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Home , Discovery (observation), God, Omnipotence, Omniscience, Randomness

Article and ’s James Bradley James Bradley

Observations of apparently random phenomena are commonplace in . However, randomness and Christian are often seen as incompatible, both by naturalists and by theists. This article argues that the scientific concept of randomness and the historic Christian understanding of God’s nature are compatible. It argues that the of randomness cannot be settled scientifically; nevertheless, it clarifies randomness as a mathematical concept, argues that it provides a plausible interpreta- tion of scientific data, and argues that its existence is consistent with God’s nature as it is commonly understood by systematic theologians.

1. The Problem Observations of apparently random phe- Christian understanding of God’s nature nomena are commonplace in the natural are compatible. I will not provide a con- . But randomness is often seen as clusive demonstration of the existence of incompatible with the historic Christian randomness—in fact, I will argue that its understanding of God’s nature both by existence cannot be settled scientifically; naturalists and theists. rather I will argue that it provides a plau- sible interpretation of scientific data and Some naturalists accept the existence its existence is consistent with God’s of chance but deny God; for example, attributes. The more we understand of the work- ings of nature, the more we realize The argument proceeds as follows. In that the forces that shape it are those Section 2, I examine several exemplars of of blind, purposeless chance. Across randomness. This is to place the subse- a encompassing billions of quent philosophical and theological dis- years, through scales of magni- cussion of randomness within the actual tude extending from subnuclear par- practice of , , and the ticles to immense galaxies colliding natural sciences. Section 3 explores the like a clash of cymbals, there is no hint concepts these exemplars are used to of plan or purpose.1 convey and presents two interpretations Some theologians affirm God’s existence of nondeterministic models—instrumen- but deny chance; R. C. Sproul writes, talism and realism. I argue that it is The mere existence of chance is impossible to choose between them on enough to rip God from his cosmic scientific grounds alone; hence the study . Chance does not need to rule; James Bradley it does not need to be sovereign. If is Professor Emeritus of Mathematics at Calvin College. He has a BS from MIT and a PhD from the University of Rochester. it exists as a mere, impotent humble His mathematical interests primarily in the areas of and servant, it leaves God not only out of operations . He has coedited two recent books on mathematics and date but out of a . If chance exists —Mathematics in a Postmodern Age: A Christian Perspective in its frailest possible form, God is and Mathematics through the Eyes of and has served as guest editor finished.2 of Theology and Science’s recent issue on “Mathematics and Theology.” In this article, I argue that the scientific He edits the Journal of the Association of in the Mathematical Sciences. concept of randomness and the historic

Volume 64, Number 2, June 2012 75 Article Randomness and God’s Nature of randomness necessarily involves metaphysical culate . The frequentist interpretation of and/or theological reflection. Section 4 explains how probability is also introduced here—that the ½ randomness can plausibly be viewed as a key feature should be understood in terms of the law of large of the physical world. Section 5 presents the classical numbers5—that with many flips the relative fre- perspective on God’s attributes as studied in system- quency of each will approach ½. A flipped atic theology. It argues that most of God’s attributes coin could land on edge or fall into a drain. The do not pose a consistency problem with realism assumption that there are only two outcomes (heads about randomness; nevertheless, four issues—pur- and tails) introduces the idea that probabilistic repre- pose, control, foreknowledge, and —do sentations are models, simplifying and idealizing a pose potential conflicts. Sections 6 through 9 address more complex . each of these, showing how the apparent conflict can be resolved. Section 10 discusses how a realist inter- Exemplar 2: Pseudorandom pretation of randomness might influence our under- Computer games and often depend on standing of God’s relational attributes. pseudorandom numbers. These are generated by an but appear random in that they are uni- formly distributed over some (say 0 to 1) if the 2. Exemplars of Randomness algorithm works as intended; this provides a kind of “fairness” in games and simulations. Typically A popular conceptualization of randomness is not such start by selecting a number (called having a governing design, method, or purpose; a seed), entering it into a formula that generates a next unsystematic; without cause. But this concept is not number, then using that as the seed for the next, and how randomness is actually used in mathematics, so forth. If one knew the initial seed and the formula, statistics, and the sciences. In The Structure of Scientific one could compute all the numbers. But the seed is Revolutions, Thomas Kuhn drew on the notion of often chosen so as to make the numbers unpredict- exemplar, those examples in a discipline that transmit able in practice, such as selecting digits from the time its key concepts from one generation to the next. given by the computer clock at the instant the num- He wrote, ber is requested. Nevertheless, John von Neumann By [exemplar] I , initially, the concrete prob- once joked, “Anyone who considers arithmetical lem-solutions that students encounter from the methods [as] producing random digits is, of course, start of their scientific education, whether in labo- in a state of .”6 ratories, on examinations, or at the ends of chap- ters in science texts … All physicists, for example, Exemplar 3: Random begin by learning the same exemplars: problems This is the basis of statistical investigations. It is typi- such as the inclined , the conical pendulum, cally done by numbering the members of a popula- and Keplerian orbits; instruments such as the ver- nier, the calorimeter, and the Wheatstone bridge.3 tion, then using a computer or a table to generate pseudorandom numbers that are used to select a I begin with nine exemplars of randomness that show sample of the population. Statisticians view such how the term is used in mathematics, statistics, and samples as having the best chance of un- the sciences; they will illustrate key ideas later in biased—that is, being representative of the popula- this article. tion. Random sampling is so widespread that it provides a particularly familiar example of how Exemplar 1: Games of chance randomness can be used purposefully. “Games of chance” employ playing cards, , coin flips, and wheels; frequently, these introduce Exemplar 4: 4 probability to students. Textbooks pack many con- If we take a sample of Carbon-14, for example, it will cepts into the discussion of these games. Each gradually decay into Nitrogen-14 through emission involves a small, finite number of equally probable of beta particles—electrons or positrons. The rate of outcomes; for coin flips, if the coin is “fair,” the out- emission is constant, making it possible to calculate comes are equally likely. The probabilities of all out- a half-life—the time it takes for half of the radioactive comes must total one, so each has probability ½. Thus material in a sample to decay; in Carbon-14’s case, the fairness assumption introduces a method to cal- the half-life is 5,730±40 years. Nevertheless, there is

