Understanding the Relationship between Science and Religion Using Bayes’ Theorem

Introduction

Religious traditions span the total bandwidth of human diversity. Despite their differences, nearly all religious traditions agree that life's most significant goods come from virtuous living and that virtuous living is integral to human flourishing. That is, living the good life involves the cultivation of morally excellent habits, such as fairness or respect, that properly align humans to each other and to the sacred sources of our creation and persistence. Moreover, in most traditions, including Christianity, religion is a virtue, where religious habits, rituals, and disciplines are considered virtues that enable flourishing in community and with God. ¹ Practising religion is among the habits that facilitate human flourishing. However, concepts such as ‘morally excellent’, ‘the Sacred’, and ‘God’, are ontologically and morally loaded terms. Both religious (and secular) traditions attach a variety of meanings to these terms. The scientific method relies on conducting experiments, measuring effects, and interpreting results, which assumes agreement in terminology. Because conversations about virtue—and by implication, the study of religion as a virtue—are pervaded by normative assumptions, it might seem that the causes and consequences of virtuous living cannot form the object of scientific inquiry. This article argues that using evidence-based science can greatly improve theological understanding of the importance of religion in people's lives. I also claim that theological inquiries can effectively help scientists to investigate religion's social and psychological origins and consequences. I develop these ideas in relation to Bayes’ theorem, which serves as the conceptual basis for promoting collaboration between these two areas of study.

The article is structured as follows. First, I consider three credible objections to the science of human virtue. Rather than disputing these three objections, I argue for a pragmatic position that remains open to the possibility that the scientific study of virtue may prove theologically interesting even in the absence of normative and ontological agreement about moral excellence. Second, I motivate interest in collaboration by describing the findings of a longitudinal study of religion in the aftermath of a natural disaster in New Zealand. Not only are the findings of this study interesting, but its gaps also reveal opportunities for further theological and scientific investigations. Here, I introduce Bayes’ theorem, which provides a mathematical framework for quantifying how much beliefs should change in response to new evidence. Bayes’ theorem describes new possibilities for discovery arising from lingering questions from the earthquake study. Third, I consider how theological conceptions of religion as a virtue might interest longitudinal scientists who have so far limited attention to religion's extrinsic functions. Again, the motivation for such collaboration arises from lingering questions from the earthquake study.

Credible Objections to Virtue Science

In this section, I consider three credible objections to the science of virtue. I will restrict my focus to psychological science because it is the field of science in which I work and am most familiar.

The first credible objection relates to concepts and the ontological assumptions that such concepts might appear to imply. Psychological scientists do not use concepts of ‘moral excellence’ in their work. By contrast, philosophers define the concept of virtue to mean a morally excellent skill cultivated by habits that are prone to deficiency and excess. ² How might psychological scientists detect a morally excellent skill? Consider an analogy to music. Assessing a jazz musician's quality requires competence in the genre of jazz. Although we may study jazz from a behavioural or cognitive perspective, such a study would not carry us to an appreciation of excellence in the genre. Similarly, it has yet to be determined how the scientific study of human thought and behaviour would carry us to an appreciation of moral excellence. This is not to say that psychologists cannot recognise virtue when it is presented. However, it is important to remember that psychological scientists formulate hypotheses about how thinking and behaviour works, not whether thinking and behaviour are morally excellent.

A second credible challenge to the psychological science of virtue is practical. Suppose that virtue is not hidden from science. Nevertheless, it is conceivable that scientists might not be able to describe virtue in a language of scientific measurement. William James writes, “Philosophy lives in words, but truth and fact well up into our lives in ways that exceed verbal formulation. There is in the living act of perception always something that glimmers and twinkles and will not be caught, and for which reflection comes too late.” ³ A similar observation applies to the scientific study of virtue. If virtue were to pertain to experiences poorly represented in human language, then we might infer that scientific language would inevitably misconceive the experiential qualities of virtue.

