Chapter 1

Reason and Belief

Human beings have all sorts of beliefs. The way in which they arrive at them varies from reasoned argument to blind faith. Some beliefs are based on personal experience, others on education, and others on indoctrination. Many beliefs are no doubt innate: we are born with them as a result of evolutionary factors. Some beliefs we feel we can justify, others we hold because of "gut feelings."

Obviously many of our beliefs are wrong, either because they are incoherent, or because they conflict with other beliefs, or with the facts. Two and a half thousand years ago, in ancient Greece, the first systematic attempt was made to establish some sort of common grounds for belief. The Greek philosophers sought a means to formalize human reasoning by providing unassailable rules of logical deduction. By adhering to agreed procedures of rational argument, these philosophers hoped to remove the muddle, misunderstanding, and dispute that so characterize human affairs. The ultimate goal of this scheme was to arrive at a set of assumptions, or axioms, which all reasonable men and women would accept, and from which the resolution of all conflicts would flow.

It has to be said that this goal has never been attained, even if it were possible. The modern world is plagued by a greater diversity of beliefs than ever, many of them eccentric or even dangerous, and rational argument is regarded by a lot of ordinary people as pointless sophistry. Only in science, and especially mathematics, have the ideals of the Greek philosophers been upheld (and in philosophy itself, of course). When it comes to addressing the really deep issues of existence, such as the origin and meaning of the universe, the place of human beings in the world, and the structure and organization of nature, there is a strong temptation to retreat into unreasoned belief. Even scientists are not immune from this. Yet there is a long and respectable history of attempts to confront such issues by rational and dispassionate analysis. Just how far can reasoned argument take us? Can we really hope to answer the ultimate questions of existence through science and rational inquiry, or will we always encounter impenetrable mystery at some stage? And just what is human rationality anyway?

The Scientific Miracle

Throughout the ages all cultures have extolled the beauty, majesty, and ingenuity of the physical universe. It is only the modern scientific culture, however, that has made any systematic attempt to study the nature of the universe and our place within it. The success of the scientific method at unlocking the secrets of nature is so dazzling it can blind us to the greatest scientific miracle of all:science works.Scientists themselves normally take it for granted that we live in a rational, ordered cosmos subject to precise laws that can be uncovered by human reasoning. Yet why this should be so remains a tantalizing mystery. Why should human beings have the ability to discover and understand the principles on which the universe runs?

In recent years more and more scientists and philosophers have begun to study this puzzle. Is our success in explaining the world using science and mathematics just a lucky fluke, or is it inevitable that biological organisms that have emerged from the cosmic order should reflect that order in their cognitive capabilities? Is the spectacular progress of our science just an incidental quirk of history, or does it point to a deep and meaningful resonance between the human mind and the underlying organization of the natural world?

Four hundred years ago science came into conflict with religion because it seemed to threaten Mankind's cozy place within a purpose-built cosmos designed by God. The revolution begun by Copernicus and finished by Darwin had the effect of marginalizing, even trivializing, human beings. People were no longer cast at the center of the great scheme, but were relegated to an incidental and seemingly pointless role in an indifferent cosmic drama, like unscripted extras that have accidentally stumbled onto a vast movie set. This existentialist ethos -- that there is no significance in human life beyond what humans themselves invest in it -- has become the leitmotif of science. It is for this reason that ordinary people see science as threatening and debasing: it has alienated them from the universe in which they live.

In the chapters that follow I shall present a completely different view of science. Far from exposing human beings as incidental products of blind physical forces, science suggests that the existence of conscious organisms is afundamentalfeature of the universe. We have been written into the laws of nature in a deep and, I believe, meaningful way. Nor do I regard science as an alienating activity. Far from it. Science is a noble and enriching quest that helps us to make sense of the world in an objective and methodical manner. It does not deny a meaning behind existence. On the contrary. As I have stressed, the fact that science Works, and works so well, points to something profoundly significant about the organization of the cosmos. Any attempt to understand the nature of reality and the place of human beings in the universe must proceed from a sound scientific base. Science is not, of course, the only scheme of thought to command our attention. Religion flourishes even in our so-called scientific age. But as Einstein once remarked, religion without science is lame.

