain natural states, then they do so necessarily. But that gives us no reason at all to think that, given a naturalistic worldview, there are any moral properties or that they do supervene on natural states. Why think that on an atheistic view of the world the curious, non-physical property of moral goodness would supervene on a human female’s nursing her infant? Why, given naturalism, would the strange, non-physical property of moral badness supervene on a man’s leaving a shop carrying certain items for which he has not left the currency demanded by the shop owner? I see no reason to think that a full specification of all the natural properties of a situation would determine or fix any moral properties of that situation. If our approach to meta-ethical theory is to be serious metaphysics rather than just a “shopping list”
approach, whereby one simply helps oneself to the supervenient moral properties or principles needed to do the job, then some sort of explanation is required for why moral properties supervene on certain natural states or why such principles are 30. Walter Sinnott-Armstrong, “Why Traditional Theism Cannot Provide an Adequate Foundation for Morality,” in God and Ethics.
31. Walter Sinnott-Armstrong, “There Is No Good Reason to Believe in God,” in God? A Debate, 34.
32. Michael Ruse, “Is Rape Wrong on Andromeda?”
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true. It is insufficient for the naturalist to point out that we do, in fact, apprehend the goodness or obligatoriness of some feature of human existence, for that only goes to establish the objectivity of moral values and duties, which just is premise (2) of the moral argument!
Some philosophers think that moral truths, being necessarily true, cannot have an explanation of their truth. I think we can agree that many moral principles are necessarily true. But that doesn’t prove that they cannot have an explanation. The crucial presupposition of these philosophers—that necessary truths cannot stand in relations of explanatory priority to one another—is far from evident and, indeed, seems plainly false. For example, the classical theist will say that the statement “A plurality of persons exists” is necessarily true because “God exists” is necessarily true and God is essentially a Trinity. To give a non-theological example, many mathematicians would say that “2+3=5” is necessarily true because the Peano axioms for standard arithmetic are necessarily true. Or again, many metaphysicians would hold that the statement “No event precedes itself ” is necessarily true because
“Temporal becoming is an essential and objective feature of time” is necessarily true. It would be utterly implausible to suggest that the relation of explanatory priority holding between the relevant statements could go either way.
Given the arbitrariness and implausibility of non-explanatory assertions of the objectivity of human values and duties, we need to ask whether moral values and duties can be plausibly anchored in some transcendent, non-theistic ground.
Let’s call this view Atheistic Moral Platonism. Atheistic Moral Platonists affirm that objective moral values do exist but are not grounded in God. Indeed, moral values have no further foundation. They just exist.
It is difficult, however, even to comprehend this view. What does it mean to say, for example, that the moral value Justice just exists? It’s hard to know what to make of this. It is clear what is meant when it is said that a person is just; but it is bewildering when it is said that in the absence of any people, Justice itself exists.
Moral values seem to exist as properties of persons, not as mere abstractions—or at any rate it’s hard to know what it is for a moral value to exist as a mere abstraction.33 Curiously, since the abstract object Justice is not itself just, it would seem to follow that in the absence of any people justice does not exist—which seems to contradict the hypothesis. Atheistic Moral Platonists seem to lack any adequate foundation in reality for moral values but just leave them floating in an unintelligible way.
Second, the nature of moral duty or obligation seems incompatible with Atheistic Moral Platonism. Let’s suppose for the sake of argument that moral values do exist 33. Moreover, we might wonder how we could ever come to have any knowledge of this abstract realm.
Realists about mathematical objects have faced this same conundrum. The suggestion by realist mathematician Kurt Gödel that we have some mysterious intuitive access to the realm of mathematical objects has been ridiculed by naturalistic philosophers of mathematics. Similarly, it is no clearer how I could know the content of the moral realm than how I could know what is going on in some remote village in Nepal with which I have no contact.