A third credible challenge to the psychological science of virtue relates to the scope of psychological science. The gold standard for research design in psychological science is an idealised ‘random experiment’. Assignment to a treatment condition or a control condition is by chance. An average response is taken within groups. If the average response differs by condition, we say the treatment has a causal effect. As mentioned, the inference from a randomised experiment pertains to the average response. Unless the population is homogenous in its response, there will be those individuals who respond higher and those who respond lower than average. ⁴ Although the average response is the Holy Grail of psychological science, teachers and students of virtue typically want to know what works for specific individuals. The psychological science of virtue, it would seem, holds limited practical interest.

Notice that I did not consider an objection that science assumes that virtue is unreal. I did not consider an ontological objection to a psychological science of virtue. Below I clarify why the ontological objection fails. As for the other objections, I will not dispute them. Let us agree that the psychological science of virtue is limited in the three respects I just described. Nevertheless, might such a science prove philosophically and practically interesting to those who seek to cultivate morally excellent habits yet disagree about what constitutes moral excellence? It is to these questions that we next turn.

The Theological Interest of Virtue Science

Despite its limitations, virtue science may be theologically exciting and informative. However, appreciating the interest and utility of virtue science requires understanding its limitations.

First, longitudinal psychology measures people over time. It systematically investigates how beliefs and habits affect people. Even if the science of virtue is no substitute for the cultivation of virtue, the science of virtue might nevertheless clarify the mechanisms that underpin the cultivation of moral characters as an audience understands and appreciates them. Again, consider an analogy to music. Although a recording and analysis of musical virtuosity are not sufficient for educating musicians, such a recording might be helpful for educating musicians. Whether longitudinal psychology is useful for cultivating virtue remains unclear because the field is so young. However, it is at least plausible that by capturing a wider bandwidth of human experience than any one of us can individually experience, the systematic study of character formation might provoke creative theological reflection. This is because longitudinal studies may uncover patterns, trends, and insights into many people's experiences. By contrast, the individual experience of any theologian is limited. By synthesising a variety of experiences, new theological insights may arise in areas such as (1) the interplay between divine grace and human endeavour in nurturing moral virtues; (2) the impact of communal and cultural factors on the formation of moral character and spiritual maturation; and (3) the potential effects of diverse spiritual practices and disciplines on virtue development, possibly leading to a reassessment or expansion of conventional methods for fostering moral character. We will revisit several of these prospects in the subsequent discussion.

Second, let us acknowledge that the psychological science of virtue has its limitations in terms of the scope of knowledge it can provide. Is this a problem? It would arguably be unrealistic to expect science to capture more than a small fraction of what makes virtue valuable for individuals. Adopting a pragmatic approach to science, we might choose to accept the inherent limitations of knowledge and then strive to expand it where possible. Again, by exploring a more extensive range of human experiences than any individual can encounter, the systematic study of character formation would seem to potentially enrich theological perspectives.

Third, we must recognise that longitudinal psychological science investigates average population effects. There is no psychological science of individual-level causes and effects. ⁵ Teachers and students of virtues should be wary of thoughtlessly applying the results of any scientific study of virtue to some practical task. However, the average response might nevertheless prove interesting and afford some guidance. For example, on average, medically approved vaccines help more people than they harm. Some unlucky people will suffer worse harm from taking the vaccine than if they abstain. Nevertheless, most of us hedge our bets because a far more significant proportion experience harm from abstaining. We roll the dice in taking the vaccine, but the dice are loaded in our favour.

We have seen that it is credible that the psychological science of virtue might be interesting and, indeed, edifying, both scientifically and theologically. Ultimately, speculating from a theological armchair will not uncover the value of greater collaborative unions between scientists and theologians. It is only through actively probing and engaging with both the systematic study of character formation and theological perspectives that we can assess the merit of this endeavour. I am not a theologian. My interest here is not to conduct theology. Rather, my purpose has been to clarify why such collaboration might be intellectually compelling for theologians and scientists. The following section describes concretely how a psychological science of virtue might develop to clarify fundamental questions about how religious and spiritual habits contribute to human flourishing.