The scientific quest is a journey into the unknown. Each advance brings new and unexpected discoveries, and challenges our minds with unusual and sometimes difficult concepts. But through it all runs the familiar thread of rationality and order. We shall see that this cosmic order is underpinned by definite mathematical laws that interweave each other to form a subtle and harmonious unity. The laws are possessed of an elegant simplicity, and have often commended themselves to scientists on grounds of beauty alone. Yet these same simple laws permit matter and energy to self-organize into an enormous variety of complex states, including those that have the quality of consciousness, and can in turn reflect upon the very cosmic order that has produced them.

Among the more ambitious goals of such reflection is the possibility that we might be able to formulate a "Theory of Everything" -- a complete description of the world in terms of a closed system of logical truths. The search for such a TOE has become something of a holy grail for physicists. And the idea is undoubtedly beguiling. After all, if the universe is a manifestation of rational order, then we might be able to deduce the nature of the world from "pure thought" alone, without the need for observation or experiment. Most scientists reject this philosophy utterly, of course, hailing the empirical route to knowledge as the only dependable path. But as we shall see, the demands of rationality and logic certainly do impose at least some restrictions on the sort of world that we can know. On the other hand, that same logical structure contains within itself its own paradoxical limitations that ensure we can never grasp the totality of existence from deduction alone.

History has thrown up many physical images for the underlying rational order of the world: the universe as a manifestation of perfect geometrical forms, as a living organism, as a vast clockwork mechanism, and, most recently, as a gigantic computer. All of these images capture some key aspect of reality, though each is incomplete on its own. We shall examine some of the latest thinking about these metaphors, and the nature of the mathematics that describes them. This will lead us to confront the questions: What is mathematics? And why does it work so well in describing the laws of nature? And where do these laws come from anyway? In many cases the ideas are easy to describe; sometimes they are rather technical and abstract. The reader is invited to share this scientific excursion into the unknown, in search of the ultimate basis of reality. Though the going gets rough here and there, and the destination remains shrouded in mystery, I hope that the journey itself will prove exhilarating.

Human Reason and Common Sense

It is often said that the factor which most distinguishes human beings from other animals is our power to reason. Many other animals seem to be aware of the physical world to a greater or lesser extent, and to respond to it, but humans claim more than mere awareness. We also possess some sort ofunderstandingof the world, and of our place within it. We are capable of predicting events and of manipulating natural processes to our own ends, and although we are part of the natural world, we somehow distinguish between ourselves and the rest of the physical universe.

In primitive cultures, understanding of the world was limited to everyday affairs, such as the passage of the seasons, or the motion of a slingshot or an arrow. It was entirely pragmatic, and had no theoretical basis, except in magical terms. Today, in the age of science, our understanding has,vastly expanded, so that we need to divide knowledge up into distinct subjects -- astronomy, physics, chemistry, geology, psychology, and so on. This dramatic progress has come about almost entirely as a result of "the scientific method": experiment, observation, deduction, hypothesis, falsification. The details need not concern us here. What is important is that science demands rigorous standards of procedure and discussion that set reason over irrational belief.

The concept of human reasoning is itself a curious one. We are persuaded by "reasonable" arguments, and feel happiest with those that appeal to "common sense." Yet the processes of human thought are not God-given. They have their origin in the structure of the human brain, and the tasks it has evolved to perform. The operation of the brain, in turn, depends on the laws of physics and the nature of the physical world we inhabit. What we call common sense is the product of thought patterns deeply embedded in the human psyche, presumably because they confer certain advantages in dealing with everyday situations, like avoiding falling objects and hiding from predators. Some aspects of human thought will be fixed by the wiring of our brains, others inherited as "genetic software" from our ancestors of long ago.

