Randomness and Divine Providence: Game-Theoretic Perspectives
Steven J. Brams and Christina Pawlowitsch
We propose to use game theory to investigate the relationship between randomness and divine providence, especially as manifested in the Hebrew Bible. More generally, we wish to study the rational basis for divine actions, with special emphasis on how they can arise, seemingly randomly, in the natural world. Game theory is a mathematical theory for analyzing the interaction of players, and explaining the products of this interaction, including equilibrium and emergent outcomes. Specifically, we wish to show how game theory can
- reconcile God’s foreknowledge with human free will, showing how free will can contravene God’s ability to make perfect predictions. Thereby God’s choices may sometimes seem erratic—best responses to human choices that He could not predict.
- illustrate God’s choices in biblical narratives, wherein His actions may appear arbitrary or haphazard.
- analyze God’s possible use of mixed strategies in games that have no pure-strategy Nash equilibrium; and investigate the applicability of “theory of moves”—a dynamic approach to explaining the moves and countermoves of players in games—to the biblical narratives.
- study the role of randomness for the emergence of specific patterns in social interactions that cannot be explained by deterministic game dynamics (e.g., the emergence of cooperation in social dilemmas or of specific patterns in language evolution).
Discoverability and Providence
Robin Collins, Messiah College
Many physicists and philosophers have noticed that the universe seems almost miraculously discoverable, with some seeing this as evidence of divine providence. By calculating the effects of varying the fundamental parameters of physics on our ability to discover the universe, Phase 1 of the project attempts to quantify how coincidental this discoverability is, and whether the universe is in some sense optimal for discovery. As part of doing this, we will check whether the various quantifiable cases of discoverability we uncover can be explained by natural selection or “observer selection” via a multiverse; we will also develop a philosophical framework for determining the degree of coincidence of this discoverability under naturalism. Assuming it is highly coincidental, this will serve as a basis for arguing that God providentially arranged the universe to be discoverable. Much of the work on Phase 1 has already been done as part of my largely completed book on the fine-tuning of the universe for life and discoverability. The requested funding for Phase 1 is for a team of physicists – including one skeptic – and me to check over the calculations that have already been done, find new cases of discoverability, look for counterexamples to the idea that the universe is discovery optimal, and find flaws in the reasoning.
Phase 2 will examine whether this discoverability extends to seemingly chance-produced features of the earth and solar system. If there is good evidence that it does, and a framework can be developed for showing that it is highly coincidental, that will indicate that God providentially arranges for some seemingly chance processes to produce the particular result God desires; if we show it does not, that will give us reason to believe God typically does not do this; finally, even an ambiguous result would be informative.
Who Pulls the Random Strings in Neural Evolution?
Steve Donaldson and Tom Woolley, both of Samford University, Birmingham, AL and Josh Reeves, Eastern Kentucky University
Large segments of modern society refuse to accept either divinity, on the one hand, or the theory of evolution, on the other, because of a basic set of highly questionable assumptions about randomness itself, about how God could or could not work, and about human inability to undermine those assumptions. Yet claims that randomness denies a role for deity in creative processes can be made to look suspect if it can be shown that constraints on chance occurrences result in a set of boundary conditions that actually enable some level of predictability. In such a case, the constraints might constitute a kind of foreknowledge with the interaction of those constraints serving to tune the accuracy of the predictions. The problem is to show how this might actually work in practice.
To address this problem, a scientist, a statistician, and a theologian from the Samford University Center for Science and Religion will lead a major scientific and theological study to investigate the role of constrained randomness in simulations of the evolution of neural architectures. The results of this work will provide potential insights into biological evolution, thereby lending credible support for theological inferences related to the compatibility of randomness and divine providence as they pertain to emergent systems. This project raises a number of fascinating scientific and theological issues ranging from the identification and relative importance of the random factors involved to questions about the extent of God’s desire to control the creative process, and suggests that a better understanding of constrained randomness in creation could be a bridge between currently competing and seemingly incompatible views regarding God’s creative activity.
