For Further Reading

Chapter 5

Models and Analogies in Science and Religion

How do we visualize complex systems? How do we form mental images of unobserved entities as we try to understand them and then work out ways of exploring them further? One of the most intriguing aspects of the interface between science and religion is the use of ‘models’ or ‘analogies’ as visual aids to depict complex entities – whether the entity in question is an atomic nucleus or God. The philosopher of science Ernan McMullin thus points to scientific models as a way of representing and organizing observations of the world, while pointing towards the hidden structures of the world that underlie these observations.

Scientists construct theories which explain the observed features of the physical world by postulating models of the hidden structure of the entities being studied. This structure is taken to account causally for the observable phenomena, and the theoretical model provides an approximation of the phenomena from which the explanatory power of the model derives.

A similar point is made by the philosopher of science Peter Godfrey‐Smith, who points out that the scientific use of models often involves developing deliberate simplifications which are designed to make problems more tractable.

A model is an imagined or hypothetical structure that we describe and investigate in the hope of using it to understand some more complex, real‐world ‘target’ system or domain. Understanding is achieved via a resemblance relation, that is, some relevant similarity, between the model and the real‐world target system.

Godfrey‐Smith's point is that models are not meant to be exact representations of a complex entity or system; they resemble it at points, and are thus able to stimulate the formulation of research questions and methods designed to allow a deeper understanding of the more complex reality – and hence the development of more reliable models. Yet these models do not need to be physical analogies – such as the famous ‘solar system’ model of the atom, developed by Ernest Rutherford in the early twentieth century – as some scientific models take the form of mathematical representations.

In this chapter, we shall explore the different ways in which these ‘visual aids’ are developed and deployed in science and religion. Are they simply helpful ways of visualizing the invisible and inaccessible? We need to be able to imagine such things as electrons, protons, and atomic nuclei – and God. Or do they also generate a research programme, thus opening up new lines of inquiry, exploration, and understanding?

Models serve an important psychological function, in that they allow human beings to discern rational sense within what often appears to be a formless and disordered world. In 1897, the psychologist William James highlighted the perceived human need to find a way of overcoming the messiness and conceptual fluidity of the world by the use of models and theories, in order to bring its (assumed) rationality into sharper focus.

All the magnificent achievements of mathematical and physical science – our doctrines of evolution, of uniformity of law, and the rest – proceed from our indomitable desire to cast the world into a more rational shape in our minds than the shape into which it is thrown there by the crude order of our experience. The world has shown itself, to a great extent, plastic to this demand of ours for rationality.

Yet James hints that this perception of order, reinforced through the selective use of models, may originate as much in our desire to find such rational structures as in what the universe itself discloses.

The representation of reality in science and religion is often framed in terms of models, metaphors, and analogies. So do these three categories of representation represent different points on an essentially continuous spectrum of intellectual possibilities, or are they distinct approaches to the process of imaginative representation? Might scientists or theologians be misled in their thinking, by confusing the categories of metaphor and analogy – assuming that there is a genuine difference between them in the first place? Several scholars have attempted to clarify the distinct features of models, metaphors, and analogies, and how these might affect their use in science and religion. The philosopher of science Daniela Bailer‐Jones, for example, points out how these three categories are employed across disciplines, making it difficult to establish their precise nature and function. Bailer‐Jones suggests that a model can be thought of as ‘an interpretative description of a phenomenon that facilitates access to that phenomenon’. This highlights the heuristic function of a model, and helps us understand that, by focusing only on certain aspects of the phenomenon, it yields at best partial access to the phenomenon.

Bailer‐Jones considers a metaphor to be ‘a linguistic expression in which at least one part of the expression is transferred from one domain of application (source domain), where it is common, to another (target domain) in which it is unusual, or was probably unusual at an earlier time when it might have been new’. This emphasizes the creative and imaginative aspects of a metaphor, and also allows us to understand how metaphors can lose their innovative force over time. In the case of an analogy, Bailer‐Jones points to the importance of a resemblance between relations across two different domains, helping to make the transition from an unfamiliar or new phenomenon to a familiar or more readily grasped concept.

In this chapter, we shall consider the use of models, metaphors, and analogies in science and religion. It must be made clear from the outset that there is no general agreement on what the terms model, metaphor, and analogy mean, and how they are to be distinguished from each other. To explore this issue, we shall consider how models, metaphors, and analogies are developed and used in both science and theology, before turning to explore how Ian Barbour applied them to the specific case of science and religion.

The Use of Models in the Natural Sciences

Models are generally understood as ways of thinking about, or representing, complex systems, which both aid visualization of the system and also provide a provisional way of understanding the system which is based on something that is already familiar to us. This allows us to draw tentative inferences and to form testable hypotheses about the more complex system on the basis of the simpler or more familiar model.

As will be evident from the brief analysis presented above, the philosopher of science Daniela Bailer‐Jones developed a coherent understanding of models, metaphors, and analogies, although there are clear zones of overlap between these categories. Yet her views might not be shared by scientists and theologians, given the significant degree of definitional ‘fuzziness’. In a series of interviews with research‐active scientists in the United Kingdom, Bailer‐Jones invited them to set out what they understood scientific models to be, and how they considered them to function in scientific research programmes. These interviews point to a considerable variety of usage of the concept of model.

In general terms, Bailer‐Jones found that scientists tend to think of models as ‘simplifications’ of the system that is being modelled. For the biogeochemist Nancy Dise, this is a central element of her understanding of a scientific model:

Generally I would consider a model a simplification of the system, incorporating the most – what you consider to be the most – important elements of that system. So you are describing the system, but you are not describing it in all of its detail.

Bailer‐Jones's interviews with working scientists led her to draw five general conclusions about how scientists understood the role of models in their research, as follows:

As Bailer‐Jones's interviews make clear, natural scientists regularly develop and use models to depict at least certain aspects of complex systems. A model is understood to be a simplified way which has been developed by researchers with the specific purpose of representing a complex system, which allows its users to gain an increased understanding of at least some of its many aspects. These models are invented, deliberately constructed to enable their users to visualize and interpret, if only in part, a complex system, and make predictions about its behaviour.

One of the most familiar of these models is the ‘solar system’ model of the atom, which was developed in December 1910 by the Cambridge physicist Ernest Rutherford. In view of the importance of this model, we shall consider the circumstances that led Rutherford to develop it. The initial discovery that motivated Rutherford to develop his ‘solar system’ model of the atom was made by his collaborators Hans Geiger and Ernest Marsden in 1909. To understand this experiment, we need to set it in its proper context.

Rutherford's breakthrough arose through his studies of radioactivity – the process in which unstable atomic nuclei spontaneously decompose to form more stable nuclei by the release of energy and subatomic particles. One of Rutherford's most important discoveries took place in 1899, when he showed that radioactive elements – such as radium – emitted what he referred to as alpha rays, beta rays, and gamma rays. It was later realized that the so‐called ‘alpha rays’ were really positively charged helium nuclei, ‘beta rays’ were negatively charged electrons, and ‘gamma rays’ were high energy electromagnetic radiation.

In 1904, following the discovery of the electron, the British physicist J. J. Thomson proposed what has come to be known as the ‘plum pudding’ model of the atom. Thomson suggested that atoms were analogous to the familiar English delicacy of a ‘plum pudding’ (American readers might like to substitute a blueberry muffin at this point), in which the negatively charged electrons (the plums or blueberries) were dispersed throughout a positive spherical matrix (the pudding or muffin as a whole). Thomson's model successfully accommodated the two empirical findings about atoms that were known at this time: that electrons are negatively charged particles and that atoms have no overall electric charge. The concept of a dense central ‘atomic nucleus’ was not known to Thomson. For Thomson, the atom consisted of a round solid area, which was positively charged. Electrons were embedded within this solid area. The overall negative charge of the electrons was precisely balanced by the overall positive charge of the solid area, so that the atom itself possessed no overall charge.

In a series of experiments between 1908 and 1913, Rutherford and his junior colleagues Hans Geiger and Ernest Marsden looked at how positively charged alpha particles (the term ‘rays’ had been dropped by this stage) were scattered when they impacted gold atoms. A beam of alpha particles was projected at strips of gold leaf that were only a few atoms thick, and the extent of their deflection from their original line of motion measured. On the basis of Thomson's model of the atom, it was predicted that the stream of alpha particles would be consistently deflected from their original trajectories by a few degrees. Both alpha particles and the atomic nucleus were positively charged. When an alpha particle came close to the nucleus, it would experience electrostatic repulsion, and so would be deflected.