The philosopher Immanuel Kant argued that not all our categories of thought derive from sensory experience of the world. He believed that some concepts area priori,by which he meant that, although these concepts are notnecessary truthsin the strictly logical sense, nevertheless all thought would be impossible without them: they would be "necessary for thought." One example Kant gave was our intuitive understanding of three-dimensional space through the rules of Euclidean geometry. He supposed that we are born with this knowledge. Unfortunately, scientists have now discovered that Euclidean geometry is actually wrong! Today, scientists and philosophers generally suppose that even the most basic aspects of human thought must ultimately refer back to observations of the physical world. Probably the concepts that are most deeply etched in our psyche, the things that we find it hard to imagine could be otherwise -- such as "common sense" and human rationality -- are those that are genetically programmed at a very deep level in our brains.

It is interesting to speculate whether alien beings who evolved under very different circumstances would share our concept of common sense, or indeed any of our thought patterns. If, as some science-fiction writers have mused, life existed on the surface of a neutron star, one could not begin to guess how such beings would perceive and think about the world. It is possible that an alien's concept of rationality would differ from ours so greatly that this being would not be at all persuaded by what we would regard as a rational argument.

Does this mean that human reasoning is suspect? Are we being excessively chauvinistic or parochial in supposing that we can successfully apply the thought patterns ofHomo sapiensto the great issues of existence? Not necessarily. Our mental processes have evolved as they have precisely because they reflect something of the nature of the physical world we inhabit. What is a surprise is that human reasoning is so successful in framing an understanding of those parts of the world our perceptions can't directly reach. It may be no surprise that human minds can deduce the laws of falling objects, because the brain has evolved to devise strategies for dodging them. But do we have any right to expect extensions of such reasoning to work when it comes to nuclear physics, or astrophysics, for example? The fact that it does work, and works "unreasonably" well, is one of the great mysteries of the universe that I shall be investigating in this book.

But now another issue presents itself. If human reasoning reflects something of the structure of the physical world, would it be true to say that the world is a manifestation of reason? We use the word "rational" to mean "in conformity with reason," so my question is whether, or to what extent, the world is rational. Science is founded on the hope that the world is rational in all its observable aspects. It is possible that there may be some facets of reality which lie beyond the power of human reasoning. This doesn't mean that these facets are necessarily irrational in the absolute sense. Denizens of neutron stars (or supercomputers) might understand things that we, by the very nature of our brains, cannot. So we have to be aware of the possibility that there may be some things with explanations that we could never grasp, and maybe others with no explanation at all.

In this book I shall take the optimistic view that human reasoning is generally reliable. It is a fact of life that people hold beliefs, especially in the field of religion, which might be regarded as irrational. That they are held irrationally doesn't mean they are wrong. Perhaps there is a route to knowledge (such as through mysticism or revelation) that bypasses or transcends human reason? As a scientist I would rather try to take human reasoning as far as it will go. In exploring the frontiers of reason and rationality we will certainly encounter mystery and uncertainty, and in all probability at some stage reasoning will fail us and have to be replaced either by irrational belief or frank agnosticism.

If the world is rational, at least in large measure, what is the origin of that rationality? It cannot arise solely in our own minds, because our minds merely reflect what is already there. Should we seek explanation in a rational Designer? Or can rationality "create itself" by the sheer force of its own "reasonableness"? Alternatively, could it be that on some "larger scale" the world is irrational, but that we find ourselves inhabiting an oasis of apparent rationality, because that is the only "place" where conscious, reasoning beings could find themselves? To explore these sorts of questions further, let us take a more careful look at the different types of reasoning.

Thoughts About Thought

Two sorts of reasoning serve us well, and it is important to keep a clear distinction between them. The first is called "deduction." This is based on the strict rules of logic. According to standard logic, certain statements, such as "A dog is a dog" and "Everything either is, or is not, a dog," are accepted as true, while others, like "A dog is not a dog," are deemed false. A deductive argument starts out with a set of assumptions called "premises." These are statements or conditions which are held to be the case without further questioning, for the purposes of the argument. Obviously the premises should be mutually consistent.

