TheNew$Physics$ Kepler's$Refutationof$Aristotle's$Concept ... · 2!! 1.Introduction:theContext$...

The New Physics

Kepler's Refutation of Aristotle's Concept of Motion

Master Thesis

Mihaela Rusu

student number: s4161343

date: July 12, 2015

specialisation: History of Philosophy

supervisor: Christoph Lüthy

1

Table of Contents

1. Introduction: the Context 2

2. The Problem 4

3. The Classical View: Aristotle’s Concept of Motion 6

3.1 First and Second Argument: Motion and the Structure of the Universe 6

3.2 Third Argument: Celestial versus Terrestrial 13

4. A New Kind of Argument: Kepler’s Physics 14 4.1 Heliocentrism 17 4.2 The Orbits 24 4.3 Motion; the Motion of the Sun and of the Planets: the Motor Virtue 29 5. The Refutation 31 6. Conclusion 35

Bibliography 37

2

1. Introduction: the Context

In 1619 Kepler formulated the last of his three laws of planetary motion.1 By that time, he had re-‐

interpreted the concept of motion so that he could shape his theories about the planetary system,

which constitute the beginnings of modern astronomy. Kepler’s adventure began when, still a student,

he was confronted with the new Copernican theory of heliocentrism, a theory that he embraced and

whose defender he would be his whole life, as he confesses in the first part of his Epitome, in 1617: “(…)

I take it as my duty and special task to defend it before the world (and the readers) with all the powers

of my brain; for I have recognized it in my own mind as true and in contemplating it, I am filled with

unbelievable delight at its beauty.”2 Based on the heliocentric hypothesis, Kepler started re-‐ordening

the universe on paper. Seen in reverse, Johannes Kepler's trajectory in his pursuit of the truth governing

the universe could be described as having been conducted by pairs of arguments: mathematical /

geometrical, astronomical / astrological, scientific / theological, physical / metaphysical.3 Max Caspar

noticed that Kepler "was no longer willing to be satisfied with a kinematic and pure geometric

presentation of the motions; he wanted to explain these by their causes."4 Therefore, he saught not a

presentation of the motions of the planets across the skies but a deeper insight into the processes that

govern them. The step Kepler had to take in order to understand and explain these motions was in fact

the move from what we call today ancient "knowledge" or "belief" towards modern "science".

Kepler was a man of words and arguments, as he continuously questioned and doubted theories,

formulated hypotheses and worked on elaborated proofs for them. The progress he made through his

step-‐by-‐step work was the result of his struggle against preconceived theories. That was not a simple

task, as the world he lived in was not encouraging doubt. It was rather a world of written and unwritten

1 The three laws were formulated over a period of 17 years: the first law was postulated in 1602 and published in 1609 in Astronomia Nova, the second law was postulated in 1605 and published together with the first law in 1609 in Astronomia Nova, while the third law was published in 1619 in The Harmony of the World.

2 Baumgardt, Kepler, 121.

3 The dychotomy physical/metaphysical has for this paper a particular importance, as Kepler's refutation of Aristotle's views on the universe is only made possible by this pair of concepts. There lies a specific difficulty in comparing what one at the time called physical or metaphysical and what we denote nowadays as physical or metaphysical.

4 Caspar, Kepler, 129.

3

laws the validity of which was not publicly questioned. And still, he questioned well-‐settled theories

with the obstinacy of an instinct. More than that, Kepler looked always for the right argument,

formulation or set-‐up, as he did not only make observations, calculations and formulate laws, but also

tried to "dress" his scientific discoveries in forms that would be easier to understand by the audience.

Kepler made the evolution from geometrical description of the seen universe to physical causality of the

planetary movement possible by scientific thinking, a process that embraces both empirical observation

/ mathematical calculation and speculation / guessing as a basis for scientific knowledge.

A convinced Copernican, Kepler based his quest on the assumption that the Sun was the centre of

the universe, not the Earth, a belief which contradicted the simplest observation and the writings of

(among others) Aristotle. The assumption that the Earth was moving around the Sun and not vice versa

proved later on (after years of hard work) to be more than a conjecture, it proved to be the truth. A

truth that allowed Kepler to formulate the three laws that are now known as the Kepler laws. These laws

describe with accuracy the movement of the Earth and the other planets within the solar system, and

they represented key knowledge for Newton and his new mechanics.

Kepler’s laws can be shortly summarized as follows:

1. The law of the ellipse: The planets move about the Sun in elliptical orbits, with the Sun occupying

one of the foci of the ellipse;

2. The law of equal areas: A line drawn from the planet to the Sun will sweep out equal areas in

equal time;

3. The law of harmonies: The square of the period of the orbit divided by the cube of the average

distance to the Sun (T2/R3) is equal for all planets.

Kepler's way of formulating the three laws was neither purely mathematical nor purely metaphysical. He

had to combat the Aristotelian set of axioms that had never been doubted until Nicolaus Copernicus's

book On the Revolutions of the Heavenly Spheres, which was published in 1543 (Copernicus died the

same day he saw a copy of his printed book). As Max Caspar notices in his biography of Kepler: "Yet

Kepler's prodigious step forward consists precisely in the fact that with his ellipse proposition he had

overthrown for all time the two-‐thousand-‐year-‐old axiom, according to which every motion retrograde

4

in itself must of necessity be a uniform circular motion."5 Aristotelian physics is (when it comes to

motion) a set of beliefs as the universal statements that Aristotle formulated were not checked by

experience or mathematics. There was no adept of the Aristotelian geocentric system that would allow

discussion of the laws. Today we would call this system unfalsifiable: a set of beliefs that do not allow

questioning, that do not consider alternatives. Beliefs cannot be contradicted by science as they have no

scientific ground, they can be contradicted by another belief. Beliefs cannot be empirically proven to be

true, they are believed to be true. The empirical approach to astronomy was possible when observations

of the movements of the planets were thoroughly recorded. Kepler used the records made by Tycho

Brahe and these records, together with Copernicus' heliocentric hypothesis, allowed him to question

Aristotle's universal statements. When Aristotle stated that movements can only be circular or linear, or

that the Earth was the center of the universe, he did not formulate a scientific theory based on empirical

facts. It is exactly the kind of arguments that Aristotle used in formulating his statements about the

universe that would determine Kepler's refutation of Aristotle's system: Aristotle built on appearances

and he had to defend them. These arguments didn't match an empirical proof, they corresponded with

the semblance of the apparent movement of the celestial bodies.

Kepler wrote a great deal throughout his life. He made records of his discoveries but also of his

mistakes, of theories that after further inquiry proved false. There is written proof of almost every step

he took in his advancing towards the laws. His work is a testimony to his accuracy and thoroughness. His

writings are not only presentations of his discoveries, but also attempts to persuade the reader of the

truth they contain. His astronomical arguments are mainly mathematical, but there is a considerable

amount of philosophical / metaphysical argumentation.

2. The Problem

How did Kepler refer to Aristotle's worldview and how did he relate himself to it? What are the main

changes Kepler introduced into the general knowledge about the universe when compared to pre-‐

Copernican natural philosophy? The modern physicist applies the same theories and rules of matter and

motion to the Earth as he does to the rest of the universe. It is possible that the concept of science in

the modern sense was formed while Kepler, the researcher, tried to separate scientific proof (based on

observations and mathematical foundations) from metaphysical hypothesis.


5

The main object of this thesis is to expose arguments defending the view according to which

Kepler emerged as a modern physicist by refuting the Aristotelian worldview as metaphysics. A key

concept in this quest will be that of motion. A comparison of Aristotle’s concept of motion with “Kepler

motion”6 will be an instrument to reveal Kepler’s worldview. To conclude, another key concept will be

used: that of falsification as formulated by Karl Raymund Popper. Kepler’s rejection of Aristotle’s

worldview is based on Kepler’s refusal of considering the validity of a theory when the theory in

question is proven to be pure metaphysics. A metaphysical hypothesis has no alternative, it cannot be

refuted or denied by any other hypothesis, least by scientific ones. A metaphysical hypothesis (theory)

requires belief while scientific hypotheses (theories) require scientific proof. Therefore, the Aristotelian

worldview cannot be, in Kepler’s eyes, falsified by a scientific theory as the two belong to different

categories. A theory that is proven unfalsifiable is automatically being refuted.

In order to make such an attempt possible, this paper needs to shape Kepler-‐the-‐philosopher out

of the generally known image of Kepler-‐the-‐astronomer or Kepler-‐the-‐mathematician, even though to

speak of Kepler as a philosopher may seem fictious: “There is probably no such thing as Kepler's

philosophy in any pure form.”7 Luckily, Kepler’s work is fully adorned with philosophical research

speculation, a kind of discourse that Kepler was deeply fond of: “Don't sentence me completely to the

treadmill of mathematical calculations. Leave me time for philosophical speculations, my sole delight!”8

Kepler faced Aristotelian philosophy with scientific proof. He built a new worldview by questioning

assumptions and searching for new ones in, until then, unscrutinized corners. This paper tries to follow

(in big steps) Kepler’s way to his worldview, a way of assumptions, hypotheses, mathematical

6 "Kepler motion" as a concept was formulated by Bruce Stephenson in his Kepler's Physical Astronomy (page 140). The term is defined as "motion on an ellipse according to the area law." I allowed myself to use the term in a wider sense as this would embrace Kepler's conception of motion as a whole. I did this so that not only the problem of the ellipse could be ascribed to "Kepler motion", but also the one dealing with the origin of movement or with the question about which of the celestial bodies move and which are fixed. Kepler's notion of motion is not yet enough researched in the literature as far as my enquiries could go. Therefore, this paper makes use of the term while still seeking its proper coverage.

