Science and the Human Prospect

Ronald C. Pine 

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Chapter 4
image of world Cultural Roots 1. The Ancient Greeks a part of the world that had for centuries been civilized... there gradually emerged a people, not very numerous, not very powerful, not very well organized, who had a totally new conception of what human life was for, and showed for the first time what the human mind was for. H.D.F. Kitto, The Greeks
    I would not be confident in everything I say about the argument: but one thing I would fight for to the end, both in word and deed if I were able --- that if we believe we should try to find out what is not known, we would be better and braver and less idle than if we believed that what we do not know it is impossible to find out and that we need not even try.  Socrates

The entire intellectual history of Western culture is but a footnote to Plato.  Alfred North Whitehead

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Ancient Greek Philosophy
  Nothing. Fourteen billion years ago only a single point, at nowhere and nowhen. Approximately five billion years ago, the formation of the Earth and the Sun. Billions of years later, between 5 and 2.5 million years ago, a fraction of a percent of Earth's history, the lush jungle habitats of prehistoric apelike creatures began to contract in Africa due a worldwide drop in temperatures and perhaps to the moving of continents. Eventually the vast grasslands which resulted selected a new type of creature, an apelike creature that stood upright, that perhaps could run like a track star and carry things with its hands. Finally, just a few minutes ago on the Cosmic Calendar (see Chapter 1), modern Homo sapiens emerged and perhaps began to ask why there is something rather than nothing.
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Belief in Natural Law

As regards the first [principle of science], "that nature can be understood". . . The most astonishing thing about it is that it had to be invented, that it was at all necessary to invent it.  Erwin Schrodinger, Mind and Matter

For generation upon generation after this, our ancestors had only the wonder of the stars to entertain and to hint at an answer. Most of the human race answered the questions of why and how in terms of the idea that the universe is like a large puppet whose strings are pulled by a god or gods; that unexpected events, or even expected ones, are subject to the whims of a supernatural creature who has the same emotional stability problems as a human being. At a time of multicultural awareness, it is perhaps not fashionable to attribute so much to one culture, but before science could exist a very radical idea had to be accepted.

In the northeastern Mediterranean area -- Ancient Greece, the west coast of Asia Minor, and the various islands in between -- from the seventh century to the second century B.C., a mere 2500 years ago, the last five seconds or so on the Cosmic Calendar, a revolution in thought took place. Some people began to think that the universe is a rational place, with an internal order and governed by universal, natural laws. Most important, they believed that this order is knowable and objective, and that human beings can figure out these laws. These people also thought that the cosmos(1) is a good place, and they began to accept particular cognitive values: that our knowing about the universe is good, that knowing takes place, not through divine revelation and obedience to authority, but through open inquiry and critical evaluation of competing ideas, and that knowing is good not only for practical utility, but for its own sake as well. Knowledge, they believed, is an essential ingredient of happiness and the good life. As the astronomer Kepler would echo centuries later, the ancient Greeks believed that as the birds sing and the grass grows, human beings were meant to be curious and seek knowledge. In short, faith in the gods was replaced with a faith in the cosmos, and the human species discovered that reason was a tool with which to romance the universe.

The most remarkable discovery ever made by scientists was science itself.  Jacob Bronowski

Ponder all things, and establish high thy mind.  Pythagoras

Ironically, religion was instrumental in the development of this outlook. Of the many creation myths circulating in the Mediterranean area, one maintained that the present state of the cosmos evolved from chaos. From this ordered cosmos, it was thought, evolved human beings and the gods. In this creation story an ordered universe exists prior to the gods, rather than after. The gods did not create the universe; they are simply another part of it. The human species and the gods were considered both children of the cosmos, implying an important consequence for the relationship between human beings and their gods: humans and the gods were on a somewhat equal footing. Although the gods were granted immortality and carefree living, and were more powerful, humans were potentially morally superior and more intelligent. Human existence in general was more challenging and potentially happier. The Greeks prayed to their gods standing upright. Devotion was superficial. The gods were kept happy to avoid trouble, but there was no love lost between humankind and the gods. The human family had to pay its taxes but did not have to enjoy doing it.

The Greek word philosophy means "love of wisdom." The word philos, however, does not mean a sexual love (eros), nor a charitable love (agape), but a passionate never ending striving, a loving contemplation of the cosmos. Devotion to a personalized divinity was replaced by a devotion to wisdom, a seeking of knowledge and the correct use of that knowledge.

The Greeks were essentially proclaiming that humans could be happy without the help of a god or gods. Humans, as part of a purposeful nature and a rational plan, had everything they need to be happy. Happiness was simply a matter of developing the potential the cosmos gave us -- especially our ability to think critically and obtain knowledge. Actualizing the potential to know was considered fun, because in doing so human beings fulfilled nature's purpose. Continual discovery and exploration were thought of as joyful, even though there is never a completion to this process, a final resting place of understanding everything. Heaven, immortality and the afterlife, for these early contemplators of our cosmological roots were boring in comparison.

Philosophers and psychologists refer to this type of theory of happiness or the good life as a self-actualization theory. The process of moving toward the achievement of a goal is more important than the actual achievement of the goal. Consider the mind of a child. Try to remember the fresh joy of every new experience. We are all born curious, full of questions, with an open mind, and a built-in sense of awe and wonder about life. Each new object is a new universe, each day a new beginning. A child would not be disappointed if the daily ecstasy of experiencing and learning new things were to last forever. The Greeks in many ways were the children of our scientific culture.

From the standpoint of eternity, all of our pursuits are futile. There will be no end to learning; there will be no final day when everything is known. Moreover, some day the universe could suffer a cosmic hiccup relatively close to us (a supernova, colliding neutron stars) and we, and all our progress and knowledge, would be gone in an instant.

Many people become disenchanted with science when they learn that science does not provide absolutely certain truths, a perfectly safe harbor in the buzzing world of daily turmoil and change. They fail to realize that if it did provide final truths, science could not grow. Adults and cultures can become tired of learning (remember the Augustine quotation in Chapter 3); like children, a true scientist must relish the freshness of every new day. We are all born with this feeling of freshness. Most lose it. But it is a necessary part of the scientific attitude.