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independently of God. Suppose that values like Mercy, Justice, Love, Forbearance, and the like just exist. How does that result in any moral obligations for me? Why would I have a moral duty, say, to be merciful? Who or what lays such an obligation on me? On this view moral vices such as Greed, Hatred, and Selfishness also presumably exist as abstract objects. Why am I obligated to align my life with one set of these abstractly existing objects rather than any other? Theism, by contrast, provides a plausible basis for moral duty, as we shall see.
Thirdly, it is fantastically improbable that just that sort of creature would emerge from the blind evolutionary process that corresponds to the abstractly existing realm of moral values. This seems to be an utterly incredible coincidence when one thinks about it. It is almost as though the moral realm knew that we were coming.
As William Sorley saw, it is far more plausible to regard both the natural realm and the moral realm as under the hegemony of a divine Creator and Lawgiver than to think that these two entirely independent orders of reality just happened to mesh.
In short, on an atheistic, naturalistic worldview, there just seems to be no basis for affirming the existence of objective moral values and duties. Certainly we have a sense of morality, but on naturalism that sense is an illusion wrought by socio-biological conditioning.
Objectivity of Moral Values and Duties
Premise (2) of the moral argument asserts that, in fact, objective moral values and duties do exist. The way in which moral theorists test competing ethical theories is by assessing how well they cohere with our moral experience. I take it that in moral experience we do apprehend a realm of objective moral values and duties, just as in sensory experience we apprehend a realm of objectively existing physical objects. Just as it is impossible for us to get outside our sensory input to test its veridicality, so there is no way to test independently the veridicality of our moral perceptions. As Sorley emphasized, there is no more reason to deny the objective reality of moral values than the objective reality of the physical world. In the absence of some defeater, we rationally trust our perceptions, whether sensory or moral.
But what about the claim that moral values and duties are illusions fostered in us by socio-biological evolution? Doesn’t that constitute a defeater for premise (2)? Here we must distinguish carefully the two ways in which the claim that our moral beliefs are byproducts of socio-biological evolution might constitute a defeater of (2).34 On the one hand, such a claim might be taken as a defeater of the truth of (2). That is to say, the claim might be that since our moral beliefs have been instilled in us through socio-biological pressures, those beliefs are false and 34. See Plantinga’s understanding of what he calls the Freud and Marx objection to theistic belief. Early on, Plantinga had dismissed Freud and Marx’s objections to religious belief as instances of the genetic fallacy (“The Foundations of Theism: A Reply,” Faith and Philosophy 3 [1986]: 308), but he later came to see them as attacks upon the warrant for theistic belief ( Warranted Christian Belief [Oxford: Oxford University Press, 2000], 136–42, 151–52).
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so objective moral values and duties do not exist. So construed, the objection is a textbook example of the genetic fallacy, which is the attempt to falsify a belief by explaining how that belief originated. Such reasoning is fallacious, since a belief could be true regardless of how it came to be held. In particular, if God exists, then objective moral values and duties exist regardless of how conditioned we may be by the evolutionary process. So the objection at best proves only that our subjective perception of moral values and duties has evolved. But if moral values are gradually discovered, not invented, then our gradual and fallible apprehension of the moral realm no more undermines the objective reality of that realm than our gradual, fallible apprehension of the physical world undermines the objectivity of that realm.
But there’s a second, more powerful way in which the socio-biological claim might be construed: not as a defeater of the truth of (2) but of the warrant for (2).
That is to say, given that our moral beliefs have been determined by socio-biological pressures, we have no warrant for believing (2) to be true. Because our moral beliefs have been selected by evolution, not for their truth, but for their survival value, we can have no confidence in the deliverances of our moral experience. So even if (2) were true, we would still have no warrant for believing it to be true. The problem with this construal of the objection is that it turns out to be question-begging and even self-defeating. First, it’s question-begging because it presupposes that naturalism is true.35 If there is no God, then our moral experience is, plausibly, illusory. I said as much in my defense of premise (1). But why think that naturalism is true? To undermine the warrant which our moral experience gives to our moral beliefs, much more must be done than hold out the possibility that naturalism may be true. For if theism is true, then our moral experience, even if conditioned by biology and society, is probably not wholly illusory but is reliable to some degree.
