God and Chance: Christian Perspectives
God and Chance: Christian Perspectives
- David J. BartholomewDavid J. BartholomewLondon School of Economics and Political Science, Emeritus
In many quarters God and chance are still seen as mutually exclusive alternatives. It is common to hear that ascribing anything to “chance” rules out God’s action.
Recent scientific developments have tended to reinforce that distinction. Quantum theory introduced an irreducible uncertainty at the atomic level by requiring that certain microscopic physical events were unpredictable in principle. This was followed by the biologists’ claim that mutations, on which evolution depends, were effectively random and hence that evolutionary development was undirected. The problem this posed to Christian apologists was put most forcibly by Jacques Monod when he asserted “Pure chance,… at the root of the stupendous edifice of evolution alone is the source of every innovation.”
Several attempts have been made to include chance within a theistic account. One, advocated by the intelligent design movement, is to contend that some biological structures are too complex to have originated in the way that evolutionary theory supposes and therefore that they must be attributed to God. Another is to suppose that God acts in an undetectable way at the quantum level without destroying the random appearance of what goes on there.
A third approach is to contend that chance is real and hence is a means by which God works. A key step in this argument is the recognition that chance and order are not mutually exclusive. Reality operates at a number of different levels of aggregation so that what is attributable to chance at one level emerges as near certainty at a higher level.
Further arguments, based on what is known as the anthropic principle, are also used to judge whether or not chance is sufficient to account for existence. These are critically evaluated.
- Religion and Science
Chance has become prominent in theological discussion where it has often been set in opposition to God as an explanation of existence. This is most conspicuous, perhaps, in discussions of biological evolution, which is seen by many as the means of generating life on this planet. It is undisputed that the processes giving rise to everything, including life itself, are exceedingly complicated. Chance is often used as a hypothesis to explain this fact, thus dispensing with the need for God as creator. It has posed particular problems for some Christian believers and most of the debate has been in Christian circles; hence, this article reflects that fact. Also, in other, more subtle ways, chance has entered scientific discussion with the—often unspoken—implication that the theist’s belief that God is responsible for the world is unnecessary. An important example, where chance can be used on both sides of the argument, is in relation to the anthropic principle (discussed in a later section). The apparent solidity of the sciences now rests, at the micro level, on chance because this appears to play a central role in quantum theory, which underpins modern physics. More surprising, perhaps, is the increasing use of chance in the social sciences, where it refers to the unpredictable behavior of people. One of the earliest attempts to grapple with the implications of quantum theory for theology is found in Pollard.1 The critical challenge from biology was posed by the Nobel laureate Jacques Monod and set out in uncompromising fashion in his Le Hasard et la Nécessité.2 A review of the position in a broader context can be found in Bartholomew.3 The discussion of God and chance figures in many discussions of science and religion, of which we note an early example in Peacocke’s Creation and the World of Science.4 Subsequently there has appeared a series of volumes based on conferences and published jointly by the Vatican Observatory and the Center for Theology and the Natural Sciences, in particular, Chaos and Complexity: Scientific Perspectives on Divine Action.5 A recent book, Does God Roll Dice?, turns out to be about how the scientific viewpoint can be accommodated within a process philosophy perspective. 6
The first thing to make clear is that chance is not an agent which (or who) acts in the world to bring about changes. This common misapprehension is fostered by the semantic error of making “chance” the subject of a sentence just like any other noun. Proposing chance as an explanation (often with a capital letter) is not an explanation of anything. In fact, chance is one of a number of terms referring to situations where we are unable to identify a definite cause—the precise opposite of what its use as the subject of a sentence requires. For this reason we shall have to begin by spending some time elucidating some of the various meanings of terms in common use.
The terms probability, random, uncertainty, likelihood, unpredictable, accident, coincidence, and luck are all commonly used in discussions in this area, often combined with adjectives or used as adjectives themselves. Thus we sometimes find references to “random chance” or “lucky chance” spoken of as though the mere addition of the adjectives added something to the meaning. The term nonrandom chance, for example, is meaningless. The essence of any situation in which these terms are used is an element of unpredictability. We obviously cannot predict what is left over when all causal mechanisms have been accounted for. Thus, for example, chance is not a residual “cause” to be brought into play when all other avenues have been exhausted; to say that a chance element is involved says no more than that there is something left over that cannot be explained. For our purposes, the terms unpredictable or unpredictability will suffice, and we shall use them whenever possible. However, some of the other terms are widely used in particular contexts, so they need further comment.
