Table of Contents

Part 1 - ✯ MOTIVATION
Part 2 - ✯ Historical Background
Part 3 - ✯ All Motion is Relative
Part 4 -  ✯ Quotations
Part 5 - ✯ Absolute Rest & Absolute Motion are Fictions
Part 6 - ✯ Conclusion   Must Reading!
Part 7 - ✯ The Problem of Motion

Part 1 - MOTIVATION

Does the Earth go around the Sun, or does the Sun go around the Earth?

Rarely a day goes by without people being reminded of the Helio-GeoCentric controversy. This topic is mentioned in almost every science-versus-faith discussion. There is hardly a book that does not mention it when dealing with science-faith issues. Even Christian authors have succumbed to the myth that Galileo somehow discovered the true motions of the planets. We are admonished to submit to the pronouncements of scientists, because the Helio-GeoCentric controversy “proved” that science is a legitimate source of truth.

Before we cite quotations, we need some background information:

Part 2 - HISTORICAL BACKGROUND

Ptolemy Claudius of Alexandria (85-165 AD) made precise measurements of celestial motions and wrote an influential book called the Almagest. He believed that the Earth is a Sphere and that Planets move in Epicycles, i.e. Cycles on Cycles. He based his work on the Greek philosopher Hipparchus, (fl. 147-126 BC) who rejected Heliocentrism as proposed by Aristarchus of Samos (fl. 270 BC). That the earth is a sphere was known at least 600 years before Christ, and its circumference was accurately estimated by 300 BC.

Nicolaus Copernicus (1473-1543) was a Heliocentrist and believed that Planets move in Circular orbits of uniform motion around the sun, even though he knew that the sun was off-center of the solar system. His book called On the Revolutions of the Heavenly Spheres was published posthumously. He discovered the heliocentric concept from the Greeks.

“[…] it is the job of the astronomer […] since he cannot by any line of reasoning reach the true cause of [celestial] movements […] to think up or construct whatever hypotheses he pleases […] it is not necessary that these hypotheses should be true or even probable, it is enough if they provide a calculus which fits the observations […] let no one expect anything in the way of certainty from astronomy, since astronomy can offer us nothing certain […]”
Nicolaus Copernicus; On the Revolutions of the Heavenly Spheres; 1543

Tycho Brahe (1541-1601) Danish Astronomer, tried to hold a middle ground between Copernicus & Ptolemy. He believed that the Earth is immobile, some planets revolve around the sun and all revolve around the earth. He tried to convert Galileo from Copernicanism. He was an instrument maker, and accurate clocks were invented by his time.  He invented the Sextant which he used to make accurate measurements of stellar positions.

Johannes  Kepler (1571-1630) A Heliocentrist. He continued the work of Brahe. He was greatly enamored by astrology. He corresponded with Brahe & Galileo and proposed elliptical paths of planets around the sun, which obviated the need for epicycles.
Both Copernicus and Kepler were of the opinion that the Solar System virtually exhausted the space of the universe.

Galileo Galilei (1564-1642)   Believed in circular planetary orbits. Even though his friend Pope Urban VIII had not discouraged him from publishing his ideas, he had asked Galileo not to insist upon absolute motions. Galileo’s publication was seen as a betrayal of that trust, and he was convicted of heresy and placed under house arrest.

[…] I think that in discussions of physical problems we ought to begin not from the authority of scriptural passages, but from sense-experiences and necessary demonstrations; for the holy Bible and the phenomena of nature proceed alike from the divine Word, […] It is necessary for the Bible, in order to be accommodated to the understanding of every man, to speak many things which appear to differ from the absolute truth so far as the bare meaning of the words is concerned. But Nature, on the other hand, is inexorable and immutable; she never transgresses the laws imposed upon her, or cares a whit whether her abstruse reasons and methods of operation are understandable to men.”
Galileo Galilei; Letter to the Grand Duchess Christina; 1615

Part 3 - ALL MOTION IS RELATIVE

Since we do not know of a point in the universe which is absolutely fixed, it is impossible to determine which celestial object is actually in motion.

We can choose ANY star or planet as our reference point, assume that it is “fixed,” and then measure the “motion” of other bodies RELATIVE to that arbitrary point.

Part 4 - Here is a collection of statements by those who have understood the nature of motion.

