Reading: What is a Theory?

Chapter 4 -  WHAT IS A THEORY?

 Dr. Roy A. Clouser

4.1            INTRODUCTION

Let’s start by asking, why should we be especially concerned about the relation of religious belief to theories? Surely there is more to the interpretation of life than what is afforded by theories! And after all, aren’t theories highly technical matters understood only by scientists and philosophers? And don’t they contribute little to the understanding most people have of themselves and their everyday lives?

While some theories are, indeed, very technical and understood only by experts, many others are not. The idea that all theories are beyond the average person comes from associating the word “theory” with the latest advances in physics, chemistry, or astronomy. We should remember, however, that there are also influential theories about political rights, human happiness, morality, the understanding of art, the rearing of children, effective medical treatment, and public education, to name but a few. Many of these theories are well within the ken of the average person. What is more, it seems unlikely there is anyone who does not hold a theory on at least one of these topics. So the truth is that the average person is highly influenced by theories.

Another reason we should be concerned about the relation of religious belief to theories has to do with the authority theories are often claimed to have, especially those in the sciences. A widely held belief nowadays is that once  a scientific theory is formulated, tested, and accepted by most experts, it becomes the most authoritative standard for judging the truth of whatever it is about. This implies, of course, that if one’s religious belief is opposed by a widely accepted theory, one would be perverse to reject the theory and keep the belief. In the last century and a half this conclusion has been drawn repeatedly by advocates of Darwinian biology, Freudian psychology, and Marxist politics, to mention only the most obvious examples.

 Can those of us who believe in God accept the claim that theories are the final arbiters of truth? Are they really neutral with respect to religious belief, and so able to command the overriding allegiance that is commonly ascribed to them? If so, are they truly in a position to decide the truth (or rationality) of religious beliefs? And what about the popular view that although theories are authoritative in one realm of life, religious belief is authoritative in another realm? Is that a satisfactory way for a theist to understand how belief in God relates to theories? To answer these, and other important questions, we must first get some grasp of what theories are so we can then investigate the relation between them and per se divinity beliefs.

4.2            WHAT IS A THEORY?

The very soul of a theory is its hypotheses, and a hypothesis is an educated guess proposed in order to explain something. Of course, the fact that all hypotheses are guesses does not mean that all guesses are hypotheses, for not all guesses are intended to explain. At times we guess in order to win a prize or make a joke, for example. In what follows, we will be concerned with only the guesses made for the purpose of explaining something and which are therefore the very special guesses we call “hypotheses.”

Let me make clear right away that I will not try to correct the commonly accepted practice of using “hypothesis” and “theory” interchangeably to indicate either a single explanatory guess or a set of closely related explanatory guesses. For the most part, however, I will not be concerned here with isolated hypotheses but with complexes of them, together with their initial conditions and background assumptions, which form a highly abstract and systematic explanation that is defended with arguments and evidence. But there is another way in which “theory” is often used nowadays which I must reject completely. This is the practice employed by many writers who use the term “theory” for any sort of explanation, whether it employs hypotheses or not. For them, the term “theory” simply means any account, interpretation, or aid to understanding.

Such a use of “theory” is both confusing and misleading because it obscures what is essential to theories in contrast to other ways of explaining. For example, it leaves in the dark the difference between a theory and a myth. In many myths the workings of nature were personified and the relations between them were explained as we would explain relations among humans. It was this type of explanation the ancient Greek philosophers wanted replaced with hypotheses, which attempted to explain various data by the properties they possessed and the laws that governed them, and which they debated by producing arguments and evidence for and against them. (This is why the term “myth” eventually came to bear the connotation of an explanation that was both inferior and false.) Since we no longer make myths as explanations of nature, it may not seem important to preserve their difference from theories. But even aside from myths, we still use ways of explaining that are not theories. For example, the directions for how to get to my office or instructions as to how to operate a helicopter offer explanations but do not propose any hypotheses and so should not be called theories. Therefore, I will use “theory” to indicate only the explanations that do offer hypotheses and that try to justify them by arguments and evidence.

Given this definition of “theory,” it should be obvious that the business of making them is not the exclusive domain of scientists and philosophers. A detective may make a theory about a case she is working on; a motorist may devise one about a strange noise coming from his car’s engine, and an office worker may propose a hypothesis as to why the boss is so grouchy today. Since all of these guesses are made in order to explain something, they are theories every bit as much as the proposals of atomic theory or Freudian psychology. Moreover, both sorts of theories — the commonsense guesses as well as those of scientists and philosophers — are prompted by the same frustration: they are made when we cannot directly discover the answer to some question. When that happens, we guess at an answer.

There are important differences, however, between the way theories are made by scientists and philosophers and the commonsense way they are made around the house or office. Two such differences that have received almost universal recognition are: (1) theories in science and philosophy are more abstract than those of common sense,¹ and (2) the methods of evaluating theories offered in science and philosophy are much more complex and sophisticated. This greater sophistication is partly a result of the abstract nature of these theories, but also a response to the fact that theories purporting to explain the same data often disagree with one other. The evaluation methods are thus geared not only to judging a theory internally, but to weighing it against competing theories. Thus, not only are the hypotheses more abstract, but so are the reasons given for them.

In the remainder of this chapter, we will examine some important differences between highly abstract and commonsense theories. This is necessary because despite their wide acknowledgment, these differences are rarely examined closely nor are their consequences accorded their full significance.² I say this because it will turn out that among their consequences are features crucial to an account of how theories relate generally to religious belief. So we first need an analysis of abstraction, after which we will look at what differentiates scientific from philosophical theories. With that behind us, we will then distinguish two types of abstract hypotheses that occur in both science and philosophy. And finally we’ll close with an account of several guidelines for evaluating theories of each type.

4.3            ABSTRACTION

While everyone seems to agree that scientific and philosophical theories are highly abstract, rarely do writers attempt to spell out exactly what is meant by “abstract” or what is meant by its being “high.” One obvious starting point for this task is to consider the literal meaning of the term: to “abstract” means to extract, or remove something (mentally) from some wider background. This activity is virtually the same as focusing our attention, something we do frequently every day. For example, if we are trying to find a book that has a green cover we search the shelf by looking at all the books with green covers. In order to do that, we must first have mentally singled out (abstracted) the color green from all the other colors and also have singled out each book’s color from all the other qualities or properties the books have.

