hist phil sci

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HISTORY AND PHILOSOPHY OF SCIENCE SXEX 1400 Assoc. Prof. Dr. Paul Lettinck

Bibliography

Crombie, A. C. (1952) Augustin to Galileo, History of Science 400-1650. Q125 CRO

Dampier, W. C. (1948) A History of Science and its Relation to Philosophy and Religion.

Q125 DAM

Dampier, W. C. (1937) A Shorter History of Science. Q125 DAM

DeWitt, R. (2004) Worldviews. An Introduction to the History and Philosophy of Science.

Q125 DEW

Dijksterhuis, E. (1950, tr. 1961) The Mechanization of the World Picture. Q125 DIJ

Gale, G. (1979) Theory of Science: An Introduction to the History, Logic, and Philosophy of Science. Q175 GAL

Philosophy of science, illustrated with three examples: the new theories of Lavoisier, Pasteur andPauli.

Koyré, A. (1939) Etudes Galiléennes. Translated by John Mepham as Galileo Studies. 1978.QB36 G2 KOY

Lindberg, D. (1992) The Beginnings of Western Science: The European Scientific Tradition in

Philosophical, Religious and Institutional Context, 600 B.C to A.D. 1450. Q124.95 Res. Coll.

Losee, J. (1972) A Historical Introduction to the Philosophy of Science. Q175 LOS

Mason, S. F. (1962) A History of the Sciences. Q125 MASIncludes Indian and Chinese science

Sarton, G.A. (1927-1948) Introduction to the History of Science, 3 vols. in 5 Q125 SAR

Sarton, G.A. (1952, 1959, repr. 1993) A History of Science, 2 vols. Q125 SAR

Singer, C. (1959) A Short History of Scientific Ideas to 1900. Q125 SIN

Taton, R. (ed.) (1957-1964, tr. 1963-1966) History of Science, 4 vols. Q125 TATIncludes Indian and Chinese science

Taylor, F. Sherwood (1949) A Short History of Science and Scientific Thought. Q125 TAYWith readings from the great scientists from the Babylonians to Einstein.

Wan Fuad Wan Hassan (1990) Ringkasan Sejarah Sains. Q125 WANF

Westfall, R. S. (1971), The Construction of Modern Science: Mechanisms and Mechanics.QA802 WES

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Introduction

If one asks the question “what is science?” one will get many different answers. Lindberg (1992,

pp. 1-2) enumerates eight answers, Wan Fuad Wan Hassan (1996, pp. 3-4) mentions six answers

and certainly one may find many more answers when one looks into dictionaries, encyclopedias

and books on the history of science (see for instance, the internet encyclopedia Wikipedia under

‘science’).

It is important to keep in mind that even if one may have found a satisfactory answer on

this question regarding what people nowadays consider to be science, it will appear that such an

answer will not work for what was considered science in past centuries. What was considered to

be science then is not considered to be science now any longer. Therefore, if one studies the

history of science one has to start from a broad and general description of science.

Most people nowadays will say that science is the investigation of phenomena in thenatural world with the goal to understand and to explain these phenomena; this is done by

proposing certain general rules (laws, theories), which should be checked against the observed

facts and/or tested by experiments; if the theory is found to be correct, then it can be used to

predict other facts and phenomena, which sometimes have not yet been found.

Note that mathematics is also called a science, but does not really fulfill the description

above, which applies rather to natural science. There are no experiments in mathematics: it is a

purely theoretical discipline. It is an indispensable tool in the natural sciences.

The above description of science would apply to modern science, that is, science after

around 1600, the time of the so-called Scientific Revolution (to be discussed later). Before that

time experiments played a less crucial role and science was part of a general reflection on the

world which included philosophy and theology. In fact, the expression ‘natural philosophy’ was

often used instead of science, up until the 19th century. Therefore, if one studies the history of

science a more general description should be used. For instance, one may say that science is an

effort to describe and understand the world in a systematic way, and thereby to control the world

to a certain extent.

Since prehistoric times (that is, the time before people used writing) people have observed the

world in which they live, have tried to understand the phenomena that occurred around them and

to use these observations and this understanding for practical purposes. Maybe the first

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beginnings of science have come about due to practical requirements of the earliest civilizations:

the practice of agriculture, hunting, fishing, metalworking, weaving, pottery, healing injuries and

illnesses resulted in a big amount of knowledge. However, this knowledge was laid down and

transmitted not by means of written reports, but orally. It will not be surprising that the way

prehistoric people try to bring order in and give meaning to what they observe is different from

how modern scientists work. They do not think in terms of general ‘laws of nature’, and do not

distinguish clearly between what is human, what is natural and what is supernatural (divine). If

asked about the cause of something they will tell a story about how it began (creation myths).

Often several different stories circulated explaining the same thing, but they did not entertain the

idea that only one could be true.

In Greek civilization a new concept of knowledge and truth developed, and one thing that

seems to have made this possible was the invention of writing. First, hieroglyphs were used in

Egypt, then alphabetical writing became spread in Greece from 500 B.C. Now observations andknowledge could be recorded in permanent form, could be compared and criticized. One could

set up criteria that would distinguish ‘real knowledge’ or truth from false beliefs, and formulate

rules for correct reasoning. This formed the basis of philosophical an scientific activity. Also,

one could study written lists of observations, which led to new ways of thought and discoveries

that would be impossible within an oral tradition. For instance, the Babylonians recorded their

observations of the positions of the stars, sun, moon and planets, and were able to discover rather

complicated patterns in the motion of these bodies in the sky. This was the one of the beginnings

of astronomy and astrology.

Egypt and Mesopotamia

The first scientific activities occurred in the Egyptian and Babylonian civilizations, starting from

around 3000 B.C. The Egyptians used a decimal system to write the numbers with a symbol for

each power of 10. Any number could be written by repeating and combining these symbols.

Later additional symbols were introduced.They also knew fractions, but only unit fractions (that is, fractions with numerator 1,

denoted by putting an oval sign above the symbol for the integer denominator) and the fraction

2/3. Other fractions were reduced to these ‘natural’ unit fractions, for instance, 3/5 = 1/3 + 1/5

+1/15 and 9/10 = 1/30 + 1/5 + 2/3. Multiplication was done by successive doubling; for instance,

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if we want to calculate 19 times 14, we first double 14; then we get 28; doubling this gives 56,

doubling this gives 112, and doubling this gives 224; now we have 16 times 14; then we add 2

times 14 (=28) and one time 14, to obtain the final result 266. This kind of arithmetic was used to

solve problems such as how to divide 700 loaves of bread among four people if their shares must

have the proportion 2/3: 1/2 : 1/3: 1/4.

Other problems to be solved require what we would call an algebraic solution. For

example: determine the value of a ‘heap’, if the heap and one seventh of it equals 19. In modern

notation this would be solving x from x + x/7 = 19. The solution was found by just ‘trying’ an

arbitrary (probably false) value for x, for instance 7. Then x + x/7 is 8. Because the sum in the

problem is in fact 19 instead of 8, one finds the correct value of x by multiplying the false one by

19/8 = 2 + 1/4 + 1/8, and so the answer becomes 7 x (2 + 1/4 + 1/8) = 16 + 1/2 + 1/8. This

method was later called the method of false position.

The Egyptians also handled geometrical problems, as they regularly needed to surveytheir lands, since the overflowing of the Nile yearly deleted the boundaries. The origin of

geometry is traditionally ascribed to the ‘rope-stretchers’ of Egypt. Indeed they knew how to

calculate the surfaces of figures like triangles, trapezoids and circles (the latter in approximation

only) and the volume of pyramids.