It is widely believed that the conclusion of a logico-eductive argument contains no more than was present in the original premises, so that such an argument can never be used to prove anything genuinely new. Consider, for example, the deductive sequence (known as a "syllogism"):

1. All bachelors are men.

2. Alex is a bachelor.

3. Therefore, Alex is a man.

Statement 3 tells us no more than was present in statements 1 and 2 combined. So, according to this view, deductive reasoning is really only a way of processing facts or concepts so as to present them in a more interesting or useful form.

When deductive logic is applied to a complex set of concepts, the conclusions can often be surprising or unexpected, even if they are merely the outworking of the original premises. A good example is provided by the subject of geometry, which is founded on a collection of assumptions, known as "axioms," on which the elaborate edifice of geometrical theory is erected. In the third century B.C. the Greek geometer Euclid enumerated five axioms on which conventional school geometry is founded, including such things as "Through every two points there is a unique straight line." From these axioms, deductive logic can be used to derive all the theorems of geometry that we learn at school. One of these is Pythagoras' theorem, which, although it has no greater information content than Euclid's axioms, from which it is derived, is certainly not intuitively obvious.

Clearly a deductive argument is only as good as the premises on which it is founded. For example, in the nineteenth century some mathematicians decided to follow up the consequences of dropping Euclid's fifth axiom, which states that through every point it is possible to draw a line parallel to another given-line. The resulting "non. Euclidean geometry" turned out to be of great use in science. In fact, Einstein employed it in his general theory of relativity (a theory of gravitation), and, as mentioned, we now know that Euclid's geometry is actually wrong in the real world: crudely speaking, space is curved by gravity. Euclidean geometry is still taught in schools because it remains a very good approximation under most circumstances. The lesson of this story, however, is that it is unwise to consider any axioms as so self-evidently correct that they could not possibly be otherwise.

It is generally agreed that logico-deductive arguments constitute the most secure form of reasoning, though I should mention that even the use of standard logic has been questioned by some. In so-called quantum logic, the rule that something cannot both be and not be such-and-such is dropped. The motivation for this is that in quantum physics the notion of "to be" is more subtle than in everyday experience: physical systems can exist in superpositions of alternative states.

Another form of reasoning that we all employ is called "inductive." Like deduction, induction starts out from a set of given facts or assumptions, and arrives at conclusions from them, but it does so by a process of generalization rather than sequential argument. The prediction that the sun will rise tomorrow is an example of inductive reasoning based on the fact that the sun has faithfully risen every day so far in our experience. And when I let go of a heavy object, I expect it to fall, on the basis of my previous experiences with the pull of gravity. Scientists employ inductive reasoning when they frame hypotheses based on a limited number of observations or experiments. The laws of physics, for instance, are of this sort. The inverse-square law of electric force has been tested in a number of ways, and always confirmed. We call it a law because, on the basis of induction, we reason that the inverse-square property will always hold. However, the fact that nobody has observed a violation of the inverse-square law does not prove it must be true, in the way that, given the axioms of Euclidean geometry, Pythagoras' theorem must be true. No matter on how many individual occasions the law is confirmed, we can never be absolutely certain that it applies unfailingly. On the basis of induction, we may conclude only that it isvery probablethat the law will hold the next time it is tested.

The philosopher David Hume cautioned against inductive reasoning. That the sun has always been observed to rise on schedule, or that the inverse-square law has always been confirmed, is no guarantee that these things will continue in the future. The belief that they will is based on the assumption that "the course of nature continues always uniformly the same." But what is the justification for this assumption? True, it may be the case that a state of affairs B (e.g., dawn) has invariably been observed to follow A (e.g., dusk), but one should not construe this to imply that B is anecessaryconsequence of A. For in what sense might Bhaveto follow A? We can certainly conceive of a world where A occurs but B doesn't: there is no logically necessary connection between A and B. Might there be some other sense of necessity, a sort of natural necessity? Hume and his followers deny that there is any such thing.