7 Di Liscia, Daniel A., Johannes Kepler, The Stanford Encyclopedia of Philosophy (Summer 2014 Edition, Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2014/entries/kepler).

8 Gingerich, The Eye of Heaven, 396.

6

calculations and philosophical speculations, a way that would eventually lead him to deconstruct the

founding pillars of the Aristotelian celestial physics: circular / uniform motion and geocentrism.

3. The Classical View: Aristotle’s Concept of Motion

The cosmological system that Kepler was taught was the Aristotelian worldview. Truths and principles

had already been settled and defined thousands of years before. The changes brought on by the

Ptolemy’s Almagest around 200 AD to the (by then) classical view were not structural, they were merely

improvements that would help the visible movements of the planets fit into a mathematically based

structure. Ptolemy's Almagest is a mathematical proof of the Aristotelian worldview. The step forward

that Ptolemy did make was the attempt to formulate a proto-‐scientific theory for a hypothesis (the

Aristotelian one). But the main elements of the Aristotelian worldview were the same: geocentrism and

the circular motion.

3.1 First and Second Argument: Motion and the Structure of the Universe

The part of Aristotle's cosmology that discribes the heavens is based on two important suppositions: the

first one regards motion (the concept that ends up with the unmoved mover), the second the structure

of the universe and the three domains (the universe is divided into three areas: the Earth, the sphere of

the planets and of the fixed stars and the space inbetween).

With Copernicus, the Aristotelian concept of motion is altered only partly: the circular movement

is preserved while the arrangement of the celestial bodies is different. In the Copernican system the

Ptolemaic epicycles become obsolete and the "strange" movement of the planets (the apparent

retrograde movement) receives a proper, though not yet complete, explanation. Copernicus launched

the theory of heliocentrism but the theory that would openly discredit the Aristotelian theory of motion

was Kepler's, by means of the three laws of planetary motion. The Earth being not the center anymore,

the laws conducting the movements are different, so different that the Aristotelian concept of motion

disappears into irrelevance.

Motion is, according to Aristotle, one of the two basic elements of nature: "Nature is a principle of

motion and change."9 In other words, everything that happens in nature happens by means of change,

9 Aristotle, Physics, Book III, 200b12.

7

and there is no change in the absence of motion. In order to have two substances or bodies interact, at

least one of them has to move or be moved. Motion is therefore a necessary principle of nature and

needs full attention and thorough description. Things or bodies fall, rise, grow or develop because of the

inner principle that resides in all natural things.

Further, Aristotle relies on the concepts of potentiality and fulfilment: "some things are in

fulfilment only, others in potentiality and in fulfilment."10 Aristotle formulates a definition of motion

which is directly related to the idea of change: "the fulfilment of what is potentially, as such, is

motion."11 The change resides in potential inside the thing: "Motion, we say, is the actuality of the

movable in so far as it is movable."12 For Aristotle, being in the world is motion between the two stages:

it is actualization of the possible. This definition seems to contain two contradictions: motion is passive

and the potentiality of a thing is its actuality. In order to resolve this contradiction, motion must be seen

as a mixture of the two: “St. Thomas thus resolves the apparent contradiction between potentiality and

actuality in Aristotle's definition of motion by arguing that in every motion actuality and potentiality are

mixed or blended.”13

Potentiality and fulfilment are key concepts, which get an important connotation also in Aristotle's

worldview, not only in his theory of motion. The four elements (earth, water, air and fire) have each a

"natural locomotion", which is rectilinear movement: "fire upward and earth downward and towards

the middle of the universe."14 These four elements are in motion and they change. Their movement can

only be simple and therefore rectilinear as they are simple themselves: “An element, we take it, is a

body into which other bodies may be analysed, present in them potentially or in actuality (which of

these, is still disputable) and not itself divisible into bodies different in form. That, or something like it, is

what all men in every case mean by element.”15

10 Aristotle, Physics, Book III, 200b26.

11 Aristotle, Physics, Book III, 201a11-‐12.

12 Aristotle, Physics, Book VIII, 251a9.

13 Joe Sachs, Aristotle: Motion and its Place in Nature, Internet Encyclopedia of Philosophy, http://www.iep.utm.edu/aris-‐mot.

14 Aristotle, Physics, Book IV, 214b14-‐15.

15 Aristotle, On the Heavens, Book III, 302a15-‐19.

8

“But since every natural body has its proper movement, and movements are either simple or

mixed, mixed in mixed bodies and simple in simple, there must obviously be simple bodies; for there are

simple movements. It is plain, then, that there are elements, and why.”16 Simplicity seems to be the

basic ingredient of this definition of motion: the world is formed by four simple elements (simplicity

being here defined as not-‐further-‐divisible). These elements are in motion (transition) and this motion

can also only be simple, as simplicity is the main characteristic of the elements. Aristotle states in the

beginning of On the Heavens that there are only two simple movements: "But all movement that is in

place, all locomotion, as we term it, is either straight or circular or a combination of these two which are

the only simple movements."17 There are thus two kinds of movement: rectilinear and circular.

Movements can also be classified into natural and unnatural or forced or violent movements,

according to where the things derive their movement from:

Of things which move in their own right, some derive their motion from themselves, others from something else: and in some cases their motion is natural in others violent and unnatural. Thus in things that derive their motion from themselves, e.g., all animals, the motion is natural. (...) And the motions of things that derive their motion from something else is in some cases natural, in other unnatural: e.g. upward motion of earthy things and downward motion of fire are unnatural.18

It seems Aristotle needed to make the distinction between natural and unnatural movements in order

to resolve the problem of the origin of motion, first the origin of motion of things in general, afterwards

the theory of motion of the celestial bodies. Who (or what) is moving the celestial bodies (or how do the

celestial bodies get into motion) is actually a key question: in order to give an answer, one needs to

choose between a metaphysical or a non-‐metaphysical one, an answer that is based on scientific

attempts to explaining the phenomenon in question. Of course, the scientific knowledge of the time was

limited as not much had up to that date been mathematically proven. The solution formulated by

Aristotle was just a hypothesis that turned into a pre-‐conception. As an undiscussable pre-‐conception it

16 Aristotle, On the Heavens, Book III, 302b5-‐8.

17 Aristotle, On the Heavens, Book I, 268b16-‐19.

18 Aristotle, Physics, Book VIII, 254b12-‐23.

9

was, in Kepler’s time, still part of a generally accepted worldview.

The concept of motion ends up with the problem of the origin of motion. Do motion and change

occur continuously, do they occur now and then? Is there a beginning of change and motion? The

Stanford Encyclopedia of Philosophy (SEP) formulates Aristotle's view on the origin of motion as follows:

"Aristotle argues at the opening of Physics Book VIII that motion and change in the universe can have no

beginning, because the occurrence of change presupposes a previous process of change."19

The idea of a beginning of motion is therefore overruled, as any beginning is the result of a

change, any change is the result of a change. The beginning of change and motion takes us backwards

into an infinite regress. A conceptual impossibility which Aristotle believes to resolve:

If then everything that is in motion must be moved by something, and by something either moved by something else or not, and in the former case there must be some first mover that is not itself moved by anything else, while in the case of the first mover being of this kind there is no need of another (for it is impossible that there should be an infinite series of movers, each of which is itself moved by something else, since in an infinite series there is no first term) -‐ if then everything that is in motion is moved by something, and the first mover is moved but not by anything else, it must be moved by itself.20

In Physics, Book III, Aristotle exposes the idea of the unmoved mover:

The same thing can be both potential and fulfilled, not indeed at the same time or not in the same respect, but potentially hot and actually cold. Hence such things will act and be acted on by one another in many ways: each of them will be capable at the same time of acting and of being acted upon. Hence, too, what effects motion as a natural agent can be moved: when a thing of this kind causes motion, it is itself also moved. This, indeed, has led some people to suppose that every mover is moved. But this question depends on another set of arguments, and the truth will be made clear later. It is possible for a thing to cause motion, though it is itself incapable of being moved.21

19 Bodnar, Istvan, Aristotle's Natural Philosophy, The Stanford Encyclopedia of Philosophy (Spring 2012 Edition), Edward N. Zalta (ed.) URL=,http://plato.stanford.edu/archives/spr2012/entries/aristotle-‐natphil/.

20 Aristotle, Physics, Book VIII, 256a13-‐21.

21 Aristotle, Physics, Book III, 201a20-‐28.

10

Aristotle’s solution to the problem of the origin of movement is the unmoved mover. There is a physical

need for the unmoved mover: the impossibility of infinite regression. The chain of violent / unnatural

movement has to begin somewhere and so there is a physical need for the metaphysical unmoved

mover:

“If there is no ultimate natural cause of movement and each preceding term in the series is always

moved by constraint, we shall have an infinite process.”22 An infinite process is, according to Aristotle,

impossible. Therefore, the beginning of motion, the cause of the movement of the heavenly bodies is

the metaphysical concept of a bodyless unmoved mover, more resembling an intellect than a physical,

material wheel.