Random usually refers to some event which is, in some degree, unpredictable. The fall of a single coin tossed into the air is a good example. We know the possible outcomes—head or tail—but we do not know what the outcome will be on any particular occasion. More complicated events in nature occur that may also be described as random. Whether or not the temperature will fall below freezing in London on December 23, 2030, is unpredictable in the present state of meteorological knowledge. It might become predictable at some future time, but that is not relevant. However, neither of these two events is unpredictable in principle. In the first case, if we knew all about the air currents and the motion imparted to the tossed coin we might be able to predict how it would fall. Similarly, with a greater knowledge of how the weather is determined, the uncertainty about future temperatures might be eliminated.
An accident is also a random event, but the term is usually reserved for a situation where an unintended event occurs or where an intended event does not occur. When we plan for something to happen, we tend to assume that we know all the factors that are relevant and hence how things will turn out. An accident may occur if we disregard some relevant factor such as when someone does not act in the expected way. Thus, for example, we may plan to drive safely from A to B, but if a pedestrian unexpectedly steps in our way, we may swerve into a lamp post, resulting in an accident.
Coincidence, in a sense, is the converse of an accident. Whereas an accident may be described as the unintended convergence of two causal chains at the same point in time and space to give an unintended outcome, a coincidence is the convergence of two such chains to give an unexpected outcome.
Uncertainty is a general term used to refer, in any context, to a situation where we are not sure what will happen; primarily, therefore, it expresses a state of mind.
Probability is rather a special term. It is sometimes used rather vaguely to indicate whether something is likely to happen or not—meaning that we do not know whether or not it will occur. More precisely it refers—and should only be used to refer—to a number expressing the degree of uncertainty about the outcome.
Likelihood has both a common and a technical meaning, and the two are often confused. In ordinary usage, it is virtually synonymous with the everyday use of “probability,” but in statistical theory it refers to the set of possible probabilities, of some particular happening.
Luck, in ordinary conversation, is commonly held to be the reason for any unexpected and often welcome happening. It is never used in serious technical discussions. As we have occasion to use, or not use, these terms, their meaning and usage will become clearer.
God’s Action in the World
In prescientific times God was often spoken of as being rather like a human being. “He paints the wayside lily and lights the evening star” may now be interpreted as poetry, but there was a time when such pronouncements were taken more literally. It was natural to think of God as moving things around rather as we do. The scientific revolution accompanied a change in thinking with which this way of regarding the world did not seem appropriate. But the question persisted: How were such events brought about, and what part, if any, did God play? In short: Is God (or some other being) responsible to any degree? There was still the need to locate what is often known as the causal joint: the point at which the spring of God’s action might be located.
Having disposed of the cause mistakenly designated “chance” on semantic grounds, it might appear that the conflict is resolved and hence that there is no ground remaining for argument. But this is not the case because the universe is constantly changing and that process needs to be accounted for. The debate is about how change takes place over time. Is God in control, or do things take the course dictated by the laws of physics?
In addition, we need to note two senses in which the word “chance” is being used. We have already proposed replacing the word chance by “unpredictability” as far as possible, and so far, there has been no need to add any further qualification. Here, however there exist circumstances where it is useful to make a distinction based on whether or not it might be possible, in principle, to identify causal factors behind the outcome. For example, in genetic inheritance there exist physical reasons for individual mutations that it would be practically impossible to disentangle or enumerate. All that matters for evolutionary purposes is that the mutation that takes place is entirely independent of the survivability of the resulting organism. In that sense mutations are effectively random, even though they are predictable in principle. The “chance” involved is then described as epistemological. However, when we come down to the subatomic level, there seems to be no means of identifying any factors that influence outcomes. At the observable level we can illustrate this idea by reference to the process of radioactive decay, where the timing of the emission of particles is entirely unpredictable in the sense that we can identify no causal factors. Whenever there is no identifiable cause and yet something has happened that, in the ordinary course of events, we could have expected to have a physical cause, we speak of ontological chance.
