This Thirteenth Century illustration,
painted by an unknown master, probably in Rheims, France, is from
La Bible Moralisée
and pictures the Second Person of the Tri-une God, the Logos,
Jesus Christ, by Whom all things were made,
in the act of "setting his compass upon the face of the deep."
In the Genesis accounts of the Creation of the World
emphasis is repeatedly placed on God's acts of "dividing."
The compass symbol expresses the fundamental truth
that reality is an irrational continuum and that only by arbitrary division and measurement
are "things" cognizable by the human mind.
The original manuscript is now at the
Österreichische Nationalbibliothek in Vienna.


Please bear with me. This page is a study of the first words of the Apostles' and Nicene Creeds.
I am only now starting the process of working out my thoughts on what exactly it is we are professing
whenever we say:

The word "heaven" used in these two Creeds I think means something different from,
or, to be more precise, means something more than,
what, in everyday English, we mean by the expression "the heavens"
In this latter case, I think "the heavens" simply means the physical universe beyond the planet Earth,
i.e., "outer space," all the other planets, and the galaxies, etc., beyond.
On the other hand, I think the two Creeds' word "heaven" includes also the spirit world,
as well as the present whereabouts of the ascended body of Jesus and the assumed body of His Mother,
and, of course, someday the whereabouts of the resurrected bodies of all the saved.

Having set forth the above distinction, I think it important to note that
whatever belongs to the "heaven" that is beyond what we mean by "the heavens"
is not, and cannot be, in any way known by us humans,
except, of course, through God's Sacred Revelation.

"9 But as it is written, Eye hath not seen, nor ear heard,
neither have entered into the heart of man,
the things which God hath prepared for them that love him.
10 But God hath revealed them unto us by his Spirit:
for the Spirit searcheth all things, yea, the deep things of God."
(I Cor. ii: 9-10)

I once had an argument with an atheist who mocked Christians as being akin to those believing in squared circles or honest lies. I remember him citing our beliefs in the Ascension of Our Lord and the Assumption of Our Lady into heaven as plainly preposterous notions because, he argued, even if their physical bodies had "taken off" into the sky from from planet Earth in the first century A.D. at the speed of light (i.e., at the fastest any physical object can move), in the less than two thousand years that have elapsed since then, their bodies would still not yet have even left our galaxy.

My atheist friend, however, begged the question by presuming that the glorified bodies of the risen Christ, of His Mother, and (we pray) someday of ourselves must all have to obey the physical laws of our earth and of our heavens. He never thought to ask himself why a God who could raise the dead could not just as easily move physical objects instantaneously. The same point was made in the 1920s, during the famous Scopes "monkey" trial in Tennessee, when the atheist defense attorney Clarence Darrow, in his cross-examination of fundamentalist William Jennings Bryan, ridiculed Bryan's belief in the Bible's assertion that Joshua made the sun stand still during a battle of the Hebrews with the Canaanites. Darrow thundered that, because of the laws of gravity, if the sun and earth had ever stopped moving in relation to each other, then all of our planetary system would have fallen apart. Bryan calmly rejoined that if God could stop the sun in the sky, He could certainly have also kept everything else going as usual.

At this point I wish to introduce my greatest teacher: the late Prof. Carroll Quigley, Ph.D., whose freshman course "The Development of Civilization" I took in 1959-60 at the Georgetown University School of Foreign Service. The first several days in that course were devoted to addressing what is reality and how we humans reason.. My excerpts from his course, quoted below, take up many paragraphs; but I strongly urge you to read through them all. One can never learn so much, in so a short period of time, as from reading Quigley:

[Reality and the Dimensions of Reality]

"Much, if not all, of the physical world consists of continua. To say this is equivalent to saying that much of the physical world is irrational. It exists and it operates, but it does these things in ways that cannot be grasped by our conscious rational mental processes. This can be seen most easily if we consider first a few examples of continua in the physical world.

How many colors are there in a rainbow? Some answer three -- red, yellow, blue. Others answer six -- red, orange, yellow, green, blue, violet. When I was a child in school, for some unknown reason, we were told that there were seven colors, the teacher inserting "indigo" between blue and violet. The proper answer, of course, is that the number of colors in the rainbow is infinite. This in itself is something we cannot grasp in any rational way. But let us consider what it means.

In the first place it means that there is, in the rainbow, no real line of division between any two colors. If we wish to draw a line we may do so, but we must recognize that such a line is imaginary -- it may exist in our minds, but it does not exist in the rainbow itself.