The yearly flooding of the Nile was essential for the agriculture in Egypt, and so it was

important to predict the time of flooding. This involved some astronomical observations. The

Egyptians noticed that the flooding occurred around the time when the star Sirius, the brightest

star in the sky, rises just before the sun (this is called heliacal rising; it occurs in mid-July). This

was marked as the beginning of the year. It was observed that the next heliacal rising of Sirius

occurred 365 1/4 days later. They adopted 365 days as the length of a year, so that every new

year began a quarter of a day ‘too early’. Thus, the seasons and the flooding of the Nile occurred

one day earlier every 4 years, and returned to their original dates after 1460 years. The year was

divided into 12 months of 30 days plus 5 ‘extra’ days. However, at the same time also lunar

months were used. A lunar month is the period of time between the first appearance of the new

moon until its next first appearance. This time is about 29 ½ days, so the months were taken as29 or 30 days. Then a ‘year’ of twelve months amounts to 354 days. In order to make this ‘year’

more or less coincide with the year determined by the seasons and the heliacal rising of Sirius the

Egyptians inserted an extra month every three years.

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In Mesopotamia the oldest civilization was that of the Sumerians, who invented cuneiform

writing. Around 2300 B.C. the Sumerians were conquered by the Akkadians, a Semitic people

who took over their script. They formed the kingdom of Sumer and Akkad. The country became

known as Babylonia when Hammurabi became its ruler (around 1750 B.C.).

The Babylonians used a number system that was a combination of the decimal (based on

the number 10) and the sexagesimal (based on the number 60) system. They had symbols for 1

and 10, and with a combination of them the numbers from 1 to 59 were written. For higher

numbers the same symbols were used, with a place system (positional notation), similar to our

system. Whereas in our system a different position of a symbol in a number denotes a different

power of 10, in the Babylonian system this denotes a different power of 60, which can also be a

negative power. Thus they could write any fraction in a sexagesimal fraction notation, similar to

our decimal fractions. At first they did not have a special symbol for the ‘empty’ position (zero),

which could cause some confusion; later, from around 300 B.C. the zero was denoted by aspecial symbol.

As for the problems that we would solve algebraically, the Babylonians surpassed the

Egyptians. They were able to solve problems that involved quadratic equations. An example:

find the side of a square if the area minus the side is 14,30. In modern notation this means: solve

the equation x2 – x = 870. The solution given is equivalent to the formula given in modern

textbooks for the root of a quadratic equation; the difference is just that they did not use a

formula but wrote out everything in words. A common problem was to find two numbers when

their product is given and either their sum or their difference. This means solving the system of

equations x ± y = p, xy = q.

From Babylonian problem texts it appears that they knew the theorem of Pythagoras. One

problem mentions a ladder of 15 units long standing vertically against a wall. If the top slides

down 3 units, then how far away slides the lower end? However, there is no indication that they

knew a general proof of the theorem.

The use of astronomical observations for determining the seasons and the calender has already been mentioned. The heavenly bodies were usually considered to be divine and to possess power

in determining what happened on earth. Thus, observation of the heavenly bodies had also

religious and astrological purposes and it was carried out by temple priests. They observed the

fixed stars, the sun, the moon and and the five planets (that is, the planets that are visible with the

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naked eye). The Babylonians recorded various kinds of observations: heliacal risings and settings

of stars, times of visibility of the planets, eclipses, and positions of the planets. These data were

later used by the Greeks and played an important part in the construction of the astronomical

model of Ptolemy.

It was observed that the planets slowly moved in relation to the fixed stars within a

narrow circular band, the zodiac, with the earth as its center. The Babylonians divided the zodiac

into 12 parts of thirty degrees each, and the stellar constellations in each of these parts became

what is known as the signs of the zodiac. Then they found from their recorded tables of positions

of the planets that the motion of the sun, moon and planets along the zodiac is not regular:

sometimes they move slower, sometimes faster and the planets even move backwards during

some time. By means of extrapolation of the data of the tables predictions could be made of

future positions, and in this way, for instance, the first appearance of the new moon and the

occurrence of an eclipse could be predicted.

Greece

The first records of the civilization of the Greeks (also called Hellenic civilization) dates from

the 8th century B.C. The first Olympic Games were held in 776 B.C. The epic poems Ilias and

Odyssey were committed to writing by Homer, and Hesiod wrote the book Theogony about the

origins of the gods and the world. The worldview of the Greeks expressed in these works was

much like what was described above as the view of prehistoric man. There were twelve main

gods living on the mountain Olympus, the greatest of them being Zeus. Their behaviour much

resembled human behaviour, they interfered in human affairs and caused natural phenomena like

storms, thunder and lightning and earthquakes. The stories about these gods and their influence

on the world are called ‘mythology’.

The first Greek philosophers appeared in the sixth century B.C. A new way of thinking

was introduced, which we now call ‘philosophy’. It did not replace mythological thinking, but

existed alongside with it. These philosophers sought to understand the phenomena in the world by means of natural explanations, not supernatural (divine) ones, and they tried to find an order

(kosmos) in nature. Therefore they were called ‘natural philosophers’.

The earliest natural philosophers of the 6th and 5th centuries B.C. came from Ionia, the

west coast of Asia Minor (nowadays Turkey). They tried to answer the question “what is

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everything made of, what is the material of the world?” The first natural philosopher was Thales;

he said that everything was made of water, or came into existence from water. Anaximander

thought that the basic stuff out of which the universe arose was the ‘unlimited’ (apeiron), some

indetermined, infinite substance. Anaximenes said that the underlying stuff of the world was air.

Heraclitus thought that everything arose from fire. One may call these philosophers materialists

and monists, because they thought that the basic substance of the world is some kind of matter,

and that it is just one kind of matter.

Leucippus and Democritus were atomists. They thought that everything consists of

invisible small particles of various shapes, which they called ‘atoms’ ( = ‘indivisible things’).

These atoms move randomly in a void space, without plan or purpose, colliding and separating

again, and thus account for the variety of things and phenomena in the world.

Empedokles (from Acragas ( = Agrigentum), on Sicily) was not a monist, nor a pure

materialist. He stated that there are four elements of all material things: fire, air, earth and water.By combination and separation of these elements all things and phenomena come about. But this

combination and separation does not occur by itself; they are induced by the immaterial

principles love and strife.

Pythagoras and his school (from the Greek cities in southern Italy) claimed that the

principle of everything is not some kind of matter, but number. It is unclear what they exactly

meant by this. At least we can say that apparently they were aware that number is a fundamental

concept to understand the world and that mathematics is essential for its investigation.

In the 5th century B.C. philosophers got interested in the problem of change. The basic

stuff out of which the world is made or from which it arose is supposed to be unchangeable. So if

we observe change in the world, is that change real? And if it is real, how can one explain it?

Heraclitus stated that change is real and is a basic feature of the world: panta rhei (everything is

flowing). Parmenides and his pupil Zeno (from Elea, southern Italy), on the contrary, thought

that the change we perceive is an illusion, and that in reality change is impossible. They proved

the impossibility of change with a logical argument: Suppose A changes into B, then B did not

exist before, but if something does not exist, it is nothing, and out of nothing nothing can comeinto being. Zeno became famous for his paradoxes by means of which he claimed to prove that it

is impossible for something to move (see Lindberg p. 33). The problem how to explain change in

a world of which the basic material is unchangeable occupied many philosophers after

Parmenides.

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Apparently for Parmenides the result that one obtains by rational, logical argument

prevailed over what followed from observation and sense experience. It is one possible answer

on the problem of knowledge (epistemology): how do we acquire knowledge? By the exercise of

reason or by using our senses (rationalism or empiricism)? The Greek rationalists contributed to

the development of the rules of argumentation and justification of theories, which would become

essential for logic and philosophy of science.