The question of how God acts in the world is central to our discussion because the choice so often appears to be between epistemological and ontological chance. We need to identify the causal joint—that is, the point at which the action of God makes contact with the physical world we observe. There is certainly a great deal of unpredictability in nature, and Christians disagree about its origin and meaning. As we have already noted, the ubiquity of uncertainty raises the question of whether every detail of the creation is under God’s direct control or whether there is some degree of variation left over that still needs to be explained. Before going further we need to rehearse the essentials of the Darwinian option.
According to the Darwinian account, the character of successive generations normally depends on the genetic code of their parents. However, the process of reproduction does not always produce an exact copy but is subject to accidental variation, called mutation; this leads to additional variation in the offspring. Some of these offspring will be better equipped to survive in the environment, and it is those survivors who go on to produce the next generation. The selection of the next generation of parents in this way is known as natural selection, and it is an essential part of evolution. How the species develops will thus depend both on the genetic inheritance of individuals and on accidental copying changes that take place in the course of reproduction. The development of the species is thus partly predictable and partly unpredictable due to these changes. If, as the biological account says, the path that the successful generations follow is partly determined by the unpredictable happenings in the process of reproduction, there is an obvious problem in saying how a purposeful God could have been responsible for what happens.
A particularly vivid way of picturing the evolutionary process was used by Gould,7 who imagined evolution as having a tree structure. This would mean that, at each juncture, there would be many possible paths the process could take. Only one of these paths could actually have been realized, and thus for human life (or any other form of life, for that matter) to have occurred it would have had to appear at the tip of a particular branch. It is difficult to imagine the complexity and sheer size of the resulting tree. This implies that there would have been an extremely small probability that any particular tip would have been reached. Since there are so many possibilities, it is virtually certain that such a random path would not arrive at any desired destination. It was this feature that led Gould to observe that, if evolution were to be rerun, it was virtually certain that the same path would not be repeated twice. Even if we allow that this argument treats all destinations as different—whereas in reality many of them might be equivalent—there are still a great many possible paths.
Another phenomenon is, perhaps, less familiar but equally relevant and important to our thesis—that apparent randomness can be produced in an entirely nonrandom way, and this is commonly used in practice. Part of the statistician’s stock-in-trade is a set of random numbers. At its simplest, this is a collection of numbers, each ranging from 0 to 9, say, constructed so that all digits occur with equal frequency in the long run and that all occurrences are independent. In the short run it is impossible to predict which digit will come next. Early sets of random numbers were constructed from census tables in which the numbers were by no means random but represented, for example, the populations of regions of a country. However, by taking only the least significant digit recorded, usually the last, it was possible to construct a collection of numbers with the right property. Nowadays the same result can be obtained from a totally deterministic formula in a computer, but the idea is the same. The least significant part of any calculation can be separated off with the knowledge that it contains virtually no information about the formula that generated it. In such a case we have unpredictability for all practical purposes, which, paradoxically as it appears, is generated by an equation that at one level gives results that are entirely predictable. It is thus conceivable that, although God’s actions might be completely determined at one level, what we observe at another might be virtually unpredictable. The apparent randomness we observe might, therefore, have been deliberately generated in this fashion.
Answers to the question of how change actually happens take a variety of forms. We shall therefore divide the following discussion into two parts, dealing first with the views of those who reject the Darwinian account of evolution and second with those who accept it and seek to find a place for God’s action within it.
God’s Action When Darwinian Evolution Is Rejected
We start with the view held by the extreme conservative wing of Christianity. On this view, the distinction between epistemological and ontological chance is unnecessary because all change is attributable to God and therefore chance of either kind has no place. Many conservative Christians believe that if God is truly sovereign, he must be in total control of everything that happens at every instant of time—because that is what sovereignty means. Although this view owes a good deal to Calvin, it has been advocated more recently, and most forcefully, both by Sproul in his book Not a Chance and, in a more measured fashion, by Helm and Byl, among many others.8 According to these authors, although there may be a good deal of uncertainty in the world when viewed from the human position, all is known to God. This, they would argue, is implied by saying that God is omniscient. This view has to contend, of course, with the obvious fact that a good deal of what happens does not seem consistent with the view of God’s revealed nature as a loving heavenly Father. This objection can be met by arguing that our human view is necessarily partial and that when viewed in the context of eternity, it will become plain that the ills and misfortunes of life serve some greater end of good that could not be achieved in other ways. When faced with evil, the Christian must therefore simply trust that God knows best and must wait, with patience, until the full picture is revealed. In other words, the appearance of chance is simply a reflection of the complexity of the system in which God acts. This view is incontestable in logic because it is always arguable that God intended what has actually happened, in every detail.
