Making Images of the Cosmos

The following is the prepared text for a lecture delivered at Anthem Preparatory Academy, a Great Hearts charter high school in Anthem, AZ. The lecture was a part of a two-day colloquium for the junior and senior class, “Making Worlds,” also with guest speaker Dr. Andrew Seeley. The texts of the colloquium were selections from Tolkien’s Silmarillion and his essay “Tree and Leaf,” as well as C. S. Lewis’ The Discarded Image, which is the subject of the following.

* * *

Making Images of the Cosmos

by John G. Brungardt
Pontificia Universidad Católica de Chile
Anthem Preparatory Academy, AZ
9 January 2018

Introduction

Perhaps the questions which arose in your minds while reading our selection on “The Heavens” from C. S. Lewis’ The Discarded Image were something like this: “What is the connection between this discussion of an obsolete astronomical Model of the Universe and the Fantasy and world-building that Tolkien discusses? What has the Art of Fantasy to do with Science? Is there a connection between Models in a more scientific sense and sub-created Worlds in the Art of Fantasy?” Perhaps you would have been concerned had you read what Lewis writes earlier in his book: “In every age it will be apparent to accurate thinkers that scientific theories, being arrived at in the way I have described, are never statements of fact.”¹ Since the opposite of a fact is a fiction, as every schoolchild knows, we might suspect Lewis of some plot to undermine the place and role of science in our culture. On the other hand, perhaps some of us are inclined to feel for the old poets and philosophers. They were not lost when they wandered about in search of truth. Indeed, Tolkien claims in the essay we just discussed, that “Fantasy is a natural human activity. It certainly does not destroy or even insult Reason; and it does not either blunt the appetite for, nor obscure the perception of, scientific verity.”² That is, Tolkien claims that Fantasy is natural to human beings, just as natural as Reason. If both are natural, how can they be opposed? Possessing both Fantasy and Science in one’s soul at the same time does not cause some sort of destructive interference that weakens one or cancels the other. This latent harmony between Fantasy and Reason is my topic, and the question I wish to answer is this: Is building Models of the Cosmos a type of Art?

To introduce this topic, let us discuss its three key ideas: Cosmos, Model, and Art. First, Cosmos. In English, the study of the whole universe is usually called cosmology. The Latin word universus comes from unus and versus, meaning “turned into one, combined into one whole.” Thus, the “universe” is not merely “all things” but it is “all things insofar as they are made, somehow, into one thing.” In Greek, the word cosmos derives from the verb kosmein (κοσμεῖν), which means “to arrange” or “to order, rule” as well as “to adorn” in the sense of making beautiful. The universe or “all that exists” is a cosmos because it is one unified order, a whole beautifully arranged in order. Cosmology is the study of this order, the existing universe as such a whole.

Now, what about Model? Here, C. S. Lewis answers our question for us. He writes: “Every Model is a construct of answered questions.”³ As a “construct,” a Model is something that we human beings make or put together by two activities: asking questions and then answering them. It is constructed, like a building is constructed, but through our thought. Now, we might think, “Well, if a Model is a construct, and a construct is constructed by some type of skill like an art, then our question is answered. Making Models of the Cosmos is a type of Art.” This seems too easy. One could object: “Isn’t ‘building’ or ‘making Models’ in this sense just a metaphorical type of making or building?” Now, Lewis further claims that “The great masters do not take any Model quite so seriously as the rest of us. They know that it is, after all, only a model, possibly replaceable.”⁴ Not only do we non-experts see the Model of our own times indirectly, but the Model itself is also a halfway house. It is merely a rough draft. Recall Lewis’ astounding statement: “In every age it will be apparent to accurate thinkers that scientific theories, being arrived at in the way I have described, are never statements of fact.”⁵ So that is what Lewis thinks of Models.

Now, what about Art? Since Lewis has turned our minds to the Middle Ages, let us consider their definition of art. For the medievals, Art is contrasted against Theory. Theory is a habit of reason that knows an order that already exists in natural things for the sake of achieving the truth. The systematic study of the natural order of things (rocks, animals, man the stars; indeed, all creation) is a theoretical activity. By contrast, in an art, the mind instills order into things. Art was called ratio factiva, or making reason, by the medievals. It is a habit of reason regarding an order that does not already exist in things, for the sake of putting that order into things. In art, the order is at first known but unmade, in theory the order is at first made but unknown. Hence, all arts are types of reasoning aimed at producing order in something. Mechanical arts such as bridge-building or blacksmithing produce order in matter for useful purposes; fine arts, such as painting, produce order in matter for the sake of the pleasing and the beautiful. The liberal arts are distinguished by the medievals because of the fact that their products are not bodily.⁶ The liberal arts produce works of the mind, such as mathematical, grammatical, and logical objects: proofs, calculations, speeches, and arguments. This seems to be an important clue. Perhaps building Models of the Cosmos could non-metaphorically involve an art because the meaning of “art” can include what the soul can craft, as it were, within itself.