In the absence of a proof of naturalism, the warrant which our moral experience lends to (2) remains undefeated. Second, the objection is self-defeating because, on naturalism, all our beliefs, not just our moral beliefs, have been selected for survival value, not truth, and are therefore unwarranted.36 In particular, the belief in naturalism and the socio-biological account of moral belief is unwarranted.
So the objection undermines its own warrant and is therefore incapable of being rationally affirmed. But then it cannot defeat the warrant for premise (2).
Most of us think that in moral experience we do apprehend objective values and obligations. Ruse himself confesses in another context, “The man who says that it is morally acceptable to rape little children is just as mistaken as the man who says, 2+2=5.”37 Speaking several years ago on a Canadian university campus, I noticed a poster put up by the Sexual Assault & Information Center. It read: “Sexual 35. See Plantinga’s response to the Freud and Marx objection to theistic belief in Warranted Christian Belief, 194–98.
36. This is Plantinga’s celebrated evolutionary argument against naturalism Warrant and Proper Function (Oxford: Oxford University Press, 1993), 216–37; Warranted Christian Belief, 227–40.
37. Michael Ruse, Darwinism Defended (London: Addison-Wesley, 1982), 275.
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Assault: No One Has the Right to Abuse a Child, Woman, or Man.” Most of us recognize that sexual abuse of another person is wrong. Actions like rape, torture, child abuse, and brutality aren’t just socially unacceptable behavior—they’re moral abominations. By the same token, love, generosity, equality, and self-sacrifice are really good. People who fail to see this are just morally handicapped, and there is no reason to allow their impaired vision to call into question what we see clearly.
Ethicist David Brink thinks that the objectivity of moral values is thus the default position. “There might be no objective moral standards. . . . But this would be a revisionary conclusion, to be accepted only as the result of extended and compelling argument that the commitments of ethical objectivity are unsustainable.”38
Indeed, I think that we are and should be more confident of the truth of premise (2) than we are of the premises in any argument for moral nihilism. In light of the warrant conferred on (2) by our moral experience, arguments for moral nihilism will always include some premise which is less warranted than (2) and which is therefore to be denied.
The Euthyphro Dilemma
From the two premises it follows logically that God exists. Notice that in defending the two premises, we have not committed ourselves to any particular account of the relationship between God and moral values or duties. Nevertheless, the most popular objection raised against the moral argument is essentially a challenge to basing moral values and duties in God. The objection, first recorded in Plato’s dialogue Euthyphro, goes as follows: either something is good because God wills it or else God wills something because it is good. If it is good just because God wills it, then what is good becomes arbitrary. God could have willed that hatred and jealousy be good, and then we should have been obligated to hate and envy one another. But that seems implausible; at least some moral goods seem to be necessary. But if we say instead that God wills something because it is good, then whether something is good or bad is independent of God. In that case, it seems that moral value exists independently of God, which undermines premise (1) of our moral argument. If God were not to exist, then objective moral values and duties would exist anyway.
The Euthyphro Dilemma can thus be construed as an argument for Atheistic Moral Platonism. Now we’ve already seen that such a theory has major deficits.
This suggests that the dilemma allegedly forcing us to such a position is a false one and that we may escape the horns of the dilemma by finding a third alternative. I think that an appropriately formulated divine command theory of ethics, such as has been articulated by Robert Adams, Philip Quinn, William Alston, and others,39 supplies such an alternative: our moral duties are constituted by the 38. David O. Brink, “The Autonomy of Ethics,” in The Cambridge Companion to Atheism, ed. Michael Martin, Cambridge Companions to Philosophy (Cambridge: Cambridge University Press, 2007), 149.