Moving one stage further we come to those who interpret the uncertainty in the world in a slightly different way though from an essentially conservative position. These are the advocates of intelligent design (ID). They differ from those discussed so far in claiming that their objection to Darwinism is strictly scientific. They believe that Darwinism can be refuted on its own terms. At its simplest, ID advocates claim that Darwinian evolution simply could not work. This is because some products are simply too complicated to have emerged by the proposed means—in particular that some things, livings things in particular, are too complicated to have been constructed in any way that involves an element of chance. While it is not necessary to deny that chance may play some part (though most ID theorists appear to miss this point), it is only necessary to show that the Darwinian theory is not sufficient to explain the world as we find it. Intelligent design fills the gap by postulating an extra (intelligent) agency, which theists would identify with God, who carries out the most difficult parts of assembling living things. In this way it is possible to find a role for God and thus to break through the looming impasse. This view is countered by many scientists who claim that there are, in fact, no such gaps. They do this by pointing out that some of the gaps identified by ID exponents are not gaps at all but have already been filled by orthodox scientific methods. They also express confidence that any remaining gaps will be filled in the same fashion without the need to invoke an intelligent designer.
However, ID exponents go further than simply making the claim that living things are too complicated to have arisen by the mechanisms that Darwinists propose. They also claim to be able to show that the probability of assembling a living creature by chance is so small that it is virtually certain not to have occurred in a universe such as ours. The principal advocate of this view is William Dembski.9 The argument is highly technical and has been critically examined by Bartholomew.10 In essence, Dembski’s proof rests on the notion of what he calls the universal probability bound. This is the smallest probability of existing anything in a universe as large and old as the one in which we live could have. By showing that this probability of constructing any organism by chance must be much smaller than this bound, he deduces that such an event could not have occurred. This probability cannot be calculated exactly, of course, but it does appear possible, to Dembski at least, to place bounds on its value that are adequate for making the comparison. Some orthodox Christians also have serious doubts about this proposed solution on the grounds that such an ad hoc manner of creation seems unworthy of a Creator God and also because to them there actually seem to be better ways of achieving the same end. We now go on to consider some of the latter.
God’s Action When Darwin’s Theory Is Accepted
We now turn to those who, broadly speaking, accept the Darwinian account of evolution and who therefore have to explain how God acts by what, to us, appears to be “chance.” Many such writers have accepted that the standard biological picture of evolution is substantially correct and have then sought to find a place for a key role played by God. The essential idea, common to many of these writers, is that of what might be called “God-guided evolution.”
At first sight it is extremely difficult to reconcile the roles of God and chance. This is because for Christians, of whatever persuasion, God is the source of all created things and is therefore responsible for human beings and human history. This difficulty has nowhere been spelled out with greater clarity than by Jacques Monod in his book Le Hasard et la Nécessité.11 Indeed, the English version of this title has become a shorthand phrase for the scientific claim that God is not needed to explain evolution in Monod’s account; chance and necessity are sufficient to do it all. The mutation of genes is the random part, and necessity is represented by the selection of the fittest.
Keith Ward is a leader among those who have argued that it is perfectly possible to believe in Darwinian evolution and to assert that God is able to influence the direction of evolution in line with his purposes. This idea is worked out in Ward’s Chance and Necessity.12 Since it appears that evolution involves uncertainty, Ward sees no difficulty in supposing that God “weights the probabilities” in a manner chosen to bring about the desired outcome. It is by no means clear how such an incompletely defined method would actually work. However, it is easy to counter any such objections by attributing to God whatever insight and foresight is necessary to achieve the desired outcome. In order to see what the possibilities for God’s action might be, we now return to the notion of micro and macro levels for describing how the world works.
The macro (or, aggregate) level, we recall, concerns what goes on at the level at which we live—the everyday world of cars, tables, and potatoes. The micro level, typically, concerns the world of atoms, electrons, and so on, on which the macro world rests. It is thus the macro world that is directly observable, but the micro world can only be accessed indirectly via the macro world. This makes it possible to argue that God’s action takes place only at the micro level. By this means the results of God’s actions will be manifested at the macro level even though they are initiated at the micro level. This would explain how God might act in the world without our being able to detect the fact—even in principle.