The analogy between childhood wonder and adult creativity is biology, not metaphor.  Stephen Jay Gould

Learning is ever in the freshness of youth even for the old.  Aeschylus

For myself, I like a universe that includes much that is unknown and, at the dame time, much that is knowable. A universe in which every thing is known would be static and dull, as boring as the heaven of some weak- minded theologians.  Carl Sagan, "Can We Know the Universe? Reflections on a Grain of Salt"

However, a price must be paid for this attitude: One must be able to live with a cosmic insecurity. One must be able to use this insecurity as a creative force to keep traveling, and remember that it is better to travel than to arrive. This attitude is not easy either for a culture or an individual. Like a romantic affair, our quest for understanding is an uneasy mixture of rapture and incompleteness.

The Greeks were comfortable with a way of life that was challenging and ongoing. Every solution to a problem would lead to another challenge. Complete closure and peace of mind would lead to stagnation. Similarly, science does not provide final answers. Every solution to a mystery produces new mysteries. From this point of view, the problem of induction discussed in Chapter 2 is not really a problem. That even our best theories must be accepted tentatively and tested continually is just part of the ongoing challenging nature of life.

In Athens, the key city-state that was the center of the development of Greek culture, we find the birth place of democracy and the Olympics. Happiness to the Greeks was the striving to develop the full potential of our minds and bodies. The pursuit of truth and the development of the mind required the free exchange of ideas, and friendly physical competition served well the development of the body.

In ancient Greece and the areas influenced by Greek philosophy, the fruits of thinking in natural terms ripened quickly. Thousands of years before modern times some scientists-philosophers believed in evolution. Some believed that the Earth was a sphere and that it was not supported by any physical thing, that the Moon was a place with hills and valleys like the Earth, not a part of heaven or an original source of light, but reflected light from the Sun, a glowing hot stone. Some even believed that the Earth moved and was not the center of the cosmos. There were also scientists-philosophers who believed that everything consisted of atoms and empty space, and that light had a finite, but very great speed. Some intently studied the physical and biological world, conducting physical experiments and making detailed astronomical observations. There were estimates of the absolute dimensions of the Moon and Sun and their distances from the Earth, and successful deductions of the existence of geological change from the observation of sea-shells on mountains and fossils of seaweed and fish in stone quarries. Others studied embryos, dissected animals, and even studied the anatomy of the brain (see insert). A world view emerged for a brief time not unlike our modern view of a vast universe of change, atoms and empty space; of a Milky Way composed of millions of unresolved stars; of worlds that evolve and decay.

Most important of all, the notion of objectivity was taken for granted. An objective independent truth existed that could be discovered through a critical exchange of ideas by a community of knowledge seekers. There was not a Greek truth, a Persian truth, or an Egyptian truth. There was one world and one truth about this world. A person or a culture could be free to believe that the world is round or flat, but if the world is round, then those who believe that it is flat were just plain wrong. Some ideas were right and some were wrong, and objective evidence and argument were needed to show which was which. The cosmos was a harmonious place, and behind the apparent complexity of daily life, the show was run by objective universal natural laws.

There was, however, also much disagreement. Some thought that all physical matter was actually water in disguise; others that the ultimate stuff was air; still others that there must be at least four basic elements: earth, water, air, and fire. Some even believed that physical matter, change, and motion were an illusion and only thought, or consciousness, existed. There were wars and political turmoil as well, and some people were executed because of their beliefs. Within a few centuries, for various reasons, a crisis in confidence developed, and people soon sought safer harbors of thinking, or perhaps excuses not to think at all.

Protagoras and the Sophists

Man is the measure of all things, of all things that are, that they are, of all things that are not, that they are not.  Protagoras

What, then, is truth? A mobile army of metaphors, metonyms, and anthropomorphisms ... .truths are illusions about which one has forgotten that this is what they are...  Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense"

Confronted by confusion and uncertainty, people usually choose one of two extremes: (1) to believe what one believes adamantly and absolutely, rationalizing one's beliefs into an irrefutable fortress, or (2) completely reject the notion of objective universal truth all together and accept all beliefs as true for those who believe them. The former we will call absolutists and the latter relativists. Both pride themselves in having discovered something profound, but both positions have the same result -- the cessation of critical thinking.

A consequence of the ancient Greek crisis in confidence was a movement known as sophism. The sophists claimed to be neither scientists nor philosophers, but "educators." They traveled about the Greek city-states claiming to teach the key to a successful life. One of the most famous was Protagoras (ca. 485-410? B.C.), the author of the statement "Man is the measure of all things, of all things that are, that they are, of all things that are not, that they are not." This cryptic statement implied the complete rejection of the old Greek ideal. We cannot know what The Truth is, according to Protagoras. Objectivity is a myth. Each individual sees the world through his or her own filters, we are each locked within a cage of our own appearances, and there are no criteria to select some filters or appearances as better than others. What is true for you is thus true for you, and what is true for me is true for me. Truth is relative to the individual and the influences of the individual's culture.

Protagoras was perhaps one of the world's first cultural anthropologists; he was also a lawyer, a diplomat, and a teacher of rhetoric. He traveled widely about the Mediterranean area, coming into contact with many different cultures and life-styles. He saw that people, societies, and cultures differ. Protagoras concluded that it was presumptuous of the Greeks to think of Greek virtues as the best way to live and other societies as barbaric. As a lawyer and rhetorician, Protagoras taught that the wise man learns to be ideologically flexible. In cases of disagreement the wise man knows that there is no objective solution, no right answer. The goal of resolving disagreements is not to find out the truth, for there is no such thing. Rather, the goal is to "cure" such disagreements by having people agree. As a diplomat and rhetorician, he taught that the truly wise man is able to persuade others to accept his view of things and cure disagreements "in his favor." This persuasion must be subtle, so that the wise man is able to make his position appear right or good to anyone who formerly did not think so. Life and language have an infinite texture, and the wise person learns to use the freedom this implies. The skilled rhetorician learns how to fill the many empty spaces between the thoughts of opposing views. If one is creative enough, any position can be supported and made to appear correct. What matters in life is not what is true, but how to achieve success.