The problem of change was addressed by Plato (4th century), a pupil of Socrates. The

philosophers of the 6th and 5th century mentioned up to here are called pre-Socratics. Socrates’

philosophy was concerned with ethical and political matters rather than with matters of nature.

Plato did not deny change, but his epistemological position was clearly rationalist. He

distinguished between the world as we know it by our sense experience, which is a world in

which everything changes, and another world, the world of unchangeable, eternal Forms or

Ideas. The latter world is the true world, and it is knowable only by reason. The things in theobservable world are imperfect copies of the perfect examples in the world of Forms. These

Forms are incorporeal, insensible, changeless and eternal, but they really exist (see Lindberg pp.

35-38).

According to Plato, the world is the work of a Demiurg (Creator), who puts order in the

chaotic matter that existed eternally. Thus, the world is a product of reason, created with a

purpose, it is not a product of nature as the pre-Socratics had claimed. The world is considered to

be a living being, possessing a soul; this soul causes the motions in the world.

Plato’s philosophy was taught and further developed in the school founded by him, called

the Academy, which continued to exist for more than two centuries. In the fifth century it was

refounded by Neo-Platonists and survived until the sixth century.

We now mention some of the ideas and achievements of the pre-Socratic philosophers and Plato

in mathematics and astronomy.

Thales and Pythagoras have probably travelled to Egypt and Babylon, where they learned

about the mathematics and astronomy that had developed there. Thales is said to have provedsome geometrical propositions and to have determined the heights of the pyramids by measuring

the length of their shadows at the moment when the shadow of a vertical stick is equal to its

height. According to him, the Earth is flat, floating on water. The heaven is a hemisphere above

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the Earth, surrounded by water. Sun, Moon and stars move along it, then set and move sideways

of the earth back to the place where they rise.

According to Anaximander the Earth is a cylindrical disc, freely suspended at the center

of a spherical universe. It remains there, because it has the same distance from all points of the

heaven so that there is no reason why it should move in one direction rather than in another. The

Sun, Moon and stars are concentric wheels or rings rotating around the Earth, filled with fire and

having a hole in them. Eclipses and the phases of the moon occur when the holes are shut.

Pythagoras claimed that the Earth is a sphere. He was aware that the Sun, Moon and

planets have a motion of their own, contrary to the daily motion.

As we have seen, the theorem of Pythagoras was known to the Babylonians; whether its

proof was due to Pythagoras is not certain. Some rectangular triangles have sides of which the

lengths have proportions to each other that can be expressed by integer numbers. Such numbers

are called Pythagorean triads; they were known to the Babylonians. Example: (3, 4, 5), (5, 12,13), etc. Then the Pythagoreans realized that most rectangular triangles do not have sides with

this property; this was in fact the discovery of the irrational numbers (that is, numbers that are

not a proportion of integers). The simplest example is the proportion of a diagonal to the side of

a square, which we write as √2. It can easily be proved that √2 cannot be written as a proportion

p/q with integer p and q. This would mean that the Pythagorean doctrine “Everything is number”

is faced with a serious problem.

Still, it will not be surprising that the Pythagoreans were much concerned with numbers.

Three points may be arranged in the form of a triangle; with three additional points a larger

triangle may be formed, with four additonal ones a still larger triangle, etc. The total number of

points in each case gives the triangular numbers 1, 3, 6, 10,…. , given by the formula 1 + 2 + 3 +

…. + n = ½ n (n + 1). In a similar way one may form square numbers, pentagonal numbers, etc.

The square numbers are given by the formula 1 + 3 + 5 + …. + (2n –1) = n2. It can easily been

seen that any square number is the sum of two consecutive triangular numbers: if Sn and Tn are

the nth square and triangular number respectively, then Sn = Tn + Tn-1.

According to Heraclitus the apparent motion of the celestial bodies occurs bycondensation and evaporation of matter between Earth and heaven: earth is turned into water,

which evaporates as fire that rises upwards The heaven contains certain bowls in which the fire

is collected. These are seen as the heavenly bodies. The fire again condenses into water which

turns into earth. Every day a new Sun arises, produced in the east by exhalation from the sea.

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Like Pythagoras, Parmenides thought that the Earth is a sphere. It remains at the center of

the spherical universe, because within such a universe there is no reason for it to move in a

certain direction (cf. Anaximander’s argument). Around the earth are concentric bands (zones of

a sphere) revolving around the Earth; at certain places fire flashes out of these bands and these

are seen as the Sun, Moon and planets.

In the 5th century B.C. Anaxagoras was another of the pre-Socratic philosophers from Ionia. He

said that the celestial bodies were fiery stones. He discovered that the Moon received its light

from the Sun, and he gave the correct explanation of the eclipses. Because of his naturalistic

explanation of these heavenly phenomena he was accused of impiety and blasphemy by the

Athenians, the majority of whom adhered to idea of the divine nature of the heavenly bodies. He

was imprisoned and exiled.

Philolaos represents the Pythagorean school in a later stage. He rejects the geocentric picture of the universe adopted by the earlier Pythagoreans. He places a fire in the center of the

universe. The (spherical) Earth revolves around this central fire, performing one revolution in

one day (24 hours), while the inhabited part is always turned away from that fire (therefore

nobody has ever seen it). Then, the Moon revolves around the central fire in a larger orbit in one

month, then follow the orbits of the Sun (one rotation in one year), the five planets and the fixed

stars. This system accounts for the daily motion of the heaven, the occurrence of night and day,

and the motion of Sun, Moon and planets along the zodiac. Philolaus claimed that besides these

nine bodies a tenth body rotates around the central fire, called the counter-Earth. Its orbit is

between that of the Earth and the central fire, and it is always in line with the Earth, so that the

central fire is always hidden from any observer on the Earth. The function of the counter-Earth is

not clear. Maybe it was added to make the number of heavenly bodies ten. This number was

considered by the Pythagoreans to be a number with special powers (the fourth triangular

number 1 + 2 + 3 + 4 = 10 was called the number of the universe, since it is the sum of the

number of points that determine the geometric dimensions 0, 1, 2 and 3).

Later Pythagoreans discarded the counter-Earth and the central fire and placed the Earthin the center of the universe. Ecphantus (4th century B.C.) assumed that the Earth rotated around

its own axis in 24 hours.

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Since the 5th century Greek mathematicians were interested (among other things) in three

problems: the quadrature of the circle, the trisection of an angle and the duplication of the cube.

The first problem was to find a square with an area equal to the area of a circle. The second one

was to construct an angle which was one third as large as a given angle. The third one was to

find the edge of a cube with a volume which was double the volume of a given cube. The

construction of the solution of these problems was supposed to be done by ruler and compass

alone. Hippocrates of Chios (not to be confused with the more famous physician Hippocrates of

Cos, see later) attempted to solve the first problem. He did not succeed, but he managed to show

that sometimes other curvilinear figures could be ‘squared’, namely lunes. A lune is a figure

bounded by two circular arcs of unequal radii. In order to ‘square’ a lune one first has to prove

that the proportion of the areas of circles is equal to the proportion of the squares of their

diameters. In modern mathematics it is proved that it is impossible to solve these three problems

with ruler and compass alone.The Greeks dealt with algebraic problems in a geometric way; numbers were represented

as lines, a product of two numbers as an area, etc. In this way it is easy to prove the correctness

of formulas such as a(b + c) = ab + ac, (a + b)2 = a2 + 2ab + b2, a2 – b2 = (a + b) (a – b). Also, one

may easily find the unknown x in a : b = c : x, which is equivalent to ax = bc (finding the fourth

proportional), and in x2 = ab, which allows the construction of square roots.