76 Perspectives on Science and Christian Faith James Bradley

no known way to predict when any particular viewed as deterministic and depends on the exis- in the sample will emit such a particle. Thus the time tence of currently undiscovered hidden variables. The of emission serves as an exemplar of a continuous hope of finding such variables received a major set- (in contrast to the discrete random back in 1964, however, with the publication of Bell’s variables of the previous three examples); our inabil- Theorem. This provides an empirical test for whether ity to identify a determinate process that would quantum can be accounted for by local enable prediction of the time of a particular emission hidden variables (ones that respect the velocity of is often used to introduce the notion that indetermi- light as a maximum velocity); such testing has dem- nacy may be an inherent of processes and onstrated that the answer is no.9 Nevertheless, the not simply a matter of our ignorance. issue of how to interpret the collapse of the wave function is far from settled; two other interpretations Exemplar 5: Poisson processes are decoherence, focusing on the of the Time-dependent events such as the arrivals of cus- electron with its environment, and many-worlds. tomers at a check-out counter in a store, of cosmic In the latter, the collapse is deterministic—the wave- rays at a detector, or of telephone calls at a hub are form representation of the electron is seen as real often modeled using Poisson processes. In such pro- but its collapse is denied. Rather, reality is seen as cesses, arrivals occur randomly at a constant rate a multibranched tree in which all possible alternative over a time interval and are equally likely to occur at histories of the electron and all possible states any time in that interval. These assumptions guaran- are real. tee that inter-arrival times will follow an exponential ; if the frequency of arrivals in a fixed time Exemplar 7: Mendel’s peas interval is counted for many such intervals (all hav- Gregor Mendel (1822–1884), an Austrian Augustinian ing the same arrival rate), the frequencies will follow , is known as the “father of modern genetics.” a pattern known as a Poisson distribution. Poisson Working with peas grown in his monastery’s experi- processes illustrate the fact that randomness may mental garden, he discovered the laws of inheritance arise by aggregating events that are individually not that govern the transmission of traits from parents to random—the coincidence of large numbers of inde- children. For instance, some traits of peas (color, tex- pendent events, each determined by its own (possibly ture, etc.) occur in two genetic forms (or alleles) that deterministic) causes, produces behavior consistent can be denoted “A” for the dominant form and “a” with an assumption of randomness. for the recessive form. The genotypes governing the expression of such a trait occur as pairs—AA, Aa, or Exemplar 6: Quantum uncertainty aa. Using careful records, Mendel demonstrated that We cannot see electrons but we can represent them the offspring of hybrids (those with the form Aa) mathematically. “Spin” is a property of electrons occur randomly with ¼ taking the form AA, ½ Aa, even though (as far as we know) electrons do not spin and ¼ aa. Mendel’s work preceded the of in the same as large objects such as baseballs genes; however, their subsequent discovery pro- and planets. Electron spin can occur in one of two vided an understanding of the mechanisms under- states: spin-up or spin-down. But this does not mean lying Mendel’s laws. Random transmission of genetic that electrons exist in one state or the other; rather, information to offspring is a key component of the they are mathematically represented as a probability theoretical framework of modern evolutionary theory. distribution over the possible spin states (and other ). However, when electrons pass through Exemplar 8: Diffusion a device called a beam splitter, a transition (called the Consider a cell in the body. It needs nutrients collapse of the wave function) occurs in such a way that and oxygen delivered to it from its exterior and has the path of the electron shows it to be in either the waste products in its interior of which it needs to up or down state with each state having probability dispose. Water can pass through the semipermeable one-half. In the Copenhagen interpretation of this phe- cell membrane taking dissolved substances with it nomenon,7 the collapse is precisely what it appears and balancing the concentration of these substances to be—nondeterministic; the Copenhagen interpreta- on either side of the membrane. This process is called tion is held by most physicists and is commonly osmosis and is a form of diffusion, the random move- taught. In the Bohmian interpretation,8 the collapse is ment of particles from regions of higher concentra-

Volume 64, Number 2, June 2012 77 Article Randomness and God’s Nature tion to those of lower concentration. This of outcomes. Algorithmic motion is the result of the heat energy of molecules, (AIT) studies infinite strings of bits; these provide each moving independently, and occurs continually a mathematical model of sequences of outcomes. in all liquids and gases. Life as we know it would not AIT has introduced several concepts of randomness. be sustainable without osmosis. For example, for Martin-Löf randomness astringof bits is random if it passes all reasonable statistical Exemplar 9: theory tests for randomness. Another approach uses incom- “Chaos” is the popular of deterministic non- pressibility—a string is compressible if it can be periodicity.10 It characterizes nonlinear systems such described by a string shorter than itself;12 random as global atmospheric pressure. Such systems are strings are incompressible. These concepts have extremely sensitive to their initial conditions. They yielded powerful results such as methods to decide are deterministic in the sense that if one knew their whether one string is more random than another. governing equations and initial state precisely, their The underlying linking all of AIT’s formu- entire future behavior would be predictable. How- lationsofrandomnessisthatarandomstringlacks ever, it is impossible to measure their initial state a discernible pattern. But AIT makes the notion of with full precision; furthermore, the system amplifies “lacking a pattern” precise by giving it the mean- tiny variations in the initial state so that two systems ing of incomputable—there is no algorithm that can that start out close together become farther apart over take the first n bits of a random string and compute time. Thus, future states are, in practice, unpredict- the (n+1)st.13 able even though in principle they are predictable. These systems are deterministic but their long-term The process definition (in terms of unpredict- behavior appears random. ability) and product definition (the absence of pattern in lists of outcomes) are similar but not equivalent—an infinite bit string that lacks a pattern 3. Randomness represents multiple outcomes and its terms are The popular conception of randomness mentioned unpredictable. However, a real world process is earlier—not having a governing design, method, never perfectly repeatable, nor can it produce an infi- or purpose; unsystematic; without cause—is mis- nite sequence of outputs. Also, its outputs may truly leading. For example, rolling a fair die produces six be unpredictable but for any finite set of outputs possible outcomes, each with probability 1/6. Both there is a nonzero probability that they possess a and lay people regard that outcome as ran- discernible pattern. Furthermore, AIT offers several dom, but the die is carefully designed and purpose- nonequivalent definitions. So randomness can be ful, is far from being unsystematic, and its outcome viewed as a collection of concepts that bear a “family has a clear (arguably nondeterministic) cause. resemblance” incorporating the notions of multiple outcomes, unpredictability, and the absence of pat- Nevertheless, even among specialists, “random” tern in idealized sequences of outputs. I will simply does not enjoy a widely agreed upon univocal defi- use “indeterminacy” and “indeterminate” to refer nition. The nine exemplars involve indeterminate to this family. This will suffice for the consistency processes—characterized by multiple possible out- argument given here. comes and the impossibility of predicting which will occur. However, the term “indeterminate” is An epistemically random sequence is one that ambiguous. Physicists, for example, often think of appears random but, in fact, possesses a pattern that randomness in terms of causation or lack thereof. canbecomputedbyanalgorithm.Anontologically Thus an event is determinate if it is “determined,” random sequence has no algorithm that can compute i.e., caused; it is indeterminate if it is uncaused. its members. Thus these represent two very different Mathematicians and statisticians typically avoid the types of randomness; ontological randomness (if it causality question by focusing on unpredictability. exists in the natural world) is a property of the very nature of things; epistemic randomness is apparent “Random” can also refer to outcomes as well as randomness—it is a function of human perception processes.11 An idealized process (assuming perfect of things but not their nature.14 is the repeatability) can produce an arbitrarily long philosophical position that ontological randomness