Abraham’s Dice: Chance and Providence in the Monotheistic Traditions
Karl Giberson, John Lanci, and Maria Curtin of Stonehill College, Easton, MA
Theological conversations occur in dialog with the past and the present. Christians summon the wisdom and insight of Tradition—what G.K. Chesterton called the “Democracy of the Dead”—to illuminate the present. And that present increasingly includes our scientific understanding. This project surveys the Christian Tradition—and dips into the broader Abrahamic Faiths—to see how thinkers across the centuries have responded to perceived randomness in the natural order, as their generation understood it, in light of their understanding of providence, natural philosophy and divine action.
Our project engages this conversation at a deep interdisciplinary level, bringing into conversation world-class scholars from theology, cosmology, philosophy, biblical studies and more who have all expressed a willingness to contribute in a major way. The breadth and depth of the team we are assembling provides a powerful engagement with the topic, which will lead to an edited volume published by a major press. We intend to produce a seminal volume that will be the standard work in this area, a well-written, accessible, authoritative springboard to further investigations.
By placing the present conversation about randomness and divine action in its larger interdisciplinary context, we anticipate uncovering helpful insights and reminding ourselves of illuminating conversations from previous centuries, as well as the sheer breadth of the topic.
Divine Action and 21st Century Physics: Chaos, Quantum Mechanics, and the Effacement of the Small
Jeffrey Koperski, Professor of Philosophy, Saginaw Valley State University
This project addresses questions of special divine action in light of quantum mechanics, chaos theory, and the emergence of higher order phenomena from more fundamental levels of nature. The project is broken down into two parts.
Part one has to do with the role of chaotic dynamics and quantum mechanics in divine action. Many noninterventionists vis-à-vis divine action believe that chaos added to the randomness found in quantum mechanics provides the causal joint of divine action. The adequacy of this model, however, crucially depends on the relation between randomness and determinism—two concepts often left unanalyzed in the divine action literature. I suspect that the view of determinism and randomness at work in these debates is inherited from the 16th century and does not comport well with more rigorous definitions used in contemporary nonlinear dynamics.
Part two begins with the twin issues of reductionism/emergence. Reductionism is generally considered to be a failed project among philosophers and many are turning to the notion of emergence as an alternative. Might each of the levels of reality above fundamental physics be irreducible and emergent? What exactly does that mean? Reduction and emergence are relevant to the Randomness & Divine Providence program since emergent phenomena often have ways of masking or “effacing” randomness at lower levels. Randomness at one level may very well be inconsequential to higher, emergent ones. Understanding the relation between random and nonrandom levels in nature is crucial if, as noninterventionists often argue, God governs “from the small.”
God’s Providence in a Universe of Purpose and Randomness
Thomas Jay Oord, Northwest Nazarene University and Benjamin H. Arbour, currently a PhD candidate at University of Bristol, Bristol, UK.
Oord and Arbour will co-supervise research into the compatibility of ontological randomness in the universe as it relates to Anselmian perfect being theology, or, the idea that God is the being than which none greater can exist. Arbour anticipates leading the effort by hosting a large conference that will analyze the philosophy of science, the metaphysics of causation, and perfect being theology as it relates to ontological randomness in the universe, all within the broader framework of pro- and con- positions with respect to open theology (Oord will assist with this endeavor). We anticipate publishing the proceedings of the conference as an anthology of essays on the subject with a major university press.
Additionally, both Arbour and Oord plan to publish work on the subject of open theism in both article and monograph form. Arbour will argue that Anselmian perfect being theology precludes any version of open theism, which likely eliminates the possibility of genuine ontological randomness in the universe. This, in turn, suggests that apparent randomness is merely a limitation of human knowledge and implies an instrumentalist philosophy of science wherein randomness many be heuristically valuable, but ultimately not real. In contrast to Arbour’s view, Oord will argue that ontological randomness is genuine, and that such requires significant modification to classical conceptions of the divine nature, along the lines of what has recently come to be known as open theism.