Findings from the New Zealand Attitudes and Values Christchurch Earthquake Study

On 22 February 2011, a magnitude 6.2 earthquake struck Christchurch, New Zealand, at a shallow depth of only four kilometres. The energy released from the earthquake, combined with the unstable soil conditions in the region, resulted in extreme shaking, widespread damage, and the loss of 185 lives. ⁶

The earthquake and aftershock sequence occurred between the first and second waves of the New Zealand Attitudes and Values Study (NZAVS). The NZAVS is a national-scale longitudinal study which was started by Professor Chris G. Sibley at the end of 2009. ⁷ This study follows the same people annually, measuring health, personality, relationships, employment, behaviours, values, beliefs, and community-making. Because the study obtains information at the level of individuals over time as they age, the NZAVS longitudinal data afford researchers insight into how social, cultural, and psychological attributes, together with life events, dynamically affect each other over time. Note that a longitudinal study differs from a census since a census samples the population over time without tracking individuals.

The Christchurch earthquake illustrates the power of longitudinal data to address questions about religion's functions. Specifically, because the participant pool consisted of a national probability sample, it was possible to compare changes in Christchurch with changes in the rest of New Zealand, thus isolating earthquake-specific effects from general trends affecting the entire country. To place this study in its broader historical context, New Zealand has experienced a steady rate of proportional decline in religious affiliates since 1966 of about 1 per cent of the general population per year. ⁸

Psychologists conjecture that people turn to religion in crisis for consolation. ⁹ This crisis-consolation theory of religion would predict that the Christchurch earthquakes, which destroyed over 30 per cent of New Zealand's second-largest city ¹⁰ and dozens of churches, would cause religious conversions in this region but not others. By contrast, the earthquakes initially destroyed over thirty regional churches, including the Catholic Basilica and the city's iconic Anglican Cathedral. ¹¹ Did faith fall with these cathedrals? Because the NZAVS had measured people across the country, longitudinal data enabled NZAVS researchers to test the theory of a crisis-consolation model for religion's functions. ¹²

NZAVS researchers observed the following:

There was an annual decline in religious affiliation outside the Christchurch region of 0.9 per cent. This decline corresponded to census estimates of a 1 per cent yearly decline in religion.

The Interest of the Christchurch Earthquake Study for Human Scientists

New information may affect prior beliefs. Remarkably, a mathematical theorem, ‘Bayes’ theorem’, enables us to quantify the degree to which further information should rationally revise prior convictions. Elsewhere I have described the relevance of Bayes’ theorem to the philosophy of religion. ¹⁴ Here, it is sufficient to note that Bayes’ theorem shows that one ought to change one's beliefs in proportion to one's surprise at new evidence. Bayes’ theorem can be stated in equation form as follows (where ‘Pr’ means ‘probability of’):

Bayes’ theorem is exciting because it demonstrates that we need not hold common beliefs before we can learn from evidence. Instead, by outlining our expectations beforehand, the evidence may adjust whatever beliefs we hold in proportion to the degree to which the evidence supports or conflicts with our prior beliefs. Why is this exciting?

First, Bayes’ theorem challenges some forms of philosophical relativism and postmodernism, which argue that truth and knowledge are relative to individuals or cultures. Bayes’ theorem suggests that people can still learn and update their beliefs based on new information, even when people have diverse perspectives. This is a powerful idea. There may be an objective basis for acquiring knowledge and adjusting our understanding, even if we start with different beliefs. Bayes’ theorem proves that it is not necessary to have a shared starting point or common ground to learn from new observations or evidence.

Second, Bayes’ theorem offers a logical reason why people might not always arrive at the same beliefs after encountering new observations or evidence. According to the theorem, how individuals update their beliefs depends on their prior beliefs and the latest evidence they receive. If someone has strong prior beliefs against a certain hypothesis, they may not be significantly swayed by new evidence, even if there are multiple results suggesting that the hypothesis is wrong. Instead, one is rationally bound to update beliefs in proportion to the degree to which the evidence conflicts with beliefs. If the new evidence aligns closely with their prior beliefs, they may not feel the need to change their beliefs much, if at all. Indeed, suppose the new evidence greatly contrasts with their prior beliefs. In that case, they might not adjust their beliefs in proportion to the degree of conflict between their prior beliefs and novel evidence that challenges these prior beliefs. They might instead check their measurements and replicate the study.