39. Philip L. Quinn, Divine Commands and Moral Requirements (Oxford: Clarendon, 1978); Janine Marie Idziak, Divine Command Morality: Historical and Contemporary Readings (Lewiston, N.Y.: Edwin Mellen Press, 1980); Robert Merrihew Adams, Finite and Infinite Goods (Oxford: Oxford University Press, 2000);
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commands of an essentially just and loving God. For any action A and moral agent S, we can explicate the notions of moral requirement, prohibition, and permission of A for S as follows:
A is required of S if and only if a just and loving God commands S to do A.
A is forbidden to S if and only if a just and loving God commands S not to do A.
A is permitted for S if and only if a just and loving God does not command S
not to do A.
Since our moral duties are grounded in the divine commands, they are not independent of God.
Neither are God’s commands arbitrary, for they are the necessary expressions of his just and loving nature. God is essentially compassionate, fair, kind, impartial, and so forth, and his commandments are reflections of his own character. God’s character is definitive of moral goodness; it serves as the paradigm of moral goodness. Thus, the morally good/bad is determined by reference to God’s nature; the morally right/wrong is determined by reference to his will. The divine will or commands come into play as a source of moral obligation, not moral value. As necessary expressions of his nature, God’s commands are not arbitrary, and so we need not trouble ourselves about counterfactuals with impossible antecedents like “If God were to command child abuse . . .” On the customary understanding, counterfactuals with impossible antecedents have no non-vacuous truth value. Even if we reject the customary semantics and allow that some counterfactuals with impossible antecedents may be non-vacuously true or false, how are we to assess the truth value of a statement with an antecedent like this? It is like wondering whether, if there were a round square, its area would equal the square of one of its sides. And what would it matter how one answered, since what is imagined is logically incoherent? I don’t see that the divine command theorist is committed to the non-vacuous truth of the counterfactual in question or that anything of significance hangs on his thinking it to be non-vacuously true or false.
If the non-theist should demand, “Why pick God’s nature as definitive of the Good?” the answer is that God, by definition, is the greatest conceivable being, and a being which is the paradigm of goodness is greater than one which merely exemplifies goodness. Unless we are nihilists, we have to recognize some ultimate standard of value, and God is the least arbitrary stopping point.
William Alston, “What Euthyphro Should Have Said,” in Philosophy of Religion: A Reader and Guide, ed.
William L. Craig (Edinburgh: Edinburgh University Press, 2001; New Brunswick, N. J.: Rutgers University Press, 2001), 283–98. It is striking that Brink, “The Autonomy of Ethics,” 152–54, takes no cognizance of these authors, nor of the alternative they offer; the only theistic account he knows is voluntarism, which is not defended by any philosopher in my acquaintance.
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The moral argument thus brings us to a personal, necessarily existent being who is the locus and source of moral goodness. It thereby complements in an important way the conclusions of the cosmological and teleological arguments.
ONTOLOGICAL ARGUMENT
Some readers may be surprised to find here a defense of the ontological argument.
Many thinkers would agree with Arthur Schopenhauer’s dismissal of the argument as “a charming joke.”40 But a number of recent, prominent philosophers such as Norman Malcolm, Charles Hartshorne, and Alvin Plantinga not only take the argument seriously but consider it to be sound. Since the formulation and defense of the argument provided by Plantinga are the most sophisticated in the long history of the ontological argument, profiting from the missteps and oversights of his predecessors, Plantinga’s version of the argument has the best chance of being cogent and will therefore serve as the springboard for our discussion.
In his version of the argument, Plantinga appropriates the insight of Gottfried Wilhelm Leibniz that the ontological argument assumes that the concept of God is possible. That is to say, the argument assumes that the concept “God” or “greatest conceivable being” is a coherent concept or, employing the semantics of possible worlds, that there is a possible world in which God exists.