Moreover, any line that we draw is arbitrary, in the sense that it could have been drawn with just as much justification somewhere else, perhaps only a hairbreadth away. If we draw a line between red and orange and another between orange and yellow, we may call the gamut between those two lines orange, but, as a matter of fact, the color is quite different on either edge of that gamut. We may decide that orange is a narrower range than the gamut between our two lines and, accordingly, slice off the margins of the orange gamut, calling the severed margin on one side yellow-orange and the severed margin on the other side red-orange. But once again the color is not the same across any of these three ranges. In fact, it is impossible to cut off any gamut in a rainbow, no matter how narrow we make it, in which the color is the same across the width of the gamut. We can move no distance, however infinitesimally small it may be, across the rainbow without a change in color. This means that the number of colors in the rainbow is infinite. But it also means that the number of colors in any portion of the rainbow is infinite. That is, there are as many shades of orange as there are colors in the whole rainbow, since both are infinite. Now, this is a truth that we cannot understand rationally. It seems contrary to logic and reason that we could add all the existing shades of red and yellow to all the existing varieties of orange without increasing the number of color varieties we have. The reason is not so much that infinity added to infinity gives infinity as that there are no different varieties of colors at all, because there are, in fact, no dividing lines in the rainbow itself. When we use the plural terms "colors" and "shades" in reference to a rainbow, we are implying that there are different colors and accordingly that there are divisions in the rainbow somehow separating one shade from another and thus entitling us to speak of these in the plural. Since there are no such lines of separation, we would be more accurate if we spoke of the rainbow in the singular as "a continuum of color." But, of course, we could not do this consistently because it would make it impossible to think about or to talk about the colors of any objects. Since the continuum changes across its range, it is distinctly different in color from one portion to another, just as dresses, flowers, or neckties are different in color from one another. If we are going to talk about these very real differences, we must have different words for the different colors involved. Thus we must give different color terms to different portions of the rainbow's gamut. The important truth to remember is that, while the differences between colors are real enough, there are no real divisions between colors: these are arbitrary and imaginary.

As is well known, the gamut of radiations of visible light that we call the rainbow is not an entity in itself but is an arbitrary and imaginary portion cut out of a much wider gamut of electromagnetic radiations. The variety of colors in the rainbow arises from the fact that the radiations of visible light come at us in wave lengths of different frequency. As the wave lengths of these radiant forms of energy get smaller (and thus their frequency gets larger), we observe this difference as a shift in color toward the blue end of the visible spectrum; as the wave lengths get longer (and the frequency less), we observe a color shift toward the red end of the spectrum. If this shift of wave length continues, the radiation may pass beyond the range to which our eyes are sensitive. Beyond the red we can notice these radiations as heat (infrared); beyond the violet we might have difficulty noticing the radiations directly, but their consequence would soon appear as a kind of sunburn on our skin. Once again there is no dividing line between the visible gamut of radiations and the ultraviolet on one side and the infrared on the other side. Some persons can "see" further into these than others can, and other forms of living creatures can "see" further into one or the other range than any human could. Bees, for example, are fully sensitive to ultraviolet radiations, while humans are generally so insensitive to these that they consider glass windows, which cut off most ultraviolet, as being fully transparent.

The gamut of radiant energy is much wider than the three sub gamuts we have mentioned. Beyond the invisible ultraviolet are other radiations of even shorter wave length, including soft X rays, hard X rays, and finally the very high frequency gamma waves released by nuclear explosions. Going the other way in the radiation range, we find that there are radiations of increasing wave length beyond the infrared which we call heat. These radiations of lower frequency and longer wave length include those used to carry our radio and television broadcasts. While we sit here reading, quite unaware of their passage, these radiations are going through our bodies. They are different from the visible light that allows us to see to read only in the wave lengths and energy content of the radiations.

This great gamut or range of energy radiations, from the shortest gamma waves at one end to the longest broadcast waves at the other end, forms a continuum. The difference between a deadly gamma radiation and an enjoyable television broadcast, like the difference between red and blue, is a very real difference, but it is only a difference of wave length (and thus a difference of distance) and not a difference of kind. Accordingly, no real lines of demarcation exist in the gamut itself, and the whole range forms a single continuum.

[The Dimension of Space]

The quality of being a continuum that exists in the range of electromagnetic radiations is not a quality that has anything to do with energy or with radiations, but is true simply because these radiations exist in space and differ from one another because of space distinctions, namely, their wave lengths. This spectrum is a continuum, and therefore irrational, because space is a continuum, and therefore irrational.

The irrationality of space sounds a little strange to most of us because we are so familiar with space that we rarely stop to think that we do not really understand it. But the irrational quality of space (which arises from the fact that space is infinitely divisible) is one of the early discoveries of ancient intellectual history. By 2000 B.C. the Babylonians were familiar with the fact that the square of the hypotenuse of a right-angle triangle is equal to the sum of the squares of the other two sides. Introduced to the Greeks in a generalized form by Pythagoras before 500 B.C., this statement came to be called the "Pythagorean theorem." Unfortunately, Pythagoras also taught that reality was rational and that the truth can be found by the use of reason and logic alone, without any need for observation through the senses, which would merely serve to confuse us. This rationalist method for discovering the nature of reality was accepted by Socrates and Plato (and, in his earlier period, by Aristotle) and led to the death of ancient science by contributing to a denigration of observation, testing of hypotheses, and experiment. It is one of the great ironies of history that thinkers like Pythagoras and Plato helped to kill ancient science by propagating the belief that observation was not necessary since reality was rational, and therefore its nature could be found by the use of reason and logic alone, long after a pupil of Pythagoras, Hippasus of Metapontium, had used the Pythagorean theorem to demonstrate that space (and thus reality) is irrational.