There are many such examples from the history of science in which scientists choose to check their instruments rather than revise their theories. In 1964, astronomers Arno Penzias and Robert Wilson discovered a persistent, low-level noise while working with a sensitive radio antenna at Bell Labs. They initially attributed the noise to their equipment or interference. After examining and recalibrating their antenna, the noise persisted. They eventually learned about the work of Robert Dicke's team at Princeton University, who were searching for cosmic microwave background radiation (CMBR) as evidence of the Big Bang. Penzias and Wilson's ‘noise’ turned out to be CMBR, which revolutionised our understanding of the universe's origins and earned them a Nobel Prize in Physics in 1978. ¹⁵ Notice that the potential for novel discovery required extending the bandwidth of plausible theories. The Eureka moment required thinking outside the boxes of pre-existing conventions.

Bayes’ theorem establishes that the amount by which we should adjust our beliefs in response to new evidence depends both on the new evidence and on our prior beliefs. If our prior beliefs align reasonably well with the observed evidence, there is likely little need for us to revise our beliefs. However, when our expectations deviate from the observations, and we cannot rule out other explanations, we should update our beliefs in proportion to the level of surprise we experience. However, discoveries require more than adjustments of prior beliefs. We also require theories that tell us where to look for data and guide us in interpreting data.

Let us return to the Christchurch earthquake study. Recall that the religious consolation hypothesis maintains that a basic function of religion is to offer comfort and solace to individuals in times of need or distress. If religion provides consolation, we might expect that (1) people will be more drawn to religion at times of crisis and (2) religious people will experience greater consolation during a crisis. Suppose that our prior belief in the religious consolation hypothesis were low. This prior belief in the theory is called the primary, Pr(Hypothesis). Suppose further that we are confident that, were the hypothesis true, we would not observe different levels both of conversion and of comfort among religious and non-religious people. This prior expectation of the evidence given the hypothesis is the likelihood, Pr ( Evidence | Hypothesis ) . We collect data and discover that (1) people are drawn to religion after a crisis and (2) religious people experience greater comfort. How much should our confidence in the hypothesis change? After observing evidence, our updated belief in the hypothesis is the posterior belief, P r ( Hypothesis | Evidence ) . Bayes’ theorem tells us that how much our beliefs should change is a function of the magnitudes we assign to our prior beliefs. If our prior belief in the hypothesis were very high, our belief need only increase upward very little. If our prior beliefs were shallow, our scepticism needs only decline very little. Indeed by dividing the right-hand side of the equation in Bayes’ theorem by the background probability of the Pr(Evidence) (here a normalizing factor) we can state precisely how much our beliefs should change upward or downward depending on our starting points (see the study from footnote 15 for more details).

The key points, again, are that (1) evidence should affect our beliefs; (2) how much evidence should affect our beliefs is not a matter that requires prior agreement. To assess the impact of evidence on our belief, we must consider how much we believe in a hypothesis (our prior), how likely the data are to be observed if the hypothesis is true (the likelihood), and the background probability of the evidence (the normalising factor). Recall that we highlighted two central predictions of the religious consolation hypothesis. (1) Religion's comforting function: the consolation hypothesis predicts that religion will alleviate psychological distress and provide support in times of adversity, crisis, or loss. (2) Increased religiosity during difficult times: The consolation hypothesis predicts people will turn to religion when facing adversity, crisis, or loss. Recall further that only the second prediction was observed. What does this imply for the science of religion?

The consolation theory is not the only psychological theory of religion that psychological scientists assert. Moral-functional theories propose that religion serves to unite individuals into cooperative groups. According to moral-functional theories, increases in religious engagement during times of adversity could be attributed to the need for increased cooperation and social cohesion. ¹⁶ Such a theory would predict that a natural disaster might lead to a rise in religious affiliation because the demands for cooperation during a disaster are higher. ¹⁷ This prediction corresponds to the comfort hypothesis prediction (2) and is supported by the Christchurch earthquake study. However, because moral functionalists do not predict comfort, the evidence against the comfort hypothesis prediction (1) does not diminish moral functionalism. That is, the results of the Christchurch earthquake study align with the moral-functionalist hypothesis while conflicting with the consolation hypothesis.