Theological Values of Randomness
Joshua Rasmussen, Azusa Pacific University and Jordan Wessling, Notre Dame University
We plan to use theology, philosophy and computer science to investigate why God might value randomness in the natural world. The investigation will be divided into three parts. First, we will explore and draw attention to ways that randomness in the natural world may reflect features of the divine personality—such as playfulness and adventure, enjoyment of surprise, artistic impulse, and others. We will express our ideas in an analytic theology paper in which we expose new lines of inquiry, while building upon recent, related work. Second, we will investigate a candidate utility of randomness using original empirical research. We have begun designing a computer program that simulates self-replication of creatures we call “bugs.” Unlike other programs that simulate evolutionary processes, our program randomizes the selection function itself; in effect, we randomize the starting state. Our goal is to see if “surviving” offspring tend to exhibit “interesting” properties, such as the possession of more component blocks, symmetry or other aesthetically notable configurations. The results may reveal a further reason why God could be motivated to make use of randomness in the natural world; or they may give us new information about the potential limits of randomness in creation. Finally, we will apply what we have learned about potential values of randomness to the problem of natural evil (i.e., suffering produced by disease, floods, hurricanes, and so forth). Some philosophers of religion have suggested that natural evil might be expected in a world that operates in a deterministic or law-like manner. By contrast, we would like to focus on indeterministic elements: our goal is to assess whether randomness may be worth its benefits, despite its potential to produce suffering. Each project will result in a research article that we plan to present at a conference and then submit for publication.
Randomness, Propensities and Indeterminism in Nature: Scientific Warrants and Theological Implications
Robert Russell, Center for Theology and Natural Science, Berkeley, CA
This interdisciplinary project starts with the growing scientific evidence for randomness in nature: in dynamic, self-organizing, complex, and autopoietic systems in the everyday world and in quantum processes at the subatomic level, at the macroscopic level through the amplification of quantum entanglement, and at the level of cosmology through quantum cosmology and superstring theory/the multiverse. These processes suggest philosophically that ontological indeterminism occurs not only at the atomic level but also in the ordinary world of nature and in the universe as such. This picture will strengthen claims for emergence, downward/top-down, whole-part, and bottom-up causality, all vital to a theological understanding of both general and special providence in nature from atoms to the cosmos. Such a view of providence is consistent with science (i.e., it is non-miraculous / non-interventionist) and it makes a real difference in the development of natural processes and thus to the history of life on earth (i.e., it is objective). I call this “non-interventionist objective divine action” (i.e., NIODA ) The highlight of the project is an international conference in Berkeley in October 2014, and resulting in a manuscript for book publication in 2015. Nancey Murphy and I will co-edit the book whose tentative title is Randomness, Propensities and Indeterminism in Nature: Scientific Warrants and Theological Implications. Participants include Gerald Cleaver, Ed Davis, George Ellis, Niels Gregersen, Alicia Juarrero, Joshua Moritz, Alan Padgett, Ted Peters, and Kirk Wegter-McNelly. A pre-conference event will be open to the public and media. Post conference plans include the development of doctoral and seminary courses at the Graduate Theological Union.
Creation at Random? – Indeterminism as a Challenge to Theism
Christian Tapp & Christian Weidemann
Providence requires God to know the future in sufficient detail. According to the most popular interpretation of quantum mechanics, however, our physical universe is ontologically indeterminate. A growing number of (open) theists maintain, for reasons not easily dismissed, that God cannot foreknow future events not yet determined (freedom and foreknowledge debate). Inasmuch as randomness only affects the means by which God’s general plan is fulfilled, there seems to be no serious difficulty here. However, what if randomness extends to the realization of the providential goals themselves?
We will use as a case study an atheistic argument put forward by Quentin Smith: according to (a widespread interpretation of) the standard Big Bang model, the earliest state of the universe, the Big Bang singularity, is lawless, and its outcome is essentially unpredictable. In particular, at this earliest state, there seems to be no guarantee that complex chemistry, stars, and animate beings, let alone persons, will evolve. But, given that it is part of God’s (general) providence that animate beings would evolve, would he have started his creation with anything like the Big Bang singularity? Open theism, general divine providence, and Big Bang cosmology seem to be incompatible.
We will explore various options to answer this atheistic argument. Our focus will be on the issue of divine intervention. Why can we not simply assume that God intervened after the Big Bang to ensure that an animate universe resulted? The main problem is that such subsequent repairing looks more like an inefficient kludge than the work of a perfect designer. Does God have a reason for such a detour? Is efficiency a great-making property for a being with infinite resources?
We hope to draw lasting general lessons about randomness/indeterminism and divine providence from this case.