According to Protagoras, the wise person learns that the game of life does not involve uncovering an objective truth that is already there for all to see, but instead an expansion of a perspective by persuading others to live in that perspective.

This statement is false.  (Self-reference paradox)

The wise man does not see skilled persuasion as distortion, exploitation, or con-artistry, because these descriptions imply that there is some right view that is being distorted, and for Protagoras, there is no such thing. The goal of life is not the result of a scientific endeavor -- to discover the truth. The goal is an artistic one -- to mold reality from a particular perspective and persuade others to see this perspective. Not that the perspective of the wise man is better -- it is just more expedient in terms of personal success to have others see things your way. Agreement through diplomacy is what we seek, not truth through science and logic.

For Protagoras the relationship between the human mind and reality is like the well-known story of the four blind men attempting to know what an elephant is. One of the blind men holds on to the trunk and proclaims this is the true elephant. Another has hold of a leg, another the tail, and the other the back -- all describing what they are experiencing accurately and proclaiming that they have discovered the real elephant. Our experience of reality is always indirect and always a point of view of the whole, a perspective, not the whole itself. And our perspectives will be heavily influenced by our culture and our interests.

Of course it is not possible always to persuade others to one's particular way of thinking. In such cases, according to Protagoras, we should conform. Because one idea is no better than another, the wise action to take would be to conform to the practices of one's community most of the time. Above all, chaos and anarchy should be avoided. Because no idea is better or worse than any other, it does not matter which ideas are accepted. As long as the majority conforms there will be less chaos and confusion in the world. So we should accept the ways of our culture, not because we have discovered that they are the best way to live, but because life is easier, more predictable, and safer if everyone agreed to live by the same truths and values.

Although Protagoras was not interested in destroying the traditional Greek virtues and institutions, the epistemological relativism of his philosophy soon gave birth, by Greek standards, to more reprehensible philosophical fruits. Callicles, another sophist, taught that the key to a successful life is to realize that the conventional ideas of right and wrong of a society are designed by inferior people as a trick to control the truly strong. Ideas such as "just treatment" are actually part of a strategy to keep the strong from taking what would be rightfully theirs, if the course of nature were followed instead. In nature the superior creatures always rule over, and have more than, the inferior. Conventional ideas of right and wrong are not discoveries of reason, but rather rationalizations that the fearful inferior have devised to protect themselves.


No human being is constituted to know the truth, the whole truth, and nothing but the truth; and even the best of men must be content with fragments, with partial glimpses, never the full fruition.  William Osler

Another sophist, Thrasymachus, argued that all discussions of right and wrong, true and false, are just a lot of hot air. Rhetorical craftiness as Protagoras advocated is also not needed. All that really matters in life is power. Beliefs are true or false, actions are considered right or wrong, depending upon the best interests of those in power. Political legislation is not the result of a painstaking objective analysis into what is the truth or what is best. Rather, it is the other way around: What is considered the truth and the best are dictated by the political will of those in power. For Thrasymachus, the most important thing to learn about life is that "might is right."

Paul Feyerabend was a twentieth-century supporter of the philosophy of Protagoras. Feyerabend argued that if the philosophies of Callicles and Thrasymachus seem evil, we should consider that the greater evil is actually what modern people have done with science. In his most famous book, Against Method(2), he argued that all so-called objective methods of inquiry were actually just methods of persuasion, not paths to objective truth. History, especially the history of science, is written by those who win. According to Feyerabend, the scientific method and the whole notion of scientific objectivity that began with the Greeks, and later reinforced by the success of Galileo, have indeed changed the world. But the modern result, our scientific-technological culture, is a powerful form of cultural imperialism. Like a huge wave of ideological totalitarianism it is consuming culture after culture and leaving a dangerous uniformity in its wake. According to Feyerabend, the most basic message of the philosophy of Protagoras is that "anything goes," and this is not a call to immorality but a plea for the ideological tolerance and cultural diversity needed for creating the conditions for a truly free and enlightened humanity. Today the philosophy of Protagoras has been assimilated into what is called social constructivism. Truth is said not to be discovered, rather it is made from the dynamics of power and interests in a social situation.

Socrates and Plato

The best of the joke is, that Protagoras acknowledges the truth of their opinion who believes his opinion to be false; for in admitting that the opinions of all men are true, in effect he grants that the opinion of his opponents is true.  Plato, the Theatetus

Although it may appear that there is much that is liberating about relativism, and although the scientific attitude shares with Protagoras the rejection of absolutism, the position argued in this book is that science would be impossible if such a philosophy were taken to its logical conclusion of anything goes. If the human race had followed Protagoras, we would not know what we know today about the planets, the stars, galaxies, or our cosmological and biological roots. There would have been no incentive to search for better ideas, for more reliable ideas. Relativism is an epistemological ghost that materializes whenever people become tired of seeking or too overconfident with their ideas about life. Historically this has happened many times. Fortunately, there has thus far always been those who defend the old Greek ideal.

Protagoras recognized, in his own way, the problem of induction. As we saw in Chapter 2, evidence needs to be interpreted, facts are revealed from a perspective, and no matter how much evidence one has for a generalization or an abstract representation of nature, there is no guarantee that it is true. In addition, given any set of agreed upon facts, there are always, in principle, an infinite number of possible explanations. Because there is never an absolute guarantee, Protagoras concluded that it was impossible to separate the reasonable from the conceivable.


The real purpose of scientific method is to make sure Nature hasn't misled you into thinking you know something you don't actually know.  Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance

Science takes the more burdensome epistemological path: it assumes that even though there is no guarantee, it is possible through great effort to separate the reasonable from the merely conceivable. We genuinely think we know it is more reasonable to believe that smoking is the cause of most lung cancers rather than some inconsequential happening on someone's birthday. We genuinely believe that the relationship between lung cancer and cigarette smoking is a universal biological phenomenon and not just a socially constructed belief of contemporary Western culture. But how do we know this when admittedly we can never be absolutely sure that smoking is the cause of most lung cancers? Can we say that we have knowledge, if we do not have certainty? This challenge has always been one of the major epistemological problems of Western thought. Much of the intellectual history of Western culture can be understood by watching how each age answers this question.