Possible Worlds
For those who are unfamiliar with the semantics of possible worlds, let me explain that by “a possible world” one does not mean a planet or even a universe, but rather a maximal description of reality, or a way reality might be. Perhaps the best way to think of a possible world is as a huge conjunction p & q & r & s. . . , whose individual conjuncts are the propositions p, q, r, s, . . . A possible world is a conjunction which comprises every proposition or its contradictory, so that it yields a maximal description of reality—nothing is left out of such a description. By negating different conjuncts in a maximal description we arrive at different possible worlds: W : p & q & r & s . . .
1
W : p & ¬ q & r & ¬ s . . .
2
W : ¬ p & ¬ q & r & s . . .
3
W : p & q & ¬ r & s . . .
4
. . .
. . .
. . .
Only one of these descriptions will be composed of conjuncts all of which are true and so will be the way reality actually is, that is to say, the actual world.
40. I note that in his fifteen pages devoted to the ontological argument in The God Delusion, Richard Dawkins only ridicules but does not refute the argument (Dawkins, The God Delusion, 80–95).
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Since we’re talking about possible worlds, the various conjuncts which a possible world comprises must be capable of being true both individually and together. For example, the proposition The Prime Minister is a prime number is not even possibly true, for numbers are abstract objects which could not conceivably be identical with a concrete object like the Prime Minister. Therefore, no possible world will have that proposition as one of its conjuncts; rather its negation will be a conjunct of every possible world. Such a proposition is necessarily false, that is to say, it is false in every possible world. By contrast, the proposition George McGovern is the president of the United States is false in the actual world but could be true and so is a conjunct of some possible worlds. To say that George McGovern is the president of the United States in some possible world is to say that there is a maximal description of reality having the relevant proposition as one of its conjuncts. Similarly, to say that God exists in some possible world is to say that the proposition God exists is true in some maximal description of reality.
Leibniz’s insight into the ontological argument was that the argument assumes that the proposition God exists (or A greatest conceivable being exists or A perfect being exists) is possibly true, that is to say, God exists in some possible world. For if the concept of God is incoherent or impossible, then the word “God” cannot possibly refer to anything, any more than the words “square circle” could refer to something. The expression “greatest conceivable being” would in that case just be an incoherent combination of words.
Plantinga’s Ontological Argument
Now in his version of the argument, Plantinga conceives of God as a being which is “maximally excellent” in every possible world. Plantinga takes maximal excellence to entail such excellent-making properties as omniscience, omnipotence, and moral perfection. A being which has maximal excellence in every possible world would have what Plantinga calls “maximal greatness.” Now the property of maximal greatness, Plantinga avers, is possibly exemplified, that is to say, there is a possible world in which a maximally great being exists. But then this being must exist in a maximally excellent way in every possible world, including the actual world. Therefore, God exists.
We can formulate Plantinga’s version of the ontological argument as follows: 1) It is possible that a maximally great being exists.
2) If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
3) If a maximally great being exists in some possible world, then it exists in every possible world.
4) If a maximally great being exists in every possible world, then it exists in the actual world.
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5) If a maximally great being exists in the actual world, then a maximally great being exists.
6) Therefore, a maximally great being exists.
It might surprise you to learn that premises (2)–(5) of this argument are relatively uncontroversial. Most philosophers would agree that if God’s existence is even possible, then he must exist. The principal issue to be settled with respect to Plantinga’s ontological argument is what warrant exists for thinking the key premise “It is possible that a maximally great being exists” to be true.