78 Perspectives on Science and Christian Faith James Bradley

does not exist in the physical world; nondeterminism exists (although I will argue in the next section that is the assertion that it does exist. There are two prin- evidence in favor of it is stronger than evidence cipal interpretations of models that include random- against it). Either claim would require complete ness. For instrumentalism,randomnessisauseful of the universe. That is, suppose Profes- tool when we have limited knowledge; for realism, sor A is a nondeterminist. Consider any particular it corresponds to a deeper nondeterministic reality. example he to be nondeterministic. Profes- sor A can never exclude the possibility that some Some Christian thinkers have argued for realism future discovery will show it to be deterministic. regarding randomness; some against it. John Byl Now suppose Professor B is a determinist. In lieu rejects ontological randomness in ; he argues of complete knowledge of the universe, she can that a preference for nondeterministic interpreta- never show that deterministic causes can be found tionsofquantummechanics“…ismotivatedlargely for all physical events. So neither position can be 15 by philosophical and theological commitments.” scientifically established; metaphysical and/or theo- R. C. Sproul, quoted earlier, also denies that ran- logical reflections are necessary if we are to explore domness could be real. Hans Gregersen sees all the concept of randomness. Randomness is a scien- natural laws including any that involve randomness, tific concept that cannot be completely investigated as human expressions of . He writes, by science. … laws of nature simply pick out the regularities of nature in so far as these can be identified by There is no inconsistency with historic Christian empirical investigations. Laws of nature, on this theology if we adopt the instrumental interpreta- account, are a metaphor or shorthand for general tion—this interpretation makes no ontological descriptions of regularities; ontological assump- claims. However, the realist interpretation is con- tions are deemed unnecessary.16 troversial. In the remaining sections of this article, I will argue for the consistency of the realist interpre- Other Christian writers argue that the apparent non- tation with classical Christian views of God’s nature. determinacy in indicates a more fundamental nondeterminate reality. John Polking- horne justifies this inference on grounds he calls critical realism. He starts from realism, the idea that things are the way they appear to be; critical realism, 4. Arguments for the Existence however, acknowledges that our perceptions can be of Ontological Randomness fooled by things such as optical illusions. It also Even if we could construct a sound argument for acknowledges that very small things (at the quantum the consistency of the realist interpretation of ran- level) and very large things (at the galactic level) domness and God’s attributes, it would be of little are outside our normal experience. So while realism importance without a plausible case for ontological is basically sound, we need to apply it cautiously. randomness. Polkinghorne argues for the Copenhagen interpreta- tion on grounds that when something such as quantum On one hand, a theist could argue for the con- uncertainty has been studied by a large number of sistency of randomness and God’s attributes on the people over many years producing powerful and grounds of God’s infinitude—algorithms are neces- consistent results, a move from “x appears this way” sarily finite, human understanding is limited; thus, to “x is this way” is warranted.17 unpredictability and the creation of patterns that cannot be detected by finitistic are consistent Keith Ward argues that nondeterministic laws with God’s infinitude. On the other hand, a different allow creative freedom room to exist and to oper- theist could assert that the physical world is finite ate.18 Bartholomew argues that God uses and hence be skeptical that any physical process chance.19 His book is subtitled “Can God Have It could produce outcomes that lack a discernible Both Ways?,” referring to the existence of both ran- pattern even though God created that process. This domness and order; he answers yes. section presents three arguments based on observa- I claim that it is impossible to decide on scientific tions of the natural world that support the plausi- grounds alone whether ontological randomness bility of ontological randomness.

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1. Recent work on “quantum coin tossing” uses science, although it is easy to reconcile it with his quantum indeterminacy to generate sequences of . Consider this thought : bits that exhibit strong evidence of being random.20 an engineer is designing a system to keep a ball AIT has shown that there are random numbers; in place. He could place it on the peak of a moun- however, this could simply be an abstract mathe- tain, and with sufficient resources and vigilance, matical curiosity. Quantum coin tossing - he could maintain it there. Or he could put it in strates that it is plausible that such numbers a valley. In the first case, he might be called - correspond in a meaningful way to entities in the nipotent, but he would not be called omniscient. physical world. Through both the long-standing Managing this world given its nonlinearity, com- durability of the Copenhagen interpretation and plexity, and sensitivity to initial conditions in a this recent work on quantum coin tossing, quan- deterministic manner would be like placing the tum indeterminacy provides a powerful argument ball at the top of the hill; managing it via indetermi- for ontological randomness; it does not prove its nacy would be like placing it in the valley. That is, existence, but it shifts the burden of proof to those an omniscient engineer would know that a deter- who deny its existence. ministic system that incorporates such a high Some physicists have used quantum indetermi- degree of instability is not an . nacy to argue for indeterminacy in the natural This argument is an application of inference to world well beyond the quantum level. In this argu- the best explanation and depends on an ment, quantum indeterminacy feeds indetermi- between God’s thoughts and those of an engineer. nate initial states into chaotic systems, and that Since the existence of ontological randomness can- indeterminacy is subsequently amplified many not be settled scientifically, such arguments are fold. The argument, however, possesses a serious our only option. Nevertheless, this argument does weakness: differential equations that exhibit chaotic not address the origin of randomness in the physi- behavior (such as those describing global weather) cal world. This is a mystery which is probably approximate states of the macro world; they may impenetrable. The of mystery should not not be applicable at the quantum level.21 Of course, be surprising, however; if God is infinite, we the cumulative effect of the enormous number of would expect that much of his nature and actions small particle interactions may be sufficiently large will remain mysterious to finite creatures. that it affects macro systems. But the argument is weaker than is sometimes assumed. 3. A third argument starts from . If a person’s decision is a function of many inputs, including 2. A different argument for widespread randomness genetic and environmental factors, is such a func- begins with Poisson processes. These illustrate that tion deterministic? There are two principal per- the coincidence of multiple independent events, spectives. Compatibilism consists of the assertions each of which may be deterministic, can produce that it is deterministic and that such a position can a composite effect consistent with an assumption be reconciled with the intuition that we have free of randomness. Furthermore, the natural world will. Incompatibilism is the assertion that such deci- is extremely complex—the number of elementary sions are not deterministic. The free will argument particles has been estimated as on the order of 1089, for randomness assumes incompatibilism. almost all of which are constantly interacting with Incompatibilist free will implies that ontological other particles. Also, the differential equations used randomness exists, but the converse need not hold. to model many natural systems exhibit extreme Consider, for example, flipping a coin. Conceiv- 22 sensitivity to initial conditions. Considering these ably an engineer could design a “coin flip predic- three factors together—independence, , tor,” a machine that detects the initial position of and chaos—it is easy to see how the world could the coin, its initial upward and rotational veloci- appear random on a broad scale. ties, and the position where it will land, and pre- A determinist could argue that the world appears dicts its outcome. Thus once the coin is released, random to finite human but need not to the outcome is deterministic. But if the flipper has an infinite, omniscient God. However, this asser- incompatibilist free will, the exact and the tion does not seem consistent with God’s omni- manner of that release are inherently unpredict-