When addressing the problem of the daily rotation of the sky from east to west in On the Heavens,

Book II, Aristotle shows how the celestial bodies move even if he cannot explain why the movement

follows one direction and not the opposite, it just "seems to be the case" (as he himself puts it):

Now there are two ways of moving along a circle, from A to B or from A to C, and we have already explained that these movements are not contrary to one another. But nothing which concerns the eternal can be a matter of chance or spontaneity, and the heaven and its circular motion are eternal. We must therefore ask why this motion takes one direction and not the other. Either this is itself a principle or there is a principle behind it. It may seem evidence of excessive folly or excessive zeal to try to provide an explanation of some things, or of everything, admitting no exception. The criticism, however, is not always just: one should first consider what reason there is for speaking, and also what kind of certainty is looked for, whether human merely or of a more cogent kind. When any one shall succeed in finding proofs of greater precision, gratitude will be due to him for the discovery23 but at present we must be content with what seems to be the case.24

22 Aristotle, On the Heavens, Book III, 300b15-‐17.

23 Ironically enough, Aristotle seems to have been waiting himself for Kepler. Kepler is the one to bring proofs of greater precision in the form of the mathematical calculations of the movements of the planets. Ignorant of his dogmatic future, Aristotle expresses here his gratitude to the very one that would refute his views.

24 Aristotle, On the Heavens, Book II, 287b22-‐288a2.

11

Aristotle makes an interesting point here when attempting to find a / the principle behind the daily

rotation of the celestial bodies. Is the question about “the eternal” allowed and, if it is allowed, will

humanity ever get the chance to answer it? It seems there is a difference between certainties, they can

be human or of a more cogent kind, the difference residing in the fact that human certainty is merely

conjectural (the human certainty is merely believed to be true) while the cogent kind has the attribute

of being definite and invariably true. The future that Aristotle proclaims here is indeed open: he uses the

phrase “at present” as an encouragement for future researchers to try to break through and discover

the principle that conducts the apparent movement of the celestial vault.

The heavens and their characteristic movement are eternal and circular and not a matter of

chance so there must be a principle behind this movement. Seeking for the principle, the human has but

little data he can rely on: “On these questions it is well that we should seek to increase our

understanding, though we have but little to go upon, and are placed at so great a distance from the

facts in question.”25 Circularity is not something that we can question, it is a given feature of heavens as

the heavens belong to the gods. The circular motion (as opposite to the rectilinear movement that is

specific to the four elements) is the perfect motion and perfection is the attribute of the gods.

The three bodily domains that for Aristotle form the universe are the Earth, the sphere of the

heavenly bodies and the intermediary space in between these two. Each of the planets moves inside a

crystal sphere that keeps the planet in its specific orbit. The moving bodies that we see in the sky at

night are therefore the planets, which move, and the fixed stars, which do not move, as they are being

stuck on a crystal sphere and move altogether in one day-‐time.

The universe is ordered with the Earth in the middle. According to Aristotle’s geocentrism, all

other celestial bodies (including the Sun) move around the Earth inside the crystal spheres. The

trajectory of the movement of the bodies in space was also not following a plane (a two-‐dimensional

flat surface as it is now known that is the case), but was wandering across the surface of the sphere. The

image in Figure 1 represents Aristotle’s universe and the order of the crystal spheres: Aristotle’s

worldview was turned into a real astronomical model by Ptolemy. Ptolemy was mainly concerned with

matching the Aristotelian model with the astronomical observations. He managed to do this, partly (e.g.,

he succeded in describing the retrograde movement of the planets).

25 Aristotle, On the Heavens, Book II, 292a14-‐16.

12

Figure 1: Aristotle's universe of spheres26

Aristotle’s universe was therefore following ideal and unaltered shapes. A universe made by gods could

only contain perfect forms (spherical) and simple motions (straight, circular): the shape of the heavenly

bodies, their trajectory, their motion. The last sphere, the sphere of the fixed stars, is the limit of the

material universe. In On the Heavens, Aristotle argues for the sphere as the only form possible for the

heavenly bodies:

With regard to the shape of each star, the most reasonable view is that they are spherical. It has been shown that it is not in their nature to move themselves, and, since nature does nothing without reason or in vain, clearly she will have given things which possess no movement a shape particularly unadapted to movement. Such a shape is the sphere, since it possesses no instrument of movement. Clearly then their mass will have the form of a sphere. Again, what holds of one holds of all, and the evidence of our eyes shows us that the moon is spherical. For how else should the moon as it waxes and wanes show for the most part a crescent-‐shape or gibbous figure, and only at one moment a half-‐moon? And astronomical arguments give further confirmation; for no other hypothesis accounts for the crescent shape of the Sun’s eclipses. One, then, of the heavenly bodies being spherical, clearly the rest will be spherical too.27

26 Source: http://mitu-‐bobs.blogspot.nl/2011/02/ss-‐fn-‐flat-‐earth.html.

27 Aristotle, On the Heavens, Book II, 291b11-‐23.

13

Aristotle brings in two arguments to prove that all heavenly bodies have a spherical shape. The first

argument is based on “the most reasonable view” that says that they are all spherical because this

shape is the most unadapted to movement, and is therefore most likely to belong to bodies that do not

move (“[the sphere] possesses no instrument of movement”). The second argument is based on the

analogy between the Moon (a heavenly object whose shape is confirmed by the senses as its shape can

be easily seen) and the stars (heavenly objects that are too far from the eye, their shape is subject to

speculation as their shape cannot be seen). The Moon is round, therefore all the other heavenly bodies

are also spherical (“what holds of one holds of all”). This Aristotelian argumentation, even though of

speculative nature, proved to be right. Because of the strength of this argument he made a step forward

and assumed that all movements must be circular. The path of the movement of the heavenly bodies

can only be circular.

3.2 Third Argument: Celestial versus Terrestrial

In Book I of Parts of Animals, Aristotle makes the distinction between substances that are generated and

those that are not generated, the world at hand and the eternal:

On substances constituted by nature some are ungenerated, imperishable, and eternal, while others are subject to generation and decay. The former are excellent and divine, but less accessible to knowledge. The evidence that might throw light on them, and on the problems which we long to solve respecting them, is furnished but scantily by sensation; whereas respecting perishable plants and animals we have abundant information, living as we do in their midst, and ample data may be collected concerning all their various kinds, if only we are willing to take sufficient pains. (...) The scanty conceptions to which we can attain of celestial things give us, from their excellence, more pleasure than all our knowledge of the world in which we live; (...).28

According to Aristotle, the celestial world cannot be measured with terrestrial scales. The planets, the

sphere of the fixed stars and the universe are all parts of a different entity than the Earth. Human

cognitive possibilities are limited, we can reach no more than “scanty conceptions” about the universe

28 Aristotle, Parts of Animals, Book I, 644b21-‐31.

14

(the celestial things). Physics studies the terrestrial world that is visible to us and which we can reach

with our senses, unlike the heavens, which seem to remain unresearcheable. The heavens are of a

different nature. When, in Book 2 of On the Heavens, Aristotle discusses the nature of the heavens (he

also calls them “the upper regions”), he acknowledges the existence of a fifth element “whose natural

movement is circular.”29 This is the element the stars are made of. An element that is therefore in

contrast with the four terrestrial elements. Notions and concepts that we use to know plants and

animals on Earth cannot be applied on the heavens.

To conclude our section on Aristotle's notions of theory of motion, these can be reduced to some

principles.30 Those that are relevant for the current discussion are summarized here:

1. The Earth is in the center of the universe

2. All bodies move towards or away from or around the center of the universe

3. The celestial bodies move in circular orbits with uniform speed

4. Celestial physics is different than terrestrial physics

5. There is an unmoved mover that moves the heavenly bodies.

4. A New Kind of Argument: Kepler’s Physics

The main object of Aristotle’s physics is the terrestrial, and the movement of terrestrial elements.

Nature on Earth is indeed one easily researched, observed, described. For Aristotle, the heavens are the

opposite: they are more subject to philosophical speculation than empirical description. As we have

already seen in the previous chapter, the heavens are for Aristotle situated too far from us, the “scanty

conceptions” we can formulate about them can barely provide enough information to attain real

knowledge. With Kepler, the epistemological attitude changed: with the right hypothesis (i.e.,

heliocentrism), measure, observe and calculate (Kepler used Tycho Brahe’s observations of the

movements of the planets well), and the heavens will come closer. Even when busy with a piece of

29 Aristotle, On the Heavens, Book I, 270b5-‐7.

30 These principles are formulated for the sake of this paper as they are needed to mirror Kepler's view on motion.

15

earthly natural object (the snowflake), what Kepler looked for was the same as what he was looking for

in the skies, the archtype of which mathemathics was a foremost representative: “where there is

matter, there is symmetry.” He assumed, he conjectured and he went for the proof. What in the

beginning was a (more or less philosophical) assumption, namely the hypothesis of heliocentrism,

proved to be, together with the hypothesis of inertia, the right epistemological package, which would

later allow Newton to intuit gravity. In a letter to David Fabricius of October 11, 1605, Kepler writes: “If

one would place a stone behind the Earth and would assume that both are free from any other motion,

then not only would the stone hurry to the Earth but also the Earth would hurry to the stone; they

would divide the space lying between in inverse proportion to their weights.”31

What Kepler did change when starting on a new worldview was (1) the hypothesis and (2) the

point of view. The hypothesis he assumed and on which he started building, was heliocentrism. Kepler

did not adopt much else from the Copernican worldview, for Copernicus the center of the universe was

not the Sun but a point near the Sun: “(…) he places that common node of the planets very near to the

Sun, but not in the Sun itself.”32 But anyway, with the move to the Sun, the main step had been taken.