The demonstration of the irrationality of space arose from the proof that the diagonal of a square is incommensurable with its side. We would say that, if the side of a square is one unit long, its diagonal, by the Pythagorean theorem, is the square root of 2 units long. And the square root of 2, we say, is an irrational number. But few of us really know what we mean by the word "irrational" in this sense. There are three ways of looking at it, each a slightly different way of looking at a quite irrational situation. We sometimes say that ~ is an endless decimal which begins with 1.41421 . . . and continues forever in an infinite series of digits which never ends and never repeats itself. Or we could say that ~ is a number which cannot be expressed as a fraction&emdash;that is, as a ratio between two rational numbers. But both of these statements are simply alternative ways of talking about the utterly irrational fact that there is no common unit of distance, no matter how small we make it, which will go into the side of a square a certain number of times and will also go into the diagonal of the square a round number of times without anything left over. Rationally we would think that if we took as a unit of measurement a distance which was infinitely small -- like one-sextillionth of a cat's whisker or even one-sextillionth of that or however small a unit was needed -- that we could eventually find a unit so small that it would go evenly into both the side and the diagonal. But the fact is that there is no unit, however small, which will go evenly into both distances, so that there is no common unit between them, and we must say that they are incommensurable. But this is not a situation that is rationally comprehensible to our conscious reasoning powers, and it is quite nonlogical. But it is true.

This quality of irrationality of space is not something exceptional, either in space or in other aspects of reality. The radius of a circle is similarly incommensurable with its circumference; the irrational relationship between the two distances is signified by the ratio we call . This quality of irrationality rests on the fact that space is infinitely divisible; no matter how close together we make two points, the number of points between them remains infinite. The infinite colors of the rainbow, like the incommensurability of a square and its diagonal or of a circle and its radius, are simply applications of this irrational quality of space.

[The Dimension of Time]

A similar irrational quality is to be found in time. We usually think of time as a succession of intervals. It is really a continuous flow, and any intervals we may choose to put into it, be they seconds, hours, or centuries, are arbitrary and imaginary. And in consequence, any conclusions we derive or any inferences we may draw from such intervals may be mistaken. We have twenty-four hours in the day as a purely conventional arrangement going back to our early ancestors in the Neolithic Garden cultures who had a number system based on twelve and passed on to us, as relics of that system, such arrangements as twelve eggs in a dozen, twelve inches in a foot, twelve pennies in a shilling, twenty four parts in a carat, twelve ounces in a pound of gold, twelve deities on Mount Olympus, and many other odd facts of which one of the most pervasive today is that teenage begins with thirteen. From the Neolithic belief that day or night should each have twelve parts we derived our twenty-four-hour day, but since these divisions are arbitrary and imaginary, we could with equal justification have a day of ten hours or of twenty-three or twenty-five hours.

Most of us are familiar with the paradoxes of Zeno, especially with the one about a race between Achilles and a tortoise. Zeno argued that if the tortoise got a head start, Achilles could never catch up with him even if he could run much faster. Zeno felt that if the tortoise was a certain distance ahead when Achilles started, the tortoise would move forward a little farther while Achilles was covering the handicap distance and would, thus, still be ahead when Achilles finished the handicap distance. Accordingly, Achilles must keep on running to overcome the new increment, but by the time he had made up that increment the tortoise would have moved forward a new amount and would still be slightly ahead. According to Zeno, this process would continue forever, the tortoise advancing a decreasingly small amount while Achilles was making up the tortoise's previous increment. A mathematician might say that the distance between the two would approach zero as a limit but would reach that limit only after an infinite number of intervals (either of time or of distance) and that Achilles would, accordingly, not catch up in any finite number of intervals.

The explanation of this paradox of Zeno's rests on the fact that the space and time through which the contestants are running are both continua, but Zeno, by treating them as if they were a succession of intervals, introduced an untrue condition, and from this contrary-to-fact assumption (that time or space exists as a sequence of intervals) he derived a contrary-to-fact conclusion (that Achilles can never catch up).

Such paradoxes are good examples of the methodological rule that logic and rationality do not apply to continua. As we shall show later, this is one of the basic rules of historical method (although, it must be confessed, few historians give it much thought).