80 Perspectives on Science and Christian Faith James Bradley

able; in fact, they are not fully under the flipper’s necessarily incomplete, statements about God’s na- control. So before the coin is released, the outcome ture because God has revealed himself in scripture. is ontologically indeterminate. Since incompati- bilist free will necessitates ontological random- The prototypical approach presents a list of divine ness, denying ontological randomness necessitates attributes and then expands on each. For example, compatibilism. Thomas Oden presents sets of divine attributes orga- nizedaroundfourthemes: Some scientists have argued that the Copenhagen • The divine being (primary and essential attributes interpretation of quantum indeterminacy, if cor- of God: sufficiency, underived existence, unity, rect, allows for an account of incompatibilist free , immeasurability, , life) will. They argue the plausibility of the converse— • that ontological randomness can account for free The divine majesty (the relational attributes of God: all-, all-knowing, almighty) will. However, it is difficult to see how to carry • out such an argument. For example, one form of The divine person (free, congruent, interactive this argument starts from quantum indeterminacy ) of elementary particles in a person’s brain. How- • The divine goodness (holy, constant, - ever, to account for free will, the argument needs ate)24 to “connect the dots” between that indeterminacy “Congruent” means that God acts in ways consistent and particular free choices. It is far from clear that with his being and character—he “cannot deny him- that can be done.23 self”; “relational” refers to God’s relationship with the entirety of creation. Note that if incompatibilist free will exists, games of chance can exhibit ontological randomness since Herman Bavinck discusses God’s attributes using they are under the control of an agent acting in- the of God revealed in scripture.25 His list determinately. Furthermore, so do pseudorandom is similar to Oden’s; he also presents a thorough dis- numbers and random sampling—an ontologically cussion of the history of Christian thought about the indeterminate choice can start the random number attributes. Many other theologians, notably Thomas generator. Aquinas in his and with his Institutes of the Christian have pre- The arguments from physical processes make a stron- sented systematic treatments of God’s attributes. ger claim about randomness than the argument from Oden’s four sets of attributes provide a representa- free will—the former locate randomness in the struc- tive summary. ture of the physical world, giving it a time frame of billions of years and independence from human The essential attributes have no relationship with activity. randomness since they deal with what God is apart from creation.26 Also, attributes of the divine person An assertion that the physical world is extensively and of the divine goodness do not involve God’s indeterminate may seem incredible given the order- relationship with physical processes. Hence, in terms liness and of the physical world. Fur- of Oden’s list, the potential problems reconciling thermore, to many people, such an assertion seems randomness with God’s nature all arise with the inconsistent with God’s nature. Sections five through relational attributes—omnipotence, , and tenaddressthisissue. .

5. God’s Nature Omnipotence To say whether randomness is consistent with God’s Oden offers a succinct definition of omnipotence: nature, we need to understand that nature. System- God’s “perfect ability to do all things that are consis- atic theologians have written extensively about it; tent with the divine character.” Bavinck explains some scholars have balked on grounds that finite omnipotence in several ways. The most explicit are human beings cannot understand a transcendent, the following: infinite God. However, the consensus of historic • “He has power over all things so that Christian thought is that we can make accurate, if nothing can resist him.”

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• “Nothing is too hard for God: for him all things bare before the eyes of him to whom we must give are possible.” account.” Oden says, • “He does whatever he pleases and no one can God’s knowing is said to be (a) eternally actual, call him to account.” not merely possible; (b) eternally perfect, as distin- • “This power of God, finally, is also the source of guished from a knowledge that begins, increases, all power and authority, ability and strength, decreases, or ends; (c) complete instead of partial; in creatures.”27 and (d) both direct and immediate, instead of in- directly reflected or mediated.31 In discussing nominalism, Bavinck also explains what omnipotence does not mean. For Oden, omniscience is as well as factual knowledge: … the nominalists defined the omnipotence of God not only as his power to do whatever he wills, The wisdom of God is God’s incomparable ability but also as his power to will anything. Differentiat- to order all things in the light of good, to adjust ing between God’s “absolute” and his “ordained” causes to effects, and means to ends; so that the power, they judged that in accordance with the divine purposes are firm and never thwarted.32 former God could also sin, err, suffer, die, become Two issues arise from omniscience. The first problem a stone or an animal, change bread into the body is that, in the popular concept, chance has no govern- of Christ, do contradictory things, undo the past, ing design, method, or purpose. The existence of make false what was true and true what was false, chance, then, would contradict the position that God and so forth. According to his absolute power, has a purpose for all of creation and orders all things therefore, God is pure arbitrariness, absolute in light of that purpose. For example, Isaiah pre- potency without any content, which is nothing sents God as saying, “I will accomplish that I please” but can become anything.28 (Isa. 46:10b, NEB). Nevertheless, Bavinck does not limit God’s omnipo- Section 6 addresses our second problem—reconciling tence beyond excluding things that are contradictory randomness with God’s purposefulness. One could or inconsistent with his nature. He adds, “What is argue that even if a process appears random, God possible extends much further than what is real.” knows what will happen, so the outcomes are pre- That is, he rejects the position of Abelard that God dictable to God. If predictable to God, then perhaps cannot do anything beyond that which he does. they are predictable to human beings. This contradicts Bavinck also adds, the unpredictability that characterizes randomness. Calvin did not deny that God can do more than Bavinck supports this position, quoting Cicero: “… if he actually did, but only opposed a concept of he [God] knows it, it will certainly take place, but if it is “absolute power” that was not bound to his nature bound to take place, no such thing as chance exists.”33 and therefore could do all sorts of contradictory Section 8 addresses this issue. things. Conceived along the lines of Augustine and Thomas, this distinction was generally endorsed Omnipresence by Reformed theologians, and so understood, it is Oden defines omnipresence as “God’s of being worthy of endorsement.29 present to all aspects of both space and time. Al- Bavinck exposes one potential problem in reconciling though God is present in all space and time, God is randomness with God’s nature: While randomness not locally limited to any particular time or space.”34 is not inconsistent with God’s character, it appears to involve processes outside of God’s control—with- Aquinas writes, out pattern or predictability, there seems to be no God is in all things by his power, insofar as all control—so it seems inconsistent with divine omnipo- are subject to his power. God is in all things by his tence. This issue will be addressed in Section 7. presence, insofar as everything is naked and open to his eyes. God is in all things by his , inso- Omniscience far as God stands to all things as the cause of their Oden defines divine omniscience as “God’s complete being …35 knowledge of the world and time.”30 One biblical source is Heb. 4:13, “Nothing in all creation is hidden The Stanford Encyclopedia of Philosophy raises a philo- from God’s sight. Everything is uncovered and laid sophical question about omnipresence: “How can an