Socrates was very impressed by the philosophy of Protagoras, but he could not accept the conclusion that objective truth was a myth and that there is no better way to live. At one time in his life Socrates was a soldier. He witnessed first hand violence and cruelty. He thought, there may be many different good ways to live, but surely there are also many bad ways to live. If so, he reasoned, what general idea about "good" enables us to judge some particular way of life as good or bad? There must be some objective standard that we can use to separate the one from the other.

It is literally true, even if it sounds rather comical, that God has specially appointed me to this city, as though it were a large thourough bred horse which because of its great size is inclined to be lazy and needs stimulation of some stinging fly. It seems to me that God has attached me to this city to perform the office of such a fly, and all day long I never cease to settle here, there, and everywhere, rousing, persuading, reproving every one of you.  Socrates, the Apology

Furthermore, Socrates felt that as a soldier he had been tricked into fighting in a war for greedy, unscrupulous politicians. He was told that he was fighting for honor and patriotism, but it was really to promote the economic interests of those in power. This exploitation was wrong, and if we followed the beliefs of Protagoras, there would be no reason to rebel against injustice, because there would be no such thing as injustice. Thrasymachus may be right about the real political world -- right and wrong are determined by those who have the power -- but this does not mean that what they do is right or that we should not attempt to make life better than this. The issue should not be what we are doing, but what we ought to do.

Protagoras had argued that each of our perspectives is limited, that most people claim to know the whole truth, even though they believe what they do because of the force of their cultural tradition. He is correct, according to Socrates, about how most people claim to know the whole truth, and how, when analyzed, we find that the reasons for their beliefs are very weak, usually based only on appeals to tradition, authority, and popularity. But our limitations and the prevalence of unanalyzed beliefs do not prove the sophists' epistemological relativism. To use the same analogy of the elephant and the four blind men, for Socrates if the four blind men could realize their limited perspectives and then communicate, they could at least construct a better, more reliable image of the real elephant. Each could realize that the whole truth could be approximated through collaboration. What we first must do then is know how little we really know. We must acknowledge our ignorance and then be willing to critically examine beliefs and communicate our different perspectives.

For Socrates this was an urgent task -- the future happiness of humankind was at stake. For Socrates, it is not the myth of objective truth that produces exploitation and injustice, but the failure of most people to think critically. People in power get away with too much. We should be humble and tentative in relation to our beliefs, and tolerant of different opinions as a means of deciding what is right. But there should be a limit to tolerance.

Socrates believed it was his task in life to make people think, to make people realize their limitations as Protagoras had taught. Truth, as a community effort, was impossible unless people critically examined their beliefs and communicated their limited perspectives. He lived what he taught. In his later years he could be seen daily walking the city streets of Athens, probing all who would listen on their opinions of the ultimate questions of life. Almost always the conversation would draw a crowd of youth looking for an adventure in ideas. And almost always the result would be the same: someone in authority who initially thought they knew the answers to the great questions of life would leave embarrassed, their pretensions of knowledge destroyed by the dialectical questioning of Socrates.


Why is the death sentence the appropriate punishment for treason?

Because everyone knows this is right. (Popularity)

How does everyone know this?

Because it has always been this way. (Tradition)

Why has it always been this way?

Because it was decreed by the gods. (Authority)

Has it been decreed by the gods because it is right or only because the gods have said so?

Because it is right.

Why is the death sentence the appropriate punishment for treason? Why is it right?

One thing only I know, and that is that I know nothing.  Socrates

For man, the unexamined life is not worth living.  Socrates

Socrates would demonstrate again and again to young, inquiring minds why appeals to popularity, tradition, and authority were not the result of thinking, but an excuse not to think. If a behavior was considered right because it has always been approved, then why has it always been approved? What was the initial reason? Does this reason still apply today? If a belief is considered true, because most people have this belief, then what are the reasons for this belief? What evidence has convinced so many people? More often than not, there were no answers to these questions from those who claimed to know.

Eventually Socrates embarrassed too many influential persons. He was arrested and tried for impiety (questioning the existence of the gods), and corrupting the youth of Athens. He was convicted and put to death. Of the many young men who had followed Socrates about the city streets of Athens, one was Plato. The injustice of silencing this sincere, unpretentious man had a profound effect on Plato. Some things are just wrong, and Plato dedicated the rest of his life to righting this terrible injustice. Not in the limited and counter-productive sense of revenge, but in a deeper historical and philosophical sense: The world and all future generations would know that the death of Socrates was an injustice not only for Plato; it was an injustice for all.

In questions of just and unjust...ought we to follow the opinion of the many and to fear them; or the opinion of the one man who has understanding? Ought we not to...reverence him more than all the rest of the world; and if we desert him shall we not destroy and injure that principle in us which may be assumed to be improved by justice and deteriorated by injustice?  Plato

The philosophy of Plato can be discussed from many perspectives. So vast was his influence on succeeding generations of Western culture that no discussion of Western religion, science, or political theory is complete without documenting his influence. In this light the twentieth-century philosopher Alfred North Whitehead remarked that all of Western culture is but a footnote to Plato. Often, those of a more limited perspective, will find in Plato only a mystic who impeded the development of Western science, who alone somehow put a stop to the great initial development of ancient Greek science. From a modern perspective there is a small amount of truth to this, but the larger truth is that Plato answered the sophists and defended the old Greek ideal of objectivity and universal truth.

Plato felt he needed certainty, some sure guide through the world of conflicting opinions of truth and justice. The death of Socrates and the philosophy of Protagoras were not unrelated events for him. At the trial of Socrates the jury was persuaded by those skilled in the tricks of rhetoric to see the unjust as the just. The majority was tricked into believing that Socrates was a dangerous man. If objectivity was a myth, if there were no universal laws that all rational human beings ought to believe, then even the death of Socrates was not an unjust act, but only an unjust act for Plato.