Should psychological scientists abandon consolation theory and rush to defend moral functionalism? From a Bayesian perspective, such a question is ill-defined. To determine how much one's confidence in these theories should change, we must consider that the extent to which our beliefs should change generally depends on both the quality of the evidence and our prior beliefs. Consequently, assessing the impact of new findings on our confidence in a given theory involves careful consideration of both the evidence and our existing understandings and beliefs. Ultimately, both evidence and prior beliefs must guide reassessments. One might have independent reasons to doubt the adequacy of moral functionalism. Merely observing evidence consistent with moral functionalism might not shift one's beliefs in favour of it. The level of interest in, and the potential influence of, any scientific finding can greatly depend on one's existing beliefs and understanding of the subject matter. Thus, the significance attributed to a discovery often varies based on the pre-existing assumptions and knowledge held by the observer.

The Interest of the Christchurch Earthquake Study for Theologians

Earlier, I mentioned that one might object to a science of virtue as irrelevant to understanding virtue because science assumes that virtue is unreal, and I claimed that this is not a credible objection. We are now in a better position to understand the problems with this objection. Any adjustment to what is deemed real or unreal depends on our prior beliefs. It is crucial to recognise that science is fundamentally about testing the predictions of our theories, for which people will assign different degrees of prior plausibility. This process begins with our existing theories and aims to update them based on the discrepancies between their predictions and new observations. Science does not endorse or ban beliefs. Beliefs evolve as new evidence meets prior convictions. Here, I have been focusing on the predictions of the consolation theory of religion. As I mentioned at the outset, most religious traditions consider religion to be a virtue. If we accept this position, then the study of religious change may help to clarify the causes and consequences of the virtue of religion. If we were not to accept the proposition that religion is a virtue, then the study of religious change might appear out of place in a discussion about the causes and consequences of virtue. If we were not to believe in virtue, then religious change would simply be the study of change in certain beliefs, habits, and affiliations. The science of virtue itself does not tell us which position to accept. Our interpretations of the evidence are inevitably inflected here by our prior commitments. This is not a shortcoming. It is an empowering feature of rationality.

Setting aside the notion that science inherently opposes studying religion, consider how theologians who view religion as a virtue might want to investigate religious conversion after a natural disaster in light of psychological science. Again, this project is yet to be undertaken, and I am not a theologian. However, I can briefly sketch a proposal based on Aquinas's perspective as a possible line of inquiry. According to Aquinas, the value of religion extends beyond extrinsic rewards such as self-reported well-being or material benefits. The primary purpose of religion, in Aquinas's view, is to honour and revere God, with additional benefits arising as a consequence of this intrinsic good. A theologian adhering to Aquinas's view might examine how religious conversion following a natural disaster offered possibilities for deepening relationships with what people take to be divine, cultivating moral growth, and fostering unity. Experiences of loss and suffering could have inspired gratitude and appreciation for divine providence, leading to new expressions of religious devotion. Furthermore, such a theologian might examine whether subsequent conversions following the earthquake evoked virtuous acts such as charitable giving, moral courage, or the pursuit of justice. By incorporating diverse experiences beyond any single individual's reach, a theologian interested in science equipped with data might significantly enhance the applied theological understanding of the role of religion in people's lives. In this context, Bayes’ theorem offers a valuable framework for updating theological beliefs. We have seen that gaining knowledge isn’t solely about reflecting on prior beliefs; it requires integrating new evidence with prior convictions. I have urged that science holds the potential to vastly broaden the range of evidence available. Again, although the theological work is yet to be done, as a social scientist, I find it fascinating to think about what a theologian might do with relevant data.