It seems we are forced to concede that conclusions arrived at inductively are never absolutely secure in the logical manner of deductive conclusions, even though "common sense" is based on induction. That inductive reasoning is so often successful is a (remarkable) property of the world that one might characterize as the "dependability of nature." We all go through life holding beliefs about the world (such as the inevitability of sunrise) which are inductively derived, and considered to be wholely reasonable, and yet rest not on deductive logic, but on the way the world happens to be. As we shall see, there is no logical reason why the world may not have been otherwise. It could have been chaotic in a way that made inductive generalization impossible.

Modern philosophy has been strongly influenced by the work of Karl Popper, who argues that in practice scientists rarely use inductive reasoning in the way described. When a new discovery is made, scientists tend to work backward to construct hypotheses consistent with that discovery, and then go on to deduce other consequences of those hypotheses that can in turn be experimentally tested. If any one of these predictions turns out to be false, the theory has to be modified or abandoned. The emphasis is thus on falsification, not verification. A powerful theory is one that is highly vulnerable to falsification, and so can be tested in many detailed and specific ways. If the theory passes those tests, our confidence in the theory is reinforced. A theory that is too vague or general, or makes predictions concerning only circumstances beyond our ability to test, is of little value.

In practice, then, human intellectual endeavor does not always proceed through deductive and inductive reasoning. The key to major scientific advances often rests with free-ranging imaginative leaps or inspiration. In such cases an important fact or conjecture springs ready-made into the mind of the inquirer, and only subsequently is justification found in reasoned argument. How inspiration comes about is a mystery that raises many questions. Do ideas have a type of independent existence, so that they are "discovered" from time to time by a receptive mind? Or is inspiration a consequence of normal reasoning which takes place hidden in the subconscious, with the result being delivered to the conscious only when complete? If so, how did such an ability evolve? What biological advantages can such things as mathematical and artistic inspiration confer on humans?

A Rational World

The claim that the world is rational is connected with the fact that it is ordered. Events generally do not happen willy-nilly: they are related in some way. The sun rises on cue because the Earth spins in a regular manner. The fall of a heavy object is connected with its earlier release from a height. And so on. It is this interrelatedness of events that gives us our notion of causation. The window breaks because it is struck by a stone. The oak tree grows because the acorn is planted. The invariable conjunction of causally related events becomes so familiar that we are tempted to ascribe causative potency to material objects themselves: the stone actually brings about the breakage of the window. But this is to attribute to material objects active powers that they do not deserve. All one can really say is that there is a correlation between, say, stones rushing at windows and broken glass. Events that form such sequences are therefore not independent. If we could make a record of all events in some region of space over a period of time, we would notice that the record would be crisscrossed by patterns, these being the "causal linkages." It is the existence of these patterns that is the manifestation of the world's rational order. Without them there would be only chaos.

Closely related to causality is the notion of determinism. In its modem form this is the assumption that events are entirely determined by other, earlier events. Determinism carries the implication that the state of the world at one moment suffices to fix its state at a later moment. And because that later state fixes subsequent states, and so on, the conclusion is drawn that everything which ever happens in the future of the universe is completely determined by its present state. When Isaac Newton proposed his laws of mechanics in the seventeenth century, determinism was automatically built into them. For example, treating the solar system as an isolated system, the positions and velocities of the planets at one moment suffice to determine uniquely (through Newton's laws) their positions and velocities at all subsequent moments. Moreover, Newton's laws contain no directionality in time, so the trick works in reverse: the present state suffices to fix uniquely all past states. In this way we can, for example, predict eclipses in the future, and also retrodict their occurrences in the past.

If the world is strictly deterministic, then all events are locked in a matrix of cause and effect. The past and future are contained in the present, in the sense that the information needed to construct the past and future states of the world are folded into its present state just as rigidly as the information about Pythagoras' theorem is folded into the axioms of Euclidean geometry. The entire cosmos becomes a gigantic machine or clockwork, slavishly following a pathway of change already laid down from the beginning of time. Ilya Prigogine has expressed it more poetically: God is reduced to a mere archivist turning the pages of a cosmic history book already written.