The cosmologies of Copernicus [Heliocentrism] & Ptolemy [Geocentrism] are kinematically equivalent; both of them are descriptions of the same facts, and Ptolemy’s epicycles of the planets are the kinematic equivalents of the circular orbits of Copernicus.
Hans Reichenbach; (1891-1953); Philosophy of Space and Time; 1927/1958; p210-211

Galileo and the Inquisition are only in error in the single affirmation in which they both agreed, namely that absolute position is a physical fact – the sun for Galileo and the earth for the Inquisition.
Alfred North Whitehead; (1861-1947); An Enquiry Concerning the Principles of Natural Knowledge; 1919/1982; p31

It looks as though all the forces of Nature had entered on a conspiracy together with the one design of preventing us from measuring or even detecting our motion through the æther. […]
We now deny the existence of any unique framework of [an æther at rest]. We have failed to obtain experimental knowledge of such a framework since we cannot detect our motion relative to it. Whatever may be the nature of the æther, it is devoid of those material properties which could constitute it a framework of reference in space.
Sir Arthur Eddington; (1882-1944); Gravitation and the Principle of Relativity; Nature; v101; March 1918; p16,17.

The laboratory can devise no method for determining whether the Earth moves while the Sun stands still or whether the Sun moves while the Earth stands still. […] Neither can physics observe anything  moving in a straight line.
Gordon Clark; Christian Philosophy; 2004; v4; p322

[…] the unsuccessful attempts to discover any motion of the earth relative to the “light medium,” suggest that the phenomena of […] mechanics possess no properties corresponding to the idea of absolute rest.
Albert Einstein; (1879-1955);On the Electrodynamics of Moving Bodies; 1905

The commonly held view is that Copernicus’s heliocentric model vanquished the competition, especially the geocentric view of Ptolemy, because it yielded better predictions of the positions of the celestial bodies. In actual fact, the predictions of the Copernican model were a little worse than those obtained via the complicated series of epicycles[…] the real selling point of the Copernican model was that it was much simpler than the competition yet still gave a reasonably good account of the observational evidence.
J. L. Casti & W. DePauli; Gödel; 2000; p166

Today we cannot say that the Copernican theory is ‘right’ and the Ptolemaic theory ‘wrong’ in any meaningful physical sense.
Fred Hoyle; (1915-2001); Nicolaus Copernicus; 1973; p78

The aether was thought of as being ― except for minor local variations ― both uniform and at rest. […]
The first important critic of the orthodox theory of absolute space and time was Mach […] [who] attacks the assumption that absolute rotation is observable. All that can be observed is rotation relative to the fixed stars.
H. G. Alexander; (1925-); The Leibniz-Clarke Correspondence; 1976; pxlix

There is one more implication that modern science has perceived in the work of Copernicus. The same observational data that Ptolemy organized in his geocentric theory of deferent and epicycle can also be organized under the heliocentric theory of Copernicus. Despite the belief of the latter that the new theory was true, the modern view is that either theory will do and that there is no need to adopt the heliocentric hypothesis except to gain mathematical simplicity. Reality seems far less knowable than Copernicus believed, and today scientific theories are regarded as human inventions.
Morris Kline; (1908-1992); Mathematics and the Search for Knowledge; 1985; p85

[…] the Ptolemaic theory of the solar system was abandoned in favor of the Copernican not because it failed to “agree” with all the facts, for it explained as much as the Copernican did, but because the latter, as Copernicus himself said, was “simpler,” more elegant mathematically, and a more harmonious addition to the body of science than the former.
[…] there was no intellectual inconvenience at one time in regarding the earth as the fixed center of the universe, nor was there any particular reason, socially or otherwise, why it should not have been accepted, nor was it inconsistent with the existent body of knowledge.
J. H. Randall; (1899-1980); Philosophy: An Introduction; 1957;  p135, 139

Two thousand years ago the earth turned; then it remained immobile until recently, when it has again begun to turn.
Nicolas Malebranche; (1638-1715); The Search After Truth; 1674/1997; p371

All the known celestial movements can be explained on a geocentric theory, if it is sufficiently complex.
A. R. Lacey; Dictionary of Philosophy; 1999; p359

[…] in fact simplicity of the mathematical theory was the only argument Copernicus & Kepler could advance in favor of their heliocentric theory as opposed to the older Ptolemaic theory. Is the path of the earth around the sun an ellipse? No. Only if the earth & sun are regarded as points and only if all other bodies in the universe are ignored. Do the four seasons on earth repeat themselves year after year? Hardly. Only in their grossest aspects, which are about all men can perceive anyway, do they repeat.
Morris Kline; (1908-1992); Mathematics: The Loss of Certainty; 1982; p344, 350