Geiger and Marsden, however, found that most alpha particles passed through the gold foil with hardly any deflection, whereas a small number (about 1 in 8000) were deflected by very large angles. Rutherford was astonished by this result and realized that a new way of thinking about the structure of the atom was needed.

It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15‐inch shell at a piece of tissue paper and it came back and hit you. … I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive centre, carrying a charge.

Rutherford realized that this completely unexpected result meant that the atom's mass was not uniformly dispersed throughout the atom, but was highly concentrated in an extremely small positively charged region (the nucleus), which was surrounded by electrons. The atom did not consist of a uniformly dense substance, but had a super‐dense core surrounded by empty space. A way of visualizing the atom was required, which would help experiments to be devised to further clarify the structure and properties of the atom.

Rutherford's new model of the atom portrayed the nucleus as its centre of mass, with electrons dispersed in space around it – analogous in some ways to the sun as the centre of the solar system. Imagining an atom as a miniature solar system helped to visualize the structure of the atom, as this was revealed by the deflection of alpha particles. The atom consists of a central body (the nucleus), in which practically the entire mass of the atom is concentrated. Electrons orbit this nucleus, in much the same way as the planets orbit the sun. Whereas the orbits of the planets were determined by the gravitational attraction of the sun, Rutherford argued that the orbits of the electrons were determined by the electrostatic attraction between the negatively charged electrons and the positively charged nucleus. The model was visually simple and easy to understand and offered a theoretical framework which explained at least some of the known behaviour of atoms at this time.

Once a model has been constructed and tested, it can be developed in such a way that it includes some more complicated features of the system which were initially ignored in constructing the model. To help us reflect on this issue, we shall consider one of the simplest and most familiar scientific models – the ‘kinetic model’ of gases.

The Kinetic Model of Gases

The behaviour of gases was studied in some detail from the seventeenth century onwards, particularly by the English physicist Robert Boyle and the French physicist and inventor Jacques Charles (whose inventions included the hydrogen balloon in 1783). A series of experiments examined the way in which gases behaved when their pressure, volume, and temperature were changed. In general terms, the volume of a gas is inversely proportional to its pressure and directly proportional to its temperature, expressed in kelvin.

Detailed experiments by Boyle and Charles showed that the behaviour of gases could be described in terms of a series of laws, which applied to all gases at low pressures, irrespective of their chemical identity. The two most famous such laws are known as ‘Boyle's law’ and ‘Charles' law’, and they can be formulated as follows:

where p is the pressure of the gas, V its volume, and T its temperature, expressed in terms of the temperature scale devised by Lord Kelvin according to which 0° centigrade is 273.15 kelvin. (This scale thus identifies the temperature of ‘absolute zero’ as −273.15 °C.) The ‘perfect gas equation’, which combines these two laws and other observations, can be formulated as:

where R is the gas constant (8.31451 J K⁻¹ mole⁻¹) and n the number of moles of gas present. This equation holds universally, irrespective of the identity of the gas in question.

So how can this behaviour be explained? The ‘kinetic model’ of gases offers a way of visualizing an ideal gas, allowing its behaviour to be predicted and understood. The term ‘kinetic’ comes from the Greek term kinesis (‘movement’) and refers to the key feature of this model of a gas – namely, that gas molecules move around and are not static. The ‘kinetic model’ is grounded on three basic assumptions:

In effect, the model suggests that we think of gas molecules as pool or billiard balls, moving around within a container, and constantly colliding with its walls. It is quite easy to use this model to predict how pressure, volume, and temperature are related. For example, the pressure on the container can be calculated in terms of the rate of change of momentum of gas molecules. The gas laws noted above can be derived theoretically on the basis of this model of gases, suggesting that the kinetic theory is a good basic model for these systems.

The model is very simple, and thus does not take account of some more complex features of the behaviour of gases. For example, it assumes that the volume occupied by gas molecules is negligible, so that the portion of the overall gas volume occupied by those molecules can be disregarded in calculations. While this is true at low pressures, it becomes a more serious complication at higher pressure. The model also ignores inter‐molecular collisions and forces (which are insignificant at low pressure) and focuses on the way those molecules impact on the walls of the container. The terms ‘perfect gas’ or ‘ideal gas’ are used to make it clear that this theoretical neatness is not actually observed in real gases!

This model can be made more sophisticated, to allow for the more complicated aspects of the system to be modelled. As noted, the model does not take account of the fact that gas molecules have a definite size. This fact can be ignored at low pressures; at high pressures, however, the volume occupied by the gas molecules begins to become significant. This can be incorporated into the mathematical modelling of the system as follows. Earlier, we saw how the behaviour of gases could be predicted using the following formula:

This formula assumes that the gas molecules are of negligible size. A small adjustment to the formula allows it to take account of the finite size of the molecules. If b is the actual volume occupied by the gas molecules, then the behaviour of that gas is given by the formula:

This pattern is a basic feature of the development and application of scientific models. The basic features of the pattern that emerges can be set out as follows:

Models are clearly useful ways of visualizing or understanding complex systems. However, they can be misunderstood. Two misunderstandings can arise through the use of models in the natural sciences. First, some assume that models are identical with the systems with which they are associated. Rutherford's model of the atom helps us understand some of the features of atoms – such as the concentration of mass in a very small space – if we think of them as miniature solar systems, with electrons orbiting a central nucleus like planets orbiting the sun. Yet this is simply a helpful visual representation of an atom, which assists explanation and interpretation. It is to be taken seriously (in that it clearly bears some relation to the system that is being modelled); it is not, however, to be taken literally.

The second error that can be made is to assume that every aspect of the model is necessarily present in the system being modelled. The model and system that is being modelled will resemble each other in some ways, but not in others. To help us understand this second point, we shall consider an excellent example of this problem – the assumption that, since sound seemed to be a useful analogy for light, and sound required a medium through which it would travel, this was also true of light.

Complementarity: Light as Wave and Particle

Eighteenth‐century physicists disagreed about the nature of light. Some considered it to be beams of tiny particles; others considered light to be a form of wave motion. In his Optics (1704), Newton took the view that a beam of light consisted of a series of rapidly moving small particles or ‘corpuscules’ (from the Latin term corpuscula, ‘small bodies’). The reflection of light by a mirror was analogous to throwing balls at a wall, and observing them bounce back. The Dutch physicist Christiaan Huygens disagreed, arguing that light was made up of waves, and that some aspects of its behaviour were best accounted for on the basis of this model.

Newton's particle theory of light came to dominate physics during the eighteenth century. It led to two important predictions. The first of these predictions was made by the English natural scientist John Mitchell in a paper presented to the Royal Society in 1783. Since light consisted of a beam of particles which would be attracted by the gravitational pull of a star, Mitchell argued that some stars might be so massive that their gravitational forces would prevent beams of light from ever leaving their surfaces. Like Newton's famous apple, these particles of light would simply fall to the ground. Mitchell thus proposed the existence of ‘dark stars’, which could not be seen because light was unable to break free from the force of their gravity. Mitchell's calculations suggested that this would happen if the star was 500 times the mass of our sun. Today, these dark stars are known as ‘black holes’.

Second, if light consisted of a beam of particles, Newton's theory of gravitation predicted that these particles would travel in a straight line, unless they were deflected by gravity. In 1804, the German mathematician Johann Georg von Soldner published a paper calculating the amount by which a beam of light would be deflected by the gravitational field of a star – such as the sun. Von Soldner concluded that the predicted effect was far too small to be observed by the instruments of his time, so nobody followed through on this.

Yet during the nineteenth century, a growing body of experimental evidence suggested that light was better understood as a wave motion. In 1801, the English physicist Thomas Young devised a ‘double slit’ experiment that suggested that light behaves like ripples or waves on a pond of water. By the middle of the nineteenth century, this way of thinking about light had gained the ascendancy. Light, like sound, was understood as a form of wave motion.