The most fully worked-out version of this hypothesis is that of Robert Russell and his colleagues and associates at the Center for the Study of Theology in the Natural Sciences at Berkeley, California. This idea is expounded by Russell.13 However, the essential idea can best be explained starting with a simple example without the need to make direct reference to Russell’s work.
In passing, it is helpful to notice that the relationship between the micro and macro levels is very familiar in some other fields. Statistical mechanics, for example, provides very familiar examples. At the macro level, we observe the relationship between the volume and pressure of a gas at a constant temperature, which shows, for example, that if we halve the volume we double the pressure. This is expressed by Boyle’s law, which says that pressure is inversely proportional to volume. It is the totally haphazard, or chaotic, motion of the molecules that make up the gas at the micro level which leads to the simple relationship we observe at the macro level. In the world of gases, therefore, whether or not we need to notice the motions of the individual molecules is haphazard—it depends on whether our description is at the macro or micro levels. Much more generally, this kind of relationship is one of the principal pillars of statistical theory. This subject is based on the fact that what is chaotic at the micro level becomes ordered when observed at the macro level and is thus capable of being described in simple terms. For example, although some medical conditions may be extremely rare in a large country such as the United States and hence very uncertain on the local scale, they will nevertheless show a stable pattern of relationships at the national level, which enables effective planning of resources to be made. This is a very common kind of phenomenon, which, though hardly noticed, forms the basis of much in modern civilization.
The simple problem of gas pressure and volume is highly simplified and abstract, but it conveys the essential idea as does the coin-tossing example, to which we now return. In the coin-tossing experiment we imagined a single coin to be tossed many times. The resulting sequence of outcomes will have many observable macro properties. The simplest is that the proportion of heads will be very close to 0.5 if the sequence is long enough. Furthermore, if we count the number of tosses before the first head appears, this number will have a frequency distribution that will settle down to a simple form. Next suppose that in a very long series of tosses we change the 74th outcome from head to tail (or vice versa if it is already a tail). The overall proportion of heads will be hardly changed by this change, and thus, if the series is long enough, it will be virtually undetectable. In this way a deliberate act at the micro level has no detectable effect on the behavior of the system at the macro level. However, suppose further that there is something special about the 74th toss that triggers a change at the macro level which can be observed. We would then have the situation that the micro level change was detectable at the macro level. In the case of coin tossing this might seem rather implausible, but it is the key to understanding the approach of Russell and others. They maintain that God acts occasionally, and very specifically, at the micro level of the world in such a way that the change effected is observable at the macro level. This immediately raises the crucial question of whether, in real life, such a micro change could have an important observable effect at the macro level. This is possible because a mutation can be caused by a micro-level change at the subatomic level. Mutations are on a par with the micro events of which we have been speaking in the coin-tossing experiment, and yet their effects on evolution could be major. In this way judiciously chosen mutations could redirect evolution and yet their origin in individual mutations would be undetectable by us. Russell is convinced that this is one (but not necessarily the only) way in which God could direct evolution in the intended direction. If what happens at the micro level is governed by probabilities, then there exists the possibility that God could act by changing those probabilities, or their outcomes, in such a way as to achieve his ends.
In spite of the feasibility of this mode of action, there are good reasons to question whether this is such an attractive way of solving the problem. One difficulty is that the number of such probabilities involved is extremely large—possibly to be numbered in trillions—and all of these possibilities, and their consequences, would have to be “kept in mind” while the changes were being effected. Of course, objections of this kind are open to the response that nothing is too large or complicated for God—but this quickly begins to sound like proposing a very cumbersome and inelegant way for God to act. Furthermore, it is not totally clear whether God is held to change the probabilities or merely their outcomes on particular occasions. In the former case it is difficult to see how such changes could be guaranteed to deliver the required changes.
A “Hands-Off” Strategy
Russell was concerned with how God might “steer” evolution, particularly the evolution of human kind, in the desired direction. As we have seen, he supposed that this might be done by influencing a small number of micro events in such a way as to produce the desired result.