Copernicus gave better explanations for the irregularities of the movements of the planets (e.g., the

apparent retrograde movements of Mars). Kepler took over the idea that the Sun is in the center of the

orbits of the planets, displacing the Earth from its fixed location as described by geocentrism and

investing the Sun with the attribute of immobility.

But this was not enough to get to the truth about the motion of the celestial bodies. Kepler

needed a different point of view, too. He imagined brave thought experiments that would help him (and

us) get a better view on the universe. He imagined travelling to the Moon (in his Somnium) and he also

imagined himself being placed on another planet than the Earth in order to see the remote movement

of the other planets:


32 Kepler, Epitome, 71.

16

Even if the whole of Levania has the appearence of fixed stars in common with us, yet one observes very many movements and numbers of planets different from those which we see from Earth so that all of their astronomy has another meaning.33

Koyré also notes that:

Kepler used an extremely ingenious and original procedure, which consists in transporting ourselves to the planet Mars and observing the motion of the Earth from that standpoint in order, first of all, to ascertain several positions of the Earth on its orbit, and from them to find the orbit itself.34

The originality of this kind of thought experiment is extreme: Kepler’s mind was far superior to that of

his contemporaries, both in imagination and boldness.

In the beginning of Chapter 39 of Astronomia Nova, Kepler resumes his axioms for motion. These

axioms are formulated as axioms for the motion of the bodies of the planets, but some of them have a

strong generalizing character of the concept of motion. To resume them:

• “the body of a planet is inclined by nature to rest in every place where it is put by itself”;

• (the body of a planet) “is transported from one longitudinal position to another by that power

that originates in the Sun”;

• “if the distance of the planet to the Sun were not altered, a circular path would result from this

motion”;

• “the periodic times will be in the duplicate ratio of the distances or magnitudes of the circle”;

• “the bare and solitary power residing in the body of a planet itself is not sufficient for

transporting its body from place to place, since it lacks feet, wings, and feathers by which it

might press upon the aethereal air”;

• “the approach and recession of a planet to and from the Sun arises from that power that is

33 Kepler, Somnium, 11.

34 Koyré, The Astronomical Revolution, 181.

17

proper to the planet.”35

The fourth axiom regards the proportion between the speed of motion and the distances of the planets

from the Sun. This axiom is a consequence of the Copernican law that states that “the speed at

perihelion and slowness at aphelion are very closely proportional to the lines drawn from the center of

the world to the planet.”36 Kepler gives this variation in motion a name: libration. Libration is therefore,

the variation of a planet’s speed along its orbit (the word originates in the latin libra, meaning

“balance”; see Epitome, 130, for Kepler’s comparison with the balance). Alexandre Koyré has formulated

this law in a simpler way: “the velocity of a planet in its orbit is inversely proportional to its distance

from the body about which it revolves.”37 This axiom has a key relevance for Kepler’s advance towards

his second law and it is further discussed in 4.2.

It is at this point interesting to notice the manner in which Kepler formulates his axioms of motion.

The word power, which Newton would later turn into force, is almost everywhere present, and it

denotes interaction of a physical nature between the Sun and the planets. Animism, in what form

whatsoever, is absent. It shows up though when Kepler cannot resolve the origin of the movement of

the Sun and, only temporarily, when he tries to explain the libration. Kepler’s celestial physics separates

here from his celestial dynamics, which is still Aristotelian: “Kepler’s celestial dynamics is (almost) purely

Aristotelian: velocity is proportional to the motive force, and in the absence of any such force the

motion changes to rest.”38

These axioms are the basis of Kepler’s worldview. Heliocentrism, the elipse and the motive force

are the key concepts that Kepler used to reform our view on the universe. The following chapters try (in

a manner that is not too elaborated) to overview Kepler’s way from conjecture to physical truth.

35 Kepler, AN, 407 (Chapter 39: "By what path and by what means do the powers seated in the planets need to move them in order to produce a planetary orbit through the ethereal air that is circular, as it is commonly thought to be.")

36 Kepler, AN, 373 (Chapter 32: "The power that moves the planet in a circle diminishes with removal from its source.")

37 Koyré, The Astronomical Revolution, 185.

38 Koyré, The Astronomical Revolution, 405, footnote 3.

18

4.1 Heliocentrism

Kepler was still young when he learned about the new Copernican theory from his mathematics

professor in Tübingen, Michael Maestlin.39 Heliocentrism was taught on the side, it was still an unofficial

alternative to the Ptolemaic theory, which some teachers, in spite of the mainsteam theory, taught at

universities. Kepler adopted it immediately as a valid hypothesis, and he believed in it from the very

beginning:

Already in Tübingen when I followed attentively the instruction of the famous Magister Michael Maestlin, I perceived how clumsy in many respects is the hitherto customary notion of the structure of the universe. Hence I was so very delighted by Copernicus, whom my teacher very often mentioned in his lectures, that I not only repeatedly advocated his views in the disputations of the candidates, but also made a careful disputation about the thesis that the first motion (the revolution of the heaven of the fixed stars) results from the rotation of the Earth. I already set to work also to ascribe to the Earth on physical, or, if one prefers, metaphysical, grounds the motion of the Sun, as Copernicus does on mathematical grounds.40

All his subsequent discoveries are based on this assumption.41

In the Epitome, Kepler’s most elaborate work, both astronomically and philosophically, he proves

with more arguments that the Earth moves and that the Sun is fixed (even if the idea is the same, Kepler

builds different arguments based on the movement of the Earth and on the immobility of the Sun). In

developing these arguments, Kepler starts by discussing and comparing the Ptolemaic system to that of

39 Kepler's acquintance with Copernicanism was made exclusively through Maestlin's lectures. Later on he owned a copy of Copernicus' De Revolutionibus. This copy is still preserved in the library of the University of Leipzig. Kepler was also not familiar with Joachim Rheticus's Narratio Prima, the first account on heliocentrism that Rheticus had written and published after visiting Copernicus (1539, respectively 1540).


41 The first theoretical construction of Kepler’s worldview, The Cosmographic Mystery, is based on heliocentrism; the calculations Kepler made using the five Platonic solids (tetrahedron, cube, octahedron, dodecahedron and icosahedron) were later proven to fit reality, the distances between the planets of the solar system coincide almost exactly to Kepler’s ratios. This was only possible in a world where the Sun stands at the middle of everything.

19

Copernicus and of Tycho Brahe. Even though there is quite a big difference between Ptolemy and Brahe

and an even bigger difference between Ptolemy and Copernicus, for Kepler, eventually, both Brahe and

Copernicus seem to have made too large concessions to Ptolemy:

Finally, the reason why Copernicus and Brahe make these two centres different [the center of the Sun and the center of the orbit of the planets, m.n.] is not sufficient nor astronomical enough. For they were led to that by the fact that they wished in the forms of their hypotheses to express their everyway equipollence to the Ptolemaic form. But it was not necessary that they should step exactly in Ptolemy’s foot-‐prints. For indeed Ptolemy did not build up all the parts of his hypothesis from observations, but he based many things upon the preconceived and false opinion that it is necessary to presuppose that the movements of the planets are regular throughout the whole circle – and that is demonstrated by observations to be false.42

Copernicus and Brahe altered Ptolemy’s model from geo-‐centric to heliocentric in different ways.

Copernicus placed the Sun in the center of the planetary system but he didn’t also place the center of

the movement of the rotating planets in the Sun (this center is situated in a point close to the Sun).

Brahe’s solar system looks somewhat different: the Sun and the Moon revolve around the Earth while all

the other planets (Mercury, Venus, Mars, Jupiter and Saturn) revolve around the Sun.43 These two

systems, Copernicus’ and Brahe’s, are mathematically almost identical and they correspond with the

observations of the planetary movements. The two astronomers needed to place the center of the

movement away from the Sun because of the variation in movement of the planets: the circular

movement did not fit the observations unless the center was displaced from the Sun. Altering circularity

was not yet an option. So, the reason why Copernicus and Brahe did not set the Sun in the very center of

the movement was just a compromise so that the new theory would not definitely contradict Ptolemy,

who was also just repeating what Aristotle had spoken, that the movements of the planets “are regular

throughout the whole circle.” Kepler calls this opinion “preconceived and false” as no one did measure

the movements before Brahe did. He had the observations, the calculations, and the scientific proof.


43 This system is still geocentric, or rather geo-‐heliocentric, as the Sun together with the other planets move, in a bunch, around the Earth.

20

The attack is clear: the validity of the ancient idea of uniform movement is openly criticised. But more

about this in the next subchapter, about the orbits.

Following Copernicus and Tycho Brahe, Kepler further argued for heliocentrism, formulating

arguments of different nature. These arguments are conceived and discussed in Part II of the Epitome of

Copernican Astronomy using a combination of scientific proof, philosophical arguments and pure

common sense.44 I will only name some and will end with a summary of them.