Many physicists now pressed home the analogy between light and sound, and drew conclusions from this which are now regarded as unsafe and overextended. Sound requires a medium – such as air or metal – through which to travel. If a source of sound – such as a ringing bell – is placed in a glass vessel, and the air is pumped out, the intensity of the sound will gradually decrease and finally vanish. Sound has to travel through something, and cannot travel in a vacuum. Many physicists concluded that, since sound needed a medium to travel through, and light was analogous to sound, then light had to travel through something as well. But what? The term ‘luminiferous ether’ (‘luminiferous’ means ‘light‐bearing’) was used to refer to this invisible substance that was believed to fill empty space, and hence allow light to travel through space.

Yet this aspect of the analogy turned out to be incorrect. Light does not need to travel through any medium. There is no ‘ether’. The Michelson–Morley experiment of 1887 was designed to detect ‘ether drift’ – that is, the motion of the ether with respect to the earth as the earth moved through space. It failed, although it took some time for the implication of the negative result to be fully accepted and understood within the scientific community. Either the ether was totally at rest with regard to the movement of the earth, or it did not exist. In the end, it had to be accepted that there was no experimental support for the existence of ‘luminiferous ether’. At least in this respect, there was a fundamental distinction between light and sound.

Everything changed in 1905, when Albert Einstein offered a brilliant theoretical account for the photoelectric effect, which suggested that light had to be considered as behaving as particles under certain conditions. Einstein was careful to present this idea instrumentally – in other words, that it was a helpful way of thinking about light. Yet it rapidly morphed into a realist account of light as a stream of what later came to be known as ‘photons’.

The ‘photoelectric effect’ was first observed in 1887 by the German physicist Heinrich Hertz, and investigated more thoroughly later by Hertz's colleague Philipp Lenard. In an article of 1902, Lenard showed that if a beam of light was shone on certain metals, it was able to eject electrons from the surface of some metals. Lenard's experiments found that the rate of emission of electrons from the surface of the metal was directly proportional to the intensity of light falling on it. The brighter the light, the more electrons were dislodged from the metal surface. Yet Lenard also found that the brightness or intensity of the beam of light falling on the metal surface seemed to have no effect on the energy of these emitted electrons. The electrons emitted through exposure to a very bright light turned out to have the same energy as those emitted through exposure to a very dim light. Furthermore, photoelectrons were only emitted if the frequency of the light exceeded a threshold frequency, which varied from one metal to another.

These observations made no sense within existing understandings of the nature of light. Einstein argued that the photoelectric effect was best understood in terms of a collision between an incoming particle‐like bundle of energy (that is, light) and an electron close to the surface of the metal. The electron could only be ejected from the metal if the incoming packets of light (or particle‐like bundles of energy, now known as ‘photons’) possessed sufficient energy to dislodge this electron. The critical factor which determines whether an electron is ejected is not the intensity of the light, but its frequency. Furthermore, if the energy of the incoming bundle of light is less than a certain quantity (the ‘work function’ of the metal in question) no electrons will be emitted, no matter how intense the bombardment with light. It was a brilliant piece of analysis, and led to Einstein being awarded the Nobel Prize in Physics in 1921 ‘for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.’

Einstein's suggestion met with intense opposition before the First World War, not least because it appeared to involve the abandonment of the prevailing classical understanding of the total exclusivity of waves and particles: something could be one, or the other – but not both. Gradually, Einstein's view gained acceptance, so that light is now thought of in terms of ‘photons’, which exhibit the properties of both waves and particles. The behaviour of light is sometimes best explained as a particle, and sometimes as a wave. So how was the behaviour of light to be expressed in terms of its ontology – in other words, the nature of light?

By the 1920s, it was clear that the behaviour of light was such that it required to be explained on the basis of a wave model in some respects and a particle model in others. The work of Louis de Broglie suggested that even matter had to be regarded as behaving as a wave in some respect. These theories led the Danish theoretical physicist Niels Bohr to develop his concept of ‘complementarity’. For Bohr, the classical models of ‘waves’ and ‘particles’ were both required to explain the behaviour of light and matter. This does not mean that electrons ‘are’ particles or that they ‘are’ waves; it means that, whatever they ultimately are, their behaviour may be described on the basis of wave or particle models, and that a complete description of that behaviour requires two mutually exclusive ways of representing them to be used.

This is not an intellectually shallow and lazy expedient of affirming two mutually exclusive options instead of attempting to determine which is the superior. As has been stressed, it was – for Bohr – the inevitable outcome of a series of critical theories and experiments which demonstrated the impossibility of representing the situation in any other manner. In other words, Bohr held that the experimental data at his disposal forced him to the conclusion that a complex situation (the behaviour of light and matter) had to be represented by using two apparently contradictory and incompatible models. This principle of holding together two apparently irreconcilable models of a complex phenomenon in order to account for its behaviour is known as the ‘principle of complementarity’.

Analogical Reasoning: Galileo and the Mountains of the Moon

Galileo Galilei is widely – and rightly – regarded as one of the most significant scientific researchers of the early modern period and is particularly associated with major astronomical discoveries through the use of the newly invented telescope. Galileo was the first to observe the four major moons of the planet Jupiter during the winter of 1609–1610, the dense starry structure of the Milky Way, and the mountains of the moon.

Yet these familiar statements need further exploration. Did Galileo really observe mountains on the moon? After all, his telescope only permitted him to study the surface of the moon in two dimensions. What Galileo actually observed through his telescope was changing patterns of light and darkness on the surface of the moon, which he subsequently interpreted as evidence for the existence of mountains, analogous to those found on earth. He interpreted his observations of the changing patterns of light and darkness on the face of the moon as the result of the changing position of the sun as the moon orbited the earth, so that the shadows cast by the lunar mountains varied in extent and intensity over the period of moon's orbit around the earth.

In a careful study of the logical structure of Galileo's conclusion that he was observing mountains on the surface of the moon, and not simply shifting patterns of light and darkness, the historian and philosopher of science Marta Spranzi identified the core elements of the analogical argument that led him to these conclusions.

Galileo sets out this argument in detail in his Starry Messenger (1610), noting how the patterns seen on the surface of the moon appear to be ridges, illuminated in different ways by the light of the sun.

A great number of small darkish spots, entirely separated from the dark part, are distributed everywhere over almost the entire region [of the Moon] already bathed by the light of the Sun. … All these small spots just mentioned always agree in this, that they have a dark part on the side toward the Sun while on the side opposite the Sun they are crowned with brighter borders like shining ridges.

This pattern, Galileo argues, is already familiar to use from terrestrial mountains.

We have an almost entirely similar sight on Earth, around sunrise, when the valleys are not yet bathed in light but the surrounding mountains facing the Sun are already seen shining with light. … Just as the shadows of the earthly valleys are diminished as the Sun climbs higher, so those lunar spots lose their darkness as the luminous part grows. … Now on Earth before sunrise, aren’t the peaks of the highest mountains illuminated by the Sun's rays while shadows still cover the plain?

Galileo referred to the level areas of the lunar surface as ‘seas’. Again, his process of arguing is analogical. The nearest things on earth to these lunar features are the oceans. However, Galileo made the limits of this analogy clear: there was no reason to suppose that these lunar ‘seas’ contained water. Analogies work within limits; it is important to identify and respect these.

This argument from analogy is integral to the scientific method. Puzzling patterns in the natural world can be explained, at least in part, by proposing an analogy with a familiar set of observations. This process underlies Darwin's proposal for a process of ‘natural selection’ within the biological realm, in some way paralleling the process of ‘artificial selection’ that was widely used in British agriculture in the 1850s. In view of its importance, we shall explore this in greater detail in the following section.

Using Scientific Models Critically: Darwin's Principle of Natural Selection

In his Origin of Species (1859), Charles Darwin proposed ‘natural selection’ as the underlying process which explained the phenomenon of biological evolution. Darwin's genius lay not in showing that biological evolution occurred, but in suggesting a mechanism that lay behind it. The way in which Darwin developed the notion of ‘natural selection’ is of particular interest, as it illustrates clearly some of the issues which arise through the use of analogies or metaphors in developing scientific theories. Darwin saw his task as being that of making sense of the bewildering diversity of plants and animals, both living and extinct, which had generally been a source of mystery to those who had gone before him.

The first chapter of Origin of Species examined ‘artificial selection’ – the way in which professional stockbreeders and market gardeners created new forms of domestic livestock and plants. Darwin then argued that this process of ‘artificial selection’, which would have been familiar to his readers, was analogous to a process of ‘natural selection’ that Darwin believed was taking place within nature itself over extended periods of time. (The term ‘natural selection’ first appears in Darwin's writings after March 1840, when he read a standard manual of cattle management entitled Cattle: Their Breeds, Management and Diseases, which explained the methods and results of artificial selection.)