[The Dimension of Abstraction]

Space and time are not the only continua. Another familiar example is the system of real numbers. Since this is a continuum, we can state a rule: no two numbers can be placed so close together that there is not an infinite number of numbers between them. For example, between 3 and 4 are an infinite number of numbers. One of these is . As we have said, is irrational, and, accordingly, although it is a very exact number we cannot write it with the ordinary ten symbols used in writing numbers. If we say that is 3.14, we do not refer to a single number but are really saying that is one of the infinite number of numbers in the gamut from 3.135 to 3.145. In that gamut we could indicate that was in a much narrower gamut (which still contains an infinite number of numbers) by writing its value as 3.141592. This refers to the infinite number of numbers in the gamut of numbers ranging from 3.1415915 to 3.1415925. Since the value of is known to over a thousand decimal places, we can define the gamut of numbers within which lies more and more narrowly simply by carrying the numerical expression for to more decimal places. But each gamut, no matter how narrow it gets, refers to an infinite number of numbers, because the system of real numbers is a continuum.

To those who are not familiar with mathematics, all of this discussion of the square root of 2 and of may seem very strange, unreal, and unapplicable to anything with which they are concerned. I hope to show that the remarks I have just made about numbers are applicable not only to statements we all make about many familiar things, but also to history and every other subject.

[All Reality is a Continuum and, therefore, Irrational]

A moment's thought will show that any statement about any continuum is just the same kind of statement as that which we have just made about . Just as any value we may give to refers to a gamut containing an infinite number of numbers and this gamut can be made narrower by carrying our statement of the value of to more decimal places, so any statement about any color refers to a gamut that contains an infinite number of colors. Thus the word "orange" does not refer to a single color (any more than 3.14 refers to a single number), but rather refers to the gamut of colors between red and yellow. If we narrow this gamut by speaking of "yellow-orange," we still are referring to an infinite number of colors. And we could make the gamut narrower by referring to "orange yellow-orange" or to "yellow yellow-orange," thus bisecting the previous gamut. This process could be continued indefinitely, just as the value of can be carried to more decimal places. The value, however, of carrying either very far is not large.

We have been talking about rainbows, numbers, and space-time in order to establish what we mean by a continuum. Now we can define the term in the sense that we shall use it in discussing history. "A continuum is a heterogeneous unity each point of which differs from all the surrounding points but differs from them by such subtle gradations in any one respect that no boundaries exist in the unity itself, and it can be divided into parts only by imaginary and arbitrary boundaries."

We might add that some continua are perfect while others are highly imperfect, the distinction being that a perfect continuum has an infinite number of gradations between any two boundaries drawn in it, no matter how closely together they are drawn, while an imperfect continuum has a finite number of gradations between at least some of the boundaries drawn in the continuum. For example, the gamut of variations of light intensity during any twenty-four-hour period is a perfect continuum. But the "races" of mankind, however defined, are an imperfect continuum. For the variations in any standard we set as a criterion for race can be no more numerous than the number of individual human persons on the earth....

We deal with continua rationally either by dividing them into arbitrary intervals to which we give names, or by giving names to the two ends of the continuum and using these terms as if the middle ground did not exist at all. This last method is called "polarizing a continuum," and is frequently done even when the greatest frequency of occurrence is in the middle range. When the telephone rings in the sorority house because someone wants a "blind date," the sisters at once ask the vital question, "Is he tall or short?" They ask this question even though it is perfectly obvious that the majority of men are neither tall nor short but are nearer the middle range. Such polarization of continua is so common and so familiar that we come, frequently, to accept our categories as real instead of being arbitrary and imaginary, as they usually are. An accident report asks, "Day or night?" although accidents are most frequent when it is neither day nor night, but dusk. Many questionnaires polarize continua by asking us to check: "White -- Colored?" "Man -- Woman?" "Pro -- Con?" In English law this is done in the distinctions between "Adult -- Juvenile" or "Sane -- Insane." In the social sciences it is done in such contrasts as "monopoly -- competition" in economics, "democratic -- authoritarian" or "totalitarian -- liberal" in politics. We have already done it several times in these lectures, as in the dichotomy between natural science and social science or between objective and subjective. The familiar polarization of man into spirit and flesh dominated religious ethics for centuries.

This practice of slicing continua into parts or even into dual poles and giving names to these artificial categories is necessary if we are to think about the world or to talk about it. But we must always remain alert to the danger of believing that our terms are real or refer to reality except by rough approximation. Only by making such divisions can we deal in a rational way with the many nonrational aspects of the world.

We could, of course, renounce any desire to deal with the world rationally and content ourselves with successful non-rational dealings with it. We can deal with the irrationality of space, time, quantity, number, race, color, and so forth, simply by action. Merely to walk, or to run like Achilles, is to deal with the irrationality of space and time and to discover, by action, who will win in a race. When we merely walk along, talking with our friends, we are, by walking, dealing successfully with space and time. No one could ever walk rationally. Simply stand still and make an effort to walk rationally. What is the first thing to do? And what should be done next? What messages must be given to which muscles and in what sequence? We do not know, and we could not do such a complicated mental operation quickly enough to walk by any rational thinking process.