Plato adopted from Empedocles the view that the material world is formed from the four

elements earth, water, air and fire. He also knew that there are just five regular geometrical

solids, that is, three-dimensional figures the sides of which are formed by a number of equal

regular polygons. These solids have 4, 6, 8, 12 and 20 sides respectively. Now each of the

elements is supposed to consist of particles having the form of one of these ‘Platonic solids’, the

12-sided solid being identified with the cosmos as a whole. The elements could transform into

one another; for instance an 8-sided particle could decompose into its 8 sides and the sides could

recombine into two 4-sided particles. This is an example of mathematization of nature, in

accordance with the program of the Pythagoreans (see Lindberg pp. 40-41).The Earth, according to Plato, is a sphere, which remains stationary in the center of the

universe. The Moon, Sun, planets and fixed stars revolve around it, all taking part in a daily

motion parallel to the equator. In addition, Moon, Sun and planets have their own motion in

concentric circles in the plane of the ecliptic (zodiac), which is at a certain angle with the plane

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of the equator. Each of them moves with its own speed, but such that Mercury and Venus always

remain in the neighbourhood of the Sun. These speeds are not uniform, that is, these celestial

bodies sometimes move faster, sometimes slower, while the planets also have a retrograde

motion as a part of their orbit. The goal of astronomy, according to Plato, is to find a

mathematical description of these motions in terms of uniform, circular motions, in such a way

that it explains the irregular apparent motions.

Eudoxus, a pupil of Plato, attempted to give a geometrical model that would account for

the apparent motions of the celestial bodies, according to Plato’s prescription. Each of the

celestial bodies was supposed to be fixed on the equator of a sphere rotating around the Earth

with constant speed. However, one sphere for each of these bodies is not enough to explain the

irregularities in their motions. Eudoxus found that the retrograde motion of the planets may be

explained by assuming that the axis of the sphere on which the planet is fixed is not stationary;

its poles are supposed to be fixed on another sphere, with rotates with the same speed in oppositedirection around an axis that makes a certain angle with the axis of the first one. The motion

resulting motion has the form of the figure 8 and was called ‘hippopede’. Two more spheres

were needed for the daily motion and the motion along the ecliptic. The system of Eudoxus

contained a total number of 27 homocentric spheres. It explained the observed data rather well

for Saturn, Jupiter and Mercury, less well for Venus and not at all for Mars. The system was later

extended (Aristotle needed 55 spheres), but eventually abandoned, since certain phenomena

could never be explained within this model, especially the variable distances of the Sun, Moon

and planets. (How did they observe that these distances were variable?).

Aristotle (d. 322 B.C) was a pupil of Plato, but his philosophy is in many respects opposed to

that of Plato. He founded his own school, the Lyceum, which continued to exist for more than

two centuries. Aristotle denied the real existence of Plato’s Ideas; for him, in order to investigate

the real world one has to start with the individual sensible objects, which he called substances.

Then he distinguished between the properties of a sensible object and that which has these

properties (the subject of these properties). These two aspects he called ‘form’ and ‘matter’ andeach substance is thus ‘composed of’ form and matter.

Knowledge begins with sense experience; then the forms are abstracted from the matter

and with the help of memory this leads to knowledge of universals.

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Change is explained by means of the concepts of form and matter: if something changes,

then the matter remains, but the form is replaced by another. In order to explain why a certain

change occurs, Aristotle claims that in every change four causes, or explanatory factors, are

involved: the material cause, the formal cause, the efficient cause and the final cause. The latter

plays an important part, not only in artifacts, but also in natural processes: “Everything in nature

has a purpose” (teleology) (see Lindberg, pp. 48-54).

The universe is eternal, that is, it has always existed and it will continue to exist forever;

it does not have a beginning, nor an end in time. It is finite in size and has the form of a sphere,

with the stationary Earth in its center. The stars, planets, Sun and Moon move on homocentric

rotating spheres, according to the model of Eudoxus, as we have seen above. There is an

important distinction between the space below the sphere of the Moon and the space above it.

The space above the Moon is the heavenly region, where everything exists eternally: nothing

perishes and nothing comes into existence; the only change is the eternal rotation of the heavenly bodies. This celestial space, including these bodies, does not consist of the well known four

elements of Empedocles, but of a special fifth element, called aether. The space below the Moon

is the terrestrial region. This space is occupied by the four elements earth, water, air and fire,

arranged in concentric spheres around the center of the universe; this is their natural

arrangement. It is important to note that in this arrangement of the heavenly and earthly regions

the whole space is filled with matter. There are no spaces that are empty: vacuum is impossible.

In the terrestrial region everything is always subject to change. For instance, if water is

heated it evaporates and becomes air, which moves upward, that is, away from the center of the

universe. If air is cooled it condenses and becomes water, which moves downward, that is,

towards the center of the universe. These elements by their own nature move to the place where

they ‘belong’ in their natural arrangement. Thus their motion is rectilinear (up or down). This is

also the explanation of the fall of a stone: if a stone (a piece of ‘earth’) is placed somewhere in

the air, it moves by its own nature to the place where it belongs, namely the sphere of the earth,

which is its ‘natural’ place.

Each of the four elements is in fact matter with a combination of two of the four properties or qualities dry, wet, cold and hot. Earth is cold and dry, water is cold and wet, air is

hot and wet, fire is hot and dry. If one element changes into another it means that one of its

qualities changes into its contrary: if the cold in water is replaced by the hot, it becomes air, etc.

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For the rest, they were opposed to each other. The Epicureans were atomists: the universe

consists of discrete, passive atoms moving in a void. Everything happens by collision and

separation of these atoms. By explaining all phenomena in his mechanistic way and not allowing

anything supernatural to intervene in this world, Epicurus thought to eliminate fear for the

unknown and the supernatural, and thus to achieve happiness.

According to the Stoa, there is no void within the universe; it is competely filled with

matter, which is infinitely divisible, that is, any tiny piece of matter can always be further

divided. This matter is acted upon by some active principle that organizes it into separate objects

and gives to these objects their characterizing properties. This principle is called pneuma; it is

itself also material, but its matter is more subtle than the matter of objects; it penetrates

everything. Each object has its own pneuma; in human beings it is called soul. Also the world as

a whole has a soul. This world soul has divine properties: it makes the world rational, purposeful

and deterministic.

The mathematical knowledge of the Greeks was collected and presented as an axiomatic

deductive system by Euclid (Alexandria, around 300 B.C.) in his Elements. It does not cover all

mathematical knowledge of his time, but it may be considered as an introductory textbook. It

deals not only with geometry, but also with algebra and the theory of numbers (that is, integers);

however, these last two subjects are discussed in the language of geometry. The book starts with

definitions, followed by five ‘postulates’ and five ‘common notions’ or axioms. The postulates

and axioms are adopted without further proof (examples: see Lindberg p. 87). The propositions

that make up the content of the work are proved using only the definitions, postulates and

axioms, and previously proved propositions. This is called the deductive method of proof. For a

long time time it remained the standard for scientific demonstrations, and up to now it is at least

a part of scientific method.

Later great mathematicians were Archimedes of Syracuse (around 250 B.C.) and

Apollonius of Perga (around 210 B.C.). Archimedes determined the surface and the volume of a

sphere; he also dealt with parabolas, ellipses and the solid figures that arise when they rotatearound their principal axis.

Archimedes is also famous as a scholar of physics. Problems of statics were treated in his

On the Equilibrium of Planes. He developed the concept of the center of gravity, and discusses

the condition for equilibrium of bodies that are suspended at certain distances from a fixed point.

15



He determined the center of gravity of certain plane figures, such as rectangle and triangle, and

he proves the law of the lever (see Lindberg pp. 109-110). In his work On Floating Bodies he

considers bodies placed in a fluid and the upward force they experience. He solves many

problems about the equilibrium of floating bodies.