Plato knew that the arguments of Protagoras were a serious challenge. He saw that Socrates had not really answered Protagoras, other than to restate a faith in the existence of better ideas and a method for achieving them. Much more was needed.

To begin with, Plato concluded that the problems raised by the sophists concerning an absolute understanding of the physical world were insurmountable. Not only is every perception a matter of interpretation, not only is there the problem of induction, but false ideas work. Recall the example in Chapter 2. If I have the general belief that all the apples in the barrel are rotten, I would predict that one in the middle is rotten. My prediction could be successful, but my belief false. Plato recognized, as did Protagoras, that any general scientific belief about the physical world could be successful in making predictions, but still be false.

As we will see in the next chapter, prior to the sixteenth-century people believed that the Earth was the center of the universe. The Earth was believed to be stationary at the center, and the Sun, Moon, planets and stars circled around it. With an appropriate arrangement of circles, the nightly motion of the stars, the monthly motion of the Moon, the yearly motion of the Sun, and even the strange motion of the planets could be qualitatively understood and quantitatively predicted to a considerable degree of accuracy. It was an explanatory scheme that had power and great utility. Farmers could keep track of the seasons, navigators using principles derived from it could sail dangerous distances accurately, and astronomers could predict the appearance of the night sky of places on the Earth where no civilized person had set foot. Even solar eclipses could be predicted. Yet today we believe that the Earth is moving and there is no center to the universe. A belief that was false made many true predictions for 1500 years.

Even at Plato's time astronomers were aware of the possibility of a sun-centered system, and he knew that even though the Earth-centered system worked, this did not prove that the real physical situation corresponded to it. One could always have many workable opinions about the reality behind the appearances. Plato believed that to answer the sophists some truths must be found that were beyond all doubt. There must be ideas that are so clear, so self-evident just by thinking them, that everyone would know that there are no alternatives. These truths must not be dependent or relative to time, place, or person. Are there such truths? Plato believed that there are and we could begin by noting that they exist in mathematics. Consider the difference between the following statements:

1. 2+2=4

2. There are nine planets in our solar system.

Plato argued these statements have a different epistemological status. The second statement is considered true today, but it was considered false during Plato's time (when only five planets were known). Similarly, this statement could be false in the future in several ways. First of all, we could be wrong about there being only nine planets. There could be an undetected tenth planet. In fact from time to time claims have been made for a tenth planet orbiting the Sun outside the orbit of Pluto. A tenth planet has not been confirmed, but this could either be due to the fact that there is no tenth planet or because our technology is not sufficiently developed to detect it yet. How can we say that it is true that there are nine planets when we are not sure there are nine planets?


Wonder is the feeling of a philosopher, and philosophy begins in wonder.  Plato

Secondly, we may be correct about there being only nine planets now, but at some future date a catastrophe could occur to one of the planets and there would then only be eight. The asteroid belt between Mars and Jupiter may be the remains of a tenth planet that was destroyed by a collision with another astronomical object. Also, astronomers predict that a few billion years from now our Sun's lifespan will end. It will expand, become a red giant, and engulf all of the inner planets, perhaps as far out as Jupiter. There will then no longer be nine planets -- maybe only three, maybe none.

Plato's concern was that some future observation could always make a belief that we consider true about the physical world today false tomorrow. Plato saw that any statement about the physical world was relative to time, place, and the subjective perspective of the observer, and hence, seemed to validate the epistemological skepticism of the sophists. The sophists were right about the physical world -- we cannot say we have knowledge when we do not possess certainty.

On the other hand, the first statement seems to be true independent of any future observation. We know that it is not possible that 2+2 will equal 5 in the future. We know that some day we will not find a strange planet where in counting two rocks and two more rocks the result is five. We know that there will not someday be a culture that believes that 2+2=7. We know something now about the entire universe and all future experience. If the solar system were entirely destroyed and all human beings ceased to exist, 2+2 would still be 4. In Plato's way of thinking, if the entire physical universe ceased to exist, the thought "2+2=4" may be no longer useful, but it would surely not be false.

Plato believed he had discovered something wonderful about mathematical truths. No experience is necessary to know that some thoughts would always be true, and some thoughts are objectively true, even if there were no physical realm at all to apply them.

Consider another example. Suppose you are sitting in a room with no windows. Outside the building is a parking lot in the shape of a precise rectangle. There are 25 rows in this parking lot and each row has exactly 20 parking stalls. Suppose you are told that at this particular time every single slot contains a parked car and there are no cases of double parking. Also, the parking lot is closed and there is no one driving around or waiting inside the parking lot for someone to leave. How many cars are there in the parking lot? We know instantly there are 500 cars in the parking lot (25 x 20 = 500). Consider how strange this knowledge is. You cannot see the 500 cars. Nor do you need to go outside and observe the parking lot to make sure there are 500 cars. It would be a silly waste of time to count each car to make sure that there are 500 cars. Plus you would probably make an error in counting the cars. You know there are 500 cars, even though you have no direct physical contact with the parking lot. You would possess this knowledge whether the parking lot was in the next town, in New York, in Paris, or on Mars. If the information is true -- no double parking, the parking lot is full -- then you know there are 500 cars in the parking lot. Plus, the thought 20 x 25 = 500 would be true even if there were no parking lot anywhere. This idea is waiting, so to speak, to be put to use in situations such as the parking lot, but it would remain true even if it was never put to use.

  Mathematics and Reality

All things are numbers.  Pythagoras

Let no one without geometry enter here.
(Inscription over the entrance to Plato's Academy)

Although for Plato the examples would be from geometry, these examples should enable us to understand why mathematics was so important to Plato and the Greeks. For Plato the problem was to show relativism can be refuted with concrete examples. Mathematics was the answer. It seemed to provide the stability and certainty needed to defend objectivity. It was also powerful, rational, and mystical. To summarize some of the key characteristics the Greeks would see in the preceding examples, consider the following.