Now, Lewis describes the medieval Model of the Universe, drawn from their poetry, history, science, philosophy, and theology, as “a single, complex, harmonious mental Model of the Universe.”⁷ So we should remember that a “Model,” according to Lewis, requires other types of knowledge besides the natural sciences. The medieval mind loved to create and organize systems, and he gives two examples of such works: Dante’s Divine Comedy and Thomas Aquinas’s Summa Theologiae. Yet Lewis insists not only

[… that this] Model of the Universe is a supreme medieval work of art but that it is in a sense the central work, that in which most particular works were embedded, to which they constantly referred, from which they drew a great deal of their strength.⁸

The Model is the artwork at the center of a sphere of cultural influence: acting upon concrete works written by Dante or Aquinas, but at the same time being acted upon by those same works and other works. Everywhere is this Model described, but in no one place is it written down. For this reason Lewis also maintains that “[The Model] helps to provide what we may call a backcloth for the arts.”⁹ This implies straightaway that there is some Model-building Art which is not one of “the arts” such as the mechanical arts, the fine arts, or maybe even the liberal arts.

Recalling Tolkien now, we should ask ourselves: Is making Models of the Cosmos a type of Art? Perhaps you would answer, with Tolkien: “Obviously they are very different—science is not an art. Science has to do with the Primary World, and science works upon that world, producing primary belief, not the secondary belief that belongs to a Secondary and sub-created World, a mere fairly-tale. Besides, I am not convinced that ‘building a model’ of the Universe is non-metaphorically building something; there is no true ‘Art’ involved. So it seems: for neither a mechanical nor a fine art would fit the bill.” So we might answer at first. But remember that Tolkien does not think that Fantasy and Reason’s “scientific verity” are enemies; they are related, he claims, in virtue of being two natural activities of human beings. Remember this also: Lewis seems to think that Models are endlessly revisable; he appears to be an enemy of “scientific verity” since he claims that scientific theories are not statements of fact. So in order to answer our main question—Is building Models of the Cosmos a type of Art?—it is best to address Lewis’s claim about scientific fact first before considering examples of the activity of building Models. By the end of the discussion, I aim to show in what sense Lewis is right about scientific theories, and in what sense building Models of the Cosmos is a type of Art.

1. The Logic of Model-Building

In order to answer the first question—Is Lewis correct to claim that “scientific theories, being arrived at in the way I have described, are never statements of fact”¹⁰—we have to understand a bit of the logic of model building, or what we might call the logic of scientific discovery. While there was a tradition of scientific logic that stretched from Aristotle to Galileo (inclusively, in many ways), and historically what has been called the hypothetical-deductive method prevailed. Let us examine the essential logic of this method, which is the logic of hypothetical statements.

The hypothetical statement is composed of an antecedent and a consequent phrase, as follows: “If X, then Y.” We want to focus on some properties of this statement. Let us consider this example: “If one lone Eagles’ player outscored the opposing team, then the Eagles won the game.” Now, we need to note a few things about this hypothetical. First, it possesses a type of necessary connection going forwards. By definition, if the antecedent (the if… phrase) is true, then the consequent (the then… phrase) must be true. However, what we need is independent knowledge of whether or not the if… phrase is in fact true. Once we know the truth of the antecedent, the truth of the consequent follows of necessity. This mode of reasoning is called modus ponens. Second, however, the connection does not work the other way around. Knowing the truth of the consequent does not warrant the truth of the antecedent. If the Eagles won the game, it could be true, but it is not necessarily true, that a single player outscored the entire opposing team all by himself. There are other conditions that could exist and allow the Eagles to win the game. That is, the consequent phrase can be true even if the antecedent is actually false. If we reason incorrectly in this way it is a fallacy called affirmation of the consequent. Third, we should notice that if the consequent phrase is false, then the antecedent phrase must also be false. If the Eagles did not win the game, then some solitary Eagle athlete could not have scored a Achillean number of points; this mode of reasoning is called modus tollens.