The story of Archimedes’ determination of the quantities of gold and silver in a crown is

legendary. The procedure was to weigh the crown in air, and then in water, and noting the loss of

weight V. If one then notes the losses of weight V1 and V2 of quantities of pure gold and silver

equal in weight to the crown, the proportion (in weight) of gold to silver will be (V2-V) / (V- V1).

(Hint: write down the weight of the crown in water as the sum of the weights in water of the gold

and silver parts in it).

Apollonius’ work Conics is an extensive treatment of the conic sections ellipse,

hyperbola and parabola.

The great astronomers of Hellenistic times were Hipparchus (2nd century B.C.) and Ptolemy

(Alexandria, around 150 A.D.). The latter conceived a mathematical description of the motions

of the celestial bodies that fitted the observations so well that his model survived until the

beginning of modern science in the 16th century. It is known as the Ptolemaic model and Ptolemy

presented it in his main work Mathematical System. After it was translated into Arabic and then

into Latin it became known as the Almagest , an Arabization of the Greek megistē ( = very big,

namely treatise). Ptolemy used many observational data from Hipparchus.

The model used eccenters and epicycles. As we saw above, the model of homocentric

spheres cannot explain the variation in distance of the Sun, Moon and planets to the Earth. If we

suppose that the Sun, for instance, moves along a circle around the Earth, but such that the Earth

is not in the center of that circle, then indeed the distance of the Sun to the Earth will be variable.

Also, if the motion of the Sun along that circle is uniform in relation to the center of that circle, it

will not be uniform in relation to the Earth, and that is exactly what had been concluded from the

variable lengths of the seasons. Therefore, in the model of Ptolemy the Sun moves uniformly

along a circle, whereas the Earth is located at a certain distance from the center of that circle.Such a circle is called eccenter.

Also the Moon has a variable distance to the Earth, and it has a variable speed while it

travels along its orbit. This orbit is not exactly the ecliptic, but it is inclined to it under an angle

of 5º. In order to explain these features the Ptolemaic model assumes that there is a circle with

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the Earth as its center, at an angle 5º with the ecliptic. This circle is called deferent. The center of

another (smaller) circle moves along this circle in a uniform motion, in the direction of the signs

of the zodiac, i. e. in the same direction as the Sun’s motion along the ecliptic. This smaller circle

is called epicycle. The Moon moves along this epicycle in a direction contrary to that of the signs

of the zodiac.

For the planets the model of Ptolemy combines the eccenter and the epicycle. The center

of the epicycle C moves along an eccentric circle (that is, such that the Earth is at a certain

distance from its center) in direct motion, that is, in the direction of the signs of the zodiac. This

eccentric circle is the deferent, with center D. The planet moves uniformly along the epicycle,

also in direct motion. It is clear that if the speed of the planet on the epicycle is larger than the

speed of C along the deferent, then in a part of the planet’s orbit its motion is retrograde. In order

to get agreement with the observed data Ptolemy took the motion of C along the deferent to be

uniform not around its center D, but uniform as seen from another point Q, which was called theequant point. If E is the position of the Earth, then Q is on the line ED, such that ED = DQ.

The Greeks also studied questions such as ‘what is light?’, ‘how does vision come about?’ These

questions are studied in the science of optics.

The atomist Democritus assumed that light consists of particles emitted from the visible

object and traveling to our eye with finite velocity. These particles form a shape similar to that of

the object and when they enter the eye they cause vision, since the eye ‘feels’ the shape.

According to Aristotle, light is not something material that moves in space from the

object to the eye or vice versa, but it is the transparent condition of the medium (air, water…)

between the eye and the visible object when a light source (the sun, a fire) is present. The colour

that is present at the surface of a visible object changes the condition of the medium and this

change is instantaneously passed on to the eye.

Euclid and Ptolemy assume that rays are emitted from the eye and reach the visible

object. In this way the eye makes contact with the object and is able to perceive it. Such rays that

are emitted from the eye are called visual rays, to distinguish them from light rays, or luminousrays, which are the rays that are emitted from a light source or an illuminated object.

We see that two contrasting theories existed about light and vision: one assuming that

something is emitted from the object and then arrives in our eye, where it produces vision, the

17



other assuming that something is emitted from our eye and then reaches the visible object. These

theories are called intromission and extramission theories, respectively.

Both Euclid and Ptolemy wrote a book called Optics. Ptolemy studied experimentally the

course of light when it was reflected from a mirror and he established the well known law of

reflection. He also studied refraction, that is, what happens when light passes from one

transparent medium to another, for instance, from air into water. Then the light will be bent

(‘refracted’) into another direction. Ptolemy experimentally established a relation between the

angles of incidence and refraction in the form of tables. He did not find the mathematical ‘law of

refraction’ that was later to be found by Snellius (!7th century).

With early Greek medicine the name of Hippocrates of Cos (5th - 4th century B.C.) is associated.

The so-called Hippocratic works are probably the work of various authors which were later

collected and attributed to Hippocrates. According to Hippocratic medicine, the basicconstituents of the human body are four humors (fluids) : blood, phlegm, yellow bile and black

bile. When these humors are in balance, the body is healthy. Disease is a state of imbalance of

these humors. The cure consists in restoring the balance.

Knowledge of anatomy and physiology developed in Alexandria in the 3rd century B.C.,

where one started to practice dissection of the body.

The culmination of Greek medicine is the work of Galen (2nd century A.D., born in

Pergamum, studied in Alexandria and settled in Rome). He distinguishes three physiological

systems: (1) The brain and the nerves; they contain psychic pneuma, which is made from arterial

blood that is refined in the brain; this pneuma is sent through the nerves to all parts of the body

and is responsible for sensation and motion; (2) The heart and the arteries, which convey arterial

blood and vital pneuma (from the lungs) to all parts of the body, giving life to the tissues and

organs of the body. Arterial blood is veinous blood that has passed from the right part of the

heart to the left part through the interventricular septum (the dividing wall between the left and

right parts of the heart), and has become heated and vitalized by the innate heat of the heart;

(3) The liver and the veins, which nourish the body with veinous blood, which is made by theliver from the food in the stomach. The blood ebbs and flows through the veins, thus distributing

nourishment to all parts of the body, among which the right part of the heart.

Galen’s work was later translated into Arabic and it was an important influence on Arabic

and medieval Western medicine.

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The Roman Empire and the Early Middle Ages

Ptolemy and Galen lived in the time when the Roman empire controlled the entire area around

the Mediterranean Sea. The city of Rome is known to exist since the 7th century B.C. In later

centuries it developed into a flourishing republic; first, it controlled the whole of Italy, then, in

the time of the emperors (from around 30 B.C.), it extended around the whole Mediterranean

Sea. Although the language of the Romans was Latin, the educated classes adopted the culture

from the Greeks. They learnt the language and studied the Greek achievements in science and

philosophy, but only ‘in moderation’. They did not significantly contribute to new developments;the works on science from Roman times were mainly popularizations and encyclopedic reviews.

Varro (1st century B.C.) wrote an encyclopedic work covering nine disciplines: grammar,

rhetoric, logic, arithmetic, geometry, astronomy, music, medicine and architecture. With the

omission of the last two these dicsiplines became known as the ‘liberal arts’, divided into the

trivium (the first three) and quadrivium (the next four). These became the curriculum for the

medieval schools in the West. They were called ‘liberal’, because they were supposed to form

the general knowledge needed by every ‘free man’, that is, member of the upper class who has

free time since he does not have to work.