When we approach history and other subjects, we are dealing with a conglomeration of irrational continua. Those who deal with history by non-rational processes are the ones who make history, the actors in it. But the historian must deal with history by rational processes. Accordingly, he must be aware of the processes and difficulties to which we have referred when we try to deal with continua rationally. For history deals with changes in society. And all changes, occurring in time, involve continua.

Once again I return to Quigley:

"Before proceeding, we should review what we understand by the term "scientific method." In general, this method has three parts, which we might call (1) gathering evidence, (2) making a hypothesis, and (3) testing the hypothesis. The first of these, "gathering evidence," refers to collecting all the observations relevant to the topic being studied. The important point here is that we must have all the evidence, for, obviously, omission of a few observations, or even one vital case, might make a considerable change in our final conclusions. It is equally obvious, I hope, that we cannot judge that we have all the evidence or cannot know what observations are relevant to our subject, unless we already have some kind of tentative hypothesis or theory about the nature of that subject. In most cases a worker does have some such preliminary theory. This leads to two warnings. In the first place, the three parts of scientific methodology listed above were listed in order, not because a scientist performs them separately in sequence, but simply because we must discuss them in an orderly fashion. And, in the second place, any theories, even those regarded as final conclusions at the end of all three parts of scientific method, remain tentative. As scientific methodology is practiced, all three parts are used together at all stages, and therefore no theory, however rigorously tested, is ever final, but remains at all times tentative, subject to new observation and continued testing by such observation. No scientist ever believes that he has the final answer or the ultimate truth on anything. Rather he feels that science advances by a series of successive (and, he hopes, closer) approximations to the truth; and, since the whole truth is never finally reached, the work of scientists must indefinitely continue. Science, as one writer put it, is like a single light in darkness; as it grows brighter its shows more clearly the area of illumination and, simultaneously, lengthens the circle of surrounding darkness.

"Having gathered all the "relevant" evidence, the scientist may proceed to the second part of scientific methodology, making a hypothesis. In doing this, two rules must be followed: (a) the hypothesis must explain all the observations and (b) the hypothesis must be the simplest one that will explain them. These two rules might be summed up in the statement that a scientific hypothesis must be adequate and it must be simple. Once again let us confess that these two rules are idealistic rather than practicable, but they remain, nevertheless, the goals by which a scientist guides his activities.

"When we say that a hypothesis must be adequate, and thus must include all of the relevant observations, we are saying something simple. But carrying out this simple admonition is extremely difficult. It is quite true that every scientific hypothesis suffers from inadequate evidence -- that is, it does not include in its explanation all the relevant evidence, and would be different if it did so. It is not easy to tear any event out of the context of the universe in which it occurred without detaching it from some factor that has influenced it. This is difficult enough in the physical sciences. It is immensely more difficult in the social sciences. It is likely that in any society the factors influencing an event are so numerous that any effort to detach an event from its social context must inevitably do violence to it. The extreme specialization of most social studies today, concentrating attention on narrow fields and brief periods, is a great hindrance to our understanding of such special fields, although the fact is not so widely recognized as it should be, since any specialist's work is usually examined only by his fellow specialists who have the same biases and blind spots as he does himself. But a specialist from one area of study who examines the work being done in some other area cannot fail to notice how the overspecialized training of the experts in his new area of interest has handicapped their understanding of that area.

"The second requirement of a scientific hypothesis -- that it should be simple -- is also more difficult to carry out in practice than it is to write down in words. Essentially, it means that a hypothesis should explain the existing observations by making the fewest assumptions and by inferring the simplest relationships. This is so vital that a hypothesis is scientific or fails to be scientific on this point alone. Yet in spite of its importance, this requirement of scientific method is frequently not recognized to be important by many active scientists. The requirement that a scientific hypothesis must be "simple" or, as it is sometimes expressed, "economical" does not arise merely from a scientist's desire to be simple. Nor does it arise from some esthetic urge, although this is not so remote from the problem as might seem at first glance. When a mathematician says of a mathematical demonstration that it is "beautiful," he means exactly what the word "beautiful" means to the rest of us, and this same element is undoubtedly significant in the formulation of theory by a scientist as well.

"The rule of simplicity or economy in scientific hypothesis has a number of corollaries. One of these, called "the uniformity of nature," assumes that the whole universe is made of the same substances and obeys the same laws and, accordingly, will behave in the same way under the same conditions. Such an assumption does not have to be proved -- indeed, it could not be proved. It is made for two reasons. First, because it is simpler to assume that things are the same than it is to assume that they are different. And, second, while we cannot prove this assumption to be correct even if it is correct, we can, if it is not correct, show this by finding a single exceptional case. We could demonstrate the uniformity of nature only by comparing all parts of the universe with all other parts, something that clearly could never be achieved. But we can assume this, because it is a simpler hypothesis than its contrary; and, if it is wrong, we can show this error by producing one case of a substance or a physical law that is different in one place or time from other places or times. To speak briefly, we might say that scientific assumptions cannot be proved but they can be refuted, and they must always be put in a form that will allow such refutation.