Might a theology, such as the one based on Aquinas's perspective, interest psychological scientists who are not theologians and have no interest in a theological reflection? Consider the gaps in scientific understanding arising from the earthquake study. We have observed that an exclusive focus on the consolation theory is too restrictive, as it lacks supporting evidence. However, Aquinas's view provides a more comprehensive understanding of religion's influence on individuals by emphasising the inherent goodness of religion and its role in deepening one's connection with what people take to be divine, promoting moral growth, and nurturing community bonds. This concept can be related to an example from astronomy: just as Penzias and Wilson discovered cosmic microwave background radiation by not limiting themselves to initial assumptions and instead explored further, a more comprehensive understanding of religion may be achieved by expanding beyond a focus on the consolation theory alone. Without implying that Nobel Prizes are waiting in the wings, it would seem sensible for psychological scientists interested in religion to attend to the writings of theologians when considering the effects of religion on people's lives. Again, scientists need not adopt Aquinas's medieval beliefs to benefit from Aquinas's attention to the processes by which religious piety affects thought and behaviour. Although the work of fully integrating theology and psychological science is yet to be done, Bayes’ theorem reveals there are no a priori philosophical barriers to conducting such work. When investigating the world, people do not need to share pre-existing beliefs, nor will encounters with data rationally demand full convergence in posterior beliefs.

Finally, notice that although Bayes’ theorem reveals inducements to greater collaboration between scientists and theologians, the theorem also reveals the potentially elusive prospect of fully integrating theology and psychological science. Scholars studying religion from different disciplines may be likened to explorers charting unknown territories, each starting from different points on the map and using their own compass (Bayesian prior beliefs). As they venture into the field, they may find that the landscape (evidence) alters their course differently (Bayesian posterior beliefs). Some may cross rivers, others climb mountains, and others navigate dense forests. Their experiences shape their route and understanding. They can benefit by learning from each other, and their paths may twist and turn in unexpected ways as they adapt to new information, reflecting the iterative nature of scholarly investigations. However, ultimately, each explorer's map of the territory will be unique, reflecting not only the terrain they encountered but also their starting point and the decisions they made along the way. This mirrors how our scholarly responses to evidence and subsequent changes in understanding are influenced by our initial and subsequent beliefs. On the one hand, Bayes’ theorem is a model of mathematical certainty, an exact tool that helps scholars navigate a complex terrain of evidence. On the other hand, its application in the scholarly study of religion underscores a fascinating paradox: while Bayes’ theorem provides an exact formula for updating beliefs in proportion to our surprise, the theorem also reminds us that growth in knowledge can occur in the absence of any ultimate convergence of beliefs.

Conclusions

I hope that I have convinced you that evidence-based science can greatly enrich discussions on religion, spirituality, and their impact on human flourishing. Likewise, I hope to have convinced you that theological inquiries can effectively assist scientists in identifying religion's social and psychological origins and consequences. My work here has been to demonstrate how Bayes’ theorem opens a pathway for such collaborative work. The key message is that people need not reach a consensus before or after collecting data that may impact their beliefs. Instead, data collection can serve to update the beliefs we hold, fostering an ongoing process of refinement and understanding.

As we look ahead, longitudinal psychology offers considerable potential to enhance both scientific and theological pursuits in comprehending the role of religion in human life. Given the diversity in beliefs, practices, character, resolve, hope, and resilience among individuals, discerning the role of religion and spirituality in this complex mix is challenging. Like the earth's curvature or planets’ orbits, the principles underpinning human flourishing await a systematic science. Such a systematic science of religion and spirituality has proved elusive because the relevant datasets have only recently been compiled. For a systematic science of human flourishing, many lives must be measured over many years, and researchers must ask the right questions. A longitudinal science of spirituality and human flourishing takes a bold yet patient approach, seeking to collect such spirituality and flourishing data by repeatedly measuring the same individuals over extended timeframes. This approach facilitates the study of causal relationships and the identification of patterns that unfold over time, which are concealed in cross-sectional studies. However, the quality of any longitudinal study of human flourishing depends not only on data. The quality of such a science also depends on the theories that organise the data. Bayes’ theorem clarifies that researchers do not need to believe in a God, or the same God, to advance theological and scientific understanding. I believe that theologians may improve the quality of scientific research by sharpening focus on topics that have so far eluded psychological scientists, thus contributing to the development of evidence-based recommendations that will better promote human flourishing.