After around 250 A.D. intellectual activity in the Roman empire began to diminish due to

worsening economical and political conditions. Also, after the death of the Roman emperor

Constantine (337), the empire was disputed between his sons. From 364 on it was divided into a

Western part and an Eastern part, the latter with Constantinople as its capital. The Eastern part

became the Byzantine empire, and Greek remained the current language there. Contact between

the Western and Eastern part became less. Due to these factors the study and interest in Greek

science and philosophy declined in the Western Empire. Still, some Greek works were translatedinto Latin, such as Euclid’s Elements and some logical works of Aristotle. The translator was

Boethius (d. 524), who lived in the time that Rome had been conquered by the Ostrogoths, a

Germanic tribe.

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Christianity had become a tolerated religion in the Roman empire; in the 4th century it

became the state religion. One may ask whether the dominance of Christianity was helpful for

the development of science and natural philosophy, or rather an obstacle. It appeared that logic,

such as it arose in Greek philosophy, was an essential tool for the development of the Christian

doctrine and the defense against opponents. Also, the philosophy of Plato was attractive for

Christians (why?). The attitude of most Christians intellectuals towards (natural) philosophy was

that they were interested to study nature because knowledge about nature was useful to explain

the Bible and to develop the doctrines of faith: (natural) philosophy ‘in the service of’ theology.

Since the 4th century monasteries started to spread in the Christian world. They were

meant as a retreat from the world, so that one could live a life of devotion, worship and

contemplation. Education was part of this, and libraries and scriptoria (places where books were

copied) became attached to the monasteries. The ancient pagan literature, which was often

judged dangerous, or at least not relevant for Christians, had only a marginal place in mostmonasteries. However, there were exceptions. In certain monasteries ancient pagan authors were

studied and translated into Latin. In this way some of the ancient science or natural philosophy

was preserved and transmitted in a time in which the further development of these disciplines

had virtually come to a halt in Western Europe. Two scholars are representative for this

condition of the sciences in the early Middle Ages: Isodore of Seville (d. 636), who became

archbishop of Seville (Spain) and Bede (d. 735) (known as the Venerable Bede), who spent his

life in a monastery in northern England. They wrote encyclopedic surveys of the knowledge of

their time.

A similar situation existed in the Byzantine Empire: there was no significant new

development in natural philosophy. Scholarly activity consisted in explaining and commenting

upon the classical authors. However, sometimes these commentaries were quite critical and

proposed new ideas. The current philosophical school was Neoplatonism (a modified form of the

philosophy of Plato), but also commentaries on Aristotle’s works were written. One of the

commentators was John Philoponus (6th century, Alexandria). He criticized various issues of

Aristotle’s natural philosophy, such as the eternity of the world, the different structure of theheavenly and terrestrial regions, and Aristotle’s dynamics.

The Arabic-Islamic world

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After the decline of the Abbasid empire several regional dynasties arised. The Fātimid

khalif al-Hakīm (Egypt, 11th century) founded the dār al-`ilm (house of knowledge); he

patronized the astronomer Ibn Yūnus and invited Ibn al-Haytham to come to Egypt. Other

famous scholars of the 11th century were al-Bīrūnī and `Umar al-Khayyām.

In 12th century Spain, under the Almohad dynasty, active scholars were Ibn Rushd

(philosophy and medicine), Ibn Zuhr (medicine) and al-Bītrūjī (astronomy).

In the 13th century, under the rule of the Mongols, an observatory was founded in

Marāgha (now Azerbeidzjan). Here worked Nasīr al-Dīn al-Tūsī and other astronomers who

made significant contributions in modifying the Ptolemaic model.

In the 14th century Ulugh Beg founded an observatory in Samarkand. The mathematician

al-Kāshī worked there.

Factors that contributed to the spread of learning in the Arabic-Islamic world were:(1) the use of paper, an invention taken from the Chinese in the middle of the 8th century. It

meant that manuscripts were easily available and books such as the Almagest could be easily

bought.

(2) libraries, which were more or less public, and other institutions of learning, such as

observatories and madrasahs.

Observatories included a library and astronomical instruments. Madrasahs were

established by Nizām al-Mulk in the second half of the 11th century under the dynasty of the

Seljuks in Iraq and Persia. They were institutes of Islamic law, and the “ancient sciences” were

not part of the curriculum. However, the scholars of Islamic law ( fuqahā’ , sg. faqīh) were

interested in arithmetics and algebra as a means to calculate the legal portions according to the

laws of inheritance, and in astronomy in order to determine the direction of the qibla and the

times of the prayers. Therefore astronomers became attached to madrasahs and mosques as

timekeepers (muwaqqit s), such as Ibn al-Shātir (14th century Damascus).

This sketch of the origin, rise and flourishing of Islamic science pertains to what was called the“foreign sciences” or “ancient sciences”, that is, the sciences such as they originated and

developed in Greece. This included what was known as falsafa, a philosophy based on

Aristotle’s system, mixed with Neo-Platonic ideas.

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However the word ‘science’ (Arabic: `ilm, pl. `ulūm) in the medieval Islamic world often

also included the so-called “Arabic sciences” or “religious sciences”, such as law or

jurisprudence ( fiqh), theology (kalām), grammar, history of the Arabs. These sciences were

included in treatises on the classification of the sciences. They have an earlier origin than the

beginning of the “foreign sciences” in Islamic civilization and are related with the rise of Islam

as a religion.

If one takes science in the sense that includes the “religious sciences”, then one might say

that the first scientific activity in Islam was the collection of the Qur’ān. In the time of the

Uthmān, the third khalif, a commission produced four copies of the Qur’ān (± 650), intended for

each of the cities Kufa, Basra, Damascus and Mekka. These copies were not unified in spelling

and pronunciation. Therefore, linguists and grammarians engaged to establish the “correct

version”. Finally seven “readings” were accepted.

Then, the Qur’ān needed to be explained. The model for the language in the Qur’ān was pre-Islamic poetry. Thus, certain explanations of the Qur’ān were done by philological methods

using this poetry, and lexicons were composed for this poetry. From this grammar and

lexicography further developed, also independent from the study of the Qur’ān.

The sources for Islamic law were Qur’ān and hadīth (“tradition”: sayings and deeds of

Muhammad and his companions). For many practical cases no rule was available in these

sources. In such cases the jurists had to come to a judgment themselves and follow their own

opinion. To avoid getting arbitrary decisions one originated the principle of consensus, or one

used the procedure of arguing by analogy, that is, one compared a case with a similar, earlier

case for which there was already a judgment. This is how one felt the need for logical reasoning

and it is one of the reasons that Greek (Aristotelian) logic was introduced in the Islamic world.

The theological school of the Mu`tazila (starting in the 8th century) tried to formulate the

dogmas of Islam, not relying on what tradition said, but using rational argumentation, and they

aimed at a rational view of the world. Again, Greek logic was a tool they used in their theology.

Transmission of ancient science into the Arabic-Islamic world

After Alexander’s death his empire was divided among his generals; eventually Persia and part

of Mesopotamia was ruled by the Parthians from the last half of the 3rd century B.C. until 224

A.D., when the Sassanids took over. As we saw above, in the meantime the Roman empire had

23



developed in Italy and expanded its territories around the whole of the Mediterranean Sea,

including Egypt, Syria, Greece and Asia Minor. At the eastern border there was always a conflict

between the Romans and first the Parthians, then the Sassanians.

We have also seen that in the 4th century the Roman Empire became divided into a

Western part (Latin-speaking, with Rome as its capital) and an Eastern part (the Byzantine

Empire, Greek-speaking, with Constantinople as its capital).

Christianity had become the state religion in the 4th century. The church became

organized, with Rome, Antioch, Alexandria and Constantinople as its ‘capitals’. Theological

treatises were written, using Greek language.