[…] there are no conceivable operations by which the absolute velocity of the earth could be measured since the attempt to measure this velocity in the aether has failed. The concept of absolute velocity must therefore be rejected from physical theories, and all actual velocities of bodies defined by the operations used to measure them relative to some other body.
Mary Hesse; (1924-2016); Science and the Human Imagination; 1954; p72

[…] when describing the motion of the Sun, moon, and planets relative to the Earth, it makes little practical difference whether one adopts a geocentric or a heliocentric model of the Solar System.
[…] the model of Copernicus is about as complicated, and not appreciably more accurate, than that described in [Ptolemy’s] The Almagest. In this respect, Copernicus cannot be said to have demonstrated the correctness of his heliocentric approach on the basis of observational data.
Richard Fitzpatrick; A Modern Almagest; {2006}; p10,11
http://farside.ph.utexas.edu/Books/Syntaxis/Almagest.pdf
[6/27/21]

[Copernicus] was able, in fact, to cite as a distinct advantage only the greater simplicity of his system.
[…] Here lies one of the reasons which led scientists to accept the Copernican system, even though it must be conceded that, from the modern standpoint, practically identical results could be obtained by means of a somewhat revised Ptolemaic system.
Hans Reichenbach; (1891-1953); From Copernicus to Einstein; 1927/1970; p18

The merit of the Copernican hypothesis is not truth, but simplicity; in view of the relativity of motion, no question of truth is involved.
Bertrand Russell; (1872-1970);  A History of Western Philosophy; 1945; p217

[…] relative to the earth the stars are in motion. We therefore need to know first of all what is meant by ‘real motion’ […] it turns out that we cannot quite say what is meant by it […] the question whether the earth is really moving but not the stars or the other way around does not make any sense […]
Hans Hahn; (1879-1934); Empiricism, Logic and Mathematics; 1933/1980; p48

Part 5 - ABSOLUTE REST AND ABSOLUTE MOTION ARE FICTIONS

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.
[…] the two propositions: “the earth turns around” and “it’s more convenient to suppose the earth turns around” have the same meaning; there is nothing more in the one than in the other.
Henri Poincaré; (1854-1912); Science & Hypothesis; 1905/1952; p116-117

We must also mention here as a peculiar and valuable auxiliary idea, the fiction of an absolutely fixed point.
The empirical perception of all change and motion is always connected with empirical points of reference, and it is only when related to these that we can recognize it as motion. In other words all observed motion is relative, relative to us, to an imaginary origin, relative to a fixed background or relative to the apparently stationary earth or sun. These are all mere points of reference which we must assume in succession. Man begins by assuming himself as a point of reference and science constantly postulates other points of reference because those taken first prove to be illusory, since they turn out to be in motion themselves. In order to prove definitely and absolutely the existence of motion, we must have an absolutely fixed point by means of which the speed and direction of the motion can be measured. Since, however, according to modern views, no such absolutely fixed body can be discovered in the universe, science is faced with a peculiar difficulty.
Hans Vaihinger; (1852-1933); The Philosophy of “As If”; 1924; p225

[…] the problem of motion remains unsolved. The reason is that we do not know what motion is. We have no concept of motion. We have nothing clearly in mind when we use the word. We simply do not know what we are talking about. Perhaps motion, and science along with it, is just nonsense.
Gordon Clark; (1902-1985); The Philosophy of Science and Belief in God; 1966; p19

Galileo said that the earth moves and that the sun is fixed; the Inquisition said that the earth is fixed and the sun moves; and Newtonian astronomers […] said that both the sun and the earth move. But now we say that any one of these three statements is equally true, provided that you have fixed your sense of ‘rest’ and ‘motion’ in the way required by the statement adopted.
Alfred North Whitehead; (1861-1947); Science and the Modern World; 1925/1944; p263

Let it be understood at the outset that it makes no difference, from the point of view of describing planetary motion, whether we take the Earth or the Sun as the center of the solar system. Since the issue is one of relative motion only, there are infinitely many exactly equivalent descriptions referred to different centers - in principle any point will do, the Moon, Jupiter… So the passions loosed on the world by the publication of Copernicus’ book, De revolutionibus orbium caelestium libri VI,  were logically irrelevant…
Astronomer, Fred Hoyle

The Church fathers were convinced that the Copernican worldview conflicted with the teaching of the Bible (after all, Joshua told the sun, not the earth, to stand still). Galileo was equally convinced that Copernicus was right, that the earth moves around the sun rather than the sun around the earth. At first, the Church fathers took a relaxed approach to Galileo’s apostasy. They were willing to allow Galileo to teach the Copernican system as a way of computing the motions of the planets as long as Galileo did not teach that the planets actually move in the way the Copernican system describes.