This level of abstraction is so common that we ordinarily pay no attention to it. For example, we often perform such actions as avoiding something because it smells bad, judging something too large for a container, or preferring a course of action because it is fair. Common as such actions are, they all require that we have first abstracted odor, size, or fairness from among all the other properties exhibited by whatever it is that smells bad, is too large, or is fairer. In such cases the extraction of those properties in our thought is not done so as to isolate them from the things or events that display them, however. That is, this level of abstraction does not focus on a thing’s odor or size or whatnot to such a degree as to disrupt the continuity of those properties with all the other properties of the things that have them. At this level of abstraction, a property, though distinguished and singled out, is still experienced as a characteristic  of the thing that exhibits it. I will call this the lower level of abstraction. By contrast, we are also capable of intensifying the focus of our attention to such a degree that we actually do isolate a property from whatever exhibits it, and thus focus our attention on the property itself. This is what I will call “high” abstraction.

Since this higher level of abstraction is such an important feature of scientific and philosophical theories, I’ll now illustrate its difference from low level abstraction in greater detail. Take the case of someone who has just bought a new car and is showing it to a group of friends. One of the friends says that she loves the color of the car, another comments that the car is beautiful, while yet others ask how expensive it was and how much it weighs. All of these remarks show that the speakers have singled out at a low level abstraction different properties of the car: its color, beauty, cost, and weight. But none of these properties has been isolated from the car; they are still both experienced and conceived as properties of the car.

If, however, someone were to focus on the property of, say, weight itself, apart from the car (or any other particular object), he would be conceiving of weight in the highly abstract way. Other properties such as velocity, mass, density, and volume could likewise be isolated. In this way highly abstract thinking can supply us with a distinctly different sort of concept over and above those which are available without it. It adds a new dimension to theorizing by making it possible for hypotheses to be guesses of (or about) highly abstracted properties, functions, relations, etc., in addition to being about the things and events which have them. It is thus possible for highly abstract concepts to be used to explain both other abstractions and the things and events we continue to experience in the unbroken connectedness of all their properties. Thus, by abstracting properties, we create the possibility of asking about the relations between these properties, and of looking for patterns of connections among those relations, all of which are being conceived in isolation from any things or events in which they may occur.³ For theories, the most important of the relations that can be discovered in this way are laws. In the case of the sample properties just named, laws holding among them would include:

momentum = mass × velocity

or

density = mass / volume

Laws holding among yet other properties would include the laws of motion or of thermodynamics, or Einstein’s famous E=mc2. Thus high abstraction makes it possible for us to ask questions about properties that could not have been asked had we not isolated them from the things that exhibit them, and to answer those questions by further isolating specific relations among them — especially law relations. Thus, for most theories of science and philosophy, neither the questions posed nor the answers offered to them could be conceived without high abstraction. Furthermore, producing arguments and evidence for (or against) the truth of such theories also involves high abstraction; in fact, the arguments for theories are often more sophisticated and ingenious than the hypotheses themselves.

The theories of science and philosophy thus differ from commonsense theories by employing high abstraction in any one (or combination) of at least three ways: (1) to ask the question(s) the theory is proposed to answer, (2) to invent the hypotheses proposed as answers to questions, or (3) to evaluate the truth of the hypotheses by arguments and evidence. From now on I will be dealing only with theories that employ high abstraction, so I will not continue to draw the distinction. The term “theories” will always refer to the highly abstract type, and the term “abstraction” will always refer to high abstraction rather than to the mere singling out of a property of a thing without isolating it from the thing.

4.4            ASPECTS OF EXPERIENCE

In addition to the three ways just listed, high abstraction plays yet another crucial role in theory making. For we not only abstract individual properties, relations, and patterns, we also abstract kinds of them. Take the properties we were just considering: weight, mass, momentum, and density. We can see that they, and the laws that hold between them, all share in common the further property of being physical. Distinguishing this large-scale, over-arching kind of properties and laws is thus a further abstraction from the abstracted properties and laws of that kind. So while individual properties and laws can be abstracted directly from things and events of our ordinary experience, the idea of the kind to which they belong is an abstraction from abstractions. Once recognized, such kind-ideas further serve theory making by delimiting a distinct domain or field of inquiry and research; in the example above, it was the physical domain of our experience that was isolated as a field of study — the field for theories of physics, including all its subdivisions and branches.

In the same way, many other kinds of properties-and-laws have been abstracted and made into specific areas of study. For example, biological properties and laws are the field of study of biology, while spatial properties and laws distinguish the field of study for geometry. Likewise, theories in economics or ethics have resulted from isolating properties and laws of those kinds and constructing theories about how various properties within each kind relate to one another and to the things that possess them. Over the past twenty-six centuries, such kinds have continued to be abstracted and become distinct fields of investigation and theory making for the disciplines formed to be devoted to them. The major examples of kinds of properties-and-laws that have been isolated as fields for theory making include (at least) those on the following list (the members and order of which will be discussed in more detail in later chapters):

fiduciary, ethical, justitial, aesthetic, economic, social, linguistic, historical, logical, sensory, biotic, physical, kinetic, spatial, quantitative

I will call these kinds of properties and laws “aspects” of the things we experience, and I am going to refer to the disciplines devoted to their study  as “sciences.” The term “aspect” will serve to emphasize that the kinds are exhibited by, and (indirectly) extracted from, the objects of our pre-theoretical experience. The term “science” will mean any specific discipline, delimited by one or more aspects, in which theories are constructed.

The list above should not be understood as a dogmatic pronouncement about whether these aspects are all genuine, since there are thinkers who would offer a somewhat different list. Rather, it is intended, first, as a description of (not a theory about) the way we come to experience properties of things in isolation as well as in their connectedness in objects. And second, it is a report of the list of aspects most thinkers have regarded as genuine fields for investigation and theory making. The list, then, is only intended to help us understand the major branches of present-day theory making, not to arrive at the one true list of genuine aspects of the world. So from now on when I use such expressions as “aspects of things,” or “aspects of the world,” or “aspects of our experience,” these expressions must be understood to refer to aspects in the same way the list does. That is, they refer to the distinct kinds of properties and laws most thinkers have taken to be exhibited by the objects of our experience prior to any theorizing. The list does not dogmatically require that no alternative listing could be correct, that our ordinary experience could not possibly be mistaken in some respect, or that no theory could show that the world is different in some respect from the way it is presented to our pre-theoretical experience.