82 Perspectives on Science and Christian Faith James Bradley

immaterial being be present at or located in space?” Robert Bishop articulates several of God’s pur- It explains Aquinas’ answer: poses for creation: (1) to exhibit his , (2) to serve This way of understanding God’s presence by as his , (3) “to become uniquely what it is reference to his power and his knowledge treats called to be in Christ,” (4) to populate creation with the predicate ‘is present’ as applied to God as ana- life, and (5) “to be an arena for comprehensive re- logical with its application to ordinary physical demption.”38 Randomness contributes to achieving things. It is neither univocal (used with the same (at least) the first and fourth of these by maintaining meaning as in ordinary contexts) nor equivocal dynamic equilibria in complex systems. Consider (used with an unrelated meaning). Rather, its these examples. meaning can be explained by reference to its ordi- • Every cell in living organisms needs to transport nary sense: God is present at a place just in case nutrients to its interior and to dispose of waste. there is a physical object that is at that place and These operations are carried out by osmosis that God has power over that object, knows what is involves the random motion of molecules as dis- going on in that object, and God is the cause of that cussed in Section 2. object’s existence.36 • More generally, diffusion is an ubiquitous phe- Omnipresence in the sense of being present to all nomenon that operates to equalize temperature things in space and time is not inconsistent with and air pressure distributions. For instance, diffu- randomness. However, God’s presence at every act sion makes the uniform shape of a balloon possible of causality raises a fourth problem: In deterministic in spite of the random motion of air molecules causation, if A occurs, B necessarily follows and either within it. A is the mechanism producing B or it triggers such • Genetic diversity allows populations to adapt a mechanism.37 In probabilistic causation, if A occurs, to changing environmental conditions.39 For ex- the probability of B increases. For instance, smoking ample, based on skeletal remains, ornithologists causes lung cancer, but not everyone who smokes have estimated that before Polynesians migrated gets lung cancer; neither is every lung cancer suf- to Hawaii sometime in the first millennium AD, ferer a smoker. But smoking increases the probability over one hundred species of honeycreeper inhab- of lung cancer. Deterministically caused processes ited the Hawaiian Islands. Ornithologists consider (such as discussed in Exemplar 9) can exhibit epis- them a subfamily, Drepanidinae,ofFringillidae, the temological randomness, but probabilistically caused finch family. Finches are seed eaters. Hawaiian processes (if they are more than simply an expres- honeycreepers include not only seed eaters but sion of human limitations) can exhibit ontological also insectivores, nectivores, eaters, and even randomness. However, because God is omniscient, snail eaters, as well as birds that probe decaying he completely understands the mechanisms by which wood for insects. Ornithologists account for the all physical processes operate. This casts doubt on uniqueness and diversity of Hawaiian honey- the existence of probabilistic causation, thereby cast- creepers by positing that at one time, a pair ing doubt on randomness. Section 9 addresses this (or more) of finches was blown onto the islands. issue. Given the lack of competition they encountered, Hawaiian honeycreepers evolved to exploit the rich resources available in ecological niches that finches do not normally inhabit. Genetic random- 6. Purpose ness enabled this diversity to arise. It provided for People use randomness purposefully in many ways, good use of resources, but it also produced an for example, games of chance, pseudorandom num- amazing variety of beautiful birds.40 bers, and random sampling. In this section, I argue that God uses randomness to fulfill his purposes, Further examples of purposeful roles for random- and thus objections to randomness based on God’s ness from artificial intelligence, theory, purposefulness are unfounded. I assume the ex- game theory, and quantum mechanics could be amples of randomness discussed in this section are cited, but these will suffice. Thus randomness, often ontological and argue for the consistency of that seen as synonymous with disorder and instability, assumption with God’s nature. is the mechanism that brings about order, stability,

Volume 64, Number 2, June 2012 83 Article Randomness and God’s Nature and diversity in physical situations on which life trol, so randomness appears to conflict with divine depends. So we can like this: God is Creator omnipotence. Oden writes, of all things, and we have articulated some of his God’s power is not bound always to exercise every purposes for that creation. We see how randomness conceivable form of power in every situation … supports the achievement of these purposes. There- God even allows wills contrary to the divine will fore we can reason analogically from how purposes to act and express influence within fleeting tempo- function for us, to how they might function for God, ral limits.44 and conclude that God has created randomness to Aquinas regarded God as empowering and sustain- accomplish his ends. ing nature rather than controlling it; creatures can be causative agents in and of themselves.45 For Aquinas, While the above examples are well understood, God is not just another cause or being in the universe some authors have advanced additional speculative but endows all else with being, order, and the capac- ideasastohowGodmightuserandomness. • ity to be a secondary cause. This section will explore In his chapter, Order out of Chaos, David Bartholo- the perspective that Aquinas and Oden represent in mew cites examples of how unanticipated orderly more detail. structures arise out of chaotic arrangements of entities such as light bulbs and buttons. He writes, First, randomness can involve order. If one rolls “Randomness achieves easily that which, by a fair die, apart from a drastically unusual event design, might have been very difficult.”41 Bartholo- such as the family dog swallowing the die, there are mew uses this as an analogy for how God can only six possible outcomes and each has probability have both randomness and order. 1/6. The situation is closer to deterministic order • Speaking of scientific law, John Polkinghorne than to complete chaos. But all order originates in writes, “Chance … is the means for the exploration God and that includes the order in randomness. As and realization of inherent possibility, through Heller points out, the laws of probability continually changing (and therefore at any time are still laws.46 contingent) individual circumstances.”42 That is, Polkinghorne views God as endowing the creation David Bartholomew argues that God “can have with possibilities; randomness provides the means it both ways”—have both randomness and order— for exploring them, thereby enabling creativity in by introducing the concept of level. At the level of the physical world. individual entities, a situation can be random, but at 47 • William Pollard, a well-known physicist and an an aggregate level, it can be orderly. For example, • Episcopal priest, argued for quantum indetermi- Globally, about 106 male children are born for nacy. But he also argued that macrolevel random- each 100 female children. However, males have ness provides room for providential action not a slightly higher rate of childhood mortality, so easily recognizable as extraordinary.43 Thus, Pol- that when both reach adulthood, the num- lard suggests, the world is not deterministic, and bers of males and females are almost equal. Thus continual divine action takes place in the form the of an individual birth can be non- of God’s providential care. However, randomness determinate while the aggregate produces a simple makes it possible for God to hide such actions. order. Hence, God ensures that the interpretation of • The gas law was first stated by Émile events as providential depends on faith; it is not Clapeyron in 1834. For gas in a closed container, forced on anyone. PV = NRT where P denotes pressure; V, volume; N, the amount of gas present; R, the gas constant; So randomness need not contradict God’s purpose- and T, temperature. A gas consists of enormous fulness. numbers of molecules moving randomly in the container; the gas law describes its aggregate 7. Sovereignty behavior in a simple, orderly way. Our second potential problem is that randomness Figure 1 presents a . Note its appears to involve processes outside of God’s con- erratic, uneven quality. Using a computer, I selected