After all, Ptolemy presented his system as a way of calculating the position of the planets, not as a description of how the system really worked. So the Church fathers were really asking Galileo to approach the question in the same fashion as Ptolemy had. Galileo, however, was not noted for his inclination to compromise. He was persuaded that Copernicus had not only the better description of nature, but also the right description. The Church disagreed and in those days the Church did not have to brook disagreement from anyone. In 1633, the Inquisition forced Galileo to renounce the Copernican view.

Galileo’s refusal to temper his viewpoint is often held up as an example of scientific integrity in the face of religious dogma, but the situation was not quite that simple. First, the idea that we cannot tell which of two bodies is in motion is critically important to Copernicus’s model ― we cannot tell from the apparent motion of the sun whether the sun or the earth is moving. Second, Galileo himself developed arguments demonstrating that we cannot tell whether something is in uniform motion or at rest on the basis of observations made within the system. This principle is familiar to anyone who has ever traveled in an airplane moving at over 500 miles per hour. In this situation, an object dropped from a tray falls to the floor in exactly the same way the object would fall if the plane were motionless on the ground. As long as the air is smooth and the plane is not turning, climbing, or descending, we cannot tell, without looking outside, whether the plane is still or is in motion.

Against these arguments, Galileo’s intransigence seems courageous but not completely rational.

Bruce Gregory; Inventing Reality; 1988; p14

QUORA Q&A

Q>> The Earth is rotating. If a helicopter takes off in LA and stays in the air (with what reference frame and velocity?) for 10 hours, will it land in NY?

A >> No one can prove if the earth is rotating or moving thru space.


RESPONSE
Well, the Ball Earthers show the Foucault Pendulum, where it swings in a straight line, making it look like the Earth is rotating under it.

Have you come across a way to convince people that it’s NOT Earth rotating? If so, then you’ll have a great way to explain how ‘no one can prove if the Earth is rotating’.

The other example they give, is how the stars seem to also rotate around a ‘south pole’, making it look like it must be a sphere.

And (bonus!) the Ball Earthers say this proves Earth is a sphere, too.

Have we got a way, yet, to explain why it CAN’T look like this?

As for orbiting the Sun, the Ball Earther explanation is longer, so I’ll wait & see how much help you can give, debunking them, and promoting the Flat Earth Model!

REPLY
It is impossible to demonstrate or “prove” absolute rest or absolute motion. Those are undefinable and thus meaningless concepts in our universe.

On the other hand, if you are advocating for a Flat Earth, I will not converse with you.

See this page on the nature of motion.
All Motion Is Relative

I will answer only rational question after you have read the page.

REPLY
Interesting ideas, Berj!

But how do we explain the cases for rotation, such as Foucault and Coriolis?

Anyone can see how an object will continue in a straight line (as per Newton), yet there is clearly visible rotation of another object (the Earth)?

I hope we have more than, “Well, that can’t be happening due to X Y Z, so there must be some mysterious thing going on.”

See the problem, Berj?

You are clearly more knowledgeable than me, so what explanation(s) have you used in the past that convinced people that the Earth can be motionless yet look rotating?

—

The other thing is orbits. Anyone can go onto sites like “The Planets Today”, and verify it uses the gravity-based, heliocentric model. And that it 100% exactly matches everything we all see, every day of our lives, from any location on Earth. Yikes!

Do you happen to know of a Geocentric model that makes the same predictions? How does it work, then?

This is a tough one, I think!

Especially the retrograde movement of planets, that only makes sense if all of them (including Earth) orbit the Sun.

—

I looked over that site, but it’s what I call “Dead Scientist Quotes”, and there are a few problems - maybe you know? For one thing, everybody should “do their own research” by setting up their own experiments. Quotes from DS’s discourage that, right?