"Other examples or applications of the rule of uniformity of nature would be the scientific assumptions that "man is part of nature" or that "all men have the same potentialities." Neither of these could be proved, because this would involve the impossible task of comparing all men with one another (including both past and future men) and with nonhuman nature, but these assumptions can be made under the rule of simplicity of scientific hypothesis or its corollary, the rule of the uniformity of nature. Thus they do not require proof. But, on the other hand, if these assumptions are not correct, they could be disproved by one, or a few clear-cut cases of exceptions to the rule.

"Thus, in the final analysis, these rules about scientific hypotheses are not derived from any sense of economy or of aesthetics, but rather arise from the nature of demonstration and proof. The familiar judicial rule that a man is to be assumed innocent until he has been proved guilty is based on the same fundamental principles as these rules about scientific hypotheses, and, like these, rests ultimately on the nature of proof. We must assume that a man is innocent (not guilty) until we have proof of his guilt because it is always simpler to assume that things are not so than to assume that they are, and also because no man can prove the negative "not guilty" except by the impossible procedure of producing proof of innocence during every moment of his past life. (If he omits a moment, the charge of guilt could then be focused on the period for which proof of innocence is unobtainable.) But by making the general and negative assumption of innocence for all men, we can disprove this for any single man by the much easier procedure of producing evidence of guilt for a single time, place, and deed. Since it is true that a general negative cannot be demonstrated, we are entitled to make that general negative assumption under the rule of the simplicity of scientific hypothesis, and to demand refutation of such an assumption by specific positive proof.

"A familiar example of this method could be seen in the fact that we cannot be required to prove that ghosts and sea serpents and clairvoyance do not exist. Scientifically we assume that these things do not exist, and require no evidence to justify this assumption, while the burden of producing proofs must fall on anyone who says that such things do exist.

"The rule of simplicity in scientific hypotheses is by no means something new. First formulated in the late Middle Ages, it was known as "Occam's razor" and was applied chiefly to logic. Later it was applied to the natural sciences. Most persons believe that Galileo and his contemporaries made their great contributions to science by refuting Aristotle. This "refutation of Aristotle," or, more correctly, "refutation of Plato and of the Pythagorean rationalists," was only incidental to the much more significant achievement of making the commonly accepted rules about the universe more scientific by applying Occam's razor to them. This was done by assuming that the heavenly bodies and terrestrial objects operate under the same laws (laws that were later enunciated by Newton). This application of Occam's razor to natural phenomena was a major step forward in making the study of nature scientific. Application of this rule to the social sciences (that is, to phenomena involving subjective factors) still remains to be done, and would provide a similar impetus to the advance of this area of human thinking. It has already been done in judicial procedure (by such rules as the assumption of innocence and the needlessness of proving negatives), and the chief task in American law at the present time is to protect and, if necessary, extend the application of Occam's razor to judicial procedure. Many persons in recent years have felt uncomfortable over the demand that certain persons should "prove" that they are not "communists," but few realized that the unfairness of such a demand rests on the nature of scientific assumption and the nature of proof and, above all, on the violation of Occam's razor.

"These rules about the nature of scientific hypothesis are so important that science would perish if they were not observed. This already once happened in the past. During the period 600-400 B.C. in the Greek-speaking world, the Ionian scientists applied these rules about scientific hypothesis by assuming that the heavens and the earth were made of the same substance and obeyed the same laws and that man was part of nature. The enemies of science about the year 400 B.C. made assumptions quite different from those of the Ionians; namely, that the heavens were made of a substance different from those on earth and, accordingly, obeyed different laws, and, furthermore, that man was not part of nature (supposedly just because he was a spiritual being). They accepted an old idea that our world was made up of various combinations of four elements (earth, water, air, fire), but assumed that the heavens were made of a quite different fifth element, called "quintessence." They admitted that the earth was changeable but insisted that the celestial areas were rigidly unchanging. They claimed that the laws of motion in the two were quite different, objects on the earth moving naturally in straight lines at decreasing velocity to their natural condition of rest, while objects in the heavens moved in perfect circles at constant speed as their natural condition. These nonscientific assumptions, made about 400 B.C. without any proof or even evidence and by violating the fundamental rules of scientific method, set up a nonscientific world view which, of course, could not be disproved. The Pythagorean rationalists were able to do this and to destroy science because the scientists of that day, like many scientists of today, had no clear idea of scientific method and were therefore in no position to defend it. Even today few scientists and perhaps even fewer non scientists realize that science is a method and nothing else. Even in books pretending to be authoritative, we are told that science is a body of knowledge or that science is certain areas of study. It is neither of these. Science clearly could be a body of knowledge only if we were willing to use the name for something that is constantly changing. From week to week, even from day to day, the body of knowledge to which we attribute the name science is changing, many of the beliefs of one day being, sooner or later, abandoned for quite different beliefs.