Now, these logical properties of hypothetical statements are important because they can give us insight into the basic logic of scientific theories. Here, we have to introduce a very abstract hypothetical: “If my theory about B is correct, then we will observe A doing C.”¹¹ What happens when we apply the three logical properties to this statement? Let’s start with the third feature, using modus tollens. If we do not observe A doing C, then we must conclude that my theory about B is not correct. It’s back to the drawing board, or at least some part of the drawing board.

Second, we should notice that our modus ponens reasoning no longer works. This is because we can’t know at the outset if our proposed theory about B is true. You might think: well, just flip the statement around: “If we observe A doing C, then my theory about B is correct.” However, this mode of reasoning is infelicitous because it cannot discriminate between theories (that is, what about theories D or E or F that try to connect A and C?). We want the first way of formulating things (“If my theory about B is correct, then we will observe A doing C”) so that we can test theories in a logical way, using modus tollens. Notice also that, in contrast to our previous example (“If one lone Eagles’ player outscored the opposing team, then the Eagles won the game.”) the hypothetical involving my theory about B is not a tautology. Indeed, by saying “my theory about B,” I’m really including a whole group of statements. Some of those statements might be true, others false. This network of statements is what constitutes my “theory about B”. This helps us to understand why Lewis defines a Model as a construct of answers to questions. Some of the answers in the construct we may discover to be false, and we need to figure out a way to replace them. Perhaps this is where the notion of an Art used by science comes into play. There is an Art to building Models of the Cosmos, and similar to the medieval liberal arts, this Art used by science produces a mental object, namely, the Model itself. Let us keep this idea of a mental product in mind.

What about the fallacy of affirming the consequent? This is the most striking and important feature for now. If we do observe A doing C, then it does not follow with necessity that my theory about B is true. Just as with our previous example that it might have been true that one player outpaced the opposing squad in scoring, but this is not necessarily true, so also the actual fulfillment of the prediction of a theory does not necessitate the truth of the theory. Some theory, heretofore unknown, might work better because we are missing relevant details.¹² So, my proposed theory can be supported using this mode of reasoning, but not proven apodictically. It is for this reason that we might sometimes hear that scientific theories can “only be disproven and never confirmed.” This hypothetical mode of reasoning, therefore, is why Lewis writes “In every age it will be apparent to accurate thinkers that scientific theories, being arrived at in the way I have described, are never statements of fact.”¹³ Now, we surely want something stronger—are there not facts in our knowledge of the natural world? If we think so, we will have to discover a non-hypothetical mode of logical reasoning. It seems to me this logic is implied by the Art of building Models of the Cosmos. To that topic we should now turn.

2. Building Models of the Cosmos

In order to answer our second question—Is building Models of the Cosmos a type of Art?—I would like to discuss three things which have recurred throughout all human Models of the Cosmos. They are time, space (or place) and substance. I have chosen this thematic discussion in lieu of a discussion of how—using the logic of discovery—various scientific models have “broken down” (for example, the problem with quintessence in Aristotelian cosmology, the gravitational paradox in Newtonian cosmology, or the vacuum catastrophe in modern Einsteinian cosmology). In contrast, the thematic discussion will cast more light on the ideas of the hierarchy and intelligibility of the cosmos, features that will help us answer our question.

First, let us consider Time. In classical Newtonian mechanics, Newton thought that time, true time, is something that flows or changes on its own separately from things in the universe. Time exists somehow apart from things like people, stars, and planets whose motions are measured by the passage of time. Now, some thought that this view of time was too much. Time, they thought, is rather the ordered relationship between events that happen to objects. Time is a special type of relation within the universe, not something outside it. However, whether time exists as a thing separate from or a special relation within the universe can be ignored when actually doing mathematical physics. In practice, time is contained in a symbol, t, and is measured by clocks. In this sense, time can be applied to any object or feature of reality that a clock can be used to measure: falling rocks by a stopwatch, heartbeats in an echocardiogram, thoughts in your brain on the MRI. What to make of this Newtonian model and its time? Is this time the time of human history? Is this time the time of the beginning of the world?

However, we might have heard that Einstein’s theory, the theory of relativity, has modified this Newtonian view of time. Einstein’s view of time is our current best physical theory. In the Newtonian model, there is one time for the entire universe, a single comic now. Einstein’s model (most say) does not contain a single cosmic “now.” Instead, the “nows” of different parts of the universe are not directly comparable; furthermore, each “now” is connected to the behavior of massive objects. Indeed, time and the behavior of objects are so connected in Einstein’s model that this model of the Cosmos does not contain objects which do things at a certain times, but rather a vast array of “events” or points in a four-dimensional continuum: the spacetime continuum. Instead of objects, we now have merely events. The universe, on this Einsteinian model, is sometimes called “the four-dimensional block universe.” The block “exists” all at once, with all of its events and their four number-coordinates (one of time and three of space). Consequently, some philosophers and scientists claim that time is a subjective, psychological illusion. “Future” events exist in the four-dimensional block universe “already” and “the past” is still there. What, on this view, becomes of human history? What does a fixed set of events make of human freedom?