Although many sciences are delineated by, and devoted to, a particular aspect, and even take their name from it, there are others that stake out their field and take their name from a particular class of things they want to investigate. Entomology, paleontology, and botany are examples.⁵ But that fact doesn’t count against the role of aspects in theorizing which I’ve just been emphasizing. For even when a science names its field by a particular type of thing, it still cannot study every aspect of those things. It is always some specific aspect(s) of insects, or fossils, or plants which they investigate — the biotic, for example. On the other hand, sciences need not be confined to only one aspect. For example, cultural anthropology deals with several aspects of ancient cultures and includes theories about how certain data relate across aspects. This, too, does not diminish the role and importance of abstracting aspects in theory making. For whether a science takes its name from a particular aspect, or from a certain range of things, or from several aspects of a certain range of things, in every case the aspectual delimitations remain crucial. At every point a theory must make clear the kind(s) of properties it is dealing with, and the kind(s) of laws it is using to relate and/or explain its data.

Having made this emphasis on the role of abstraction in isolating aspects, I now freely admit that many people working in the sciences would say, if asked, that they are unaware of abstracting entire aspects. I think this is true, but that it fails to count against the necessity and importance of such abstraction. The reason someone may be unaware of abstracting an entire aspect is that this act is usually done so automatically that it is not noticed by the thinker who does it — something like the way we are often unaware of moving our eyes while we read. In both cases there is a sub-event taking place within a larger act for the sake of that larger act. We move our eyes in order to read, and our attention is fixed upon our intended purpose rather than upon the eye movement done in order to accomplish that purpose. In the same way, and for the same reason, the abstraction of an aspect can go unnoticed because it is done for the sake of investigating and theorizing about the properties and laws that fall within it. So it is not surprising that someone engaged in a science may notice the role abstraction plays in the conceptualization of specific properties or relations, but not notice its role in isolating entire aspects. That role is so basic it can go unnoticed.

I will now offer some examples to illustrate how the abstraction of aspects is involved in the sciences. To appreciate the purpose of these examples, one must keep in mind the point made earlier that abstracting an aspect does not result in the thinker’s experience or thought being emptied of everything but the aspect which is abstracted. What these examples will be showing instead is how abstracting an entire aspect is added to our experience and is an addition that is indispensable for the enterprise of scientific theorizing.

For the first illustration, take the case of a biologist looking at microbes through a microscope. As she experiences them, the microbes appear to have spatial size and shape, sensory color, physical mass, etc. It may also be significant what quantity of them exist in a certain area. But these properties are all understood from the standpoint of her abstractive focus on the biological aspect of the microbes. It is that focus which guides and directs her thinking. Even though the size, mass, color, and number of the microbes are not themselves biological properties, they are all important insofar as they contribute to her understanding the life-processes of those objects. It is the focus on their biological aspect which guides the questions she will pose about them and the explanatory guesses she may make to answer those questions.

To see that this point applies equally to other sciences, consider a case in which a thinker’s focus is guided by distinguishing the economic aspect. The economist may even be concerned with the same set of microbes the biologist was examining. But rather than being concerned with them as data to be covered by a biological explanation, he will instead be offering an economic theory about them — an explanation whose explanatory principles include the law of supply and demand and the law of diminishing returns. Thus the microbes will be covered by the economist’s explanation because of their economic properties, even though their economic properties might change were the microbes dead rather than alive.

These are illustrations of a role played by abstraction in theory making that is often not sufficiently appreciated. Without the abstraction of entire aspects, it would not be possible to specify the kind of properties being investigated or the kind of laws being used to explain whatever a theory is seeking to explain. For these reasons — and others we will shortly discover — the abstraction of aspects is essential to theorizing. No matter exactly what list of aspects a thinker adopts, theorizing necessarily presupposes some list or other.

4.5            TYPES OF THEORIES

First, let’s consider the difference between scientific and philosophical theories. Both are highly abstract, of course, but whereas scientists stake out one or more specific aspects as their domain, philosophers seem to lack such a “home ground.” In fact, scanning the list of aspects given earlier could tempt one to suspect that since there appear to be sciences devoted to every aspect of our experience, there is nothing left for philosophy to be about. To make matters worse, many of the subjects about which philosophers write are the same as those that thinkers investigating a single aspect write about. For example, there are scores of works devoted to the philosophy of mathematics, the philosophy of history, the philosophy of law, and so on. This makes it appear that philosophy lacks its own domain, and so poaches on everyone else’s. Nevertheless, I am happy to report that philosophy does have a territory of its own, and that once its territory is properly understood the difference between a scientific theory in an aspect and a philosophical theory about the same aspect becomes clear.

Earlier we saw that some sciences theorize across aspects as well as within them. This allowed us to notice the possibility of developing a more general theory not restricted to a specific aspect, but one that gives an account of how properties of different aspects interconnect in certain data. That point raises the possibility of a wholly general theory, a theory about how all the aspects connect. And that is precisely what distinguishes philosophy from the sciences. Whereas the sciences are devoted to only one or a few specific aspects, philosophy aims at an all-encompassing overview; it offers theories which seek to explain the general connection of all the aspects and therefore of all the sciences. And while a few philosophers have occasionally disagreed with this definition and tried to argue that philosophy should have a less ambitious goal, their arguments are themselves testimony to the fact that from the beginning philosophical theories have tried to develop this sort of overview. As Gilbert Ryle put it:

The famous psychologist Jean Piaget also recognized this feature of philosophy when he said that

The two sorts of theories invented by philosophers to “synthesize” or connect all the aspects of experience into an overview are: (1) a general theory of reality and (2) a general theory of knowledge. The technical terms for these theories are, respectively, “ontology” (also nicknamed “metaphysics”) and “epistemology.” It is the development of ontologies and epistemologies which distinguishes philosophical theorizing and is its distinctive “home ground.” You might object that this is a home ground that encompasses all other home grounds — and you’d be right! But that’s exactly why a philosophical theory about math, physics, logic, or ethics isn’t simply poaching on the domains of those sciences. It’s not merely intruding into them because it is bringing the results of a general theory of reality or knowledge to bear on the study of those aspects. For this same reason, whenever scientists become involved with issues that require them to take a position on how their specific field of study relates to any others, taking that position has brought them across the border from science into philosophy.

This observation is not intended as a criticism; there is nothing wrong with theories within a specific aspect relating to a wider perspective. In fact, I will be arguing that it is impossible to make theories within a particular aspect that do not at least assume (even if unconsciously) some answer to the question of how that aspect relates to all the others. The difference is therefore one of emphasis. For even though scientific theories can’t avoid some general overview on how all the aspects connect, that overview may remain a background assumption which is never consciously raised, questioned, or defended. But whereas a scientist may merely assume an overview, the philosopher specializes in it. Philosophers make it the first order of business to justify the overview they invent or adopt, and all their other theories are developed in accordance with what is required by the overview developed in their theories of reality and/or knowledge.