We now explore the possibility that such detailed control may not be necessary; this means that a desired outcome might be achieved without God’s deliberate intervention at any level. A closely related idea was developed by Peacocke, who envisaged something analogous to “play” in God’s creative activity.14 He linked this to earlier ideas to be found in the Greek fathers and in Indian thought. This is akin to what we call a “hands-off” strategy. It is clear that such a strategy allows only a rather general kind of providence to be exercised because it lacks the means of fine-tuning that would be possible by direct intervention as and whenever needed. On the other hand, there are two other considerations to be borne in mind. First, there remains the possibility of providential action using other channels such as interaction with human minds. Second, there might also be compensating benefits that can only be achieved by a “hands-off” strategy. One way in which this might happen can be seen by going back to Gould’s example. Gould imagined evolution as represented by a tree structure in which, at each juncture, there are several paths that could be taken. Human life would thus appear at the tip of one of the resulting branches at the end of one such route. Because there were so many of them, there would be a vanishingly small probability that any particular endpoint would be reached. However, this argument is a gross oversimplification because of the evolutionary phenomenon known as convergence. Conway Morris has adduced considerable empirical evidence from nature to show that the number of branches can be drastically reduced to a point where the few remaining routes might lead to virtually equivalent ends, for all practical purposes. 15 For example, the mere fact that creatures of particular kinds already exist may place severe restrictions on the kinds of new creatures that can survive and prosper. The environment, in which the “fittest” are selected, is thus, itself, partly the product of the evolutionary process. It may be the case that the universe was set up, in the beginning, in such a fashion that God’s principal objective could be achieved without the micromanagement implicit in the other approaches which we have described above. If it also turned out that there were considerable additional benefits to be derived from creating a “random” environment for human beings to develop in, this might well be the preferred strategy.
Unpredictability is an all-pervasive part of life, and it contributes much to the excitement and interest of living. From games of chance, where the outcomes depend on the throw of a die or the shuffling of a pack of cards, to the choice of ends in a football match, chance contributes much to the richness and enjoyment of life. In a more fundamental way, human-generated randomness is used in many fields of research to explore and simulate the complexity of life—for example, to find the effect of variable weather, over centuries, on a physical construction such as a bridge. This may well be a mimicking of God’s ongoing creative activity on the cosmic scale. The idea that God may have actually used chance, and still be using chance, may help to dispel the negative role it often plays in current theology.
The Anthropic Principle
This principle has been used as a powerful argument for theism and, in an extended form, for atheism. It is somewhat different from the problems discussed earlier in this article, but, like them, it builds on the placing of God and chance in opposition to it. The principle stems from the fact that our universe may be characterized by a number of parameters, some of which must have values that fall in a very narrow range for the universe and, especially ourselves, to exist at all. The argument goes that if our universe had arisen “by chance,” it would have been virtually impossible that these crucial parameters to have taken values that permitted our existence. Therefore, the values must have been deliberately selected by a creator to allow us to exist. Atheists, on the other hand, point out that this argument fails if our universe was one of infinitely many whose individual parameter values were selected “by chance” in exactly the same way as envisaged above (the so-called multiverse hypothesis). On this supposition a universe such as ours would have occurred sooner or later, and it is in such a particular universe that we happen to find ourselves. Therefore there is no need to posit a creator—what we know to be the case would have happened in any case. Finally, and in the spirit of a “hands-off” theology, the theist can reply that this would have been a feasible (if somewhat extravagant) strategy of creation. By this means one could have certainly produced a universe like ours.
All of these lines of reasoning make an untestable assumption about the creation of universes in general. This lies entirely outside of science, and therefore the validity of any of these arguments depends on an assumption for which there is, and can be, no physical evidence whatsoever. The fallacy turns on what is meant in this context by “chance.” It assumes that a universe is selected “by chance” just as we might envisage it happening on earth, that is, that all possible parameter values might be subject to some kind of celestial lottery conducted in the absence of anyone or “thing” that could be regarded as the instigator of that lottery. It requires a heroic act of imagination to envisage what this might mean, never mind how it might actually happen! There is certainly is no empirical evidence available to help us—nor can there be.
It should certainly not be surprising that coincidences should occur in the values of these parameters, for without their occurrence we should not be here to observe them. Their occurrence therefore tells us nothing of itself. They can only be rendered meaningful if we first invoke the notion, derived from our particular universe, about what it means to select values “by chance.”
- Bracken, J. A. Does God Roll Dice? Collegeville, MN: Liturgical Press, 2012.
- Russell, R. J., Nancey Murphy, A. R. Peacocke, eds. Chaos and Complexity: Perspectives on Divine Action. Vatican City State: Vatican Observatory, 1995.