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10,000 random samples of size 30 from a population But, says Bartholomew, randomness at low levels so distributed. Figure 2 presents the distribution of also expresses God’s sovereignty. Nevertheless, the means of these samples. It is similar to the famil- while Bartholomew’s discussion of levels is helpful iar bell-shaped curve. The in seeing how “God can have it both ways,” viewed tells us that for any probability distribution, if we in isolation, it can oversimplify the of take independent random samples of size n from reality. Creation cannot be neatly divided into two that population, the distribution of means of those levels—a lower one where God operates via ran- samples approaches a as n gets domness and an upper one where deterministic larger. Processes that average together large number laws prevail. of similar items are common. For example, tempera- ture is the average motion of molecules. Thus, the Robert Bishop’s notion of contingent rationality— central limit theorem provides a powerful explana- the order and structure that God has freely given tion for why normal distributions arise so frequently creation—helps here. He writes, “… creation has its in nature. It demonstrates how aggregation trans- own rationality, its own particular order, structure forms disorder at one level to order at a higher level. and functionality, which are at least partially intelli- gible to us.”48 God works through that rationality Bartholomew argues that God’s sovereignty oper- and that includes the laws of probability and the ates differently at different levels. A believer can orderliness of random processes. Randomness does easily affirm that the order and structure at aggre- not mean arbitrariness. Rather, random phenomena gate levels expresses God’s orderliness and goodness. are constrained to act within boundaries according to their nature. Molecules can vibrate in any direc- tion in three-dimensional space, but that is all they can do; a smooth-skinned pea may nondeterminis- tically produce offspring that are smooth or rough, but it cannot produce a gorilla. God’s sovereign controloverrandomnessisexpressedinbothtypes of probabilistic laws—those that operate at the level of the individual entity and those that govern aggregation.

8. Foreknowledge Reconciling randomness with divine foreknowledge is a generalization of the classical problem of recon- Figure 1. A Probability Distribution ciling human free will with divine foreknowledge— all of the same questions arise. In On Free Choice of the Will, Augustine formulates the problem in the words of his interlocutor, Evodius: I very much wonder how God can have foreknow- ledge of everything in the future and yet we do not sin by necessity. It would be an irreligious and completely insane attack on God’s foreknowledge to say that something could happen otherwise than as God foreknew. So suppose that God fore- knew that the first human being was going to sin. Anyone who admits, as I do, that God foreknows everything in the future will have to grant me that. Now … since God foreknew that he was going to sin, his sin necessarily had to happen. How then Figure 2. The Distribution of Averages of Random Samples is the will free when such inescapable necessity from Figure 1. is found in it?49

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Replace sinning by random events and free will imagine God after he has chosen the one we live by processes that produced them and we have the in (“after” is used here in a logical rather than problem of reconciling randomness with God’s fore- a temporal sense); his knowledge of this is his free knowledge. Three ways to reconcile God’s foreknow- knowledge (since he has freely chosen which one to ledge and human free will apply to randomness in create). In between these, Molinists argue, is God’s the natural world as well.50 middle knowledge, knowledge of events (which may 1. Open theists assert that the future does not exist. be random) in each . Molinists They affirm that God has knowledge of many argue that in choosing the particular world God future events—he knows his plans for the future; chose to create, he took this middle knowledge into he knows the laws of nature fully, so he can predict account. Thus he is able to create randomness, the future of all objects under the control to foreknow its outcomes, and to ensure that his of those laws. He also knows the aggregate behav- will is accomplished—not in spite of randomness, iors of nondeterministic systems. But he does not but as we saw in Section 6, because randomness have knowledge obtainable by observing a future is one of the means of accomplishing his will. event—if I plan to flip a coin in the next five min- Scholars are far from a consensus on which of these utes, open theists would argue, God cannot say accounts is the most compelling. Open con- whether that coin will come up heads or tails. tradicts classical ’s affirmation Advocates of this approach argue that it does not that God’s omniscience includes knowledge of the violate God’s omniscience—God knows all that future; given the extent of classical unity on this is knowable, but because indeterminate future question, it would require a very compelling case events do not exist, they are not knowable. They to reject it. To my mind, the case for , also present numerous biblical texts referring to however, does not seem that compelling. Simple God regretting actions, changing his mind, and so foreknowledge affirms free will (and by inference forth, that they interpret as providing support for randomness), but it has not provided a clear account an open future. of the relationship between God’s knowledge and 2. Another approach is simple foreknowledge—God’s that freedom. has been critiqued on vari- complete and infallible knowledge of the future ous grounds, notably the question of why God, “… uncomplicated by exceptions, additions, quali- knowing his creatures’ free choices in advance, fications, et cetera …”51 Arguments for simple fore- would create that are lost. knowledge argue that foreknowledge does not constrain events. Consider any particular event I lean toward Molinism—it provides a powerful that one might want to regard as random—say account of how God’s foreknowledge and ontologi- observing the measurement of the spin of a par- cal randomness can be reconciled; it also seems that ticular electron. Imagine that God, in spite of God’s omniscience would include middle knowl- his omniscience, chooses to ignore this particular edgeandthatGodwouldusethatknowledgeincre- event. (Perhaps he cannot, but let’s accept it as ation. The matter is far from settled, but the three a hypothesis for the sake of this argument.) God approaches demonstrate that compelling arguments has no foreknowledge of whether this electron can be presented to reconcile randomness and God’s will be measured as spin-up or spin-down, and so foreknowledge. the randomness of that outcome does not conflict with his foreknowledge. But the event is exactly the same whether God knows about it or not. 9. Causality So the randomness of the event is independent Oden writes that God’s omnipresence means (among of God’s foreknowledge. other things) that God is present in every act of 3. A third approach is Molinism, after the Jesuit causation. Historically, Christian thinkers identify scholar Luis de Molina of the late sixteenth God as the first cause of all actions, although century. Imagine God contemplating all possible observed events may have secondary causes. Physi- worlds he could create. Molinists call the knowl- cists who endorse the Copenhagen interpretation of edge of these worlds God’s natural knowledge. Now quantum mechanics typically associate quantum

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indeterminacy with causelessness; many Christian garden to move slightly; the pollen grains on its back thinkers object. For example, John Byl argues against would differ and his peas would receive different quantum randomness: genetic material than they would have received Indeed, a basic principle of rational enquiry is that without the wind. everything has a sufficient reason. The Principle of Sufficient Reason implies the Principle of Causal- By considering counterfactuals, we can see how ity, which affirms that every event has a sufficient probabilistic causation can exist without violating cause. To say that a quantum choice is made by God’s presence to the causation. chance is to say that “nothing” makes and actuates the choice. This contradicts the Principle of Suffi- cient Reason. To say that an event has no cause is 10. Conclusions to give up on science and to invoke magic, in this How might the existence of ontological randomness 52 case magic without even a magician. in the physical world influence how we see God?