But just what is meant by a “general theory of reality”? It is a theory that tries to discover the essential nature of reality. Its aim may be stated as trying to find what kinds of things there are. But saying it this way must not be mistaken for asking what types of things exist. Types of things would be an enormous list that would include: shoes, mountains, animals, clouds, people, etc. So the question here is not what types of things there are, but what is the most basic nature of them all. The traditional approach to answering that question can be thought of this way: if the various aspects of the things we experience are represented as beads on a necklace, then a general theory of reality wants to know “What is the string?” What is it these aspects are all aspects of ? This is because, traditionally, theories of reality have tried to answer this question by proposing some one or two of the aspects themselves as the string — as the basic nature of all things. For example, some theories have proposed that all things are basically physical, others that the nature of reality combines physical with logical properties and laws, still others that everything is basically mathematical, or sensory, etc.

The same is true of a general theory of knowledge. This is a theory that tries to account for what is essential to all knowledge, not just a specific kind such as mathematical knowledge, aesthetical knowledge, or ethical knowledge. Instead it tries to answer such questions as: “What characterizes knowledge as distinguished from mere opinion?” “How do we get knowledge?” and “What is truth?” To answer these questions, an epistemology has to account for the general connection of all the different (aspectual) kinds of knowledge. As in the case of traditional theories of reality, traditional theories of knowledge have also taken the approach of proposing one or another aspectual kind(s) of knowing as the key to all the rest. Some of them have held knowledge to be essentially mathematical, for example, while others have said it is sensory, or logical, or historical.⁸

It should be clear, then, that theories of knowledge and reality seek to explain the general connectedness between the aspects forming the domains of all sciences in a way that parallels the way most sciences try to explain the relations of data within a particular aspect.

A second distinction we can make concerning theories is between two types of hypotheses, each of which occurs in both science and philosophy. I will call the first of these an “entity hypothesis.” The term “entity” is used here because it is the widest and most indefinite term we have in English to refer to any sort of reality: it is used of things, events, states of affairs, relations, properties, laws, and anything else one wants to speak of. An entity hypothesis, then, is one which proposes some new reality as the solution to a question or puzzlement. In other words, this type of hypothesis postulates some underlying hidden reality as the explanation for whatever we are trying to explain. In this way the gaps in our knowledge concerning what we experience are filled by educated guesses about entities we do not experience. It is as though we have been given a jigsaw puzzle to put together which has no picture to guide us although we know what its overall outline should be. When we find we cannot make the pieces fit so as to produce that outline, we guess that there is a missing piece which, were it of such and such a shape, would go into a particular spot and enable all the other pieces to form the correct configuration. Most of the theories that are well known to the public are of this type. Atomic theory and the Big Bang theory in physics, the theory of evolution in biology, and Freud’s psychological theory postulating such entities as id, ego, and superego, are all examples of theories proposing entities we do not experience in order to explain features of things we do experience.

Here’s a simple example of how such an entity theory can get cooked up. Suppose we observe that red paint mixed with blue paint turns purple, and we want to know why. No amount of closer observation will answer this question. Even if we stick our heads in the mixing trough, we won’t see why the paint turns purple rather than any other color. So we invent a theory. We say that paint is made up of parts so tiny we can’t see them, and that these parts are shaped so that they reflect different wavelengths of light. So the red paint looks red because its tiny parts reflect light of the wavelength associated with our seeing red, while the paint that appears blue does so because its tiny parts are shaped so as to reflect the wavelength of light associated with our seeing blue. We then propose that, when mixed, the two differently shaped tiny parts combine so as to form a new shape — a shape that reflects the wavelength of light associated with our seeing purple.

This theory has now postulated a number of entities: tiny paint-parts, wavelengths of light, associations of specific wavelengths with perceived colors, and laws for how paint parts combine to form parts with a new shape. Notice that the form of the explanation is roughly that of a logical argument. In an argument we list premises as reasons for the truth of a conclusion, and then specify the logical rules by which the conclusion follows from those premises. In an entity theory, the initial conditions take the place of premises, and what needs to be explained takes the place of the conclusion. So we get:

C.   The paint turns purple

What we don’t know, however, is why 1, 2, and 3 produce the effect stated in C. So we ask ourselves what else is going on that we can’t observe? What other factors are involved which, in addition to 1, 2, and 3, produce C? Our guesses of what these might be then constitute our hypotheses as to the missing pieces of information which, could we conjoin them to 1, 2, and 3, would lead by logical laws to C. In this example, our theory proposes what those missing pieces of information are. It then tries to show that statements of these hypotheses, together with statements of the initial conditions (1, 2, 3), lead by logical rules to the statement of C. It is in this sense that the theory is said to explain C.

It should be clear even from this (overly simple) account that such theories involve — as was said earlier — not just hypotheses, but also initial conditions (such as 1, 2, 3) and background assumptions (such as rules of proof). My emphasis on the role of the hypotheses is because their nature is often misunderstood, and because it is especially hypotheses that can be shown to be importantly regulated by religious belief. It should also be noticed that entity theories can connect their hypotheses to what is to be explained by mathematical rules as well as logical rules, or by determining their probability rather than by logical or mathematical deduction. Probability arguments still fall within the same format, however, since the theory as a whole is still (roughly) in the form of a logical argument. That is, the argument purports to show that, given the relevant factors, the theory in fact has a probability of X, not that it probably has a probability of X.

Whenever some new entity is proposed, thinkers in that field want to find out whether the entities they’ve proposed are real. But since the entities usually proposed by theories cannot be directly experienced, their reality can be checked only indirectly.⁹ The most general description of such indirect evaluation is to say that a theory is assessed by how well it explains what it was invented to explain, including whether it explains better than any rival theories. The usual evaluation check-list includes such items as the theory’s consistency, how thoroughly it explains its data, and also how broadly its hypotheses can be applied. This last step is often the most persuasive one, and is one I call “extent beyond intent.” It means that when a theory offered to explain one puzzle is unexpectedly found to explain several others as well, it then becomes hard to deny that the theory has hit on something that corresponds to reality.¹⁰ Another especially persuasive form of confirmation is when a hypothesis that initially had a small range of evidence becomes the beneficiary of new evidence from unexpected sources. This “convergence of evidence” is then also hard to resist. Just as it’s hard to believe that a hypothesis is wholly false that unexpectedly explains things it wasn’t invented to explain, so also it’s hard to believe it’s entirely false when many sorts of evidence from widely different sources all converge to support it. But this is not to suggest that such evidence could ever prove a theory beyond all doubt. It can’t do that even when the evidence consists of successful experiments. Here’s why.

