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Models and Presuppositions

In Science and Theology

(This paper was presented at The XIIth European Conference on Science and Theology, Sigtuna, Sweden, May 3, 2008)

John Byl, Ph.D.

The world in which we live is very complex. To simplify the study of reality, both science and theology often make use of models. This paper examines the role of models in acquiring scientific and theological knowledge. We shall examine particularly the connection between models and worldview presuppositions. This subjective link suggests that conflicts between science and theology may be largely resolved by adopting worldview assumptions that are sufficiently broad to support a mutually complementary science and theology.


1. Models in science and theology

The word "model" has a variety of meanings. In science, we shall be concerned primarily with what Ian Barbour (1974:29) terms theoretical models. A theoretical model is a framework of ideas and concepts from which we interpret our observations and experimental results. They are imaginative mental constructs invented to account for observed phenomena. Often they involve mechanisms or processes, postulated by analogy with more familiar phenomena (e.g., the billiard ball model for gas, Maxwell’s mechanical model for electro-magnetic forces, etc.). Especially in physics, theoretical models often generate mathematical equations that quantify the model, thus enabling precise predictions and applications. In its highest form, a physical model is expressed as a set of natural laws (e.g. Newtonian mechanics, general relativity or quantum mechanics).

Theoretical models are useful also in representing aspects of reality that are hard to visualize. In that respect they function as metaphors and analogies, serving as conceptual frameworks that can lead to important physical discoveries. They are symbolic representations of physical systems, aiming to represent the underlying structure of the world. The physical theory should be based on a minimum number of physical assumptions, and, ideally, should broaden our understanding of the physical phenomenon. In this paper, for purposes of simplicity, we shall not distinguish between theories and models.

In short, in science a model is taken to be a simplified representation, or analogy, that often makes use of mathematical equations. We thus distinguish between observational data, inferences made from the data, and theoretical models that extend and explain the data. Although models can be very useful in making predictions, their chief use is to help us understand the world.

Theological knowledge exhibits a structure similar to scientific knowledge.  In (biblical) theology we similarly distinguish between religious experiences and biblical assertions, inferences made from these, and theological models that explain and extend. As examples of theological models Barbour (1974:154) enumerates various models for Christ's atonement: penal substitution, sacrificial victim, liberator and moral example. In ethics, the servant model may clarify how Christians are to behave. Marc Cortez (2005:349) notes that in contextual theology we have a translation model, which focuses on articulating absolute biblical truths in a culturally intelligible manner, and a praxis model, which is more concerned with transforming these truths into action. According to Cortez (2005:360), "The purpose of a theological model is to explicate, clarify, and extend the conceptual content and implications of a paradigm." A primary value of theoretical models is that of "suggesting potentially fruitful lines of inquiry and the making of new discoveries" (Cortez 2005:354).

Thus, in both science and theology, models may be metaphors, analogies, or simplified representations of a limited aspect of reality. They serve as conceptual frameworks that can lead to further insights and discoveries.


2. The power of models.

Models can be extremely useful, particularly in science. Consider, for example, quantum mechanics as a model for atomic matter or general relativity as a broad framework for mechanics. The power of such scientific models is due to their mathematical quantization, which enables precise predictions and applications. Here scientific models have a distinct edge over theological models, where mathematics rarely comes into play.

The huge success of scientific models is remarkable. Eugene Wigner (1960), a Nobel-prize winner in physics, exclaimed about "the unreasonable effectiveness of mathematics in the science". He concluded that the amazing applicability of mathematics to the physical world is a mysterious, undeserved and inexplicable gift. More recently, Mark Steiner (1998) noted the major role played by human mathematics in the discovery of new phenomena. The astounding success of mathematical models suggests that the universe has an objective, underlying mathematical structure. This, in turn, suggests that theoretical models reflect, to at least a limited degree, a deeper reality that goes beyond mere appearances.


3. The fallacy of misplaced concreteness

Nevertheless, we must be careful not to over-rate theoretical models. Consider, for example, Roger Penrose's notion that the mathematical world is the primary, real world, the physical world and the world of our consciousness being mere shadows of it (1994: 417). Or Oxford chemist Peter Atkins' assertion that the ultimate reality is mathematics and that the universe originates from a mathematical set of points (Atkins 1994: 128). Such views illustrate a peril facing scientists, particularly mathematical physicists. This danger is what Keith Ward (1996:28) calls "the fallacy of misplaced concreteness": one is so impressed by the beauty and predictive power of one's theoretical model of reality that one comes to see one's model as the true reality. The fallacy is to mistake the abstract model for the concrete reality. Abstractions, such as Hamiltonian vector fields in multi-dimensional phase space, then become the reality, whereas one's actual concrete experiences, upon which the model was initially based, are relegated to the realm of mere subjective illusion.  