On the medieval view, time in the Cosmos is partly a child of the mind and partly a child of physical objects. Time, Aristotle or Thomas Aquinas would say, really only exists in the momentary “now.” The past did exist but is no longer except in memory, while the future will exist but does not yet except in anticipation. Time “flows” because physical objects exist in a more important way and those physical objects can undergo change. If the universe were made entirely of creatures that could not undergo change or corruption, then time would not exist. The time experienced by a being depends upon what kind of being it is. Hence, on this medieval view, there would be a hierarchy of times in the Cosmos. The material changes of rocks is different than the time of human experience and human history, and human time is again different than the age of an angel or the eternity of God. All these times are related to each other, and the higher times “contain” the lower forms of time, all in that grand total order of things which the medievals called “Cosmos.”

What about space? On the medieval view, the Heavens did not “have“ or “take up” space.¹⁴ Rather, they were a place, like an environment or habitat. Ancient Aristotelian cosmologists deduced the nature of this heavenly place using long empirical observation and logical reasoning. They reasoned that different types of substances should exhibit different types of motions. Since the heavens exhibit a motion that is very different from that of terrestrial elements (which naturally go either up or down), the heavens are made of heavenly stuff: aether or quintessence. Furthermore, in all the cosmos, there were natural places (what we might call a natural environment or habitat) for each kind of element. What this shows is that place in the medieval Cosmos had the aspect of “home”—there were natural or fitting places for things to be and exist, where it was good for them to be.

Now, on the Newtonian view all of this fell apart. There is no longer a difference between heavenly and earthly matter. Space is an empty void, not a homelike place. Space is also inert: it does not change, move, or act and react with material objects. The place for the Earth, on such a view, seems more the result of random occurrence (although Newton would not have said so). However, this Newtonian view of space was changed by Einstein’s model. Einstein’s model says that space is no longer inert and changeless, as it is in the Newtonian model. Rather, space expands, contracts, and warps in the presence of matter: “Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve.”¹⁵ Not only this, but this much more physical type of space produces matter in the extreme early conditions of the universe, and indeed produces the matter needed for the stars. Stars, in turn, can only form in certain regions and under certain conditions, and upon their death they produce the elements necessary for life. Einstein’s stars still have a natural order in place and time and thereupon produce the heavier elements necessary for life.

Lastly, what about substances? Usually, when we think of substance we think that material substances are the most important and numerous. However, the medievals viewed things the other way around. While material things are more obvious to us, they are not, so to speak, more obvious to Nature.¹⁶ The medieval Model claimed that the Cosmos existed because the Cosmos and all its parts was a created imitation of the Divine Mind. As an imitation, creatures were, most fittingly, intellectual beings with minds. The highest created minds were entirely spiritual, without matter—the intelligences or angels—and were the most powerful and the most like God. Their knowledge was contained within themselves. This hierarchy of minds descended in rank of nobility, intellectual insight and power, all the way until you reached a mind so weak—so naturally ignorant—that this mind possessed no knowledge within itself but had to to search outside itself for knowledge, and thus this mind had to be united to a body, and that body placed in a vast, ordered, beautiful cosmos so that this mind might learn something. This mind, of course, is the human mind. To top this all off, Thomas Aquinas argued that the Cosmos would not be complete unless the Divine Mind created all of these minds, from the highest angel to the human mind stuck inside a material cosmos. This idea is paralleled in modern cosmology only in a distant way. Modern cosmologists speak of the “anthropic principle,” namely, that in order for life to exist, the various physical forces in our universe can only exist within certain ranges or limits. The debate cosmologists have is whether or not this necessity is absolutely necessary or hypothetically necessary. Nonetheless, the principle is there: the existence of the physical universe and the existence of the human mind are tied together.

This concludes our tour of time, place, and substance. On the one hand, the medieval Models emphasized hierarchy more than the others, while all the Models imply the intelligibility of nature. On the other hand, even the modern Model cannot escape the fact that our own human existence is tied up with the existence of time and space and substance. Perhaps the hierarchy of the Cosmos still exists, albeit in a way that the medieval Model did not adequately capture.