In dealing with this issue, it’s crucial that we distinguish clearly between metaphysical and merely epistemic possibility. The first concerns what is really possible; the second concerns what is consistent with what we know. One is tempted to say,
“It’s possible that God exists, and it’s possible that he doesn’t exist!” But this assertion is true only with respect to epistemic possibility: for all we know, God may exist or he may not exist. On the other hand, if God is conceived as a maximally great being, then his existence is either necessary or impossible, regardless of our epistemic uncertainty. To illustrate: some extraordinarily difficult mathematical equation may be beyond our ability to grasp, and so we say that it’s possible that the equation is true and it’s possible that it is false. But we thereby merely confess our epistemic uncertainty concerning the equation’s truth value. As a piece of mathematics, the equation itself is either necessarily true or necessarily false. In the same way, the epistemic entertainability of premise (1) (or its denial) does not guarantee its metaphysical possibility.
Intuitive Warrant for Premise (1)
That being said, however, it remains the case that the concept of a maximally great being is intuitively a coherent notion and, hence, it might be argued, possibly instantiated. In order for the ontological argument to fail, the concept of a maximally great being must be incoherent, like the concept of a married bachelor. The concept of a married bachelor is not a strictly self-contradictory concept (as is the concept of a married unmarried man), and yet it is obvious, once one understands the meaning of the words “married” and “bachelor,” that nothing corresponding to that concept can exist. By contrast, the concept of a maximally great being does not seem even remotely incoherent. This provides some prima facie warrant for thinking that it is possible that a maximally great being exists.
But won’t this appeal to intuition lead to metaphysical excess? One of the most important strategies employed by detractors of the ontological argument has been to construct parodies of the argument which are designed to defeat the prima facie warrant which premise (1) is said to enjoy. By showing that analogous ideas like the idea of “a most perfect island” or the idea of “a necessarily existent lion” also seem prima facie to be coherent concepts, critics have tried to show that one is
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forced by the logic of the ontological argument to postulate the existence of all sorts of ridiculous beings.
But we may plausibly reply that the idea of God differs crucially from the parodies traditionally put forward by the argument’s detractors. For one thing, the properties that go to make up maximal excellence as Plantinga defines it have intrinsic maximum values, whereas the excellent-making properties of things like islands do not. For example, omniscience is the property of knowing only and all truths. It’s impossible to know any more truths than that. By contrast, in the case of islands, there could always be more palm trees or native dancing girls! Thus, there cannot be a most perfect or greatest conceivable island. Moreover, it is far from clear that there even are objective excellent-making properties of things like islands, for the excellence of islands seems to be relative to one’s interests—does one prefer a desert island or an island boasting the finest resort hotels?
The idea of something like a necessarily existent lion also seems incoherent.
For as a necessary being, such a beast would have to exist in every possible world we can conceive. But any animal which could exist in a possible world in which the universe is composed wholly of a singularity of infinite spacetime curvature, density, and temperature just is not a lion. By contrast, a maximally excellent being, if it is immaterial, could transcend such physical limitations and so be conceived as necessarily existent.
Perhaps the greatest challenge to the appeal to intuition as warrant for premise (1) is that it seems intuitively coherent in the same way to conceive of what we might call a quasi-maximally great being, for example, one which is in every other respect maximally excellent except that it does not know truths about future contingent events. Why is the key premise of the ontological argument more plausibly true than a parallel premise “It is possible that a quasi-maximally great being exists”? If we are warranted in thinking that a maximally great being exists, aren’t we equally warranted in thinking that a quasi-maximally great being exists?
Maybe not; for maximal greatness is logically incompatible with quasi-maximal greatness. Since a maximally great being is by definition omnipotent, no concrete object can exist independently of its creative power. As an omnipotent being, a maximally great being must have the power to freely refrain from creating anything at all, so that there must be possible worlds in which nothing other than the maximally great being exists. But that entails that if maximal greatness is possibly exemplified, then quasi-maximal greatness is not. A quasi-excellent being (that is, a being which has lots of excellent properties but which does not exist in every possible world) may exist in many worlds (worlds in which the maximally great being has chosen to create it), but such a being would lack necessary existence and thus not be quasi-maximally great. Hence, if maximal greatness is possibly exemplified, quasi-maximal greatness is impossible. Thus, our intuition that a maximally great being is possible is not undermined by the claim that a quasi-maximally great being is also intuitively possible, for we see that the latter intuition
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depends on the assumption that a maximally great being cannot possibly exist, which begs the question.