Darwin introduced the term ‘natural selection’ as a metaphorical and non‐literal means of referring to a process which he believed to be the most convincing means of explaining the patterns of diversity he observed within nature.

All my notions about how species changed derive from long‐continued study of the works of agriculturalists and horticulturalists; and I believe I see my way pretty clearly on the means used by nature to change her species and adapt them to the wondrous and exquisitely beautiful contingencies to which every living being is exposed.

This passage is significant for two reasons. First, it makes it clear that Darwin clearly saw an analogy between the familiar process of ‘artificial selection’ and the inferred or proposed – but unobserved and intrinsically unobservable – process of natural selection. Second, it also implies the notion of a conscious process of selection. At points, Darwin speaks explicitly of nature changing her species and adapting them. The analogy is apparently being allowed to imply that the active selection of the animal or plant breeder is somehow paralleled within nature itself. This is certainly suggested by his frequent references to ‘nature’ as an agent who actively ‘selects’ good variants.

But is this analogy being pressed too far? Can one speak of nature ‘selecting’ anything, when ‘selection’ would seem to imply purpose, choice, and intelligence? Darwin's colleague Alfred Russell Wallace was one of many who was alarmed at Darwin's apparent suggestion of an active process of selection on the part of a personified nature, which was thus understood to have the powers of rational analysis and an intended goal.

The analogy of ‘natural selection’ developed by Darwin transfers the notions of intention, active selection, and ultimate purpose from the model (the established procedures of artificial selection) to what the model is meant to explain or illuminate (the natural order). At both the verbal and conceptual level, the anthropomorphic concept of ‘purpose’ is retained, despite Darwin's apparent intention to eliminate any notion of purpose or deliberate design. Darwin himself came to realize the dangers of his somewhat anthropomorphic manner of speaking about ‘nature’, and added a preface to the third edition of Origin of Species (1861) in which he stressed that the idea of ‘natural selection’ did not imply that nature chose what it wished to produce.

Darwin's use of the analogy of ‘natural selection’ helpfully illustrates both the positive and negative aspects of an argument from analogy. Positively, the analogy allows a complex situation to be illuminated or partly understood by an appeal to a known and understood event, process, or action. Yet negatively, it can lead to the transference of inappropriate aspects of the model to what the model is intended to explain. Darwin clearly did not intend his readers to understand that nature acted purposefully and rationally in ‘selecting’ variants. Yet that, as Darwin discovered, was precisely what the analogy suggested to many of his readers.

A vivid analogy can easily be misunderstood. The evidence suggests that at least some of Darwin's readers failed to realize that ‘natural selection’ was a metaphor and saw it as a literal truth, implying that nature actively chose its preferred outcomes. We know how Darwin wanted his readers to interpret the metaphor of ‘natural selection’. As we noted earlier, Darwin added an explanatory preface to the third and subsequent editions of Origin of Species, clarifying – and hence restricting – the meaning of ‘natural selection’. His words merit close study at this point.

Several writers have misapprehended or objected to the term Natural Selection. … Others have objected that the term selection implies conscious choice in the animals which become modified; and it has even been urged that, as plants have no volition, natural selection is not applicable to them! In the literal sense of the word, no doubt, natural selection is a false term; but who ever objected to chemists speaking of the elective affinities of the various elements? and yet an acid cannot strictly be said to elect the base with which it in preference combines. It has been said that I speak of natural selection as an active power or Deity; but who objects to an author speaking of the attraction of gravity as ruling the movement of the planets? Everyone knows what is meant and is implied by such metaphorical expressions; and they are almost necessary for brevity. So again it is difficult to avoid personifying the word Nature; but I mean by Nature, only the aggregate action and product of many natural laws, and by laws the sequence of events as ascertained by us.

This passage is of considerable importance, on account of its explicit affirmation of the analogical or metaphorical nature of the term ‘natural selection’. It is a ‘false term’ – that is, a term which cannot be pressed to its literal limits of meaning. Darwin makes it clear that, while the metaphor seems to endorse and embrace the ideas of ‘active choice’ and any personification of the selecting agent (which might be argued to be essential to the notion of ‘selection’), he did not intend these to be affirmed by the use of the term ‘natural selection’.

So what happens if we are presented with an analogy for something that we cannot directly see – such as God or salvation – and have to figure out how to interpret it on our own? Darwin was able to interpret his own analogy for the benefit of his readers. Yet in the case of religious analogies, to which we now turn, there is no authoritative interpreter who can tell us precisely how the analogy of God as ‘shepherd’ or salvation as ‘adoption’ is to be interpreted. As will become clear, this helps us understand why religious models, metaphors, and analogies are so powerful in their appeal to the imagination yet are resistant to yielding closed interpretations.

The Use of Models and Metaphors in Christian Theology

Christianity, like most religions, uses analogical or metaphorical language to speak about God and related themes – such as the nature of salvation. Why? Because these realities exceed the capacity of the human mind to comprehend them. For this reason, these realities need to be adapted to human abilities – a process often known as ‘accommodation’. The Christian Bible and the long tradition of reflection on this text make extensive use of analogies and models, clearly intended to convey insights about God in simple and accessible ways. This has two significant outcomes, both of which are important for any understanding of the religious use of models or analogies. First, these analogies are seen to be reliable yet incomplete ways of thinking about God or the transcendent. Second, there is far more to God or the transcendent than these analogies are able to convey. The human mind is unable to comprehend God fully, and can only partly grasp the reality of God, in a way that is informed and guided by the appropriate use of models, analogies, and metaphors.

This immediately opens up the question of ‘mystery’ – here understood not as something that is puzzling, but rather something that is so vast or complex that the human mind struggles to take it in. When faced with such a situation, we tend to reduce the mystery to what we can cope with, in effect reducing God to the level of our conceptualities, rather than expanding our conceptualities so that they may render the nature of God more effectively. The Swiss theologian Emil Brunner was alert to the human tendency to reduce God to what we found to be intellectually manageable. For example, he argued that the doctrine of the Trinity was to be seen as a ‘security doctrine’, designed to prevent us from diluting or distorting the majesty and glory of God through our well‐meaning attempts to make God intelligible. We shall return to this point later in this chapter.

Yet the use of analogies and metaphors in theology also highlights the importance of the human imagination in religious reflection. Images of any kind invite engagement, opening up rather than closing down reflection. Many Enlightenment writers who endorsed this Age of Reason's quest for concise objective answers to questions resisted the use of metaphors, anxious about their conceptual fluidity. The seventeenth‐century political philosopher Thomas Hobbes, for example, spoke of metaphors as ‘senseless and ambiguous words’, so that ‘reasoning upon them is wandering amongst innumerable absurdities’. What Hobbes saw as a vice, others saw as a virtue – a capacity to allow the imaginative exploration of an image, identifying its multiple possible meanings, and exploring how these might be evaluated and applied.

So are analogies simply useful illustrations, having no ontological connection with what they are used to explain? Or is there something deeper going on, so that analogies or metaphors are meant to have some connection with what they signify? The specifically Christian use of metaphors is, many theologians argue, rooted in a doctrine of creation which confers on certain aspects of the natural and social world a capacity to signify God as their creator. In what follows, we shall explore this idea, which is often termed the ‘analogy of being’ (analogia entis). Its most familiar statement is found in the writings of the thirteenth‐century theologian Thomas Aquinas.

Thomas Aquinas on the Analogia Entis (‘Analogy of Being’) 

How can we describe God using human terms? Many would argue that this limits God to the realm of the human or the natural and fails to take account of God's transcendence of the natural order. If I were to say ‘God is good’, I run the risk of describing or even defining God in terms of human conceptions of goodness, which are often flawed and self‐serving. For this reason, Thomas Aquinas argued that terms that were applied to God cannot mean exactly the same as if they were applied to things in the world of human experience. For this reason, Aquinas argues that the words we use to refer to God must be analogical, used in different but related senses to those encountered in everyday life.