Many entity hypotheses include experimentation among their methods for evaluation. But as there are widespread misunderstandings about the role of experiments, I want to take time to dispel two of the most common of them. The first is the notion that unless there is an experiment to test a theory, that theory cannot really count as scientific. The truth is, however, that experiments, although desirable, are often not possible and a theory is not discarded just because it is not subject to experimental testing. The second misunderstanding is that if an experiment is successful then the theory has been proven beyond doubt and should henceforth count as indubitable truth. This mistake is often combined with yet another, namely, the idea that experimental proof distinguishes scientific theories from those of philosophy. According to this compound error, scientific theories can be proven by experiment but philosophical theories are unprovable because they are not subject to experiment. But while it is true that there are philosophical theories that have opposed one another for centuries, this is not because theories of science are always provable while the philosophical theories never are, nor is it because of the presence or lack of experiments. And this brings us to the final misunderstanding: the idea that experiments can prove a theory true beyond all doubt. The fact is, however, that experiments perform a different service.

In order to understand why experiments cannot prove a theory true, we must first understand two simple logical rules. The first says that if it is true that “If A then B,” and A is true, then B must be true. For example, A could mean “It is raining” and B could mean “The sidewalk is getting wet.” In that case, “If A then B” would translate: “If it is raining then the sidewalk is getting wet.” Now the rule says that if that is true, and if it’s true that it’s raining, then it must be true that the sidewalk is getting wet. Written as a formula the rule looks like this:

The crucial thing about this rule is that while it works from left to right, it does not work from right to left. We are not entitled to say: 

For even if the sidewalk is getting wet, that will not tell us that it is raining (other things could cause the sidewalk to get wet besides rain). But to claim that a successful experiment has proven a theory is to make the mistake represented in 4, 5, and 6 above. The argument would run:

Thus the notion that a successful experiment can prove a theory true is a logical mistake. There is, however, another logical rule that does go from right to left. It runs like this:

Applied to our sample argument, this would translate into: if it is true that rain will wet the sidewalk, and if it is true that the sidewalk is not getting wet, then it is also true that it is not raining. When the value of an experiment is understood in this way, we can get a logically valid argument that looks like this:

Here we have an important role for experiments in theories. They cannot prove a theory true, but they can prove that it is (at least partly) false. But even this value is subject to limitations. Showing a theory to be partly false will not, all by itself, show exactly which part of it is wrong. And it is always possible that the experiment was not properly conducted, or that it was not properly conceived in the first place. Besides, even if the experiment is both well planned and carried out, theories often have such great explanatory power that they are not given up merely on the basis of a few failed experiments. So the real role of experiments in theory making is more subtle. It is this: when  a theory survives a number of (well-planned and well-executed) attempts to prove it false, theorists in that field regard themselves as justified in being more confident about it. The theory is then said to be confirmed by experiments. (Experiments can have other employments as well, of course. They can, e.g., help decide between competing theories.) But no set of successful experiments can ever reach the point of conclusively proving a theory true.

At this point some readers might feel like asking, “Why is it, then, that refutation by experiment seems to happen more often in the sciences than in philosophy?” The answer is that there is another type of theory besides entity theories, a type often not able to be checked by experiment at all. And although both entity theories and theories of this other type occur in both science and philosophy, the most famous theories in science are entity theories while the most famous philosophical theories are of the other type. This other type does not begin by proposing the existence of some previously unsuspected and unexperienced reality, but explains its data in another way. Think again of our analogy of a jigsaw puzzle. If what is to be explained is represented by the overall outline of the puzzle, then this second type of theory seeks to arrive  at the puzzle’s outline by viewing one of its pieces as the key to the proper placement of all the others. Rather than propose some new entity, this sort of theory proposes a new perspective on the mutual juxtaposition and arrangement of all the pieces it already has. That is, this approach regards the pieces present as sufficient for solving the puzzle provided we identify the key piece for arranging the others in the right way. So I call this second type of theory a “perspectival” hypothesis.

An example of a perspectival hypothesis is the Marxist interpretation of history. According to this theory, the key factor in understanding history is always economics. This means that the economic factor is seen as decisive in explaining the course of history so that other possible explanatory factors, such as religious beliefs, racial hatred, political rivalry, desire for power, or the talent and influence of powerful individuals, are always controlled by the economics of the situation, rather than the other way around. Clearly, this is not an entity hypothesis; that economic forces play a role in human history is no guess. But it is a hypothesis that they alone determine the entire course of history.

It is important to distinguish perspectival from entity theories for several reasons. One is that it allows us to recognize that the theories which are central to philosophy — the theories that provide an overview of reality or knowledge — are perspectival theories. We already touched on this point in connection with the prevailing assumption in Western philosophy about how to construct general theories of reality or knowledge. The assumption is that the way to arrive at the basic nature of reality or knowledge is to select one or two aspects (from whatever list of them a thinker adopts) as identifying that nature. In terms of our earlier analogy, the assumption is that some one or two of what appear to be only beads of the necklace in fact comprise its string. This assumption thus identifies the nature of reality or knowledge by assigning a priority to one or two aspects over all the others. It then defends its priority assignment by arguing that its chosen aspect accounts for the connectedness between all the others because all the others are either identical with or generated by the one(s) assigned priority. The priority is therefore an ontological priority.

Since the latter point is important I don’t want it to go by too fast, so here it is again stated from a different angle. The assumption that the nature of reality or knowledge is identical with one or two aspects of our experience dictates a specific strategy for defending whatever aspects are chosen by a theory to play that role. It requires the strategy of arguing for such a theory in either of two ways. The more popular way theories argue for their selected aspect(s) is to admit that reality has many genuine aspects, but argue that their selected aspects have priority because they generate all the others. Theories taking this first way may therefore be seen as arguing that their favored aspects constitute the basic nature of reality or knowledge. By contrast, the second way a theory can employ the strategy is to argue that its favored aspect is the only genuine one, so that all the (alleged) others collapse to it. According to this second way, the chosen aspect would not merely be the basic nature of all reality but its exclusive nature. The common core of both these options, and thus the heart of the strategy, is therefore the claim that any aspect assigned priority could exist apart from the others, but the others could not exist apart from the one(s) with priority. And this is why the priority assigned in both these ways is ontological, and also why it simultaneously confers the status of nondependent reality and thus of divinity per se on whatever aspect(s) are selected to receive it.¹¹

Finally, recognizing the distinctiveness of perspectival theories is important because it allows us to notice how overviews on the nature of reality or knowledge pervade the concepts and theories of the sciences and are not confined only to philosophy. In fact, it is especially via views of the nature of reality that the influence of religious belief is conveyed to scientific theories. In other words, our central claim about the religious control of theories has two steps: scientific theories necessarily presuppose an overview of reality, while overviews of reality necessarily presuppose some per se divinity belief. Religious belief thus regulates overviews of reality directly, and through the mediation of some overview regulates scientific theories indirectly.