In contrast, Robert Kane distinguishes the principle First, the apostle Paul writes, of sufficient reason and the axiom of sufficient rea- Oh, the depths of the riches of the wisdom and knowledge . The first says that if p, then there is a sufficient of God! reason for p. The second is its converse; it says that if How unsearchable his judgments, there is a sufficient reason for p, then p. Kane writes, And his paths beyond tracing out! (Rom. 11:33, NIV) … it will be logically possible that something be Randomness can be viewed as a subtle expression of the case (e.g., a chance event) which does not have God’s wisdom—numbers consist of bits that cannot a sufficient cause or explanation for its existence. be generated by any algorithmic process, enormously … We may say that the axiom of sufficient reason complex systems have components that act independ- defines the sufficiency of a sufficient reason. By con- ently according to their own laws yet aggregate to trast, it does not seem that one can derive from the produce a simple order, dynamically stable systems definition of a sufficient reason that everything depend on randomness for their stability, God’s sov- existing must have one, which is what the principle ereignty is expressed in dramatically different ways of sufficient reason requires.53 at different levels, and probabilistic laws define how Byl seems to raise the principle of sufficient reason order can exist in the midst of apparent disorder. to the level of an axiom. The principle assumes deter- Such factors expand our understanding of Paul’s minism; an argument against chance based on it words and can lead to richer . begs the question. Secondly, Calvin writes, Consider this thought experiment. A male bear Suppose a man falls among thieves, or wild beasts; walks through the woods in mating season to liaison is shipwrecked at sea by a sudden gale; is killed with a female. A deer steps on a stick which snaps. by a falling house or tree. Suppose another man wandering through the desert finds help in his The bear stops, listens, and moves on. During that straits; having been tossed by the waves, reaches hesitation, his sperm swim around so that the harbor; miraculously escapes by a finger’s genetic material he passes on differs from what it breadth. Carnal reason ascribes all such happen- would have been. In explaining his cub’s genetic ings, whether prosperous or adverse, to fortune. makeup, the stick would not appear in a causative But anyone who has been taught by Christ’s lips explanation. Now suppose the deer had stepped that all the hairs of his head are numbered a half inch further and missed the stick. That non- [Matt. 10:30] will look further afield for a cause, event would also not appear in the explanation. and will consider that all events are governed by That is, one could construct a causative explanation God’s secret plan.54 for the cub’s DNA makeup and yet, indeterminacy would still be present. In fact, arbitrarily many such The view of randomness presented here can nuance counterfactuals could alter the cub’s DNA. But none Calvin’s statement. We need not set “fortune” against would appear in a causative account. As another ex- Christ by associating it with “carnal reason.” Rather, ample, a puff of wind could cause a bee in Mendel’s randomness suggests we should look at the events

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Calvin cites systemically—God has ordained that 8Articulated by Louis de Broglie in 1927 and rediscovered such events occur but, rather than seeing each event by David Bohm in 1952. 9Nancey Murphy argues that God is such a nonlocal variable as God’s particular will, we see the broad system in “Divine Action in the Natural Order: Buridan’s Ass and in which such events occur randomly as God’s will. Schrödinger’s Cat,” in Chaos and Complexity: Scientific A nondeterministic world provides an arena in which Perspectives on Divine Action,2nd ed., ed. Robert John Russell God can demonstrate providential care.55 et al. (: Vatican Observatory Publications, 2000), 325–58. 10 Thirdly, Newton saw his theory of gravita- The name was popularized in James Gleick, Chaos: Making a New Science (New York: Viking Penguin, 1987). tion as explaining God’s work in the physical 11In the Stanford Encyclopedia of Philosophy article on chance, universe. But subsequent scholars used his laws to Antony Eagle applies chance to processes and random to undergird . The use of nondeterministic pro- data. 12 cesses to account for events in the physical world For instance, the string 010101010 … can be finitely described as an infinite repetition of 01 even though the could also lead to deism. But it need not. Rather, string itself is infinite. along the lines that Aquinas suggests, nondeter- 13AIT removes any remaining ambiguity in the idea of com- minism can enhance respect for the freedom God putability by defining it with Turing machines—an abstract gives his creation and recognition of God’s provi- model of computation that serves as the theoretical founda- dential care. tion for computer science. 14Ontological randomness, as defined here, is not merely a limitation in human knowledge. If there is no algorithm And lastly, randomness offers the potential of a for computing a pattern, God cannot compute it either. more nuanced than does determinism. But Of course, it is conceivable that God could know the list this will require development beyond this article. ù of outcomes in another way, for example, by possessing timeless knowledge that encompasses all past, present, and future outcomes of a process. Whether such knowledge can exist is controversial; I will return to this question in Acknowledgments Section 8. I would like to thank Kenneth Constantine, Russell 15John Byl, “Indeterminacy, Divine Action and Human Free- Howell, Roger Konyndyk, and Mary Vanden Berg dom,” Science and Christian Belief 15, no. 2 (October 2003). for comments on the first draft of this article. I would 16Niels Henrik Gregersen, “Laws of Physics, Principles of Self-Organization, and Natural Capacities: On Explaining also like to thank three anonymous referees for their a Self-Organizing World,” in Creation: Law and Probability, very helpful comments. ed. Fraser Watts (Minneapolis, MN: Fortress Press, 2008), 81. 17John Polkinghorne, “The of Divine Action,” Notes in Chaos and Complexity: Scientific Perspectives on Divine 1David Stover and Erika Erdmann, A Mind for Tomorrow: Action, ed. Robert John Russell, Nancey Murphy, and Facts, Values, and the Future (Westport, CT: Praeger Pub- Arthur R. Peacocke (Berkeley, CA: The Center for Theology lishers, 2000), 37. and the Natural Sciences, 1996). 18 2R. C. Sproul, Not a Chance: The Myth of Chance in Modern Keith Ward, “Why God Must Exist,” Science and Christian Science and (Grand Rapids, MI: Baker Books, Belief 11, no. 1 (April 1999): 5–13. 19 1994), 3. David Bartholomew, God, Chance, and Purpose: Can God 3This quotation appears in a postscript to the second edition Have It Both Ways? (Cambridge: Cambridge University of Thomas Kuhn, The Structure of Scientific Revolutions Press, 2008). 20 (Chicago, IL: University of Chicago Press, 1970). See, for example, “Random Numbers Certified by Bell’s 4The modern concept of probability was formulated by Theorem,” Nature 464 (April 15, 2010): 1021–4. Also see Andrey Nikolaevich Kolmogorov in the 1930s. The earliest Cristian S. Calude, Michael J. Dinneen, Monica Dumitrescu, widely used textbooks were written in 1950 by William and Karl Svozil, “Experimental Evidence of Quantum Ran- Feller in the United States and Boris Gnedenko in the Soviet domness Incomputability,” Physical Review A 82, 022102 Union. Feller mentions all of the games of chance discussed (2010), http://tph.tuwien.ac.at/~svozil/publ/2010-qrat-j here as well as other examples in chapter 1. Gnedenko uses .pdf. 21 dice and cards as his principal examples. John Polkinghorne, Science and Providence: God’s Interaction 5In the Bayesian interpretation, probabilities refer to subjective with the World, 2nd ed. (West Conshohocken, PA: Templeton degrees of belief. Foundation Press, 2005), xii. 22 6John von Neumann, “Various Techniques Used in Connec- There are several excellent articles on this phenomenon in tion with Random Digits,” Applied Mathematics Series, no. 12 Russell et al., Chaos and Complexity. Crutchfield et al. in an (1951): 36–8. article simply titled “Chaos,” pp. 35–48, mention several 7Developed by Niels Bohr and Werner Heisenberg in natural systems including the atmosphere, dripping 1924–1927. faucets, turbulence in fluid mechanics, and the heart.