Aquinas thus affirmed the analogical nature of theological language. When I say that ‘God is good’, I am not defining God by human standards of goodness, as if there is a direct correspondence between divine and human goodness. Rather, I am saying that there is an analogical relationship – a similarity, but not an identity – between these notions. This allows us to avoid two inadequate ways of speaking about God – univocity, in which we think that our words mean exactly the same thing when they are used to refer to either God or creatures; and equivocity, in which we think our words are so indeterminate that we cannot speak meaningfully of God at all.

Yet perhaps Aquinas's most significant contribution to the discussion of analogies between God and the world of creation is found in his later writings, such as the Summa contra Gentiles and the Summa Theologiae. Aquinas here links the analogous nature of God and the created order with a doctrine of causal similitude, emphasizing the active transmission of properties from God to creatures. Creation is an act of causation, which leads to the created order bearing a likeness to its creator.

God is thus an analogical cause. In other words, God's creation of the world involves the creation of a realm that is analogous to the creator, and this inbuilt analogical correspondence between God and the natural order underlies our legitimate use of analogical language. The German Catholic philosopher Erich Przywara described the ‘analogy of being’ as ‘Catholicism's metaphysical a priori’, and extended Aquinas's approach to include wider issues than theological language. Our concern in this section, however, is with Aquinas's account of the idea, not the more developed form associated with Przywara.

Aquinas's approach gives theological legitimacy to the use of analogies drawn from the world of creation to help us think about God. The utility of this approach is not a fortunate accident; it is grounded in a distinct characteristic of the world of nature – namely, that it is God's creation, and thus bears God's imprint in some way and to some extent.

This theological insight, however, does not solve the question of how theological analogies such as ‘God as a shepherd’ are to be interpreted. It lays the foundation for this process but does not itself determine its outcomes. There are two main interpretative tasks that need to be undertaken:

Ian T. Ramsey on the Model of the Divine Economy

Earlier in this chapter, we noted how in 1910 Ernest Rutherford set out his influential model of the atom as a miniature solar system. Rutherford had observed patterns of deflection of alpha particles fired at thin gold foil that were not consistent with the model of an atom which was then generally accepted – J. J. Thomson's ‘plum pudding’ model of 1904. The basic elements of Rutherford's emerging understanding of the atom fell into place as a result of that experiment – such as the atom's mass being concentrated in a ‘minute massive centre’, with electrons orbiting this central nucleus, and the remainder of the atom consisting of empty space. Yet Rutherford knew that he needed to develop a visual representation of this new understanding.

He therefore took a model developed for a completely different purpose – the Copernican model of the solar system – and adapted it. Copernicus's model of the solar system offered Rutherford an existing conceptual pattern, a scientifically familiar visual image, with three core elements: a massive object at its centre, vast areas of space, and smaller bodies orbiting this central mass. There were difficulties – for example, did electrons really orbit the nucleus? But it was good enough for Rutherford's purpose. His new theoretical model of the atom could be represented visually using a familiar analogy.

So is this process of constructing models also found in Christian theology? At first sight, the answer might appear to be ‘no’. Most theological models are drawn from the Christian Bible. Yet there are examples of theological models which are borrowed from other contexts, often to correlate biblical insights using a familiar image or concept drawn from a theologian's cultural context. In what follows, we shall consider the Oxford philosophical theologian Ian T. Ramsey's reflections on the idea of the ‘divine economy’ – a model of divine activity that found wide acceptance in the Greek‐speaking Christian churches of the first five centuries.

During the 1960s, Ramsey wrote a number of works on the problem of religious language and the relationship between science and religion, often focusing on issues that arose from the dominance of logical positivism, which called the legitimacy of religious language into question. Ramsey devoted two works to these topics: Religious Language (1957) and Models and Mystery (1964). Religion, he argues, is like any other discipline – it develops its own distinctive language in response to its area of discourse and it uses models to help grasp aspects of a complex reality.

Various disciplines, despite their necessary and characteristic differences, nevertheless have a common feature of great significance, a feature which is often overlooked and frequently misunderstood: the use they make of models. It is by the use of models that each discipline provides its understanding of a mystery which confronts them all.

Ramsey's defence of the legitimacy of theological language is important in its own right; our concern here, however, is with the way in which he resolves the issue of how to correlate multiple models of God.

Ramsey's final reflections on this topic were published posthumously in Models for Divine Activity (1973). After noting how the Bible makes extensive use of ‘models’ of God – such as the Holy Spirit – Ramsey explores how early Christian theologians took a purely secular concept and developed it as a model of divine activity. The Greek term oikonomia – perhaps best translated as an ‘ordered administration’ – was widely used in secular culture to refer to the organization and administration of societies. Theologians quickly realized that this provided a framework for developing an interconnected account of God's action in the world, particularly in relation to salvation. The phase ‘economy of salvation’ began to be used to refer to the ordered patterns of divine activity – including creation, the act of redemption in Christ, and the subsequent ministry of the Christian church. The model of the ‘divine economy’ was not itself biblical but was rather a secular framework that enabled early Christian theologians to display the coherence of the biblical pattern of divine action in creation and redemption. Yet with the passing of the cultural context of this model in late classical antiquity, the model lost its plausibility, and seems to have dropped out of use in Christian theological discourse.

Note that Ramsey was not suggesting that early Christian theologians invented certain beliefs about God with reference to secular ideas. His point is much more subtle and interesting. Ramsey argues that early Christian theologians had well‐developed understandings of God's action in creation, the nature of God's redemption of the world in Christ, and a growing understanding of the role of the church in sustaining the life of faith. What they needed – and what they found in the secular model of oikonomia – was a conceptual framework that allowed them to hold these all together, as three distinct yet interconnected elements of a greater whole. This integrative capacity of models or analogies is important in both science and theology. The basic elements were already known; what was new was the framework which allowed them to be seen as part of an integral whole.

Arthur Peacocke on the Theological Application of Models and Analogies

Arthur Robert Peacocke went up to Exeter College, Oxford University, in 1942 to study chemistry. At that stage, the Oxford University chemistry course lasted four years. After the initial three years of teaching, the final year consisted of a substantial research project. Peacocke was supervised by the Nobel laureate Sir Cyril Hinshelwood (1897–1967) in the Physical Chemistry Laboratory for his final year of undergraduate work, and remained with him for his subsequent doctoral research. In 1973, he accepted the position of Dean of Clare College, Cambridge, which allowed him to develop his interest in the interface of science and religion. He served as director of the Ian Ramsey Centre at Oxford, which has a special interest in fostering study of issues at the interface of science and religion, from 1985–1999.

In common with many of those working at the interface of science and religion, Peacocke argues the case for a form of ‘critical realism’, in which models play an important role as intermediaries in the process of knowledge production. Science and theology alike use imagery in an attempt to offer a reliable and responsible picture of the world as it really is.

I think that both science and theology aim to depict reality; that they both do so in metaphorical language with the use of models; and that their metaphors and models are revisable within the context of the continuous communities which have generated them. This philosophy of science (‘critical realism’) has the virtue of being the implicit, though often not articulated, working philosophy of working scientists who aim to depict reality but know only too well their fallibility in doing so.

Having argued that some form of critical realism is integral to the scientific method, Peacocke argues that theology also aims to depict reality using models or analogies. The images used to visualize reality may, however, be culturally conditioned and thus may require revision or modification to secure continuing use. Yet the realization of the provisionality of our representations of reality does not force us to abandon any idea of a real world, which is somehow represented in this way.

Theology, the intellectual formulation of religious experience and beliefs, also employs models which may be similarly described. I urge that a critical realism is also the most appropriate and adequate philosophy concerning religious language and theological propositions. Theological concepts and models should be regarded as partial, adequate and revisable but necessary and, indeed, the only ways of referring to the reality that is named as ‘God’ and God's dealings with humanity.

While recognizing the diversity of types of scientific realism, Peacocke argued for a ‘common core’ of claims – most notably, that scientific change is progressive and accumulative, and that the aim of science is to depict reality. Peacocke makes a similar case for critical realism in theology. As in science, theological concepts and models are partial, inadequate, and revisable. Yet, unlike those in science, they include a strong, affective function, engaging the emotions as much as the mind. For Peacocke, both science and religion operate on the basis of a ‘critical realism’ which recognizes that models are ‘partial, adequate, revisable and necessary’ means of depicting reality. Each of these terms merits a little further exploration.