The simplest argument is the first one, which stipulates that the Earth shares the main characteristic

with the other five planets, namely motion. All planets move around the Sun in a “line very close to a

circle.” This argument is also presented in Astronomia Nova, Chapter 33, where Kepler wants to prove

Brahe wrong in his belief that the Sun rotates around the Earth, eliminating even alternative forms of

geocentrism. Kepler’s position is pretty simple, he sets a choice before the reader:

(…) From this it follows that motion of the Sun itself (if it is moved) is intensified and remitted according as it is nearer or farther from the Earth, and hence that the Sun is moved by the Earth. But if, on the other hand, the Earth is in motion, it too will be moved by the Sun with greater or less velocity according as it is nearer or farther from it (…). Between these two possibilities, therefore, there is no intermediate. I myself agree with Copernicus, and allow that the Earth is one of the planets.45

The argument is not strong enough to stand alone in a debate, indeed. It needs the upcoming series of

arguments to be able to defeat the opposite. But the interesting point here is the fact that Kepler wants

his reader to accept the option that common sense tends to validate: it is more difficult to move a

heavier body than a lighter body. It is an argument that needs rather to be felt than reasoned.

The third argument Kepler brings forward discusses the “diurnal movement of incalculable speed

of the fixed stars.” Kepler asserts that it is much easier to believe that the moving of the Earth is the

cause of us seeing the fixed stars moving than to attribute movement to such an immense body:

44 Kepler, Epitome, [542]-‐[549].

45 Kepler, AN, 379.

21

(…); so now, an annual movement being granted to this same Earth after the model of the other planets, we have ended that very slow movement of the fixed stars, which is called by Copernicus the procession of the equinoxes. (…) For it is much more believable to attribute them (these things) to the axis of the Earth, a very small body, than to such a great bulk.46

Again the same simplicity of reasoning that implies that a small body can be moved more easily: the

difference in size between the Earth and the sphere of the fixed stars is too significant to accept a

different conclusion. The Earth must therefore be moving and this is the cause of us seeing the stars

slowly rotating around the Earth, rather than the other way around.

The next argument (the fourth) is connected to the sixth and they both deal with the revolution of

smaller bodies around the bigger bodies: “For it is more believable that the body around which the

smaller bodies revolve should be great.”47 Kepler makes an analogy between the Earth and the Moon

revolving around it, and the Sun and the planets: the Moon is smaller than the Earth and it moves

around the Earth, the planets are all smaller than the Sun, therefore they have to move around the Sun.

Kepler often uses this kind of argument: there is no physical or metaphysical explanation given for the

process in question, there is again just the common sense logic that conducts the reasoning. When

compared to Aristotle’s same type of argument (i.e., how the elements move in the following directions:

earth downwards towards the centre of the universe as being heavy, fire upwards as being light),

Kepler’s reasoning has obviously evolved, not necessarily by its use of scientific observations and

arguments (he does not always do that) but simply in its approach to natural laws. Kepler’s thinking is

modern, his mind operates differently than the Aristotelian: the heavenly bodies interact with each

other in a physical way. This specific argument in the Epitome is also not discussing the causes of the

movement, it only describes how the heavy interacts with the light (Earth / Moon, Sun / planets).

Kepler’s eighth argument for heliocentrism stands out, for it is of a special nature: it brings us back

to the Harmonies of the World, where Kepler made an attempt to find the physical harmonies that

conduct the movement of the planets (a theory he always tried to sustain with mathematical

arguments): “Eightly, the same things are to be said concerning the harmony of the celestial


47 Ibid., 73.

22

movements, which are made up of the same numbers and proportions as our musical scale.”48 The

Earth’s semitone is needed for the harmony of the universe and its place is determined by the

difference between the maximum and the minimum of its angular speed in its orbit around the Sun. This

difference varies by about a semitone (a ratio of 16:15), from mi to fa. Needless to say that this

argument does not weigh much in the present refutation of Aristoteles’s motion theory. It is still an

argument that reveals Kepler as a scientist who needs to find mathematical proof (the musical scale is

mathematical) for his assumptions and hypotheses. Accordig to this argument, there is a mathematical

need for the Earth to be situated inbetween Venus and Mars.

Directly connected to the previous argument, Kepler formulates the tenth argument for

heliocentrism, which is an argument “taken from the periodic times”: each planet needs a specific

amount of time (number of days) to revolve around the Sun; according to this scale of numbers, the

planets can be arranged following an order. In this order, the Earth finds its natural place in between

Venus and Mars:

The tenth argument, taken from the periodic time, is as follows: the apparent movement of the Sun has 365 days, which is the mean measure between Venus’ period of 225 days and Mars’ period of 687 days. Therefore does not the nature of things shout out loud that the circuit in which those 365 days are taken up has the mean position between the circuits of Mars and of Venus around the Sun: and thus this is not the circuit of the Sun around the Earth (…) but the circuit of the Earth around the resting Sun (…)?49

This argument resides on Tycho Brahe’s model of the solar system, where the five planets move around

the Sun, while the Sun and the Moon move around the Earth. Kepler uses it: if the number of days that

the Earth and the Sun complete a rotation fits perfectly in between the numbers representing the

periodic times of Venus and of Mars, it must be concluded from here that the Earth moves, together

with the other planets, around the Sun.

Kepler formulates the fifteenth argument using libration:


49 Ibid., 75.

23

It has already been said in part, and it will be demonstrated below more fully, that all the planets have a movement of libration in a straight line, which proceeds towards the Sun and by means of this libration obey the laws of their speed and slowness in any position on the eccentric circle. And thus it is certain that the Sun is the cause of this variation in all five planets.50

The variation in speed of the movement of the planets could not be explained by any of the

astronomers before Kepler. Kepler uses it to argue for heliocentrism: if the Sun (“which is the source of

movement of the five planets and is many times greater than the Earth”51) is moving the other planets

(as in the Brahe model), then with what kind of logic should we imply that the Earth is the moving cause

of the Sun?

The Earth moves and the Sun is “necessarily at rest.” In several arguments, Kepler sketches

heliocentrism as described by Copernicus and denies Brahe’s model as well as that of Ptolemy.

Also the Aristotelian idea of the crystal spheres is refuted, with the help of Tycho Brahe’s

observations. In the Epitome, Kepler names the three reasons that made Brahe reject the spheres: “Are

there solid spheres [orbes] whereon the planets are carried? And are there empty spaces between the

spheres? Tycho Brahe disproved the solidity of the spheres by the following reasons: first from the

movement of comets; the second from the fact that the light is not refracted; the third from the ratio of

the spheres.”52 Tycho Brahe was the first to measure the location of a comet crossing the heavens, a

fact that allowed him to conclude that the spheres were not existing (he observed the Great Comet of

1577 on November 13 in Prague and compared his records with the records of other observers from

other places on the world), and even if he could not precisely tell its distance from the Earth, he could

still state that the comet travels through the space between the planets. Another argument is based on

observations of the movement of the planet Mars relatively to the Earth: the observations tell that Mars

travels sometimes closer to the Earth than the Sun, movement that would not be possible if the spheres

existed. Nevertheless, Kepler played himself with the idea of the spheres in his Mysterium

Cosmographicum, which he wrote when young (published in 1596) and in which he demonstrates that


51 Ibid.


24

the five planets are aranged in space, around the Sun, inside spheres that are positioned towards each

other at specific distances: the distances are determined by the five Platonic solids. Strangely enough,

the distance between the five planets proved to match reality. A model is shown in Figure 2.

Figure 2: The planet's orbitals within the Platonic solids 53

4.2 The orbits

When Kepler met Tycho Brahe for the first time and they started working together, a happy

circumstance occured (Caspar calls it “a most propitious piece of good luck”) that brought Kepler to

working on the theory of the planet Mars54: another co-‐worker of Brahe, Christen Sorensen Longberg, or

Longomontanus, who was assigned the difficult task of solving the special issues of Mars, got stuck in his

work and was assigned the theory of the Moon instead. “At his own wish,” Kepler was allowed to

further study the movements of the planet. It was this circumstantial turn that would lead Kepler to

formulate the laws of the planets. Brahe’s observations together with trigonometry and Euclid’s

53 Source: http://cs.cas.cz/portal/algomath/geometry/spatialgeometry/polyhedra/polyhedraindex.htm.

54 It is maybe interesting and useful to explain briefly why the study of the orbit of the planet Mars was the only one that could bring Kepler to his “new astronomy”. Out of the six Copernican planets, “Mars en Mercurius are the only planets whose orbits differ enough from circles for that difference to have an effect observable by Tycho’s instruments. Mercury is too near the Sun to afford reliable observations of its entire orbit” (Donahue, AN, 43).

25

geometry enabled Kepler’s computational abilities to unfold the shape of the orbit of Mars. At this

moment, an important change occurs in Kepler’s view on the universe: when busy with describing the

movements of planet Mars (with the question “how does the planet move?”) and proceeding from

Copernicus’s mean Sun to the true Sun, Kepler realized that it was the body of the Sun that made the

planets move. It was the idea of the Sun as a physical object that overshadowed the mathematical Sun

in its representational form of a point. The thinking turned from being descriptive to searching causality.