"Closely related to the erroneous idea that science is a body of knowledge is the equally erroneous idea that scientific theories are true. One example of this belief is the idea that such theories begin as hypotheses and somehow are "proved" and thereby become "laws." There is no way in which any scientific theory could be proved, and as a result such theories always remain hypotheses. The fact that such theories "work" and permit us to manipulate and even transform the physical world is no proof that these theories are true. Many theories that were clearly untrue have "worked" and continue to work for long periods. The belief that the world is a flat surface did not prevent men from moving about on its surface successfully. The acceptance of "Aristotelian" beliefs about falling bodies did not keep people from dealing with such bodies, and doing so with considerable success. Men could have played baseball on a flat world under Aristotle's laws and still pitched curves and hit home runs with as much skill as they do today. Eventually, to be sure, erroneous theories will fail to work and their falseness will be revealed, but it may take a very long time for this to happen, especially if men continue to operate in the limited areas in which the erroneous theories were formulated.

"Thus scientific theories must be recognized as hypotheses and as subjective human creations no matter how long they remain unrefuted. Failure to recognize this helped to kill ancient science in the days of the Greeks. At that time the chief enemies of science were the rationalists. These men, with all the prestige of Pythagoras and Plato behind them, argued that the human senses are not dependable but are erroneous and misleading and that, accordingly, the truth must be sought without using the senses and observation, and by the use of reason and logic alone. The scientists of the day were trying to reduce the complexity of innumerable observed qualities to the simplicity of quantitative differences of a few fundamental elements. This is, of course, exactly what scientists have always done, seeking to explain the subjective complexity of qualitative differences, such as temperature, color, texture, and hardness, in quantitative terms. But in doing this they introduced a dichotomy between "appearance" and "reality" that became one of the fundamental categories of ancient intellectual controversy. All things, as the scientists said, may be made up of different proportions of the four basic elements -- earth, water, air, fire -- but they certainly do not appear to be. The same problem arises in our own day when scientists tell us that the most solid piece of rock or metal is actually very largely made up of empty space between minute electrical charges.

"The Pythagoreans argued that if things are really not what they seem, our senses are at fault because they reveal to us the appearance (which is not true) rather than the reality (which is true). This being so, the senses are undependable and erroneous and should not be used by us to determine the nature of reality; instead we should use the same reason and logic that showed us that reality was not like the appearance of things. It was this recourse to rational processes independent of observation that led the ancient rationalists to assume the theories violating Occam's razor that became established as "Aristotelian" and dominated men's ideas of the universe until, almost two thousand years later, they were refuted by Galileo and others who reestablished observation and Occam's razor in scientific procedure.

"The third part of scientific method is testing the hypothesis. This can be done in three ways: (a) by checking back, (b) by foretelling new observations, and (c) by experimentation with controls. Of these the first two are simple enough. We check back by examining all the evidence used in formulating the hypothesis to make sure that the hypothesis can explain each observation.

"A second kind of test, which is much more convincing, is to use the hypothesis to foretell new observations. If a theory of the solar system allows us, as Newton's did, to predict the exact time and place for a-future eclipse of the sun, or if the theory makes it possible for us to calculate the size and position of an unknown planet that is subsequently found through the telescope, we may regard our hypotheses as greatly strengthened.

"The third type of test of a hypothesis, experimentation with controls, is somewhat more complicated. If a man had a virus he believed to be the cause of some disease, he might test it by injecting some of it into the members of a group. Even if each person who had been injected came down with the disease, the experiment would not be a scientific one and would prove nothing. The persons injected could have been exposed to another common source of infection, and the injection might have had nothing to do with the disease. In order to have a scientific experiment, we must not inject every member of the group but only every other member, keeping the uninjected alternate members under identical conditions except for the fact that they have not been injected with the virus. The injected members we call the experimental group; the uninjected persons we call the control group. If all other conditions are the same for both groups, and the injected experimental group contract the disease while the control group do not, we have fairly certain evidence that the virus causes the disease. Notice that the conditions of the control group and the experimental group are the same except for one factor that is different (the injection), a fact allowing us to attribute any difference in final result to the one factor that is different.

"The nature of experimentation with controls must be clearly understood, because it has frequently been distorted from ignorance or malice. A number of years ago a book called Science Is a Sacred Cow made a malicious attack on science. In this work the method of experimental science was explained somewhat like this: on Monday I drink whiskey and water and get drunk; on Tuesday I drink gin and water and get drunk; on Wednesday I drink vodka and water and get drunk; on Thursday I think about this and decide that water makes me drunk, since this is the only common action I did every day. This perversion of scientific method is the exact opposite of a scientific experiment. In this performance we assumed that all conditions were different except one, and attributed cause to the one condition that was the same. In scientific method we establish all conditions the same except one, and attribute causation to the one factor that is different. In the perversion of scientific method we made an assumption that was not proved and probably could not be proved&emdash;that all conditions, except drinking water, were different&emdash;and then we tried to attribute causation to the one common factor. But there never could be only one factor the same, since, as an experimental animal, I was breathing air each day and doing a number of other common actions, including drinking alcohol.