Sallie McFague on Metaphors in Theology

One of the most influential discussions of the role of metaphor in a constructive and critical Christian theology is due to Sallie McFague, who served as Carpenter Professor of Theology at Vanderbilt Divinity School before becoming Distinguished Theologian in Residence at Vancouver School of Theology. For McFague, we have to come to terms with the inevitability of metaphorical approaches to theology, living in a ‘tensive’ relationship with theological metaphors that cannot be directly identified with what they point towards, and engaging the critical imagination rather than the discursive reason.

In an important study of 1975, McFague made clear her dissatisfaction with the naïve rationalism of the Enlightenment, which valued the acquisition of ‘clear and distinct ideas’ but failed to appreciate the difficulties in securing this, given the limits placed on the human situation:

The days of supposing we are free of finite limitations, of supposing that we have some direct access to ‘Truth,’ that there might be words that correspond to ‘what is,’ that ‘clear and distinct ideas’ can be many or very interesting – such a time is over (if it ever existed except in the most rationalistic circles). … What we have and all that we have is the grid or screen provided by this metaphor and by that metaphor. The metaphor is the thing, or at least the only access that we highly relative and limited beings have to it.

McFague argues that an appreciation of the central and inevitable role of the concept of ‘metaphor’ in theology moves us decisively away from the theological precision favoured by Enlightenment writers, inviting us to embrace an ‘open‐ended, tentative, indirect’ encounter with reality which could never be captured or fully expressed in terms of well‐defined ideas. Theology is thus called to ‘understand the centrality of models in religion and the particular models in the Christian tradition’, to criticize ‘literalized, exclusive models’, and to ‘chart the relationships among metaphors, models, and concepts’. Interestingly, for McFague, ‘scientific models refer to the quantitative dimension of the world while theological models refer to the qualitative dimension’.

Having explored some aspects of the function and use of models and metaphors in religion, we now need to consider a case study in more detail, so that the points in question can be more fully appreciated. We therefore turn to two aspects of Christian theology to explore this more fully. We will look at the doctrine of creation and what are often known as ‘theories of the atonement’ – understandings of the meaning and significance of the death of Christ.

Using Religious Models Critically: Creation

The idea that the world is created is of fundamental importance to many religions, especially Christianity and Judaism. The theme of ‘God as creator’ is of major importance within the Old Testament and is thought to have become particularly significant to Israel's self‐understanding during the period of the Babylonian Exile. Of particular interest for our purposes is the Old Testament theme of ‘creation as ordering’, and the manner in which the critically important theme of ‘order’ is established on and justified with reference to cosmological foundations.

The Old Testament often depicts creation in terms of God's victory over forces of chaos, understood either as an imposition of order on a formless chaos or conflict with a series of chaotic forces, often depicted as a dragon or other monster. While there are parallels between the Old Testament account of God engaging with the forces of chaos and Ugaritic and Canaanite mythology, there are significant divergences at points of importance, such the Old Testament's insistence that creation is not be to understood in terms of different gods warring against each other for mastery of a (future) universe, but in terms of God's mastery of chaos and ordering of the world.

The theologians of the early church affirmed that the natural order possessed a goodness, rationality, and stable order which resulted directly from its creation by God. The truth, goodness, and beauty of God (to use the ‘Platonic triad’ of categories which so influenced many writers of this period) could be discerned within the natural order, in consequence of that order having been established by God. In the third century, Origen argued that it was God's creation of the world which structured the natural order in such a manner that it could be comprehended by the human mind, by conferring upon that order an intrinsic rationality and order which derived from and reflected the divine nature itself.

This insight is of central importance to the interaction of Christian theology and the natural sciences, highlighting the importance of the Christian doctrine of creation in grounding both the rationality of the cosmos, and the capacity of the human mind to discern this rationality. For example, Athanasius of Alexandria and Augustine of Hippo both hold that a rational God created a coherent and rational (logikos) universe, whose structures reflect the character of its creator and are capable of being grasped by the human mind, and their significance appreciated, if only dimly and partially. This framework of belief affirms that the being of the universe ultimately derives from the being of God, and that humanity, in bearing the image of God, has a created capacity to engage, interpret, and understand the universe. Many scholars believe that this framework for engaging nature may help explain why Christian theology was so intellectually hospitable towards the emerging natural sciences at the time of the Renaissance.

The idea of creation is thus important theologically, as well as in relation to the field of science and religion. But how is creation to be understood? What models can be used to help us visualize this concept and so open up a deeper understanding of its significance? In what follows, we shall consider three models that have been used at various points within the Christian tradition, and look at issues that arise from them which indicate the need for a critical approach to these models.

Each of these models is to be understood as an analogy, not an identity. There are clear continuities and discontinuities between the model and what is being modelled. Each model offers a partial account of some aspects of the concept of God's creation of the world, while failing to illuminate other aspects, and occasionally introducing ideas that run counter to some core Christian insights. Two such insights are of particular importance: first, that God is to be considered as a personal agent; and second, that creation is about bringing things into existence ex nihilo (‘from nothing’), rather than representing a re‐ordering or rearrangement of existing matter.

This second point needs further discussion. The prologue to John's gospel (John 1:1–14) speaks of everything being created by God from nothing through Christ. Yet this idea ran counter to the Hellenistic idea, clearly expressed in Plato's dialogue Timaeus, that the world was made out of pre‐existent matter, which was fashioned into the present form of the world. This idea was picked up by Gnostic writers, especially in the second century. However, as early Christian writers became increasingly aware of the shortcomings of Gnosticism, they adopted more sophisticated readings of the Old Testament creation narratives and taught that creation was about bringing things into existence from nothing.

Each of the three models noted above has points of value, while at the same time requiring critical interpretation. It is necessary to exclude certain readings of the model in order for the model in question to be genuinely illuminating. The idea of creation as emanation, for example, unhelpfully suggests a constant process of natural production, rather than a purposeful divine decision to create. The image of the sun radiating light implies an involuntary emanation – something which just happens naturally. The Christian tradition has consistently emphasized that the act of creation rests upon a prior decision on the part of God to create, which this model cannot adequately express. In effect, this model of creation – like all such models – needs to be approached through a theological filter.

The same issue arises when thinking of creation as construction or artistic expression. Here, creation could be understood as giving shape and form to something which is already there – an idea which stands in tension with the Christian doctrine of creation ex nihilo. The image of God as a builder would seem to imply the assembly of the world from material which already exists. The model of artistic expression can be associated with the idea of creation from pre‐existent matter, as in the case of a sculptor with a statue carved from an already existing block of stone. Nevertheless, this model expresses the insight that the character of the creator is, in some manner, expressed in the natural world, just as that of an artist is communicated or embodied in her work. This weakness can, however, be addressed. One of the many merits of Dorothy L. Sayer's Mind of the Maker is that it can accommodate the idea of creation from nothing, as with the analogy of author who writes a novel or the composer who creates a melody and harmony.

Using Religious Models Critically: Theories of the Atonement

The need to adopt a critical approach to theological models is also evident in the case of interpretations of the significance of the death of Christ – an area of theology traditionally known as ‘theories of the atonement’ or ‘the work of Christ’. The New Testament deploys a rich range of visual images to enable a full understanding of the consequences of the work of Christ – such as justification, salvation, reconciliation, and adoption.

The Christian message of salvation was contextualized in language that was accessible to ordinary people. Imagery, metaphors, and comparisons that those early Christians could understand and relate to became important tools in the hands of the evangelists for explaining to these new converts what had happened to them.

Yet the issue of the extent to which these analogies can be pressed remains important, in that any given soteriological analogy does not indicate the limits of its scope, or its proper mode of interpretation. To illustrate this point, we may consider one such image: the notion that Christ gave his life as a ‘ransom’ for sinners (Mark 10:45; 1 Timothy 2:6).

So what does this analogy mean? How is it to be interpreted? The everyday use of the word ‘ransom’ suggests four ideas.

These four ideas all appear to be implied by speaking of Christ's death as a ‘ransom’ for sinners. But are we meant to interpret this analogy in this way? Might the analogy be pressed too far at certain points?

There is no doubt that the New Testament proclaims that we have been liberated from captivity through the death and resurrection of Christ. We have been set free from captivity to sin and the fear of death (Romans 8:21; Hebrews 2:15). It is also clear that the New Testament understands the death of Christ as the price which had to be paid to achieve our liberation (1 Corinthians 6:20; 7:23). Our liberation is a costly and a precious matter. In three of these four respects, the scriptural use of ‘ransom’ broadly corresponds to the everyday use of the word. But what of the idea that Christ's death was a ransom that was paid to someone? Who was paid in this manner?