Also, how do we know the ‘scientists’ aren’t wrong? Or outdated? Or flat-out liars? We can only trust ourselves!

Any help you can offer on this whole “heliocentric” thing is appreciated!

REPLY
Thanks for your kind questions.
So many I can only give a very brief reply.
Before all else though, it must be admitted that Absolute Motion and Absolute Rest are fictions. There is no possible way to demonstrate either one because of the way our universe is created. We cannot expect to experience either one, and we do not experience either one!
I am not surprised by your questions because we never hear that Geo-centrism is just as viable a model of the solar system as Helio-centrism. I think few have ever investigated this topic to the extent that I have done thru the years. The quotations by these most prominent astronomers and physicists show that to insist on either Geo- or Helio-centrism as true or false is not a logical point of view.
I want to make clear again, because I do not want to be accused of insisting on one model as opposed to the other model. Neither model can be true and neither model can be false. All motion is relative. It is simply a matter of convenience which model we want to use for the purpose at hand.

The Foucault Pendulum cannot demonstrate absolute motion. All such pendulums are Driven, Damped and Tuned because no pendulum can be perfectly balanced, no pendulum can ever swing in a perfect plane due to friction at the apex and air resistance in the chord, and the fact that the bob has volume.
The equation for a pendulum assumes that there is no tension in the cable, the apex has no friction, and the bob has no volume. But such a pendulum is an imaginary pendulum, having little in common with pendulums which are used to “prove” that the earth is rotating on axis. i.e. a perfectly balanced pendulum is needed to prove absolute motion, and that is an impossibility.

If the pendulum is not DAMPED, it begins to swing in a figure 8 path, goes out of control and becomes useless. It needs to be DRIVEN because it loses momentum with every swing and its path becomes shorter and shorter. It needs to be TUNED so that it swings the “exact same” arc length each time. In addition, pendulums precess both clockwise and counter-clockwise!! That I am sure is a shock to most inquirers!!

Of course each one of these intrusions into the pendulum’s natural motion make the pendulum an irrelevant tool in determining the absolute rotation of the earth.
In addition, celestial forces which control the tides of the oceans will also be working on a pendulum, making it a useless tool in determining absolute motion. The same forces apply to Coriolis motions.

There is just no possible way to prove absolute motion. People much brighter than me have tried it over and over. Finally they realized that all their efforts were a waste of time and money because they were longing to prove the unprovable. The quotes on my webpage prove beyond a shadow of a doubt that absolute motion and rest are impossible to experience.

A good scientist should first be a good philosopher. Sadly good epistemology and philosophy of science is hardly ever taught in our schools!!
Dismissing quotes by dead astronomers is not how we do scholarly work. Address the point made by each writer. Do not indulge in personal attacks.
If we do not agree that All motion is relative, there is no point in continuing this conversation. I deal only with facts and not with fantasies.

Stephen Toulmin; (1922-2009); & June Goodfield; (1927-2025); The Fabric of the Heavens; 1961; p169

From the point of view of modern science[…] there is no absolute frame of reference, only frames which are more or less convenient to use for the purpose at hand. A geocentric frame is useful for everyday activities, while a heliocentric frame is [useful] for solar-system mechanics […]
Wikipedia; Geocentric Model

[…] it does not appear to me that there can be any motion other than relative; so that to conceive motion there must be at least conceived two bodies, whereof the distance or position in regard to each other is varied. Hence, if there was one only body in being it could not possibly be moved. This seems evident, in that the idea I have of motion does necessarily include relation.
George Berkeley (1685-1753); The Principles of Human Knowledge 1710/; s112


No one is competent to predicate things about absolute space and absolute motion; they are pure things of thought, pure mental constructs, that cannot be produced in experience.

But if we take our stand on the basis of facts, we shall find we have knowledge only of relative spaces and motions. Relativity, not considering the unknown and neglected medium of space, the motions of the universe are the same whether we adopt the Ptolemaic or the Copernican mode of view. Both views are, indeed, equally correct; only the latter is more simple and more practical.
Ernst Mach; (1838-1916); The Science of Mechanics; 1893/1942; p229; p284

Part 6 - CONCLUSION

That should be sufficient for any thoughtful person to understand that the Helio-GeoCentric controversy took place because both sides of the dispute insisted upon the fallacies of absolute rest and absolute motion.