3. The part that understands the whole

Let us return to Lewis’ definition of a Model in hopes that we can now answer whether or not making Models of the Cosmos is a type of Art. He says that every Model is a construct of answered questions. Recall also what art is: an art is productive reason. An art puts order into things when that order was not there beforehand. Now, perhaps we can see from our examples that the natural sciences involve Model-making and Image-building. These Models are held together within many human minds through discovery and education and are then corrected and critiqued by Nature. Nature herself tells us that some of the pieces are wrong, and we change our Model. Unlike the art critic of Secondary Worlds, Nature is the Critic of what scientists produce. However, unlike human critics, Nature cannot “speak” or “write”. In order to hear Nature’s critique, don’t we need to study Nature more? However, will this not require that we make another Image or Model of Nature? If so, we now have a problem. Someone could claim that listening to Nature—that is, seeing what is wrong with our Models of the Cosmos—itself requires a Model or Image of nature. But then, how do we know if that Image is correct? If we correct that Model by another Model, how do we know that the new Model is correct? Is it Models all the way down? Have we recourse only to hypothetical modes of logic?

Let us place Lewis’s definition of “Model” in context:

Every Model is a construct of answered questions. The expert is engaged either in raising new questions or in giving new answers to old ones. When he is doing the first, the old, agreed Model is of no interest to him; when he is doing the second, he is beginning an operation which will finally destroy the old Model altogether.¹⁷

This actually implies four possibilities:

Questions|Answers	Old	New
Old	1. Asking old questions that have old answers	2. Asking old questions that have new answers
New	3. Asking new questions that have old answers	4. Asking new questions that have new answers

Lewis is claiming that those experts engaged in making new Models of the Universe operate mainly within box #2. Of course, new questions could also receive new, heretofore unknown answers (box #4). But what about boxes #1 and #3? What would it mean for questions (old or new) to receive old answers? Here is my suggestion: to ask old or new questions and to find that the answers to those questions are the same old answers is an indicator of perennial truth. That is, even for the natural sciences—one among the many forms of human knowledge—there is the logical possibility of an unchanging foundation to truth. As scientists make new Images of the Universe, they must invariably rely upon a foundation of old answers. At the bottom of this tradition of old answers will be answers so old and so fundamental that they have never changed and can never change. Such answers can never change because they rest upon the very foundation of our Primary Belief in the Primary World.

What is an example of such an answer, old and true? Recall how I said that Nature critiques our Models by holding them up, as it were, in comparison against the order that already exists in things, an order that human beings have not put there. However, this general expectation that an order exists in Nature that we did not put there, that Nature is knowable and has her own logic that we can learn, is one of the oldest answers that exist in the history of the natural sciences, and it is a true one. This example of an old, true answer—the existence of a knowable order in nature that is not man-made—suffices for our purposes. It allows us to say how making Models is and is not an Art, as Fantasy is an Art, and how the natural sciences are part of making Models of the Cosmos.

Model-building requires Art insofar as we make a Model World by composing together answers to questions about the Cosmos, and those answers come from heterogenous sources. The natural sciences contribute in a principal way; they contribute to this Model not as a sub-creation, but as a mental object built to imitate the Primary World as such, without seeking the independence of a Secondary World. The Model can therefore be one means by which we theorize about the nature of the Primary World. To improve the Model, instead of appealing to Secondary Belief for its “inner consistency,” we turn to Nature herself as judge of our Art. We listen to Nature’s approval or disapproval of our Model by utilizing our foundation of “old answers.” Our Models are applicable to the truth of the Cosmos but they are not adequate to that truth in all its detail. Such detail is known only through the Primary Art, that Art which would build Primary Worlds. Here, Lewis and Tolkien might approve of quoting Thomas Aquinas, who writes:

Nature is nothing other than the reason of a certain art, namely the divine art instilled into things by which the things themselves are moved to a determinate end: as if the shipbuilder were able to bestow upon timbers such ability that they were to move of themselves so as to take on the form of a ship.¹⁸

The Models of the Cosmos that human beings make using the natural sciences—along with other kinds of knowledge and our “old answers”—are woven into the backcloth of human culture; they catch the shadows on the walls of our cultural caves. Nonetheless, through the shadows our attention is drawn towards that of which they are the Models—the deeper truths of the Primary World, which instills Primary Belief through the very existence of knowable things. This is important because both the Art of building Models of the Cosmos and the Art of Fantasy are natural human activities. And we humans are a part of the Cosmos. It seems good to say, therefore, with Tolkien and Lewis, that both Reason and Fantasy, meant in the way we have described, are necessary for our contemplation of the Universe.

— — —