In Nisibis (S.E. Turkey) a theological school was founded for the Christians in the East,

whose language was Syriac. This school was later transferred to Edessa (S. Turkey). It became a

center for theological study. Greek theological works were translated into Syriac; also some

logical works of Aristotle were translated, for logic was used in theological argumentation.In the 5th century a conflict arose within the Church about the nature of Christ (human or

divine?). Nestorius, patriarch of Constantinople, defended the idea that Christ was more human

than divine. A council was held where he was condemned. Many of the Syriac Christian did not

agree and separated themselves from the ‘orthodox’ church. They became known as Nestorians,

with Edessa as their center. The Nestorian school in Edesssa was eventually not tolerated and

closed by the Byzantine emperor. The Nestorians then moved to Nisibis, within the Persian

empire. They gained influence on Persian cultural life, and introduced Greek learning into Persia.

Apart from the logical works of Aristotle now also medical works and mathematical and

astronomical treatises were translated from Greek into Syriac. When Persia was conquered by

the Arabs and later the `Abbasid reign was established in Baghdad, many of those who translated

Greek works into Arabic were Nestorians (Hunayn ibn Ishāq). This explains that often the

translation from Greek into Arabic was made via Syriac as an intermediate language. The

practitioners of medicine in Baghdad were mostly Nestorians, such as the Bukhtishū` family,

who were court physicians to the khalifs.

After the rise of Islam, starting from the Arabian peninsula in the 7th century, the Arabsconquered Egypt, Syria and Mesopotamia on the Byzantine empire and Persia on the

Sassanids..The first khalifate was that of the Umayyads, with Damascus as its capital. In that

time there was a free discussion between Muslims and Christians; Muslims were introduced to

Christian theology and Greek philosophy. It was in Basra and Kufa (now in Iraq) that the

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nowadays. There are symbols for the numbers 1 until 9 and for zero. These symbols were

probably derived from the symbols used in India. The Arabic symbols such as used in medieval

Spain further developed into the western numerals.

(3) Arithmetic ‘of the astronomers’, or ‘of degrees and minutes’. This system is the

sexagesimal system of the Babylonians. Numbers from one until 59 are written by means of

letters of the alfabet in a non-positional decimal system. Higher numbers and fractions were

written in a positional sexagesimal system. The positions were named as degrees (600), minutes

(60-1), seconds (60-2), thirds (60-3), etc.

An arithmetical system that used decimal fractions like we do was described by al-Kāshī

in his work The Key to Arithmetic (15th century, Samarkand). He remarked that just as fractions

could be expressed in a sexagesimal system, as above, they could also be expressed, in a

completely analogous way, in a decimal system, the positions denoting powers of 10 instead of

60.

Algebra

The first author in the Arabic world who wrote a work on algebra was al-Khwārizmī. The title of

the work was Kitāb al-mukhtasar fī l-jabr wa-l-muqābala (Compendium on Restoring and

Balancing); from this title the word ‘algebra’ is derived. He describes how to solve linear and

quadratic equations. He does not use algebraic symbols, but explains everything in words.

Negative numbers are unknown, so only positive terms are recognized, and he finds only the

positive solutions. The term jabr (restoring) refers to the elimination of subtracted terms by

moving them to the other side of the equation, whereas muqābala (balancing) refers to reducing

similar terms on both sides of the equation.

Example (in modern notation): 45 + 3x2 + 2x = 84 – 8x + 2x2

Jabr : 45 + 3x2 + 2x + 8x = 84 + 2x2

Muqābala: x2 + 10x = 39

Now the solution is obtained by a geometrical method, similar to the methods used by Euclid: xis supposed to be the unknown side of a square, and the procedure is that of ‘completing the

square’. We take one half of 10, which is 5. We add two rectangles with sides 5 and x on two

adjoining sides of the square and ‘complete’ a larger square by adding a square with sides equal

to 5. Then the equation says that the area of the original square with side x plus that of the two

26



rectangles equals 39. Thus, the area of the larger, ‘completed’ square equals 39 + 25 = 64.

Therefore the side of the larger square equals 8, which is x + 5. Thus, x = 3.

Further developments in algebra were made by `Umar al-Khayyām, who solved third

grade equations by intersecting two of the conic sections (ellips, parabola or hyperbola), and a

fourth grade equation by intersecting a circle and a hyperbola.

Geometry and Trigonometry

Geometrical problems from Euclid, Archimedes and Apollonius were further discussed and

developed by Arabic scholars. A new problem was discussed by Ibn al-Haytham, whose most

famous work is about optics. The problem, known as the problem of Alhazen, was to draw lines

from two points in the plane of a circle meeting at a point on the circumference and making

equal angles with the normal at that point.Trigonometry arose in connection with astronomy. The sine-function was not known to

the Greeks; Ptolemy used a table of chords. The Arabs use the sine. This concept originated in

India. The Sanskrit word jīva (chord) was adopted in Arabic and became jaib. The Arabic word

jaib, however, means ‘breast’ or ‘bosom’, and the Latin translators rendered this as sinus. The

astronomer al-Battānī (9th-10th century) used sine, as well as cotangent, called zill (shadow), since

the shadow of a vertical stick is calculated with the cotangent of the angle under which the rays

of the sun fall on the earth.

Spherical trigonometry, needed for astronomical caclulations, was further developed in

Islamic times.

Al-Kāshī gave methods to compute trigonometric tables. The sine-table of Ulugh Beg

remained the most accurate for a whole century.

Astronomy

Arabic translations of Ptolemy’s Almagest were made under al-Ma’mūn (9th century). Earlier translations from Indian and Persian astronomical works had been made, but eventually the

Ptolemaic model became the accepted one among Arabic astronomers.

There were two main types of astronomical texts in the Arabic world: hay`a-texts and zīj-

texts. The former discuss the structure of the universe and give models to explain the motions of

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the celestial bodies, following the example of the Almagest . They often criticized Ptolemy and

proposed alternative models that solved certain alleged deficiencies in the Ptolemaic model.

Zīj-texts are in fact astronomical tables; they are similar to the tables given in the

Almagest and other Greek works. They have a more practical use: they give the positions of the

celestial bodies at any given time, but also include data concerning calenders, tables of

trigonometric functions, tables of eclipses and of visibility (of the Moon and planets), tables

giving the position of the fixed stars, etc.

The data in these tables came from observations that were made at various places and

times in the Islamic world. The goal of these observations was to check and improve the

parameters of the Ptolemaic model. Occasionally the new observations led to a proposal of a

change in the Ptolemaic model itself.

This model was also criticized for theoretical reasons. One thought that certain aspects of

Ptolemy’s model were inconsistent with the principles of astronomy laid down before. For instance, Ibn al-Haytham wrote the work Doubts about Ptolemy, in which he showed that some

parts of Ptolemy’s model were not in agreement with the principle that the motions of the

celestial bodies must be explained by means of uniform circular motions.

Starting from this criticism new models were proposed that were different from the

model of Ptolemy. Among those who devised non-Ptolemaic models were Nasīr al-Dīn al-Tūsī,

who was attached to the Marāgha observatory, and Ibn al-Shātir, who was timekeeper attached to

the mosque in Damascus.

Also in Spain astronomy was flourishing. In the 11th century a group of astronomers,

among whom al-Zarqālī, formed a kind of school in Toledo, where they did observations. The

results were laid down in the ‘Toledan Tables’; this work was translated into Latin and became

the main influence on astronomy in Europe, until they were superseded by the ‘Alfonsine tables’

about two centuries later.

In the 12th century a revival of Aristotelianism occurred in Spain, with Ibn Bājja

(Avempace), Ibn Rushd (Averroës) and Ibn Maimūn (Maimonides). Under their influence the

astronomer al-Bitrūjī constructed a system of homocentric spheres moving around the Earth astheir center, completely disregarding the model of Ptolemy. The model could not account for all

the observed details of planetary motion which could be explained by Ptolemy’s model.