In my classes I have often found resistance to the idea that scientific theories cannot avoid presupposing a view of the nature of reality and thus of divinity. Even people who are comfortable conceding that philosophical theories of reality might unavoidably presuppose a religious belief often balk at extending the point to science. So while the full defense of this claim must wait till chapter 10, at least a rough, preliminary explanation of the claim seems called for now. To show this is not true only of philosophical theories, I’ll first illustrate it using the concept of an ordinary object (a saltshaker), and then by using the concept of an atom. This will allow us to see how analyzing the concepts of them invokes the question of how the properties of different aspectual kinds included in them relate to one another. That is the question — the question  of what kind of relations connect properties of different aspects — that has provoked so many thinkers to identify one or two aspects as generating all the rest. This is because relating properties of the same aspectual kind has never been as problematic as doing so for properties of different aspects. Within the same aspect properties can be seen to be related causally, to be mutually incompatible, to occur in typical patterns, etc. This is because the relations are of the same kind as the properties involved. But across aspects the relations themselves become the problem: what kind of relations are they? How, e.g., can properties of one kind produce properties of a different aspect? It is to answer such questions thinkers have made what I called priority assignments. They postulate that the properties and laws of some one (or two) aspects have a reality independent of the others and that they can actually produce the others. This is how they identify the kind of relation that holds between different aspectual properties as we find in things or postulate them in theories. And that is why doing this thereby identifies the kind of reality that experienced things or hypothetical entities depend on. This sort of answer is therefore the same as an overview of the nature of reality, and thus also identifies the nature of what is taken to be divine per se.

If I am sitting at dinner with, say, a materialist and I ask him to please pass the salt, he is perfectly able to understand my request for several reasons. First, he is just as much in the presence of the saltshaker as I am, and his perception is in proper working order. As a consequence, he too has formed the belief that there is a saltshaker at his end of the table. Neither of us forms that belief because of what we hold to be divine, but because we see it there. Moreover, our perception of it is not wholly sensory, but includes properties of many different (aspectual) kinds which the saltshaker exhibits. These are logically distinguished and combined by each of us into a concept of the saltshaker in such a way that there is a large overlap between our concepts, an overlap sufficient to confirm us in the belief that we are dealing with the same object. At this level of experience and thought, therefore, no philosophical or religious issue arises. He passes me the salt. But were we to begin to analyze more extensively our concepts of the saltshaker, we would soon find that while I believe none of the kinds of properties and laws it exhibits to be generated by any other but that all are the creations of God, he believes them all to be generated by, or identical with, something physical. So while at the initial level of everyday experience he might agree with me were I to have commented that the saltshaker is beautiful or overpriced, a more extensive probing would show why his concept of it would force him either to deny there are such nonphysical properties as beauty and cost, or to insist that they are dependent on the physical properties and laws true of the saltshaker. This is because, on his view, nonphysical properties either don’t exist or, if they exist at all, owe their existence to the physical.¹² We would discover this, however, only if we analyzed our concepts in far greater detail than is ever needed by ordinary thought in everyday experience.

Now theories also start with our common experience of the world around us. They, too, are based on our perceptions and the perception reports of others, and on the recognition that the objects of experience exhibit properties and law-conformities of different aspectual kinds. But unlike our concept of the saltshaker, the concepts of hypothetical entities are our own inventions. We place in them just the properties we wish to combine as the nature of the entity we’re proposing to fill the relevant gap in our knowledge. That is, we never simply propose an entity without specifying its nature; we can’t just say “there are atoms,” for example. We’d have to know what kind of a thing an atom is supposed to be in order to understand what it explains and how it explains it. So the concept of a hypothetical entity displays much more immediately and clearly the kind of relation assumed to hold between the various kinds of properties included in it than do our concepts of objects of pre-theoretical experience. In the concept of an atom its physical properties, e.g., must be thought of as relating in specific ways to its mathematical and spatial properties, as well as to yet other kinds of properties such as the sensory properties of our observations. That is, such inter-aspectual relations must themselves be conceived in a specific way, and whatever answer is given (or assumed) to that question is a position about the basic nature of reality. For both atoms and the things they comprise depend upon the connectedness of all their properties, so that whatever is supposed to qualify that kind of connectedness is also the ultimate qualifier (nature) of the world we experience.

Here’s the same point paraphrased from another angle. A thinker who sees a particular aspect as the ultimate nature of reality would be compelled to have a view of reality consistent with that belief. And this would be true whether or not the thinker actually worked out an entire philosophical overview. Even without elaborating such a theory, even if the overview of reality remained unconscious, it could not then fail to be implicit in whatever hypothetical concepts the scientist accepts. For in any concept of a hypothetical entity, the way its properties are combined to constitute its nature will reflect which kind(s) of them are thought to have independent existence and which owe their existence to the independent kind(s) of properties and laws. If the aspectual kind of properties constituting the nature of the entity is understood as the only real kind, or as the kind that generates all other kinds, then that aspect is being regarded as qualifying the nature of all reality and for that reason has the status of per se divinity. On the other hand, if the kind of properties the concept combines as the nature of the entity is presented as owing its existence to properties and laws of some other kind(s), then the nature of the hypothetical entity is non-divine. But in that case, its explanatory power is relativized to the divine kind(s) of properties and laws upon which it ultimately depends. In either case the issue of the nature of the relation between aspects cannot be avoided.