- Bartholomew, David J. God of Chance. London: SCM, 1984.
- Bartholomew, David J. God, Chance and Purpose. Cambridge, U.K.: Cambridge University Press, 2008.
- Byl, John. “Indeterminacy, Divine Action and Human Freedom.” Science and Christian Belief 15 (2003): 101–115.
- Conway Morris, Simon. Life’s Solution. Inevitable Humans in a Lonely Universe. Cambridge, U.K.: Cambridge University Press, 2003.
- Dembski, William A. Design Inference: Eliminating Chance Through Small Probabilities. Cambridge, U.K.: Cambridge University Press, 1998.
- Dembski, William A. Intelligent Design: The Bridge Between Science and Theology. Downers Grove, IL: Intervarsity Press, 1999.
- Dembski, William A. No Free Lunch: Why Specified Complexity Cannot Be Purchased Without Intelligence. Downers Grove, IL: Intervarsity Press, 2002.
- Dembski, William A. The Design Revolution: Answering the Toughest Questions About Intelligent Design. Downers Grove, IL: Intervarsity Press, 2004.
- Helm, Paul. The Providence of God. Leicester, UK: Intervarsity Press, 1993.
- Gould, Stephen J. Wonderful Life: The Burgess Shale and the Nature of History. Harmondsworth, UK: Penguin, 1989.
- Monod, Jacques. Le Hasard et la Nécessité. Paris: Editions du Seuil, 1970. (English translation, London: Collins, 1972.)
- Peacocke, A. Creation and the World of Science. Oxford: Oxford University Press, 1979.
- Pollard, William G. Chance and Providence. London: Faber and Faber, 1959.
- Russell, Robert J. Cosmology from Alpha to Omega. Minneapolis: Fortress, 2008.
- Sproul, R. C., with assistance from Keith Mathison. Not a Chance, The Myth of Chance in Modern Science. 2d ed. Grand Rapids, MI: Baker, 2014.
- Ward, Keith. Chance and Necessity. Oxford: One World, 1996.
1. William G. Pollard, Chance and Providence (London: Faber and Faber, 1959).
2. Jacques Monod, Le Hasard et la Nécessitė (Paris: Editions du Seuil, 1970).
3. David J. Bartholomew, God of Chance (London: SCM, 1984).
4. A. Peacocke, Creation and the World of Science (Oxford: Oxford University Press, 1979).
5. R. J. Russell, Nancey Murphy, A. R. Peacocke, eds, Chaos and Complexity: Perspectives on Divine Action (Vatican City State: Vatican Observatory, 1995).
6. J. A. Bracken, Does God Roll Dice? (Collegeville, MN: Liturgical Press, 2012).
7. Stephen J. Gould, Wonderful Life: The Burgess Shale and the Nature of History (Harmondsworth, UK: Penguin, 1989).
8. R. C. Sproul, Not a Chance, The Myth of Chance in Modern Science, 2d ed. (Grand Rapids, MI: Baker, 2014); Paul Helm, The Providence of God (Leicester, UK: Intervarsity Press, 1993); John Byl, “Indeterminacy, Divine Action and Human Freedom,” Science and Christian Belief 15 (2003): 101–115.
9. William A. Dembski, Design Inference: Eliminating Chance Through Small Probabilities (Cambridge, U.K.: Cambridge University Press, 1998); William A. Dembski, Intelligent Design: The Bridge Between Science and Theology (Downers Grove, IL: Intervarsity Press, 1999); William A. Dembski, No Free Lunch: Why Specified Complexity Cannot Be Purchased Without Intelligence (Downers Grove, IL: Intervarsity Press, 2002); William A. Dembski, The Design Revolution: Answering the Toughest Questions About Intelligent Design (Downers Grove, IL: Intervarsity Press, 2004).
10. David J. Bartholomew, God, Chance and Purpose (Cambridge, U.K.: Cambridge University Press, 2008).
11. Monod, Le Hasard et la Nécessité.
12. Keith Ward, Chance and Necessity (Oxford: One World, 1996).
13. Robert J. Russell, Cosmology from Alpha to Omega (Minneapolis: Fortress, 2008).
14. Peacocke, Creation and the World of Science, 109.
15. Simon Conway Morris, Life’s Solution. Inevitable Humans in a Lonely Universe (Cambridge, U.K.: Cambridge University Press, 2003).