The New Testament is silent over any suggestion that Christ's death was the price paid to anyone in order to achieve our liberation. Some of the writers of the first four centuries, however, assumed that they could press this analogy to its limits. Origen, perhaps the most speculative of early patristic writers, argued that since Christ's death was a ransom, it must have been paid to someone. But to whom? It could not have been paid to God, in that God was not holding sinners to ransom. Origen concluded that it had to be paid to the devil.

Later writers – such as Rufinus of Aquileia and Gregory the Great – developed this idea still further. The devil had acquired rights over fallen humanity, which God was obliged to respect. The only means by which humanity could be released from this satanic domination and oppression was through the devil exceeding the limits of his authority, and thus being obliged to forfeit his rights. So how could this be achieved? Gregory suggests that it could come about if a sinless person were to enter the world, yet in the form of a normal sinful person. The devil would not notice until it was too late: in claiming authority over this sinless person, the devil would have overstepped the limits of his authority, and thus be obliged to forfeit his rights to humanity. Rufinus suggests the image of a baited hook: Christ's humanity is the bait and his divinity the hook. The aspect of this approach to the meaning of the cross that caused the most disquiet subsequently was the apparent implication that God was guilty of deceiving the devil.

Following the penetrating theological criticism of this idea by Anselm of Canterbury in the eleventh century, this theory was generally abandoned by academic theologians, although it retained considerable popular appeal. This unsatisfactory theory clearly resulted from an analogy being pressed far beyond its intended limits. But how do we know whether a theological analogy has been pressed too far? How can the limits of such analogies be tested? Such questions have been debated throughout Christian history. An important twentieth‐century discussion of this point may be found in the writings of the philosopher Ian T. Ramsey, who we noted earlier in this chapter. In his Christian Discourse: Some Logical Explorations (1965), Ramsey set out the idea that models or analogies are not independent and freestanding but interact with and qualify each other.

Ramsey argues that Scripture does not give us one single analogy (or ‘model’) for God or for salvation but rather uses a range of analogies. Each of these casts light on certain aspects of our understanding of God or the nature of salvation – but not all. However, these analogies also interact with each other. They modify each other. They help us understand the limits of other analogies. No analogy or parable is exhaustive in itself; taken together, however, the range of analogies and parables builds up to give a comprehensive and consistent understanding of God and salvation.

Models and Mystery: The Limits of Representation of Reality

How do we represent a complex reality, such as the strange and perplexing world around us? There is a deep human longing to be able to visualize things, in a process which draws more on the imagination than reason. When we attempt to ‘picture’ something that lies beyond our capacity to see fully, we naturally try to scale it down to something manageable. This underlies the scientific use of models as heuristic devices to help us grasp the core features of complicated systems.

In this chapter, we have explored how models and analogies can help us visualize at least some aspects of a complex reality. We have noted some of their limits, particularly those which arise from confusing a model with what is being modelled. Yet a further concern remains: what if models and analogies are fundamentally incapable of rendering the complexity of our universe? We have already alluded to the concept of ‘mystery’ in this chapter; this theme clearly needs further discussion.

Any discussion of the human attempt to investigate and represent reality needs to take account of the limited capacity of human beings to grasp complex entities. The theoretical physicist Werner Heisenberg – best known for formulating the uncertainty principle – argued that while a good scientific theory would do justice to ‘every accessible domain of the world’, there remain certain ‘phenomena that defy formulation in language’. Scientific thinking ‘always hovers over a bottomless depth’, being confronted by the limits placed on human understanding.

Every time when there is an understanding of a new reality, their sphere of validity appears to be pushed yet one more step into an impenetrable darkness that lies behind the ideas language is able to express.

Richard Dawkins has also clearly appreciated the importance of this point, and the need to recognize the validity of the category of mystery in science.

Modern physics teaches us that there is more to truth than meets the eye; or than meets the all too limited human mind, evolved as it was to cope with medium‐sized objects moving at medium speeds through medium distances in Africa. In the face of these profound and sublime mysteries, the low‐grade intellectual poodling of pseudo‐philosophical poseurs seems unworthy of adult attention.

Some scientists use the word ‘mystery’ to mean something that is presently not understood, but which will become resolved and intelligible through scientific advance. For example, Charles Darwin commented that the question of the historical origin of species was the ‘mystery of mysteries’, borrowing a phrase from the astronomer Sir John Herschel. For Darwin, a mystery could be solved by discovering a higher‐order theory that allows what presently seems incomprehensible or incoherent to be seen in a new way. Darwin's answer to Herschel's riddle was to find a theory which made intelligible what otherwise might seem mysterious – the theory of descent with modification by natural selection. Certain ‘mysteries’ thus cease to be mysterious once they are explained by discovering an intellectual framework within which they are rendered intelligible or predictable.

Other scientists, however, regard a mystery as something which lies beyond the scope of reductive explanation. Albert Einstein, for example, constantly stressed the limits of the human grasp of the rationality of the universe, and the importance of maintaining a sense of mystery and wonder in the face of its vastness. Although he was not a mystic in any meaningful sense of the term, Einstein was clear that a sense of ‘the mysterious’ was the source of all true art and science, just as an ‘experience of mysteriousness’ lay at the heart of religion. ‘What I see in nature is a magnificent structure that we can only grasp imperfectly.’

Another issue needs to be noted at this point. A common assumption underlying contemporary evolutionary biology is that human cognitive capacities evolved primarily for the purposes of survival, not for the pursuit and acquisition of truth. Yet human cognitive capacities far exceed those required for mere survival – as evident, for example, in the remarkable successes of mathematics. Yet Dawkins's point remains. The ‘all too limited human mind’ is well adapted for simple scenarios. But what about those which are too vast and too complex to be grasped by this limited human mind? Can the use of models and analogies help us grasp something that ultimately lies beyond our full comprehension?

For Christian theologians such as Maximus the Confessor, the term ‘mystery’ fundamentally refers to the conceptual immensity or ontological vastness of God. A mystery is resistant to interpretative closure or intellectual reduction, ultimately transcending any attempt at a limiting definition – precisely because this limits what must be allowed to remain open. The English theologian Charles Gore also highlighted the importance of this point, noting the limits of language to comprehend the mystery of the divine:

Human language never can express adequately divine realities. A constant tendency to apologize for human speech, a great element of agnosticism, an awful sense of unfathomed depths beyond the little that is made known, is always present to the mind of theologians who know what they are about, in conceiving or expressing God.

Augustine of Hippo's famous declaration si comprehendis non est Deus (‘if you can understand it, it is not God’) makes the important point that anything that humanity can grasp fully and completely cannot be God, precisely because it would be so limited and impoverished if it can be fully grasped by the human mind.

The potential importance of the issue for religion can be seen in Rudolf Otto's Idea of the Holy (1917), which developed the concept of the numinous as a means of expressing what he considered to be foundational to religious experience and existence. For Otto, the numinous can be understood as an experience of a mysterious terror and awe (mysterium tremendum et fascinans) in the presence of that which is ‘totally other’ and thus not capable of being expressed directly using human language or analogies. Otto's conception of an irrational or numinous aspect of religion that lies beyond conceptual description and is only accessible through experience has proved significant in the study of religion; it is, however, of particular importance to any serious attempt to reflect on the religious category of mystery. Otto does not use the term ‘irrational’ to mean ‘rationally deficient’; indeed, his use of complementary terms such as ‘non‐rational’ or ‘trans‐rational’ makes it clear that the mystery at the heart of religion is something that overwhelms and saturates human rational capacities.

The French theologian and philosopher Gabriel Marcel (1889–1973) distinguished between the scientific and religious uses of the term ‘mystery’ using the categories of ‘problems’ and ‘mysteries’. For Marcel, the natural sciences deal with the world of problems. A problem is something which can be viewed objectively, and for which we can find a possible solution. A mystery, however, is something which we cannot view objectively, precisely because we cannot separate ourselves from it. While problems can be resolved through universal or generalized solutions, mysteries cannot. Life, according to Marcel, is thus not a problem to be solved but a mystery to be lived. The existence of suffering, for example, is thus to be seen as a mystery that can never be fully grasped, rather than as an intellectual problem that can be mastered and subdued.