This paraphrase may seem to beg the question, however, as it uses the illustration of a thinker who already has a priority assignment owing to a belief about the ultimate nature of reality. So it may seem that it only explains how, for thinkers who already have an overview of reality and a per se divinity belief, such a belief will impact their scientific concepts. But this is not correct. What was illustrated prior to the paraphrase already showed why the concept of a hypothetical entity can’t avoid presupposing some idea of how the different aspectual kinds of properties relate within that entity. And this will be true of any such concept regardless of whether the person accepting it (consciously) holds a view of the nature of reality based on assigning priority to one or another aspect. For it is unavoidable that properties comprising the nature of a hypothetical entity are thought of as: (1) belonging to the only real kind of properties or to the kind that generates all the other kinds, or (2) owing their existence to properties and laws of some other aspect which has independent existence, or (3) owing their existence and connectedness to something other than any aspect whatever. Which of these is assumed is not a trivial issue, as it is crucial to understanding the explanatory range and power of an entity to know whether (and which) properties included in its nature are independent, and if not, to know what they are (ultimately) dependent upon. In this way, how the properties included in the concept of an entity are related to one another presupposes some overview of how the aspects relate generally, which, as I’ve been saying, is the same as an overview identifying the nature of reality. Thus the issue of how the various aspects relate is not avoidable. Whether an answer is tacitly assumed or overtly defended, some view of it guides how the concept of any entity is formed. This is why even the simplest and most basic concepts in the sciences are understood differently depending on the overview of reality assumed by the thinker.¹³ (We will see a number of examples of this in the casebook chapters when we examine theory conflicts in mathematics, physics, and psychology.)

Let me be clear, however, that although I’ve been dealing mostly with theories and concepts framed on the assumption of options (1) or (2), that is because it is those which have long dominated science and philosophy. But they are not the only ones, as option (3) makes clear. And as it is my contention that(1) and (2) presuppose a pagan religious commitment, I also contend that they should be rejected by theists. So we will investigate what theories and concepts framed upon option (3) could look like in the final three chapters.

Throughout this preliminary sketch I’ve been speaking only of the concepts of entity hypotheses. I’ve been saying that the impact of religious belief on entity theories derives from the way aspectual priority assignments appear within concepts, and not just from contact with philosophical theories.¹⁴ But this point applies equally to the perspectival theories that occur in the sciences as well as to their entity theories. As was mentioned earlier, perspectival hypotheses occur in the sciences as well as philosophy. For example, a botanist may propose something as simple as that it’s the color of a flower that attracts the bees rather than its smell. That would be a perspectival hypothesis, but certainly is not an overview theory about the relation of all the aspects. Nevertheless, even in such a simple case, a more extensive analysis of the concepts employed in it would — like that of the saltshaker or an atom — reflect what is being presupposed about the relations between properties of different aspectual kinds. This is the reason the overview issue can’t be eliminated, and so is the reason why the sciences can never be completely independent of philosophy. And since we’ve already seen why such overviews in turn presuppose some per se divinity belief, it’s also why perspectival theories can also never be free of religious regulation whether or not a thinker wants them to be, admits it, or is even conscious of it.

4.6            CRITERIA FOR JUDGING THEORIES

The methods for confirming entity theories seem to be more precise and definite than those for perspectival overview theories. As was already mentioned, the thoroughness of explanation for entity theories can be checked by using logic and/or mathematics to tell whether known facts are implied when an entity proposal is added to the initial data a theory is dealing with. Arguments may also attempt to show that an entity hypothesis is more probable than its rivals. In addition, entity theories often lead to predictions which can be checked by experiments. Breadth of application is also easier to determine for an entity theory. It can be obvious whether a proposed entity, when utilized by another theory, yields confirmable results. Theorists also evaluate an entity theory according to how many new entities it needs to propose. Their rule is that if two rival theories explain things equally well, the one with fewer hypotheses is to be preferred. In these ways, entity hypotheses can be evaluated, improved, or disproved.

By contrast, these standard procedures for judging entity hypotheses do not seem to work for perspectival overviews at all. Since proposing a perspectival slant on the nature of reality is not a matter of conjoining proposed entities to initial conditions to see if they entail specific results, perspectival overviews are not cast in the format of a logical argument as entity theories are. For   that reason they are almost never able to be confirmed by experiment. And when rival perspectives are compared for thoroughness, whichever one looks true to a person will seem to explain things better even if another explains more thoroughly. In fact, when an alternative perspective gives a more detailed explanation of more things, that only makes it seem false in greater detail to someone who rejects it.15 Moreover, the breadth of any overview perspective is (at least potentially) universal; all reality can be viewed from the standpoint of, say, its quantitative, spatial, physical, sensory, or logical aspects, etc. And, finally, it makes no sense to compare two perspectives to see which proposes fewer entities, since neither proposes any.

So it seems clear that perspectival overviews need their own guidelines. Of course, they share with entity theories the need to be logically consistent. A theory that contradicts itself can’t be right as it stands. But that is hardly news. Over and above logical consistency, the only rule specific to an overview theory up till now has been to see whether there are data that don’t seem to have any plausible account at all from its standpoint. For example, it’s clear that older forms of materialism could not give any plausible account of concepts. But modern materialists now point to the capabilities of computers and claim that human concept formation is essentially the same process. Whether that can be successfully defended or not, materialism now has some sort of account of conceptual thought whereas previously it had none. This rule for evaluation is, of course, looser than the ways entity theories are judged, and yields less definite results. As was already noted, although it counts against a perspective if it has no account whatever for some range of data, even what it can give an account of will still look false to anyone holding another perspective. Moreover, there are no sharp criteria for what is or isn’t a “plausible account.” To compound these difficulties it’s also the case that even if it could be shown that all presently existing accounts of certain data from a particular perspective are not plausible, that would not show that no plausible account could ever be given from that point of view. So the debates between overview perspectives go on century after century.

I believe it is possible, however, to offer some additional guidelines which can sharpen the evaluation of overview hypotheses. Each of these guidelines will be the statement of a type of incoherency to be avoided. (Of course, these incoherencies should be avoided by shorter-range perspectival theories and entity theories as well, but they will be presented here mainly with their application to perspectival overviews of reality or knowledge in mind.)

I find there are (at least) three incoherencies over and above logical inconsistency that need to be exposed, defined, and avoided. Moreover, these three are often more subtle and harder to detect than straightforward logical contradiction. It’s also the case that logical inconsistency is usually easy to correct, and its correction rarely requires serious alteration of a theory in which it occurs. By contrast, the three incoherencies I’m about to formulate are not easily corrected. They often occur at the heart of a theory and can’t be eliminated without serious alteration or surrender of the theory’s main claims. Two of these incoherencies have been noticed by philosophers in the past, but are not yet taken seriously enough in my opinion. The third is relatively new, having been first defined and deployed by Herman Dooyeweerd about fifty years ago.¹⁶

The first of these criteria rules out any theory that makes a claim which, while not contradicting any other statement of the theory, is incompatible with itself. Following a number of recent thinkers, I will call such a claim “self-referentially incoherent.” I find there is both a strong and a weak sense in which a claim can violate this requirement. In the strong sense, a claim is self-referentially incoherent if it is itself an exception to what it asserts. In that case it cancels the possibility of its own truth. In the weak sense, a statement committing this incoherency doesn’t require its own falsehood, but cancels the possibility of anyone ever knowing it to be true. Thus, even though it could possibly be true, the fact that we can never know whether it’s true makes it a very bad explanatory guess.