First, there is certainty. If all the information given to us is correct, we cannot be wrong about the conclusion of the number of cars in the parking lot. We would be far less certain of our conclusion if we physically counted each car.

Second, mathematics seems to provide us with an unusual power of perception. With mathematics as a means we are able to transport our minds to places where we may never set foot physically. Think of the achievement of Eratosthenes in calculating the size of the Earth. In his day there was no physical way for him to travel and experience the Earth's 25,000-mile circumference. Yet by sitting at a desk in the library at Alexandria, he knew. In a sense he could transport his mind around the world while his physical body stayed in one place. Consider also the achievement of the third century B.C. astronomer Aristarchus of Samos, who devised a geometrically correct method for estimating the relative distances of the Sun and the Moon from the Earth. Although his actual results were incorrect, because of the primitive state of measurement, through geometry he could "see" these distances were very large. For Plato, such achievements meant that one could contact a realm of truth by thinking. He was a rationalist to use the language introduced in Chapter 2. Our reasoning ability can reveal to us truths that experience cannot.


The created world is but a small parenthesis in eternity.  Sir Thomas Brown

Third, although the physical circumstances in which one applied mathematical thoughts could change, the thoughts themselves seemed to be eternal. The physical universe could cease to exist, but the geometrical theorems used by Eratosthenes and Aristarchus would continue to exist. The Earth could explode, but the geometric theorem used by Eratosthenes could be applied to another physical sphere. There are an infinite number of physical things that "2+2=4" can be applied to, and the concept remains the same even when the physical things change or disappear. Thus, and this is the fourth point, mathematical principles are not things. They are thoughts. Finally, mathematical principles are universal public entities. The geometry used by Eratosthenes and Aristarchus were not private truths. They are public ideas, discoverable by, and applicable for, any person, from any culture, at any time, past, present, or future. Squares and triangles are the same in Greece and China.

But what kind of existence does an idea or thought have? Consider how difficult it must be initially for a child to grasp the concept of "two." A mother may point to a piece of chalk and say repeatedly "chalk...chalk." Eventually the child will begin to mimic the mother and associate the verbal expression with the object. But imagine the potential confusion when the mother picks up another piece of chalk and says "two"! The objects were just referred to as "chalk" -- now the name is "two"? Where is the object "two"? Imagine the further confusion when she points to two tables or chairs and says "two." Eventually we understand the abstraction and many others, and if we are fortunate to have the right teachers, we will understand and appreciate the beautiful achievements of Eratosthenes, Aristarchus, and even today that of modern scientists who with a few facts can calculate backwards in time to the physical circumstances of the first billionth of a second of the existence of a universe 14 billion years old.

Until philosophers are kings, or the kings and princes of this world have the spirit of philosophy, and political greatness and wisdom meet in one . . . cities will never have rest from their evils -- nor the human race

So important was mathematics for Plato that it served as a basis for the rest of his philosophy. This was not an idle ivory tower game. For Plato the entire future of the human race was at stake. Truth and justice were not myths, games, or rationalizations as the sophists argued. He thus founded in the fourth century B.C. the first university of public knowledge, where people from all over the Mediterranean came for many centuries to study and exchange ideas. It was called the Academy and over its main entrance was an inscription that specified a background in mathematics was required before one could enter.

Plato's main concern was ethical judgement and a political system that would maximize correct ethical judgement. He concluded that if there is a realm of truth which we have access to through thought, then there must also be an objective basis for ethical standards and justice. There must be eternal standards of right and wrong, just as there are eternal mathematical principles. Similarly, knowledge of these standards must proceed in the same way as knowledge of mathematical truths. For me to know "2+2=4," I must, of course, first experience particular examples of counting. But at some point I do not need to examine any further examples. I understand the concept and know that it will always be true. Similarly, to know that any particular action is a just action, there must be a common property of just actions that we are capable of knowing as in a mathematical principle. By examining particular cases and communicating our opinions we can obtain a better idea of what justice really is. For Plato, real justice was not a matter of personal opinion, or relative to a culture or time, or a matter of power, but the result of a rational insight. As in the words of the United States Declaration of Independence, justice was a "self-evident truth." Today, the United Nations has a declaration of universal rights. The origin of such a concept of a universal right derives in large part from the concerns of Socrates and Plato.


Mind, for anything perception can compass, our spatial world more ghostly than a ghost. Invisible, intangible, it is thing not even of outline; it is not a 'thing'. It remains without sensual confirmation and remains without it forever.  Sir Charles Sherrington

Although Plato's main concern was the practical matter of just treatment, we see that his theory of justice was backed by a metaphysics, a theory of reality. Mathematical truths are eternal, applying at all times and places, and true for all people. Yet they are thoughts, ideas, or concepts. We can apply them to the physical world, but they are not physical things. Because they are not physical, they do not change and are not subject to the doubts of experience. Yet they can be known with certainty through thinking and they can be communicated. But if they are not in the physical world, where are they?

According to Plato, the culmination of these insights is the realization that there is another realm of existence, a dimensionless, timeless, nonmaterial reality of pure thought, a realm of ideas. For Plato, the skepticism of the sophists and paradoxes such as Zeno's paradox of motion are simply nature's way of revealing one of her secrets: a realm of true being, a realm of self-evident formal truth, one with which we can participate through thought. This realm is contrasted with the world of our normal experience which Plato called becoming. Any statement we make about the physical world is subject to doubt and change, because the physical world is an illusion or shadow of a higher reality. A strange conclusion no doubt, conflicting with common sense, but according to Plato, it is what reason leads us to step by step.