A similar point was made by the great German physicist Max Planck, widely regarded as the founder of quantum mechanics. Like Einstein, Planck held that there were limits to the capacity of science to fully understand our universe. ‘Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are part of nature and therefore part of the mystery that we are trying to solve.’

Marcel's ideas were developed in a more explicitly theological manner by the English philosophical theologian Austin Farrer, who defined the realm of the problematic as the field in which there are right answers. The realm of mystery, however, involves engagement with reality at such a level that it cannot be investigated in terms of ‘determinate and soluble problems’. The theologian, Farrer argues, is not faced with the limited and manageable relation which arises between a conceptual instrument and physical objects. We are rather confronted with the ‘object itself, in all its fullness’, consisting not of ‘a cluster of problems’, each of which can be solved scientifically or rationally, but of a ‘single though manifold mystery’. It is tempting to try to reduce a mystery to a set of problems on the basis of the mistaken belief that the mystery is the mere sum of the individual (soluble) problems.

The analysis presented by Marcel and Farrer illuminates the theological task, in that each generation is called upon to wrestle with a mystery, knowing that it possesses a certain inexhaustibility which cannot be grasped or fully comprehended by any one writer or era. The Catholic theologian Thomas Weinandy makes this point as follows: ‘Because God, who can never be fully comprehended, lies at the heart of all theological enquiry, theology by its nature is not a problem‐solving enterprise, but rather a mystery‐discerning enterprise.’ The problematical is the domain of science and rational inquiry. Once a problem is solved there is no more interest in it.

A mystery, however, challenges, refreshes, and reinvigorates the theological task, not least through the expectation that fresh light has yet to break forth from mysteries which have been wrestled with by previous generations. The process of wrestling with a mystery thus remains open, not closed. What one generation inherits from another is not so much definitive answers as a shared commitment to the process of wrestling.

One theological response to the category of mystery is to develop models which attempt to represent or allow visualization of certain aspects of a greater reality, while conceding that this reality as a whole remains resistant to reduction in this way. Theologians can thus speak of different ‘models’ of the Trinity. While there is a clear difference between theological modelling and modelling in the natural sciences, some analytical models of God seek to comprehend their target ‘scientifically’ – in other words, fully and completely.

A good example of a theological model of the Trinity is that developed by Jeffrey Brower and Michael Rea, based on the Aristotelian notion of ‘numerical sameness without identity’. This model suggests that we can understand a key aspect of the doctrine of the Trinity – namely, the relationship between the three divine persons and the one divine nature – as analogous to the relationship between a bronze statue and the bronze metal from which it is constructed. The statue and the bronze count as exactly one object (they are numerically the same). Yet the statue is not strictly identical to the bronze, since they do not share exactly the same properties or persistence conditions. It is, for example, possible to melt down the statue without destroying the bronze. In the same way, we can think of the divine essence as playing the role of matter in a form–matter compound, so that the persons of the Trinity can be understood as numerically distinct beings constituted by three numerically distinct forms.

Yet theologians have expressed concerns about attempts to model God, noting how this tends to reduce God as something existing within the world, and failing to do justice to God's transcendence. The philosopher of religion William Wood notes these concerns, highlighting the importance of ‘apophatic’ considerations – in other words, recognizing the limits of our attempts to speak of God. Human beings, because of their finitude and sinfulness, cannot comprehend God's essence or being. God is ‘unknowable’ in the sense of lying beyond human categories and sense‐making methods.

In recent decades, contemporary academic theologians have reasserted the absolute transcendence and unknowability of God, which goes hand‐in‐hand with a newfound respect for apophatic theology. The more we insist that God is unknowable, the more problematic the practice of modeling God becomes. The existing literature on theological modeling has not really come to terms with this renewal of apophatic thought.

Wood's point is important, as it raises the question of whether the scientific practice of developing models as heuristic devices aiming at intelligibility can be applied legitimately within theology. As the philosopher of science Peter Godfrey‐Smith notes, the natural sciences often develop models that represent a ‘deliberate simplification, or other imaginative modification of reality, in order to make some relationships visible or problems tractable.’ Many classical theologians would suggest that making God ‘tractable’ is likely to entail distortion and diminishment.

Ian Barbour on Models in Science and Religion

Ian Barbour has had a significant impact on the field of science and religion, mainly through his ground‐breaking works Issues in Science and Religion (1966) and the later Myths, Models, and Paradigms (1974). Barbour has given considerable attention to the development of an intellectual basis for the facilitation and consolidation of a positive and constructive interaction between science and religion. Far from being a pragmatic response to the need for two powerful cultural forces to engage in dialogue, Barbour argues that there is an intellectual bridge between the two, which makes the dialogue necessary and proper.

Barbour argues that there are important continuities (though not identities) in terms of epistemology (the kinds of knowledge we have), methodology (how this knowledge is obtained and justified), and language (how this knowledge is expressed). Taken together, these commonalities provide a bridge between science and religion which is capable of sustaining significant intellectual traffic between them. Although some consider Barbour's achievement in bridging these disciplines to lie primarily in his notion of ‘critical realism’, others suggest that it lies in his use of the categories of models, metaphors, and analogies – in other words, in the way in which we visualize our world.

Barbour's discussion of the category of model shows both an awareness of the concept's potential for illumination and the generation of research programmes, while at the same time noting important differences between the ways in which models are understood in science and religion. Scientific models, he suggests, are ‘neither literal pictures of reality’ nor ‘useful fictions’, but partial and provisional ways of imagining what is not observable; they are symbolic representations of aspects of the world which are not directly accessible to us. They serve a heuristic function, in that they are ‘mental constructs devised to account for observed phenomena in the natural world’. Barbour emphasizes that such models are constructed by scientific communities as interpretative tools; they are not a priori concepts which derive their plausibility from beyond scientific practice.

Janet Martin Soskice argues that it is important to distinguish ‘model’ from ‘metaphor’, and criticizes Barbour for conflating these two, in effect regarding their difference as only a matter of degree. For Soskice, ‘an object or state of affairs is said to be a model when it is viewed in terms of some other object or state of affairs. A model need not be a metaphor, for a model need not be linguistic at all.’

Religious models, according to Barbour, are also neither literal pictures of reality nor useful fictions; they have an additional function, however, of serving as organizing images to interpret patterns of human experience, especially those associated with a variety of religious emotions – such as awe and reverence.

Models in religion are also analogical. They are organizing images used to order and interpret patterns of experience in human life. Like scientific models, they are neither literal pictures of reality nor useful fictions. One of the main functions of religious models is the interpretation of distinctive types of experience: awe and reverence, moral obligation, reorientation and reconciliation, interpersonal relationships, key historical events, and order and creativity in the world.

Yet these models are often given to the religious community of interpretation through tradition, raising the question of whether they can be revised or replaced – or whether their renewal and ongoing use is dependent on their constant reinterpretation. As we saw earlier in this chapter, such a position is taken by Arthur Peacocke.

Barber pointed out three similarities between the scientific and religious use of models.

Barbour also noted three areas of divergence between the use of models in scientific and religious contexts. At this point, a degree of generalization about the nature of religion may perhaps lead to some incautious conclusions, although there is no doubt that, at least in some cases, the points which Barbour makes are valid.

A further point of importance in this comparison concerns the way in which analogies or models are chosen. In the sciences, analogies or models are chosen and validated partly on the basis of certain criteria of fidelity – such as whether they offer a good empirical fit with the target of representation, for example, by sharing as many of its significant features as possible. These two themes – selection and validation – are of considerable importance, not least in that they highlight a significant difference between the natural sciences and religion. Analogies are generated within the scientific community; if they prove to be unsatisfactory, they will be discarded, and replaced by new ones.

These key themes of formulation and validation have no direct parallel in classical Christian thought. Christianity has traditionally held that the controlling analogies or generative models in question are ‘given’, not chosen; the two tasks which confront the theologian are those of establishing the limits of the analogy and correlating it with other such given analogies. Not all theologians would support this traditional view; some would argue that we are at liberty to develop new models which avoid certain features of traditional models which are deemed to be unsatisfactory.

For Further Reading

General Themes

Models, Analogies, and Metaphors in Science and Religion

Models, Analogies, and Metaphors in Science

Models, Analogies, and Metaphors in Religion

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