Standing in opposition to determinism is indeterminism, or chance. We might say that an event happened by "pure chance" or "by accident" if it was not obviously determined by anything else. Throwing a die and flipping a coin are familiar examples. But are these cases of genuine indeterminism, or is it merely that the factors and forces that determine their outcome are hidden from us, so that their behavior simplyappearsrandom to us?

Before this century most scientists would have answered yes to the latter question. They supposed that, at rock bottom, the world was strictly deterministic, and that the appearance of random or chance events was entirely the result of ignorance about the details of the system concerned. If the motion of every atom could be known, they reasoned, then even coin tossing would become predictable. The fact that it is unpredictable in practice is because of our limited information about the world. Random behavior is traced to systems that are highly unstable, and therefore at the mercy of minute fluctuations in the forces that assail them from their environment.

This point of view was largely abandoned in the late 1920s with the discovery of quantum mechanics, which deals with atomic-scale phenomena and has indeterminism built into it at a fundamental level. One expression of this indeterminism is known as Heisenberg's uncertainty principle, after the German quantum physicist Werner Heisenberg. Roughly speaking, this states that all measurable quantities are subject to unpredictable fluctuations, and hence to uncertainty in their values. To quantify this uncertainty, observables are grouped into pairs: position and momentum form a pair, as do energy and time. The principle requires that attempts to reduce the level of uncertainty of one member of the pair serves to increase the uncertainty of the other. Thus an accurate measurement of the position of a particle such as an electron, say, has the effect of making its momentum highly uncertain, and vice versa. Because you need to know both the positions and the momenta of the particles in a system precisely if you want to predict its future states, Heisenberg's uncertainty principle puts paid to the notion that the present determines the future exactly. Of course, this supposes that quantum uncertainty is genuinely intrinsic to nature, and not merely the result of some hidden level of deterministic activity. In recent years a number of key experiments have been performed to test this point, and they have confirmed that uncertainty is indeed inherent in quantum systems. The universe really is indeterministic at its most basic level.

So does this mean that the universe is irrational after all? No, it doesn't. There is a difference between the role of chance in quantum mechanics and the unrestricted chaos of a lawless universe. Although there is generally no certainty about the future states of a quantum system, the relative probabilities of the different possible states are still determined. Thus the betting odds can be given that, say, an atom will be in an excited or a nonexcited state, even if the outcome in a particular instance is unknown. This statistical lawfulness implies that, on a macroscopic scale where quantum effects are usually not noticeable, nature seems to conform to deterministic laws.

The job of the physicist is to uncover the patterns in nature and try to fit them to simple mathematical schemes. The question ofwhythere are patterns, and why such mathematical schemes are possible, lies outside the scope of physics, belonging to a subject known as metaphysics.

Metaphysics: Who Needs It?

In Greek philosophy, the term "metaphysics" originally meant "that which comes after physics." It refers to the fact that Aristotle's metaphysics was found, untitled, placed after his treatise on physics. But metaphysics soon came to mean those topics that lie beyond physics (we would today say beyond science) and yet may have a bearing on the nature of scientific inquiry. So metaphysics means the study of topicsaboutphysics (or science generally), as opposed to the scientific subject itself. Traditional metaphysical problems have included the origin, nature, and purpose of the universe, how the world of appearances presented to our senses relates to its underlying "reality" and order, the relationship between mind and matter, and the existence of free will. Clearly science is deeply involved in such issues, but empirical science alone may not be able to answer them, or any "meaning-of-life" questions.

In the nineteenth century the entire metaphysical enterprise began to filter after being critically called into question by David Hume and Immanuel Kant. These philosophers cast doubt not on any particular metaphysical system as such, but on the very meaningfulness of metaphysics. Hume argued that meaning can be attached only to those ideas that stem directly from our observa

Excerpted from The Mind of God: The Scientific Basis for a Rational World by Paul Davies
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Mind of God The Scientific Basis for a Rational World

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