"There would, perhaps, be no reason to pay attention to this perversion of science if it were an isolated case. But it is not an isolated case. Indeed, the book in question, Science Is a Sacred Cow, attracted undeserved attention and was publicized in America's most widely read picture magazine as a worthy book and a salutary effort to readjust the balance of America's idolatry of science. The magazine article in question reprinted extracts from the book, including the section on experimental method, and seriously presented to millions of readers the experimental proof that water is an intoxicant as an example of scientific method. Scientific method as we have presented it, consisting of observation, making hypotheses, and testing, is as applicable to the social sciences as it is to the natural sciences. To be sure, certain variations in applying it to the social sciences are necessary. But this is equally true of various parts of the natural sciences. These variations are most needed in testing hypotheses. Even in the natural sciences we frequently cannot use two of the three kinds of testing: we cannot use forecasting in the study of earthquakes or geology in general; we cannot use controlled experiments in these fields or in astronomy. But these deficiencies do not prevent us from regarding geology or astronomy, seismology or meteorology as sciences. Nor should similar deficiencies, especially difficulty in forecasting and the impossibility of controlled experimentation, prevent us from applying the scientific method to the social sciences.

"The applicability of scientific method to the study of society has also been questioned on the ground that theories of the social sciences are too changeable. We are told that every generation must rewrite the history of the past or even that every individual must form his own picture of history. This may be true to some extent, but it is almost equally true of the natural sciences. Science is a method, not a body of knowledge or a picture of the world. The method remains largely unchanged, except for refinements, generation after generation, but the body of scientific knowledge resulting from the use of this method or the world picture it provides is changing from month to month and almost from day to day. The scientific picture of the universe today is quite different from that of even so recent a man as Einstein, and immensely different from those of Pasteur and Newton. And even at a given moment the body of knowledge possessed by any single scientist or the world picture he has made from that knowledge is quite different from that possessed by other scientists. Yet such persons are all worthy to be called scientists if they use scientific method. The same is true in the social sciences.

"The one major difference between the natural sciences and the social sciences is the assumption, made in the former, that human thoughts cannot influence what happens. This is an assumption, justified by the rule of simplicity, although few persons recognize that it is. There is a considerable body of evidence that human thoughts can influence the physical world, but this evidence, segregated into such fields as parapsychology or the psychic world, is not acceptable to the natural sciences. As a result, phenomena such as poltergeist manifestations (largely because they cannot be repeated on request) go unexplained and are generally ignored by the natural sciences. The latter continue to assume that physical processes are immune to spiritual influences.

"In the social sciences, on the other hand, it is perfectly clear that human thoughts can influence what happens; and, accordingly, the social scientist must face the more complicated situation created by this admission. Thus we assume that a rock, dropped from a high window, will fall even if everyone in the world expected it to rise or wanted it to rise. On the other hand, we are quite prepared to see the price of General Motors common stock rise if any large group of people expects it to rise. In a somewhat similar fashion, expectation of a war or desire for a war will make war more likely.

"This difference between the social sciences and the natural sciences makes it possible to draw up fairly definite conditions distinguishing between the two: the natural sciences are concerned with phenomena where we do not expect subjective factors to influence what happens, while the social sciences are concerned with phenomena where subjective factors may affect the outcome."

I asked you to read through all the above so that, in what follows, you will know how I do my thinking. In past generations, one could assume that all those with whom one spoke or wrote one's thoughts would share the same logic and epistemology or in recent centuries would, at least, know which system of logic and epistemology one's audience or readers used. Even as recently as 30 years ago, Carroll Quigley could write a thousand page history book setting forth his historical methodology and cite only one footnote (to St. Thomas Aquinas), knowing by that one footnote any reader would know how the author's mind worked. That is not the case to-day, when we might have readers themselves totally unaware they are part of some idiosyncratic gnostic movement completely alien to Western Civilization, the scientific method, even rationality.

Having said all this, I can proceed to my big question: What is the universe (the heaven and earth, all that is visible or invisible) that we believe God created? The universe is obviously not just the sum of all the individual moon rocks, and chairs, and bacteria, and tigers, and lilies of the field in existence. After all, we now know that all such "things" are in reality just various combinations and patterns of certain electrical particles. Furthermore, we also are about to confirm that even all these particles are themselves just combinations and patterns (fields) of electromagnetic and/or gravitational energy waves. What then is the universe (our heavens and earth)? Just "fields" of immaterial energy? Just formulae, whether or not in the "mind" of "someone"? Sort of, like music or mathematics? (Did the formula 3 x 3 = 9 "exist" before the first human thought of it? Would it still exist if all humanity died out? If all copies of Beethoven's 9th Symphony were destroyed and all humans alive were utterly unaware of it, would it still exist?)


(More Coming)



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