As an example of the strong sense of this incoherency, take the claim sometimes made by Taoists that “Nothing can be said of the Tao.” Taken without qualification (which is not the way it is intended), this is self-referentially incoherent since to say “Nothing can be said of the Tao” is to say something of the Tao. Thus, when taken in reference to itself, the statement cancels its own truth. As an example of the weak version of self-referential incoherency, take the claim once made by Freud that every belief is a product of the believer’s unconscious emotional needs. If this claim were true, it would have to be true of itself since it is a belief of Freud’s. It therefore requires itself to be nothing more than the product of Freud’s unconscious emotional needs. This would not necessarily make the claim false, but it would mean that even if it were true neither Freud nor anyone else could ever know that it is. The most it would allow anyone to say is that he or she couldn’t help but believe it.

The next criterion says that a theory must not be incompatible with any belief we have to assume for the theory to be true. I will call a theory that violates this rule “self-assumptively incoherent.” As an example of this incoherence, consider the claim made by some philosophers that all things are exclusively physical. This has been explained by its advocates to mean that nothing has any property or is governed by any law that is not a physical property or a physical law. But the very sentence expressing this claim, the sentence “All things are exclusively physical,” must be assumed to possess a linguistic meaning. This is not a physical property, but unless the sentence had it, it would not be a sentence; it would be nothing but physical sounds or marks that would not linguistically signify any meaning whatever and thus could not express any claim — just as a group of pebbles, or clouds, or leaves, fails to signify any meaning or express any claim. Moreover, to assert this exclusivist materialism is the same as claiming it is true, which is another nonphysical property; and the claim that it is true further assumes that its denial would have to be false, which is a relation guaranteed by logical, not physical, laws. (Indeed, any theory which denies the existence of logical laws is instantly and irredeemably self-assumptively incoherent since that very denial is proposed as true in a way that logically excludes its being false.) What this shows is that the claim “All things are exclusively physical” must itself be assumed to have nonphysical properties and be governed by nonphysical laws or it could neither be understood nor be true. Thus, no matter how clever the supporting arguments for this claim may seem, the claim itself is incompatible with assumptions that are required for it to be true. It is therefore self-assumptively incoherent in the strong sense.¹⁷

The fact that the previous example had to do with a theory that denied a genuine plurality of aspects is no accident. Although such theories are not the only ones to violate this criterion, theories denying that the world we experience really contains things with a plurality of kinds of properties and laws are invariably self-assumptively incoherent. This criterion is thus our first defense for regarding our experience of a plurality of aspects as genuine: any attempt to deny there are any aspects, or to reduce them all to only one allegedly genuine aspect, always turns out to commit this incoherency.

The last of the three criteria, like the previous one, also has to do with the compatibility of a theory with a factor that lies outside its explicit content. But rather than being concerned with the compatibility of a theory with its own unstated assumptions, this final one concerns the compatibility of a theory with conditions necessary for its production. In other words, it says that a theory must be compatible with any state that would have to be true of a thinker, or any activity the thinker would have to perform, in order to have formulated the theory’s claims. To borrow and recast an old Marxist expression, a theory must be compatible with “the means of its production.” Any theory that violates this criterion will be said to be “self-performatively incoherent.”

In order to start with as simple an illustration of this rule as possible, let’s take the trivial case of someone saying that no one can speak, or that there is no such thing as language. Since one has to speak in order to say it cannot be done, and since one has to speak in a language in order to say there are none, these claims violate the criterion in the strong sense and could not possibly be true. To illustrate the weak version of the criterion, take the case in which we are asked to determine the temperature of water in a glass by using a thermometer. The fact is, once we put the thermometer into the water we cannot coherently claim to know what the temperature was prior to performing that act. The act itself has changed the temperature of the water. So the very activity necessary to discovering what we want to know prevents us from ever being able to know it (it produces an “uncertainty relation”). Thus to claim that “The thermometer shows that the water in the glass was twenty degrees C” is to ignore the fact that the action by which this information was obtained prevents us from ever knowing the claim to be true.

A more serious example of the strong sense of this incoherency is the one offered by Descartes (but without his recognizing or defining it as a specific, distinct criterion). In reflecting on what can and cannot be reasonably doubted, Descartes saw that one thing that could not reasonably be doubted was his own existence. This was because he had to exist in order to perform the act of doubting. He also had to exist in order to think or say “I do not exist.” Thus his state of existing and his acts of thinking or speaking were all incompatible with the claim “I do not exist.” He therefore held that “I do not exist” had to be false, in which case he could not reasonably doubt the truth of “I exist” whenever he thought of it. This example is important because it highlights the way this criterion can yield significant results by comparing a theory’s claims to conditions which not only stand outside the theory itself, but are not even beliefs. Like the previous criteria, the demand for self-performative coherency does not set aside, but assumes logical laws and distinctions. Nevertheless, it gives us a way to test theories which goes beyond mere logical consistency. It reminds us that a theory may avoid explicitly violating any logical rules and even remain compatible with its own assumptions, but still be fatally flawed. Notice that there is nothing logically self-contradictory about the sentence “I do not exist”; the truth of “I exist” is not required by logical rules alone. All the same, Descartes saw that the first claim could not be true and the second claim could not be false in some more-than-logical sense — a sense now identified and named.

The test of whether a theory is self-performatively coherent is one we will find particularly illuminating when we examine traditional theories of reality in more detail in chapter 10. There we will use this criterion to show both why the issue of inter-aspectual connectedness can’t be avoided and why ascribing independent existence to any aspect is always self-performatively incoherent in the weak sense. Its employment will show that any attempt to justify the claim that an abstracted aspect is self-existent (and thus divine) is always incompatible with the activity of abstraction required to make the claim rendering the claim unjustifiable as a theory.¹⁸ And this, as I said earlier, will further confirm both the religious character of those claims, and the position that they are grounded upon experience rather than on the sort of justification sought by theories.

Before this position can be defended, however,  it is necessary to clarify   it further. This is the task of the next two chapters. Chapter 5 will contrast this position with its major rivals concerning the relation of religious belief to theories. Then chapter 6 will give a more detailed account of what is meant by saying some religious belief always “controls” or “regulates” abstract theories.

With these clarifications behind us, we will then be prepared for the casebook chapters which illustrate that control at work in several scientific theories in math, physics, and psychology.