This fallacy occurs in its strongest form in materialist reductionism, which attempts to explain all of reality--including our minds--in terms of purely physical laws. For example, the Nobel prize-winning biologist Sir Francis Crick opens his book The Astonishing Hypothesis with:

“The Astonishing Hypothesis is that “You”, your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behaviour of a vast assembly of nerve cells…” (Crick 1994:3)

This implies that the ultimate reality consists only of atoms and their interactions, the real “you” being just an illusion caused by nerve cells. This curt dismissal of our "self" as a real entity clashes starkly with our strongest, most intimate, conscious experiences.It is thus essential that one must never forget the proper limits of models. Models of the universe function like maps of landscapes. A map is just an abstract representation of the landscape and, as such, should never be mistaken for the real thing.


4. The role of worldviews

A further significant feature of models is that the same data can often be explained by many competing models. For example, in mechanics, various forms of post-newtonian approximations have the same observational consequences as general relativity. Also, a very successful theoretical model, such as quantum mechanics, may be given a variety of different philosophical and physical interpretations. The construction and interpretation of models involves a significant element of creative imagination. Models are not simply deduced from the data. Rather, the criteria for ranking models are often largely extra-observational, based primarily on subjective, philosophical factors.

Human knowledge has a perspectival aspect. All our experiences are filtered through a worldview grid, which reflects our most basic beliefs about such things as ontology, epistemology, and God. Our worldview presuppositions determine what we consider to be real and what we take as only apparent; they determine what we accept to be genuine knowledge. Consequently, our choice of models is strongly influenced by our worldview presuppositions: we prefer models that best reflect our fundamental beliefs about how the universe functions. Models thus bridge the gap between our worldview beliefs and our experiences of reality. Establishing such theoretical connections serves to increase the plausibility of our worldview. These factors are discussed in more detail by G.Y. Nieuweland (2000).


5. Resolving incompatible knowledge claims

Models offer a simplified view of reality; they are constructed to facilitate the exploration of limited aspects of reality. For example, models in physics are incomplete in that they cannot deal with such topics as ethics, beauty, meaning and purpose. Models in theology, on the other hand, primarily concern our understanding of God and our relation to Him, rarely involving physical reality. Models in science and theology offer largely complementary descriptions of reality.

However, science and theology do have points of contact. One of these concerns causality. Models in physics provide a causally incomplete description of reality because they ignore human intentionality. For example, the laws of physics cannot predict when human choices--based on ethical considerations--will detonate a nuclear bomb. This problem becomes even larger when we consider divine action in the world. Is God's action limited to merely upholding regularities or does it include also supernatural intervention, whether through unobservable quantum choices or large-scale miracles? 

Here knowledge claims of science and theology may overlap. How are these to be resolved? We recall the various levels of knowledge: (1) observational data (and biblical assertion), (2) inferences from these, and (3) theoretical models. Since scientific models are generally more mathematically sophisticated than theological ones, and thus generally more precise, scientific models seem to carry more weight. Further, direct observational data surely outweigh biblical assertion. From such considerations many conclude that scientific claims should always trump theological ones. It is not obvious, however, whether that should necessarily be the case when biblical assertions are pitted against scientific models.

To take a specific example, consider the eschatological resurrection of all humans. Most Christians believe this doctrine to be a clear biblical assertion (cf I Cor.15). Wolfhart Pannenberg (1981) raised the question as to how this can be reconciled with the apparently contrary predictions of Big Bang cosmology. Hans Kűng resolves the conflict in favor of Big Bang cosmology by demoting the biblical eschatology to metaphorical images that should not be taken literally (Kűng 2007:199-205). This, however, seems to rob Christianity of its central hope.

John Polkinghorne and R.J. Russell, on the other hand, choose to reject Big Bang cosmology. Russell defends his choice by asserting that the challenge is not really from science but, rather, from the philosophical assumption of "nomological universality"--that the same laws of nature that govern the past will govern the future. Russell counters this assumption by contending that a strong case can be made on philosophical grounds that the laws of nature are only descriptive of what has thus far occurred, rather than prescriptive of what must necessarily always happen. Indeed, this was argued already by David Hume in his "Treatise of Human Nature" (1739).