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23See Harald Atmanspacher, “Quantum Approaches to Grove, IL: InterVarsity Press, 2001). It also presents the ,” Stanford Encyclopedia of Philosophy, ed. case for determinism; because my goal here is to show that Edward N. Zalta (Summer 2011), http://plato.stanford.edu ontological randomness is consistent with historic views of /archives/sum2011/entries/qt-consciousness/. God’s nature, I will not address that case. 24Thomas C. Oden, Classic : A 51David Hunt in Divine Foreknowledge: Four Views, 67. (New York: HarperOne, 1992), 35ff. 52Byl, “Indeterminacy, Divine Action and Human Freedom,” 25Herman Bavinck, Reformed Dogmatics, Volume 2: God and 102–3. Creation (Grand Rapids, MI: Baker Academic, 2004). 53Robert Kane, “Principles of Reason,” Erkenntnis 24 (1986): 26Some writers speak of God’s attributes “prior to” creation. 117. But time, too, is usually seen as part of the created order. 54Institutes, I, XVI, 2. So “prior to creation,” in the sense of time, has no meaning. 55For a further exploration of these ideas, see Paul Ewart, Nevertheless, these writers use the term not in a temporal “The Necessity of Chance: Randomness, Purpose, and the way but in the sense of creation being dependent on God Sovereignty of God,” Science and Christian Belief 21, no. 2 and not the reverse. I prefer to avoid the ambiguity by (October 2009). using “apart from” to refer to those attributes that would ASA Members: Submit comments and questions on this article characterize God even if there had been no creation. at www.asa3.org à FORUMS à PSCF DISCUSSION. 27Bavinck, God and Creation, 246. 28Ibid., 247. 29Ibid., 249. 30Oden, Classic Christianity, 46. 31Ibid., 49. American Scientific Affiliation 67th Annual Meeting 32Ibid. 33Bavinck, God and Creation, 202. 34Oden, Classic Christianity, 43. Science, Faith, and the Media: 35Thomas Aquinas, The Treatise on the Divine Nature, Summa Communicating beyond Books Theologiae 1, trans. Brian Shanley (Indianapolis, IN: O.P. Hackett Publishing, 2006), 1–13. “Therefore each of you must put off falsehood and 36Edward Wierenga, “Omnipresence,” Stanford Encyclopedia speak truthfully to his neighbor, for we are all members of Philosophy, ed. Edward N. Zalta (2009), http://plato of one body.” Ephesians 4:25, NIV .stanford.edu/entries/omnipresence/. 37The clause about mechanism is essential. For instance, if Point Loma Nazarene University A is the fact that the air pressure in a certain location drops San Diego, CA and B is the fact that a occurs, B necessarily follows A, July 20–23, 2012 but A does not cause B. 38Robert C. Bishop, “Recovering the Doctrine of Creation: A Theological View of Science,” http://biologos.org PLENARY SPEAKERS /uploads/static-content/bishop_white_paper.pdf. 39This bulleted item also appears in James Bradley and JACK JOHNSON Russell Howell, Mathematics through the Eyes of Faith Professor, Department of Molecular Biology, (New York: HarperOne, 2011), 108. Copyright 2011 by the Lab of Structural Virology, The Scripps Research Council for Christian Colleges and Universities. Reprinted Institute, La Jolla, CA by permission of HarperOne. 40Another clear example of this phenomenon can be found DEAN NELSON in Jonathan Weiner, The Beak of the Finch: A Story of Evolution Journalism Professor, Point Loma; Coauthor of in Our Time (New York: Alfred A. Knopf, 1994). Quantum Leap: How John Polkinghorne Found God 41Bartholomew, God, Chance, and Purpose, 49. in Science and Religion 42Polkinghorne, Science and Providence, 46. 43William Pollard, Chance and Providence: God’s Action in a CHRIS PEREZ World Governed by Scientific Law (New York: Scribner, 1958). Public Relations and Interactive Marketing 44Oden, Classic Christianity, 53. Counselor and Educator 45I am grateful to William Stoeger, S.J. for explaining Aquinas’s thought on this matter to me. REBECCA VER STRATEN-MCSPARRAN 46Michael Heller, Creative Tension: Essays on Science and Reli- ; Theologian; Instructor; and gion (West Conshohocken, PA: John Templeton Foundation Director of the Los Angeles Film Studies Center Press, 2003), chap. 11. 47Much of the material in this section also appears in Bradley RALPH WINTER and Howell, Mathematics through the Eyes of Faith, 105–6. Producer of 4 X-Men, Star Trek III, IV, V & VI, 48 Bishop, “Recovering the Doctrine of Creation.” 2 Fantastic Fours, Cool It, Left Behind,and 49 Augustine, On Free Choice of the Will, trans. Thomas Mother Mary of Christ Williams (Indianapolis, IN: Hackett, 1993), 73. 50All three are clearly presented in Divine Foreknowledge: Four Views, ed. James K. Beilby and Paul R. Eddy (Downers www.asa3.org

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