Still, skeptics about our ability to discern what is possible/impossible will insist that we have no way of knowing a priori whether maximal greatness or quasi-maximal greatness is possibly exemplified. It cannot be both, but we have no idea if either is possible. Our intuitions about modal notions like possibility are unreliable guides.
We might plausibly reply to this objection that the intuition that a maximally great being possibly exists has priority over any intuition that a quasi-maximally great being possibly exists. The latter intuition seems to depend on the former, and yet upon reflection we come to lose the latter intuition through the realization that if a maximally great being is possible then a quasi-maximally great being is not. Thus, our prima facie warrant for premise (1) remains.
A Posteriori Warrant for Premise (1)
Still, we might wonder whether, in the face of such skepticism, anything more can be offered in defense of premise (1) than our modal intuitions alone. Plantinga provides a clue when he says that if we “carefully ponder” premise (1) and the alleged objections to it, if we “consider its connections with other propositions we accept or reject” and we still find it compelling, then we are within our rational rights in accepting it.41 Such a procedure is a far cry from the sort of a priori speculations decried by the modal skeptic. Even if we cannot determine a priori whether maximal greatness is possibly exemplified, we may come to believe on the basis of a posteriori considerations that it is possible that a maximally great being exist.
For example, other theistic arguments like Leibniz’s cosmological argument, the moral argument, and conceptualist arguments for God as a ground of abstract objects or necessary truths may lead us to think that it is plausible that a maximally great being exists. We’ve already looked at the Leibnizian cosmological argument and the moral argument. A conceptualist argument for God’s existence might be formulated as follows:
1) Abstract objects, such as numbers and propositions, are either independently existing realities or else concepts in some mind.
2) Abstract objects are not independently existing realities.
3) If abstract objects are concepts in some mind, then an omniscient, metaphysically necessary being exists.
4) Therefore, an omniscient, metaphysically necessary being exists.
41. Plantinga, The Nature of Necessity, 221.
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A defense of premise (1) would involve a refutation of nominalism, the view that abstract objects do not exist at all. Premise (2) rejects Platonism with respect to abstract objects, most plausibly on the grounds of their causal isolation and hence irrelevance to what exists or transpires in the world. Premise (3) excludes the grounding of abstract objects in some human mind, for there are too many such objects to be grounded in anything less than an infinite intelligence and, since many of these objects exist necessarily, they cannot in any case be grounded in the mind of a merely contingent being. Thus, one is brought to the existence of an omniscient, necessary mind as the foundation of the existence of abstract objects. I remain uncertain of this argument, chiefly due to reservations about its first premise, which would require us to reject various nominalistic alternatives to conceptualism such as fictionalism, constructibilism, figuralism, and so forth. Still, prominent philosophers such as Plantinga have endorsed it.
Thus, the cosmological argument leads to a metaphysically necessary being which is the ground of existence for any concrete reality, the moral argument to a locus of moral value which must be as metaphysically necessary as the moral values it grounds, and the conceptualist argument to an omniscient, metaphysically necessary intelligence as the foundation of abstract objects.
Considerations of simplicity might also come into play here. For example, it is simpler to posit one metaphysically necessary, infinite, omniscient, morally perfect being than to think that three separate necessary beings exist exemplifying these respective excellent-making properties. Similarly, with respect to quasi-maximally great beings, Swinburne’s contention seems plausible that it is simpler (or perhaps less ad hoc) to posit either zero or infinity as the measure of a degreed property than to posit some inexplicably finite measure. Thus, it would be more plausible to think that maximal greatness is possibly instantiated than quasi-maximal greatness.
On the basis of considerations like these, we might well consider ourselves to be warranted in believing that it is possible that a maximally great being exists.