Men’s longing for material absolutes has manifested itself over the ages with presumptions of “absolute” Space, “absolute” Time and “absolute” Motion. None of these “absolutes” could possibly exist, yet to this day, those who should know better, continue to pay homage to these and other figments of their imaginations and urge others to join in their idolatry.

Does the Earth go around the Sun,
or does the Sun go around the Earth?
Take your pick, whichever is most useful for the purpose at hand.

To ask the question expecting an Either/Or answer, or to answer the question as Either/Or is clear evidence that the Nature of Motion has NOT been understood.

Part 7 - The Problem of Motion
Gordon H. Clark

Among those who accept and defend the historic position of Protestantism, interest has recently increased in the philosophy of science. This interest does not arise merely or even mainly from the implications of biological evolution, but rather in part springs from a broader concern with philosophy as a whole and in part from the presence and activity of the scientists among us. The importance of formulating a philosophy of science, whether by Christian thinkers or by secular thinkers, needs no emphasis. What is needed, is, rather, a warning of the difficulties and dangers that attend the attempt. One of these dangers is seen in the frequent neglect of a most basic problem. And the aim of this paper is to bring to the fore the general problem of motion.

The main proposition, the justice of which this paper hopes to support, is that no philosophy of science can be acceptable unless it satisfactorily disposes of the problem of motion.

Although the ancients gave serious thought to this matter, recent philosophy has unfortunately made little progress in explaining motion and modern science has made none at all. On this subject the scientists seem satisfied with a famous statement of Sir Isaac Newton. Near the beginning of his Principia, in the Scholium after Definition VIII, he says, “I do not define time, space, place, and motion, as being well known to all. ” Now, Sir Isaac Newton was a scientific genius of first order, and therefore he is entitled to make a blunder of first order without diminishing his fame. Such a blunder was this assertion, for time, space, and motion are by no means well known to anybody. Recent physics has to some extent seen the need of examining the meaning of time and space; but if any uneasiness about motion has been felt, it is at least safe to say that no explanation has been achieved. The situation today remains about the same as antiquity left it. That situation was a stalemate. The Eleatic arguments against the possibility of motion still oppose the Aristotelian explanation of motion. Since the latter is not too convincing, the Eleatic arguments are dismissed as poor jokes that scientists ought not to bother with. To forget is to solve.

The original joke was Zeno’s paradox of Achilles and the tortoise. In that notable race, when Achilles had once allowed his competitor a head start, it slowly dawned on him that he could never overtake the tortoise. Two thousand years have passed since Zeno first told this story, and still no refutation of it commands universal assent. The replies are superficial. One calculates how far Achilles could run in ten or thirty minutes and places him far ahead of the tortoise. Another balances the infinite divisibility of space against the infinite divisibility of time. Aristotle (Physics VIII) addressing himself to the simpler form of the paradox, that of a single body exhausting an infinite series of points as it moved toward a fixed terminus, argued that the moving body does not actually pass through an infinite series of points. Zeno, says Aristotle, treats one point, the midpoint, as two. He takes it as both the end and the beginning of a motion. But this can be so only if the moving body stops at this point and then begins again. If the body is in continuous motion, none of these mid-points is “actualized.” The points and the divisions are only potential and do not actually exist. Therefore although it is impossible to pass through or exhaust an infinite number of actual points, there is no difficulty in passing through an infinite number of potential points.

There is another attempt to answer Zeno. One may protest since an infinite series does not have a last term, Zeno cannot require the moving body to reach the last term before it starts to move. He cannot erect as a barrier to motion a factor that admittedly does not exist. And yet, did Zeno say that it was necessary to reach the last term? Will not his paradox remain if he simply asserts that motion can not begin so long as there are more terms in the series. And this is long enough.

Well, perhaps a slightly different expedient will allow the body to move. Let us grant that in any finite space an infinite number of points actually exist. Let us also grant that to move from here to there a body must pass through all of these points. But let us deny that the body must pass through each of these points. That is, we claim, Zeno confused a collective all with a distributive each. He supposed, mistakenly, that whatever is true of one must be true of the other. Yet there are many examples where the collective all has qualities quite different from the distributive each. Each nail in this keg is easy to pick up; but it is difficult to pick up all of them. Similarly what is true in every case is not necessarily true in general. Aristotle argues that although a theorem be proved for each of the three types of triangle, it has not on that account been proved a triangle generally. Or, finally, each element of a compound may be poisonous (NaCl), but the whole may be good to eat. Zeno therefore was mistaken because he insisted that a moving body must pass every point, when as a matter of fact it need only pass all of them.