Later this thought was to give birth to one of his arguments for heliocentrism: the planets (celestial

bodies) do not revolve around a geometrical point but around another celestial body55. There is

interaction between the planets. Together with the Copernican axiom that states that the planets move

faster when closer to the Sun and slower when further away56, Kepler deduced that there must be a sort

of interaction between the planets and the Sun the nature of which he had to study. As mentioned

before, Kepler called this variation in distance to the Sun (and speed) libration, which is the variation in

altitude. For the sake of clarity: the other variation that movement of the planet presents was the

variation in latitude, which means that each planet deviates from the equatorial plane of the Sun where

they are all suppose to move within.

Kepler’s research of planet Mars’s orbit followed a long and troubled path. The “critical

phenomenon” in the movement of planet Mars was the fact “that the planet moved swiftly when near

the Sun and slowly when distant from it,”57 thus faster at perigee than at apogee, and this phenomenon

was far from having been explained properly. Kepler’s inventivity had to come up with ways to

overview, formulate and, if possible, solve the problem. Therefore, he used what he had at hand:

geometry and trigonometry, techniques of Archimedes to calculate the area of a circle and Copernicus’

55 The three systems that preceded Kepler’s (Ptolemy’s, Brahe’s and Copernicus’) were all exclusively geometrically conceived. For the three of them the center of the orbits of the planets were virtual points of virtual circles. Kepler is the first one to treat the center of the orbit in a different way.

56 Kepler was able to reach this conclusion by mixing Ptolemaic, Braheic and Copernican descriptions of the movements of the planets and their positions with reference to the Sun. For further information see Kepler's Astronomia Nova, Chapters 39 and 45, and Bruce Stephenson's Kepler's Physical Astronomy (Chapter 3, especially the chapter Conquest of Mars).

57 Stephenson, Kepler, 29.

26

eccentric system (the Sun is not situated at the center of the orbit but somewhere near it).58

At this point of his inquiry, Kepler needed again to speculate, this time on the nature (or cause) of

the libration, the irregularity that disorders the speed of the planets on the orbit, an axiom taken over

from Copernicus. What (or who) is actually controlling and dictating the libration? In Kepler’s words: “By

what means or measure may a planet grasp its distance from the Sun?”59

Kepler tries (in Chapter 39 of Astronomia Nova) to find the answer to this question by formulating

suppositions and eliminating those that prove non-‐valid (using a “trial and error” method). Allusions to

Aristotelianism are obvious: those who are

so attracted to the supposition of a perfectly circular orbit as to associate a mind with the planet

(…) can say only this: that this planetary mind observes the increasing and decreasing size of the

solar diameter, and understands, using this as an indication, what distances from the Sun it should

arrive at at any given time.60

The mind in the planet observes, understands and lets the planet take the right position, the planets

receive thus anthropomophic features; this seems indeed a reasonable solution to the problem, it would

resove libration. But then, Kepler uses the comparison with the sailors on the seas that cannot know

their exact position from the sea itself as the sea has by itself no system of reference. The sailors can

observe and measure time, the direction of the wind and other quantifiable circumstances. In just the

same way, Kepler sums up some alternatives that allow the mind of a planet to change its own position

relatively to the Sun: (a) the mind of the planet can (just like the sailor) observe and measure and direct

the movement, (b) the planet is moved by a physical machine or (c) it makes use of “some suitable

58 Kepler switches actually often between the two models: the model that makes use of epicycles (both Ptolemy’s and Tycho Brahe’s) and the Copernican model – where the centre of the orbits of the planets is not the Sun but a point in its vicinity; this was not an accident, he allowed himself this approach because the two models can be similar in specific circumstances. But the switching can make the reading of Kepler’s work difficult for a non-‐astronomer.

59 Donahue, AN, 73.

60 Donahue, AN, 73.

27

means of indication that varies with the distance of the planet from the Sun.”61 As the only observable

and measurable reference in space is the Sun’s apparent diameter, this third alternative seems to be the

only left to be considered. The idea of the mind is just too simple a solution to the problem of the

libration. As Donahue observes referring to the “mind of the planet”: “this was the standard view of the

day.”62 At the time, natural movements were considered regular and it was thought that anomalies

could only belong to forces like the intellect: only a mind can determinate a position in space, objects

cannot do that. To discredit the idea of a mind conducting the planets through the universe definitely,

some lines later Kepler writes: “So then, Kepler, would you give each of the planets a pair of eyes? By no

means, nor is this necessary, no more than that they need feet or wings in order to move.”63 The

solution Kepler gives to the irregularity in the movement of planets is the vis insita (an own inherent

force): “Kepler concluded that each planet required its own innate force, a vis insita to move it or stir it –

he was not certain which – through its wandering course.”64 The way Kepler balances here between a

mechanistic view and an animistic one seems to cover a certain uncertainty: he has not yet decided on

which side he should be as he was aware that he could not give all the observed physical phenomena a

good explanation. The solution he reached eventually is indeed close to the idea of inertia, but the

argumention lacks the strength of Kepler’s usual heuristic. So much concerning the “mind of the planet”

as (temporary) explanation for libration.

Kepler’s idea of the inherent force of the planet that causes the irregularities in motion about the

Sun returns in the Epitome. Here Kepler rediscusses the issue and formulates the theory of inertia:

(…) it has already been pointed out that, in addition to the rotating force of the Sun, there is in the planets themselves a natural inertia [opposing] this motion, through which they are constrained,

61 Donahue, AN, 74.

62 "This was the standard view of the day, included in all the introductory university textbooks in natural philosophy. The planetary mind was usually identified with the biblical angels, thus bringing Aristotle into harmony with scripture. However, some theorists believe that the mind is united with the planet as soul is with body. This view was widely regarded as heretical, as it suggested that the Prime Mover is the soul of the world (anima mundi), and thus that the universe is somehow God’s body” (Donahue, AN, 74, footnote 5).

63 Donahue, AN, 75.


28

by reason of their material substance, to remain in their place. Consequently, the vectorial power of the Sun, and the weakness or material inertia of the planet vie with each other. Each shares its victory; the former displaces the planet from its position; the latter releases part of its body, i.e. of the planet, from the chains which bound it to the Sun.65

Kepler could use the equation of proportion between the planet’s speed and its distance from the Sun:

“the delay, or time, required to traverse a small arc was proportional to the planet’s distance from the

Sun.”66 Planets moved irregularly in two ways: (a) sometimes closer to the Sun, sometimes further away

and as a consequence, their speed “varied, in inverse proportion to distance;”67 (b) the planets did not

always follow the Sun’s equatorial plane, small oscillations occurred at times. The myth of the uniform

motion was at stake. Mars’ movement was not uniform at all in fact. None of the planets moved in a

uniform way. Ptolemy’s mission to save the appearances of the observable movements of the celestial

bodies was about to be annihilated by the evidence of the observations: Kepler’s calculations, based on

three known positions of Mars68 (he only needed the coordinates of three positions to represent the

circle of the orbit), ended up in a conclusion that would change astronomy for good. Eventually the

results of his calculations were confronted with the observed positions of Mars: they didn’t correspond.

The tendency was to blame the records of the planet’s positions, as such observations were always

subject to human mistake. Especially when the error was only a difference of eight minutes of arch

between the orbit described by the actual observations and mathematical calculations:

For if I had thought I could ignore eight minutes of longitude, in bisecting the eccentricity I would already have made enough of a correction in the [vicarious] hypothesis found in Chapter 16. Now, because they could not have been ignored, these eight minutes alone will have led the way to the



67 Ibid.

68 Kepler took over the known positions of Mars on its orbiting the Sun from Aristotle’s and Ptolemy’s old records. As he himself relates in Chapter 69 of Astronomia Nova,“(…) there have survived no more than five observations of the star Mars, as well as one of extreme antiquity noted by Aristotle, who saw Mars occulted by the dark part of the half moon. (…) The other four were by Ptolemy himself, using an astrolabe to measure Mars’s distances from fixed stars” (AN, 642-‐643).

29

reformation of all of astronomy, and have constituted the material for a great part of the present work.69

Kepler’s accuracy is remarkable, as it was generally known that even Ptolemy himself knew he should

not go below 10' [minutes in accuracy] in his observations. At this point it becomes obvious that there

was an error in the setup of the problem: either the orbit of Mars was not a circle or Ptolemy’s theory of

the equant was not valid. Kepler had to choose between these two possibilities or accept them both.