Further, Russell claims on theological grounds that the processes that science describes do not obey autonomous "laws of nature" but are the results of God's ongoing action as Creator. The regularity of nature is the result of God's faithfulness but God is free to act in radically new ways in the ongoing history of the universe, such as in the Easter event. Hence the predictions of the laws based on God's prior action need not apply in the future. In other words, the predictions of all scientific laws hold only "all else being equal". If God, at the eschaton, chooses to act in radically new ways to transform the world then all else is not equal (Russell 2002: 19). Polkinghorne (2000:39) likewise argues for a future "discontinuous change in natural law."

This approach challenges methodological naturalism, the rule that science should limit itself to purely natural explanations of natural events. Since we generally cannot predict when the supernatural may intervene, methodological naturalism is a plausible working assumption for science. It is, however, only an assumption. Thus scientific inferences based on it are valid only to the extent that there has in fact been no relevant supernatural interaction. Metaphysical naturalism, the further naturalistic assumption that there are no supernatural events is at heart a theological assumption, in that it concerns the attributes of God.

The clash between contrary knowledge claims is here not between science and theology as such but, rather, between two competing worldviews: naturalism versus theism. These have quite different presuppositions regarding such fundamentals as ontology, causation, epistemology and God.

How are we to judge between these worldviews? A worldview seeks to explain all of reality; hence its set of worldview presuppositions should be broad enough to provide a coherent framework for a mutually complementary science and theology. As stressed by David Griffin (2000:99), one's worldview must be able to account for such things as common sense, the activity of scientists and theologians, and the acquisition of knowledge. The concept of knowledge entails the existence of a purposeful knower, a reliable mind, objective truth, and absolute rational values and logical laws. Any viable worldview must therefore accommodate these. A major weakness of naturalism-- particularly its most common, materialist form--is its difficulty in accounting for such things as logical absolutes, ethical norms, and the power of mind over matter. Consequently, the rational defense of some forms of naturalism (e.g., the materialist reductionism of Francis Crick) is self-refuting to the extent that such defense implies the existence of entities (e.g., a purposeful mind) that the worldview itself explicitly denies. Theism, on the other hand, provides richer metaphysics and epistemology that can credibly explain the full range of reality, including particularly the nature and condition of humanity.


6. Conclusions

Models and presuppositions play an important role in both science and theology. However, they also have limitations, since they are ultimately constructed, chosen, and interpreted on the basis of worldview presuppositions. Our worldview presuppositions must be broad enough to encompass both science and theology. What are commonly perceived as clashes between science and theology are often clashes between opposing worldviews. Worldviews must be judged as to how well they account for all of reality.



Atkins, Peter1994. Creation Revisited. Harmondsworth: Penguin.

Barbour, Ian G. 1974. Myths, Models and Paradigms. New York: Harper & Row.

Cortez, Marc 2005. "Contextual theology and the nature of theological discourse". Westminster Theological Journal 67:347-362.

Crick, Francis. 1994. The Astonishing Hypothesis. New York: Touchstone.

Griffin, David R. 2000. Religion and Scientific Naturalism. Albany, NY: SUNY Press.

Kűng, Hans 2007. The Beginning of All Things. Trans. by J. Bowden. Grand Rapids: Eerdmans.

Nieuweland, G.Y. 2000. "Do Mathematical Models Tell the Truth?" Nieuwe Archief voor Wiskunde 5/1: 406-411 and 5/2: 59-64.

Penrose, Roger 1994. Shadows of the Mind. London, UK: Vintage.

Pannenberg, Wolfhart 1981. "Theological Questions to Scientists" in The Sciences and Theology in the Twentieth Century, ed. A. R. Peacocke. Notre Dame: University of Notre Dame Press.

Polkinghorne, John 2000. "Eschatology: Some Questions and Some Insights from Science" in The End of the World and the Ends of God: Science and Theology and Eschatology, eds. John Polkinghorne and Michael Welker. Harrisburg, Trinity Press International.

Russell, Robert John 2002. “Bodily Resurrection, Eschatology and Scientific Cosmology" in Resurrection: Theological and Scientific Assessments, eds.Ted Peters et al. Grand Rapids: Eerdmans.

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Ward, Keith 1996. God, Chance and Necessity.  Oxford: One World.

Wigner, Eugene 1960. "The Unreasonable Effectiveness of Mathematics", Communications on Pure and Applied Mathematics 13: 1-14.



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