Perhaps this last solution is not so suspicious as the previous ones were. But even so, it would only remove an Eleatic objection to motion: it would not furnish a theory, a definition, an explanation of motion. And this last is what is needed. Professional, practicing scientists like Newton may no doubt be excused if they refuse to tell us what motion is; but a philosophy of science cannot decide to bury a problem simply because it has remained so long unsolved. And if motion is basic to all science, one wonders how any natural phenomenon can be explained before this. We cannot, then, dodge the question, What is motion?

In the Physics, Book III, Aristotle begins a determined attack on the problem of motion. He spares no effort to arrive at a solution. And effort is required, for the explanation of motion must make use of the concepts of continuity, infinity, place, time, and perhaps void. This is a constant trouble with philosophic subjects. One hardly begins a topic before one discovers that another matter calls for prior attention. We are always being pushed back or forward, until it seems impossible to solve any one problem without solving all. Omniscience is the prerequisite, and omniscience is hard to come by. But Aristotle makes a brave beginning. The Pre-Socratics had failed to unravel the enigma of motion, chiefly because they did not know what motion is. Their halting hints were faulty as definitions. Within this section (Physics III, 1) Aristotle formulates the definition of motion three times. First, he says that motion is the actualization – literally, he says the actuality – of the potential qua potential. This cryptic phrase is then explained. When that which is buildable, insofar as it is buildable, is actual, it is being built; and this is the motion or change called building. Note that the completed house is not buildable; it is built, and the motion is completed. Nor is the actuality of brick and wood motion: insofar as the materials as such are concerned, the motion has not yet begun. This motion therefore is the actualization of the buildable qua buildable.

Aristotle must insist on the importance of the insofar as, the qua, the as such. Bronze is potentially a statue; but the actuality of bronze qua bronze is neither a statue nor motion. To be bronze and to be movable do not mean the same thing. Or, again, to be potentially healthy is not the same as to be potentially sick; for, if it were, to be actually healthy would be to be actually sick. Of course the same person may be sick or well; but the potentialities are different. Motion thus is the actualization of the potential qua potential.

The second time Aristotle formulates the definition he says, “Motion is the actuality of a potential being when it operates in actuality not insofar as it is itself, but insofar as it is movable.” The third formulation, a few lines below, is essentially a repetition of the first. Now, the second of these three formulations is clearly untenable: it is obviously circular. To define motion as the actuality of the moveable is to use the concept of motion in its own definition. How could one know what moveable means, i.e., able to move, unless one first understood motion? This circularity is present also in the example given under the first formulation. What buildable means cannot be known until the motions of building are understood. Either then Aristotle has made a circular blunder, or the first and third formulations must somehow escape this criticism. It is not at all certain that the second formulation is a mere slip of the pen which is excusable in the light of the other two. In Physics VIII, 1 (251a8), a passage presumably referring to Physics III 1, Aristotle again defines motion as the actuality of the moveable qua moveable. Similarly, a few pages later (257b8) he says “Motion is the incomplete actuality of the moveable.” It would seem therefore that the taint of circularity is more than merely superficial.

However, Aristotle should be given every opportunity to rebut this charge before a final judgment is entered. Since he furnished two other formulations, these also should be examined. And it must be admitted, they contain at least no apparent circularity. Motion is the actualization of the potential qua potential. It is requisite, however, to state what is meant by the term potential. In fact, two requirements must be met. First, the term potential must be defined without using the idea of motion, or else the circularity will reappear; and, second, the idea of potentiality must be set forth clearly and unambiguously, or else all physics will remain vague and confused. The clarification of the concept of potentiality is found more in the Metaphysics than in these discussions on motion. In Book Delta he says, “Potentiality is a source of motion and change which is in another thing than the thing moved, or in the same thing qua other … Potentiality then means the source of change or motion…” It would seem, however, that this is not altogether satisfactory. In the Physics Aristotle defined motion in terms of potentiality, and now in the Metaphysics he is defining potentiality in terms of motion. Circularity therefore has not been avoided, and we still do not know what motion is.