  Common Sense and Reality: the Allegory of the Cave

Philosophy subverts man's satisfaction with himself, exposes custom as a questionable dream, and offers not so much solutions as a different life.  Walter Kaufman

If the doors of perception were cleansed, everything would appear to man as it is, infinite. For man has closed himself up till he sees all things through the narrow chinks of his cavern.  William Blake

In one of his most famous writings, The Republic, Plato warns the people of his time, and all future generations, that a true seeker of the truth must deal with the fact that new discoveries will always conflict uncomfortably with common sense. In what has come to be called the "Allegory of the Cave," he asks us to imagine a race of people imprisoned deep in a dark cave, all chained together facing a wall of the cave. Behind them is a large fire and another race of people moving about, such that shadows are cast on the walls of the cave. The chained people do not realize that they are captives of the other race. The only reality they have ever experienced is the shadows on the wall. By observing the shadows carefully, they have been able to recognize generalities in the movements of the shadows and have been able to develop a practical science: They can predict what shadows will appear at different times and when food and water become available. Because their science works, because there is regularity to their experience, there is little reason for them to believe that this science is false, that what they are seeing is an illusion, an appearance only, reflected from a more fundamental reality.

Suppose now that by accident one person escapes from the grip of his chains enough to turn around and see for the first time what is actually causing the shadows. His first reaction is one of uncertainty, confusion, and fear. He quickly turns back to what is familiar. All his life he has known only the shadows as real. He must be going crazy. It must be a bad dream. He concludes that he must never turn around again. Eventually though his natural curiosity becomes too much to suppress and he turns around once more. This time, because he is more familiar with the sight, he does not quickly turn back to the shadows. He realizes that he has made a great discovery. With great excitement he turns back to his companions, announces his discovery, and attempts to get them to turn around. At first they laugh at him. Then they reason with him, pointing out that the shadows are what everyone knows to be real and practical. Then, as he persists, they ignore him, concluding that he has lost his mind. At first the force of this community rejection causes him to doubt what he has experienced. Maybe he is crazy. But it seemed so real.

Socrates said that he was not an Athenian or a Greek, but a citizen of the world.  Plutarch

Eventually though he turns for the final time, and with the resolve of an explorer, he frees himself completely from his chains and leaves his people to investigate this new reality. He discovers that he is in a cave, finds the passage way out of the cave, and slowly and tentatively makes his way, eventually reaching the outside world. At first it is too much to bear -- so many new things, and the light of the Sun blinds him. When he finally adjusts, he is overjoyed by this simple, clear, beautiful new reality compared to the dim, confining reality of the cave's shadows. He must share this discovery. So back into the cave he goes to try once more to convince his former companions, and most likely to experience rejection once again.

Mathematics Today: Why does it work so well?

Philosophy [the universe] is written in that great book which ever lies before our eyes .... we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language ... without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.  Galileo, The Assayer

Technically the metaphysics Plato advocated is called idealism. All that is said to exist is a realm of thought or consciousness. The physical realm is an illusion. This metaphysical philosophy serves as a foundation today for the religions of Hinduism and Christian Science. Idealism is usually opposed to the metaphysical position known as materialism, the belief that the only thing that exists is the physical world. Although it is a mistake to believe that all scientists are materialists and that science necessarily endorses materialism, most scientists today would not accept Plato's metaphysics. Universally objectionable from a scientific outlook based on empiricism would be Plato's rationalist epistemology: that genuine knowledge could be obtained by just thinking. As a type of mysticism that claims a nonphysical realm exits, Plato's philosophy influenced the development of Christianity during the middle ages. By the time of the Renaissance, the realm of ideas had become ideas in the mind of God, and when one did mathematics one was thought to be actually reading the mind of God. What is fascinating about Plato is that he achieved this other-worldly philosophy not by contemplating religious issues, but by studying the nature of mathematics.

Today physicists routinely use higher mathematical functions to explore strange dimensions of space and time, dimensions that conflict radically with common sense. Whether these dimensions are real or not is much debated by physicists and philosophers of science. That physicists can conduct such investigations, however, without fear of ridicule is just one of the many legacies we owe to Plato. However, most contemporary philosophers of science believe Plato was wrong about the nature of mathematics and the impossibility of an objective physical science. Because of his need for certainty, Plato, as a rationalist, believed too much about mathematics and not enough about the possibility of a science of the physical world that sought out reliable beliefs. Advances in mathematics have demonstrated that contradictory mathematical systems can be created and applied to the physical world. The geometry used by Eratosthenes works in mapping the circumference of the Earth, but a different geometry is needed to understand the strong gravitational fields and regions of space and time as analyzed by Einstein.(3)

Plato recognized that mathematical principles could be applied to different hypothetical situations, even contradictory ones, but he thought the mathematical principles themselves were always consistent. As we will see in the next chapter, the geometry of a circle can be used to construct an Earth-centered model and a Sun-centered model of the motion of the planets. Because only the geometry was stable, Plato concluded that only its principles were real. Today the mathematical situation is analogous to having one mathematical system where "2+2=4" is true and another where "2+2=5" is true. It is doubtful that Plato would have had room in his perfect realm of being for contradictory ideas.

Whereas Protagoras concludes that certainty, and hence knowledge, is impossible, and Plato concludes that certainty, and hence knowledge, is possible, modern science assumes that although certainty is not possible, knowledge is possible nevertheless.
For Plato, mathematical ideas were eternal thoughts independent of human minds. The goal was to discover these thoughts and use them to organize the world of physical appearances, or to "save the appearances" to use his own words. Today, most philosophers of science believe that mathematical ideas are the result of free creations of the human mind. They are tools that we create to map the world. Just as a hammer is needed in one situation, a saw is needed in another. Experience is needed for knowledge. Modern empiricists argue that without some input of initial data derived from experience, our mathematical tools are useless. In the previous example of the parking lot, someone must first experience the parking lot and see that it is a rectangle, that it has 25 rows with 20 parking stalls each, and that it is full with no double parking. If any of this information is incorrect, the conclusion that there are 500 cars in the parking lot could be wrong. Accepting the basic epistemology of empiricism, most contemporary philosophers of science believe that mathematical equations do not convey any more certainty than is already contained in the initial data. In a sense, the conclusion that there are 500 cars in the parking lot is already contained in our knowledge of the initial data. The mathematics is simply a way of making explicit what is implicit in the data.(4)

When the bagel is eaten, the hole does not remain to be reincarnated in a doughnut.  Gregory Bateson

What we believe today is not as important for the history of science as what Plato believed. Although possibly wrong, Plato's emphasis on the importance of mathematics was one of the most influential philosophical positions ever taken in Western culture. It had a profound and lasting influence on both the development of Christianity and modern science.