Max Caspar opiniates that the choice that Kepler made at this point of his research was conducted by

logic: “Logic decided: there must be an error in the suppositions regarding the form of the orbit and the

form of the motion.”70 The problematic eight minutes could only be explained therefore by a slight

alteration of the curves of the orbit describing the movement. The orbit must be “an oval of some

kind.”71 In Chapter 44 of Astronomia Nova, Kepler formulates his first law: “Clearly, then, [what is to be

said] is this: the orbit of the planet is not a circle, but comes in gradually on both sides and returns again

to the circle’s distance at perigee72. They are accustomed to call the shape of this sort of path oval.”73

4.3 Motion; the Motion of the Sun and of the Planets: the Motor Virtue

In Kepler’s theory of motion, the starting point is the differentiation between geometry (as part of

mathematics) and physics. Motion of bodies follows different principles than when motion is dealt with

as an abstract notion. In the Introduction to his Astronomia Nova, by means of several propositions,

Kepler states the difference between mathematics and physics:

A mathematical point, whether or not it is the center of the world, can neither effect the motion of heavy bodies nor act as an object towards which they tend. (…) It is impossible that, in moving its body, the form of a stone seek out a mathematical point (in this instance, the center of the

69 Kepler, AN, 286.



72 Perigee is the point closest to the orbited body that the orbiting body can reach.

73 Donahue, AN, 86.

30

world), without respect to the body in which this point is located. Let the physicists prove that natural things have a sympathy for that which is nothing.74

This is in accordance with the adjustment he applied to the Copernican Sun: Kepler considers always the

Sun as a physical body instead of Copernicus’ “mean Sun,” which was merely a hypothetical position in

space. It is a category mistake to talk about a body that is attracted by a point, according to Kepler. A

moving body belongs to physics while a point is a conceptual abstraction. No relation whatsoever

between these two is possible. Natural objects have no sympathy and even less for something that is

nothing. For in the physical world a point can only be called to be nothing as no matter can be attributed

to it. Therefore, attraction is an attribute of objects that can only be assigned to physics. Aristotle’s

principle according to which the elements move towards or away from the center of the universe is

therefore refuted. One of the principles of Aristotelian motion is being proved wrong: "fire upward and

earth downward and towards the middle of the universe." The middle of the universe cannot exert any

force on anything (as it is only a mathematical concept), according to Kepler.

This being made clear (that bodies do not advance towards a mathematical point), Kepler moves

on to formulating the “true theory of gravity” and its axioms. This theory of gravity (that could also be

called Kepler’s theory of motion) “constitutes a complete rejection of the Aristotelian view of gravity

and plays a fundamental role in Kepler’s physical thought.”75 The first axiom of this theory is of extreme

generality: “every corporeal substance” will not move as long as it is not acted upon from the outside.

The next step Kepler takes is defining gravity (the true gravity as opposed to the gravity of Aristotle, who

was in error): “gravity is a mutual corporeal disposition among kindred bodies to unite or join together

(…). Heavy bodies (…) are not drawn towards the center of the world qua center of the world, but qua

centre of a kindred spherical body, namely, the Earth.”76 Kepler is refering here to gravity in relation to

the Earth – Moon system.

The planets (among which the Earth) move around the Sun describing an elliptical orbit. This

motion is not regular, firstly in shape (it is not a circle but an ellipse) and secondly in speed (the

74 Kepler, AN, 54.

75 Donahue, AN, 55, footnote 7.

76 Kepler, AN, 388.

31

proportionality between speed and distance to the Sun). The next question Kepler had to answer was:

what makes the planets move around the Sun? Once the Aristotelian spheres had been eliminated, a

replacement was required, a replacement that was different from the construction in Mysterium

Cosmographicum. Kepler was able to formulate a solution, first (in Astronomia Nova) in the form of a

“lucky guess” and, after years of observation (the Sun spots), with a still speculative but pertinent

theory: the Sun rotates and drags along the planets in a non-‐uniform but continuous movement.

Kepler proposes (in Astronomia Nova and also in the Epitome) several alternatives to Aristotle’s

geocentrism of the spheres. The hypothesis he starts with is that the Sun is the cause of the movement

of the planets. The physical cause that supports the planets in their orbits is not clear. Kepler gives

several solutions for this problem: magnetic fibres, an immaterial species or light itself. Kepler borrowed

the idea of the magnetic species from William Gilbert: “What Kepler takes from Gilbert’s The Magnete

(1600) is the notion that the Earth has an animate magnetic virtue and that this virtue can be

demonstrated to be immaterial (for it cannot be blocked).”77

In Astronomia Nova, for the first time, the Sun is spinning, it rotates about its own axis: “(…) since

the species of the source, or the power moving the planets, rotates about the center of the world, I

conclude with good reason, (…), that that of which it is the species, the Sun, also rotates.”78

In his Kepler’s Physical Astronomy, Bruce Stephenson notices that there is a slight difference

between Kepler’s account of the Sun rotating around its own axis in Astronomia Nova and the account

of the same hypothesis in the Epitome. Innitially, Kepler speculated over a movement of the Sun around

its own axis in Astronomia Nova (the “lucky guess” mentioned earlier). In Chapter 34, “the Sun is a

magnetic body and rotates in its space,” Kepler formulates the theory of the “motor virtue” of the Sun:

For it may appear that there lies hidden in the body of the Sun a sort of divinity, which may be compared to our soul, from which flows that species driving the planets around, just as from the soul of someone throwing pebbles a species of motion comes to inhere in the pebbles thrown by him, even when he who threw them removes his hand from them.79

77 Regier, Kepler's Theory of Force, 21.

78 Donahue, AN, 65.

79 Donahue, AN, 63.

32

In between Astronomia Nova and Epitome, “the observations of sunspots moving accross the face of the

Sun had confirmed this supposition.”80

The image of the system is now made clear: the Sun rotates around its own axis and drags the

planets with it. The Sun is fixed in space, the Earth and the other planets move around the Sun, this

being also the explanation of the apparent movement of the sphere of the fixed stars. The attractive

force of the Sun is countered by the inertia of the planets, a force directly proportional to their mass.

There is a motive force that moves the Sun, the nature of which is not yet well specified.

5. The Refutation

Kepler’s worldview, based on Copernicus’ heliocentrism, had, along his career, taken shape, changed

and developed until it became what we know today to be his image of the universe: one could call it

“evolution,” as it is now well known that Kepler worked continuously on it and, what is most important,

never stopped being critical towards others and towards himself. Starting from the hypothesis of

heliocentrism, Kepler formulated theories and dismissed them again, being able, somewhere on his way,

to formulate laws of major importance for the progress of science. A critical attitude was one of his main

characteristics. When reading Astronomia Nova, the reader is confronted with a special kind of writing:

it is difficult to say if it is a history (a personal record) or an astronomy treatise. There is care and

thoroughness in the development of the book as if the writer tried to foresee the possible objections

that could dismantle his theory. Kepler doubted and rejected theories and conjectures of others but also

his own, the critical approach and examination being an essential contribution to the progress of

knowledge. In the words of Karl Popper: “The critical method alone explains the extraordinarily rapid

growth of the scientific form of knowledge, the extraordinary progress of science. All prescientific

knowledge whether animal or human, is dogmatic; and science begins with the invention of the non-‐

dogmatic, critical method.”81

Kepler’s criticism of Aristotle uses two kinds of arguments: first, there are arguments of (natural)

physics, which Kepler presented in Part IV of the Epitome (see 4.1 Heliocentrism). Second, there are the


81 Popper, All Life, 7.

33

philosophical arguments which Kepler discusses in Part I of the Epitome. The beginning of the Epitome is

made by stating clearly, in several questions an answers, that the Sun is at the centre of the universe

and that Aristotle’s view on the universe was wrong. Kepler presents in short the position of those that

pretend that it is the Sun that is placed at the centre of the universe: “The very ancient Pythagoreans

and the Italian philosophers supply us with some of the arguments in Aristotle [On the Heavens, Book II,

Chapter 13]; and these arguments are drawn from the dignity of the Sun and that of the place, and from

the Sun’s office of vivification and illumination in the world.”82 This is the position of the Pythagoreans,

Copernicus’, and also Kepler’s. The argument of dignity states that as “the more worthy place is due to

the most worthy and most precious body," no other body can be more worthy than the Sun, which is

fire. According to Kepler, the sphere of the universe has three conceptual parts, the centre, the surface,

and the intermediary space; out of which the Sun, as one of the most important actors of the game, can

only be placed at one of the extremities, either the centre or the surface. As only the centre can fulfill

the mission of watching over all the other bodies, the Sun can only be placed in the middle. The Sun is

therefore the one to occupy the center of the world. Several pages earlier, Kepler had already shown

that the Sun is the principal body of the world (as the Earth used to be in the Aristotelian system). In this

view, Earth does not belong to the major group of actors but to the planetary part of the world (the

movable): it “should not be reckoned among the primary parts of the great world but should be added

to one of the primary parts (…) to the planetary region, the movable world.”83 Kepler opposes here the

primary parts of the great world to the primary parts of the planetary region. The Earth belongs to the

second group and it revolves the Sun together with the other planets. The Sun is the source of light (“the

eye of the world”84) and heat (“the fireplace of the world”85), movement (“the Sun is the first cause of

the movement of the planets and the first mover of the universe, even by reason of its own body”86) and

harmony of movement (only with the Sun in the centre are the “magnitudes harmonically


83 Ibid., 14.

84 Ibid., 15.

85 Ibid.


34

proportioned”87).