There is, however, another passage. In Book Theta of the Metaphysics (1048 a 30-b 6) Aristotle defines actuality. “Actuality means the existence of an object, but not in the manner we call potentiality. We say, for instance, that a statue of Hermes is potentially in the block of wood … because it can be cut out of it. We call a man a scholar even when he is not studying, if he is actually capable of studying … We must not seek a definition of everything, but be content to grasp an analogy: that as he who is building is to him who can build, and as he who sees is to him who, though not blind, has his eyes shut … so actuality is defined by one member of these antitheses and potentiality by the other.” Even in this more extended passage it is a question whether circularity has been avoided. Cutting the statue out of wood, studying, and seeing are motions; and thus potentiality and actuality are explained on the basis of motion. Motion, then, cannot properly be defined in terms of potentiality.

But, says Aristotle, this is not a definition. Potentiality cannot be defined. It must be grasped by analogy. As he who is asleep is to him who is awake, so potentiality is to actuality. Now, the man who is asleep is horizontal and the man who is awake is vertical. Is this what Aristotle means? Of course not. But it is hard to tell what he means, for there are many comparisons that can be made between men asleep and men awake. The former dream, the latter do not. How can one select which point of comparison is intended? It would seem therefore that even if Aristotle has avoided the apparent circularity, he has not given us a clear and unambiguous concept of potentiality.
This argument may now seem to have become all too intricate; but the conclusion should be disturbing enough to jolt one out of any tendency to doze. The conclusion is not that Aristotle got himself into a jam: such would be merely a piece of historical information. Nor is the conclusion simply the meaninglessness of the concept of potentiality and the uselessness of analogical definitions. Such is of course a valuable warning to any ambitious philosophers who are unknowingly starting up a blind alley. But there is the much more disturbing conclusion that the problem of motion remains unsolved. And in the recesses of our oblivion there still lurks the skeleton of Zeno’s Achilles. Perhaps motion is just nonsense.

Newton, as has been said, failed to extricate science from the difficulty because he assumed that the meaning of motion was known to all. On this assumption he proceeded to discuss particular forms of motions. The futility of this procedure is clear enough to philosophers, but perhaps scientists wonder why ancient puzzles should be allowed to hinder modern science. For the reason something, as brief as possible, should be said about two important Newtonian laws; the law of inertia and the law of gravitation. The first of these asserts that a moving body continues indefinitely in a straight line unless subjected to an impressed force; and the second is an attempt to explain the curvilinear motion of the planets.

Now, the best known of all Newton’s pronouncements is the one that reveals his failure to explain planetary motion. The law of gravitation expresses with mathematical accuracy the forces necessary to change the rectilinear or inertial motion of a planet into an elliptical path. But when one asks the question, what impresses these forces? Newton replies, Hypotheses non fingo. Cajori, Newton’s recent editor, has collected some of Newton’s letters (Principia, Appendix, not 6, pp. 632-635) in which he clearly expresses the limitations of his mathematical law. Gravity, newton declares, is not a property of bodies; if it were, one body would act on another at a distance, and this is manifestly absurd; indeed, “We are ignorant of the essential properties of matter.” Mathematics only measures the quantity of the force; it says nothing about what impresses the force. Newton himself thought it possible that God impresses this force; but this theological opinion is obviously not a part of experimental science. Therefore science has failed to show what forces the planets out of a rectilinear path.

Now, finally, what is the value of the law of inertia? This law states that a moving body continues in a straight path unless compelled to change by an impressed force. The difficulty with this law is well known. To determine a straight line a fixed point is needed. If a hawk in search of a meal flies always toward another bird, and the other bird is darting hither and yon, the hawk obviously does not fly in a straight line. And if a rocket could be fired so as always to be pointing to the moon, it would not describe a rectilinear path. The determination of a rectilinear path requires a fixed object in absolute space. But there are no fixed objects. The “fixed” stars are not fixed. Hence the law of inertia has no application. It is completely impossible to discover a body moving in a straight line.

Since this paper is but one section of a larger argument, later conclusions are not here sufficiently prepared for; yet it seems that one subsidiary but important point may be made. The problem of motion, particularly the general problem, but also even some special problems remain unsolved. Space, time, and motion are not “well known to all.” In this situation a philosophy of science that pretends to justify scientific knowledge of nature is left without any knowledge to justify. Can anything be known about nature if no one knows what space, time, and motion are? Can it even be known that science is supposed to talk about nature?

Wittgenstein, whose unwise assertions approximately equal Newton’s wise ones, is surely allowed one very wise remark to match Newton’s blunder; “Whereof one cannot speak, thereof one must be silent.”

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