Few scientists today will profess that in doing mathematics they feel as if they are reading the mind of God. But when we find them talking about mathematics, and especially its application to understanding the physical world, the legacy of Plato is clear. There is something bewildering still about using mathematics to fly a robot spacecraft to the planet Saturn, at a distance of a billion miles from Earth, and be only a few miles off upon arrival, or to the planet Uranus, close to 2 billion miles away, arriving on course and one minute ahead of schedule. Why should our mathematical thoughts work? Why should the free creations of the human mind work so well? According to Einstein, this is the greatest cosmological mystery, that our ideas should work at all.

The philosopher Aristotle, a student of Plato's at the Academy, saw too many problems with Plato's other-worldly interpretation of mathematics. According to Aristotle, universal principles such as those of mathematics work because they are built-in formal structures, and only human beings are capable of reading these formal structures. They are inseparably linked with the physical universe. So once we understand how they work on Earth, we immediately know something about the entire universe. By the Middle Ages these formal structures had become the floor plan by which God had created the universe, and as God's special creature, we were endowed with the special potential to read this floor plan. Most scientists today profess philosophical detachment from such speculations. Nevertheless, indecision and debate continue. Consider the following statements in Mathematics and the Search for Knowledge, from some of the best minds of the twentieth-century.(5)

There is inherent in nature a hidden harmony that reflects itself in our minds under the image of simple mathematical laws. That then is the reason why events in nature are predictable by a combination of observation and mathematical analysis. Again and again in the history of physics this conviction, or should I say this dream, of harmony in nature has found fulfillments beyond our expectations. Hermann Weyl

The essential fact is simply that all the pictures which science now draws of nature. . . are mathematical pictures. . . . it can hardly be disputed that nature and our conscious mathematical minds work according to the same laws. Sir James Jeans

Here arises a puzzle that has disturbed scientists of all periods. How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality? Can human reason without experience discover by pure thinking properties of real things? Albert Einstein

Is there perhaps some magical power in the subject (mathematics) that, although it had fought under the invincible banner of truth, has actually achieved its victories through some inner mysterious strength? Morris Kline

There is another difficulty in Plato's defense of objectivity against Protagoras and the sophists. Assuming the principles of mathematics are universal does not demonstrate necessarily the existence of universal ethical principles. Historically, however, it does not matter. Wrong or right, Plato was believed. Plato won the intellectual battle with the sophists. Better ideas were thought possible, given a community of knowledge seekers willing to acknowledge their limited perspectives. Our modern view of the universe is the result of believing in better ideas.

But how do better ideas come about? How do revolutions in thought take place. How do people break out of the intellectual caves of previous generations? If absolute proof is not possible, how are more reasonable ideas separated from mere conceivable ones? This is the subject of the next chapter.

Concept Summary
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© 2001, 2004, 2011 Ronald C. Pine


Notes:  (Click Back to return to text.)

1. Cosmos is a Greek word for "all that is." In this book we will use cosmos and universe interchangeably.

2. Paul Feyerabend, Against Method: Outline of an Anarchist Theory of Knowledge (London: NLB, 1975).

3. In the Euclidean geometry used by Eratosthenes the sum of the interior angles created by the line intersecting two parallel lines must equal 180 degrees. The axioms that are used to prove this also lead to the conclusion that the sum of the angles of a triangle are always 180 degrees. In the non-Euclidean geometry used by Einstein, the sum of the angles of a triangle can exceed 180 degrees.

4. In this regard, recall that the conclusions of both Eratosthenes and Aristarchus were technically incorrect because of errors of observation.

5. Morris Kline, Mathematics and the Search for Knowledge (New York: Oxford University Press, 1985).

Suggested Readings 

The Greeks
, by Humphrey David Findley Kitto, rev. ed. (New York: Penguin Books, 1957).

A classic brief introduction to the Greek culture and its significance for the development of Western civilization.

Nature and the Greeks, by Erwin Schrodinger (Cambridge, England: Cambridge University Press, 1954).

A short investigation of the scientific world-picture inherited from ancient Greek thinkers. Schrodinger, one of the main contributors to modern physics (see Chapter 8), searches for some insight into the epistemological roots of the present perplexities of modern science.

A History of Philosophy, v.1., Greece and Rome, by Frederick Charles Copleston, new rev. ed. (Garden City, N.Y.: Image Books, 1962).

Part of an eight-volume history of Western philosophy from the ancient Greeks to the twentieth century. Although there are many good introductions to the history of Western philosophy, this time-honored work is still one of the best in terms of completeness and objectivity.

For a somewhat more readable account see A History of Western Philosophy, vol.1, The Classical Mind, 2nd ed., by William Thomas Jones (New York: Harcourt, Brace & World, 1969-75). This book has a stimulating chapter on the sophists, "Education Through Violence." Throughout, Jones emphasizes that one of the ways of understanding the classical Greek philosophers is from the point of view of their struggle with defending objectivity and a public truth.

Greek Philosophy: Thales to Plato, by John Burnet (New York: Macmillan, 1964).

Although the author died in 1928, the eight reprintings of this book since then attest to the authority it still commands. Packed with scholarly twists and turns, it is still quite readable for the highly motivated student.

The Collected Dialogues of Plato, Including the Letters, ed. by Edith Hamilton, and Huntington Cairns (New York: Pantheon Books, 1964).

A must-read primary source for anyone interested in the cultural roots of Western civilization. Out of the barely penetrable mists of history comes the voice of a great intellect, asking the questions and defining the parameters of the answers that have guided our civilization for centuries. Most recommended are the following dialogues: The Apology, The Republic, The Theaetetus, and The Protagoras. Also see the 7th Letter for a surprising conclusion.