Aristotle responded to these arguments of the ancient heliocentrists, by saying that “they assume

something which is not granted”: that the two centres of the world coincide. He compares the world

with an animal body: in an animal body “the heart is inside but it is not equally distant from the

surface.”88 The animal body has therefore two centres that are not located at the same point: the centre

of vivification and the centre of the body. Similarly, even if the Sun is the centre of vivification of the

universe, it is still the Earth that is situated at its centre. Kepler’s rejection of Aristotle’s view is clearly

stated: “nothing is more probable than this.”89 Aristotle is seen as being more of a metaphysician, not

skilled in astronomy. Copernicus, on the contrary, is skilled in this discipline and he could show us the

truth: “And when we ask in what place in the world the Sun is situated, Copernicus, as being skilled in

the knowledge of the heavens, shows us that the Sun is in the midpart.”90 The astronomer is getting the

front seat, the rest are left with speculation: “The others who exhibit its [the Earth’s] place as elsewhere

are not forced to do this by astronomical arguments but by certain others [arguments] of a metaphysical

character drawn from the consideration of the Earth and its place.”91

In his Logic of Scientific Discovery, Karl Popper defines the problem of demarcation as the finding

of “a criterion which would enable us to distinguish between the empirical sciences on the other hand

and (…) metaphysical systems on the other.”92 Kepler constantly looked for the good arguments that

would refute the Aristotelian system together with any other theories that would not pass the scientific

test, even when the theory in question was his own. He struggled for sustainable, feasible arguments

that would “demarcate” between “good” theories and pseudo-‐scientific theories (or, as Popper would

call it, “prescientific knowledge”). The question of finding a method to demarcate science from pseudo-‐

science is nowadays still under discussion. This makes Kepler’s attempt to distinguish between the two

87 Ibid.


89 Ibid.


91 Ibid.

92 Popper, The Logic, 34.

35

even more remarkable. He used the method of trial and error as one of the first, being methodically

critical with empirical knowledge, corresponding to Popper’s modern view on the methodology of

science: “(…) the novelty of science and scientific method, which distinguishes it from the prescientific

approach, is its consciously critical attitude to attempted solutions; it takes an active part in attempts at

elimination, in attempts to criticize and falsify.”93 Kepler questioned and doubted the circularity and

uniformity of the movement of the planets with method, proving them wrong, eventually:

The orbit of the planet is not a perfect circle. But if mind caused the orbit, it would lay out the orbit in a perfect circle, which has beauty and perfection of the mind. On the contrary, the elliptic figure of the route of the planet and the laws of the movements whereby such a figure is caused smell (…) of material necessity rather than of the conception and determination of the mind.94

In Popper’s epistemology, even theories that are impossible to test by experience can be submitted to

the test of falsifiability in order to prove them true or false: “this means that their form must be such

that to verify them and to falsify them must both be logically possible.”95 Therefore, a theory that is not

falsifiable cannot be accepted as scientific. Kepler’s aim was not to prove the Aristotelian system to be

false, he was not a theoretician of science, his aim was to reveal how the planetary system worked and

to prove it true. In order to reveal the real system, he needed assumptions that were contradicting the

presently accepted theories, those of Aristotle and Ptolemy. He managed to refute the Aristotelian

worldview by using a smart trick: if he could show that the Aristotelian principles emerged from a

metaphysical belief rather than an empirical analysis of observations, he could subsequently show that

such a system is not to be proven wrong because of the simple reason that it didn’t have a scientific

basis. The falsification of the Aristotelian worldview is actually not possible logically because Aristotle

does not “show but seek”96 his theory. As Copernicus had already shown, the Sun is in the center of the

world and “the others who exhibit its place as elsewhere are not forced to do this by astronomical

93 Popper, All Life, 11.

94 Kepler, Epitome, 52-‐53.

95 Popper, The Logic, 40.


36

arguments but by certain others of a metaphysical character drawn from the consideration of the Earth

and its place.”97 In the Epitome, Kepler argues for Copernicanism in a modern way: he assigns the

theories of the ancients as “probable” and, as a contrary, describes the demonstration of Copernicus as

bringing in necessity.98 Kepler’s attempt to separate the “new physics” from the old, traditional theory

of motion having its origin in Aristotle’s worldview, brought science on a new path of physical causality

that would help change our view upon the universe.

6. Conclusion

Kepler’s description of the planetary system is based on a new vision of motion and its implications were

important not only for the further development of astronomy, but for the progress of science in general.

His faith in the growth of knowledge by testing, questioning, inquiring brought him eventually to the

three laws of planetary movement that provided us with a new kind of knowledge, able to look at the

depths beyond appearances:

But we are practised in the discipline which discloses the causes of things, shakes off the deceptions of eyesight, and carries the mind higher and farther, outside of the boundaries of the eyesight. Hence it should not be surprising to anyone that eyesight should learn from reason, that the pupil should learn something new from his master which he did not know before.99

His critical approach to astronomy, which is transparent in all his writings, fully used the dichotomy

between physical and metaphysical, giving it new connotations, even if the linguistic and semantic

clarity of the two concepts is still problematic. In an evolving process along his career as mathematician

and astronomer, Kepler succeded in invalidating Aristotle’s notion of celestial motion and formulate

laws of motion that contributed in an essential way to the Scientific Revolution.

97 Ibid.

98 Kepler, Epitome, 21 – 22: “The reasoning of the ancients is merely probable, but the demonstration of Copernicus, arising from his principles, brings necessity.” “The ancients do not explain and confirm as they desire the reason for their lay-‐out; Copernicus establishes his lay-‐out excellently by reasons.”


38

Bibliography

• Aristotle, The Complete Works, 2 volumes, the revised Oxford translation, Edited by Jonathan

Barnes, New Jersey: Princeton University Press, 1984.

• Baumgardt, Carola, Johannes Kepler, Life and Letters, New York: Philosophical Library, 1951.

• Bodnar, Istvan, "Aristotle's Natural Philosophy", The Stanford Encyclopedia of Philosophy (Spring

2012 Edition), Edward N. Zalta (ed.)

URL=,http://plato.stanford.edu/archives/spr2012/entries/aristotle-‐natphil/ (consulted on 12

April 2015).

• Caspar, Max, Kepler, Trans. Doris Hellman, New York: Dover Publications, 1993.

• Corvi, Roberta, An Introduction to the Thought of Karl Popper, London: Routledge, 1997.

• DeWitt, Richard, Worldviews -‐ An Introduction to the History and Philosophy of Science, Oxford:

Wiley-‐Blackwell, 2010.

• Di Liscia, Daniel A., Johannes Kepler, The Stanford Encyclopedia of Philosophy (Summer 2014

Edition), Edward N. Zalta (ed.), URL =

<http://plato.stanford.edu/archives/sum2014/entries/kepler/> (consulted on 30 March 2015).

• Donahue, W. H., Selections from Kepler's Astronomia Nova: A Science Classics Module for

Humanities Studies, Santa Fe: Green Lion Press, 2005.

• Gingerich, Owen, The Eye of Heaven. Ptolemy, Copernicus, Kepler, New York: American Institute

of Physics, 1993.

• Kepler, Johannes, Epitome of Copernican Astronomy, Trans. Charles Glenn Wallis, New York:

Prometheus Books, 1995.

• Kepler, Johannes, Harmonies of the World -‐ Book Five, Trans. Stephen Hawking, Philadelphia:

Running Press, 2002.

• Kepler, Johannes, New Astronomy, Trans. W. H. Donahue, Cambridge: Cambridge University

Press, 1992.

• Kepler, Johannes, The Six-‐cornered Snowflake, London: Oxford University Press, 1966.

• Kepler, Johannes, Somnium, Trans. Normand R. Faladeau,

https://frostydrew.org/papers.dc/papers/paper-‐somnium/ (consulted on 30 March 2015).

• Koestler, Arthur, Johannes Kepler -‐ Een nieuwe visie op het helaal, Elsevier

Natuurwetenschappelijke Pockets, 1962.

39

• Koestler, Arthur, The Sleepwalkers : a History of Man's Changing Vision of the Universe, London:

Hutchinson, 1964.

• Koyré, Alexandre, The Astronomical Revolution: Copernicus -‐ Kepler -‐ Borelli, New York: Dover

Publications, 1992.

• Piglicci, Massimo & Boudry, Maarten (editors), Philosophy of Pseudoscience -‐ Reconsidering the

Demarcation Problem, Chicago: The University of Chicago Press, 2013.

• Popper, Karl Raymund, The Logic of Scientific Discovery, London: Hutchinson, 1983.

• Popper, Karl Raymund, Realism and the Aim of Science, London: Hutchinson, 1983.

• Popper, Karl Raymund, “The Logic and Evolution of Scientific Theory” in All Life Is Problem

Solving, 3-‐22, London: Routledge, 1999

• Regier, Johathan, "Kepler’s Theory of Force and His Medical Sources," Early Science and

Medicine, 19 (2014), 1 -‐ 27.

• Rossi, Paolo, The Birth of Modern Science, Oxford: Blackwell Publishers, 2001.

• Sachs, Joe, Aristotle: Motion and its Place in Nature, Internet Encyclopedia of Philosophy,

http://www.iep.utm.edu/aris-‐mot/ (consulted on 16 May 2015).

• Stephenson, Bruce, Kepler’s Physical Astronomy, Princeton: Princeton University Press, 1994.

• Stokes, Geoffrey, Popper: Philosophy, Politics and Scientific Method, Polity Press, 1998.

• Swinford, Dean, Through the Daemon's Gate -‐ Kepler's Somnium, Medieval Dream Narratives and

the Polysemy of Allegorical Motifs, New York & London: Routledge, 2006.

• Voelkel, James R., The Composition of Kepler's Astronomia Nova, Princeton: Princeton University

Press, 2001.

TheNew$Physics$ Kepler's$Refutationof$Aristotle's$Concept ... · 2!! 1.Introduction:theContext$...

Documents

Transcript of TheNew$Physics$ Kepler's$Refutationof$Aristotle's$Concept ... · 2!! 1.Introduction:theContext$...