Therefore after some time it was not accepted any more and the Ptolemaic model became

dominating again.

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Optics

A field in which remarkable results were obtained during the flourishing of Arabic-Islamic

science was optics, largely due to the work of Ibn al-Haytham (Alhazen). Optics in this time was

mainly a theory of light and vision, trying to answer the questions ‘what is light?’ and ‘how does

vision come about?’ Besides this, geometrical optics was also studied: light rays were considered

as straight lines, and the course of these rays was studied, also during the process of reflection

and refraction. Greek works of Euclid, Archimedes and Ptolemy dealt with this subject; they

were translated into Arabic, and Arabic scholars continued to discuss the subject. For instance,

Ibn Sahl (10th century) in his work On Burning Instruments, treats parabolic and ellipsoidal

mirrors, and convex lenses. Apparently he knows the correct law for refraction, although it wasonly formulated as a law much later in the 17th century by Snellius.

Also Ibn al-Haytham wrote about burning mirrors (parabolic and spherical) and the

burning sphere; he did experiments to establish the rules of reflection and refraction occurring at

these objects.

As for the questions ‘what is light?’ and ‘how does vision come about?’ we have seen

that two kinds of theories were in use in ancient times: extramission theories and intromission

theories. One of the first scholars in the Islamic world writing on optics was the philosopher al-

Kindī (9th century). He adheres to the extramission theory and gives several arguments against

the intromission theory.

Ibn Sīnā (10th – 11th century) adopts the Aristotelian theory of light, which is a kind of

intromission theory. He gives several arguments against the extramission theory, for instance:

assuming that visual rays are material, and fill the whole space between the eye and the visible

object, then it is a huge amount of matter that is supposed to come from the eye, especially when

the object is far, such as the moon. Moreover, this is supposed to happen every time when the

eyes are opened. Also, if perception occurred at the place where the visual rays reach the object,then an object would always be perceived with the same size, irrespective of the distance.

Ibn al-Haytham wrote an extensive book under the title Optics ( Kitāb al-manāzir ), in which he

integrated the geometrical approach and the physical intromission theory. One problem with the

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intromission theory was how a ‘form’ of the visible object, the size of which may be large

compared to that of the eye, can enter in our eye, and what seems even more impossible, enter

the eye of many observers at the same time. Apparently it was assumed that those ‘forms’ were a

kind of images of the whole object, forming a coherent unity.

Ibn al-Haytham assumes that light is emitted from all points (or small parts) of a

luminous body (either self-luminous or illuminated) in straight lines into all directions. He

verifies this principle by a number of experiments with light passing through holes, with dark

chambers and shadows. He also shows by experiments that reflected and refracted light proceed

along straight lines from the point of reflection or refraction in one particular direction. Then he

examines the structure of the eye. The essential part of the eye, where vision occurs, is the

crystalline humor (lens). If all rays from all points of the object would be effective in the eye, we

would never get a coherent image of the object. Therefore it is supposed that only the rays that

fall perpendicular on the crystalline humor are effective; they are further transported through theeye to the optical nerve and then arrive in the brain. By means of these perpendicular rays there

is a one-to-one correpondence between the points of the object and the points on the surface of

the crystalline humour. The rays that are not perpendicular are refracted and weakened, and they

are considered to be not effective.

Kamāl al-Dīn al-Fārisī continued the experiments on reflection and refraction, especially

those in a transparent sphere. He applied this to the reflection and refraction of sunlight in a

raindrop and thus arrived at an understanding of the rainbow.

Structure of Matter, Chemistry, Alchemy

Ancient chemistry and alchemy

The theoretical background for chemistry and alchemy in ancient and medieval times was the

theory that all things are made up from the four elements earth, water, air and fire. We find this

theory first expressed by Empedocles (5th century B.C.). It was adopted by most philosophersand scientists in this period. An alternative to this theory was presented by the atomists

Leucippus and Democritus (5th century B.C.). According to them, everything is composed of

indivisible particles (atoms) which move in a void. The atoms are eternal and unchangeable, they

differ in size and form. They combine and separate without plan or purpose, and in this way

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account for the various substances in the world and their changes. Most philosophers rejected

this theory, since it supposed the existence of the void.

The four elements can change into one another (water becomes air, etc.). How this can

occur was explained by Aristotle as follows: he assumed that there was one fundamental matter,

which may assume certain qualities. There are four basic qualities: hot / cold, dry / wet. Earth is

matter that is dry and cold, water is wet and cold, air is wet and hot, fire is dry and hot. When

one of the qualities is replaced by another, the element changes into another. For instance, when

water is heated, the cold is replaced by the hot, and so the water becomes air. This theory

explains why substances can change into each other (chemical change).

From archeological findings it appears that early civilizations such as those in Egypt,

Babylonia and Persia knew certain chemical processes, such as those required to make pottery,

glass, and to produce metals from minerals. First, copper was produced from certain minerals,

then followed the production of bronze ( = copper / tin alloy), lead, silver, tin and iron. Gold wasfound in pure state, like electrum ( = a natural alloy of gold and silver).

Chemical substances are mentioned in written sources, starting from ancient Egyptian

and Babylonian medical texts. Later texts from Greek and Roman times show that an increasing

number of minerals was discovered, but not all substances were correctly differentiated. The

number of metals was considered to be seven; they were associated with the planets. One could

order them according to their value or degree of perfection. The most perfect metal was gold;

then comes silver; they were associated with the Sun and the Moon, respectively. Lead was the

least perfect metal, associated with Saturn. The other metals were copper (Venus), iron (Mars),

tin (Jupiter) and mercury (Mercury).

Chemical substances arise from a combination of the four elements. Elements may form a

compound, such that the compound consists of small particles of each element that keep their

own nature and identity. Elements may also be mixed into a homogeneous compound, such that

their original natures disappear and the compound gets a nature of its own. Aristotle called the

latter kind of compound a ‘mixture’; it corresponds with what we would call ‘chemical

combination’. The nature and properties of the ‘mixture’ depends on the proportion of theelements in the mixture.

In view of this theoretical (Aristotelian, philosophical) background it is not surprising

that people thought that any chemical substance may change into any other. The fundamental

matter is the same for everything. Elements may change into one another by changing the basic

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qualities, and mixtures of elements ( = chemical substances) may change by changing the

proportions of the elements in the mixture. This was the basic idea behind alchemy.

The goal of alchemy was to transform base metals, such as lead, into precious metals,

such as gold. Some Greek texts, the oldest ones dating from the first century A.D., should be

considered as precursors of truly alchemical texts. These older texts contain recipes for gilding,

silvering and colouring metals purple. They did not claim that metals were really transformed

into gold, silver, etc. What was done was only an imitation (a surface treatment or colouring).

The first truly alchemical text was written by Zosimus (± 300). Only fragments of the text

have been preserved; it was translated into Arabic. Typical features of alchemy are the role of

spirits that cause changes in chemical substances and the role of xērion ( = dry stuff, Arabic: al-

iksīr , which later became ‘elixir’). Spirits are substances that easily evaporate or sublimate. The

‘elixer’ is a kind of ferment or catalyst that is necessary to bring about the transmutation of

metals. The most important process was distillation of substances such as sulphur, mercury andarsenic. They were the spirits that worked upon the base black metal (lead, iron, etc.) and caused

it to change colour: it became white, yellow and purple. Purple colouring was the sign that the

elixir was obtained. The elixir could transform any quantity of matter into gold.

Scientific achievements of ancient alchemy were: development of distillation apparatus,

mastering the processes of distillation, sublimation, crystallization; discovery of new substances.

Arabic alchemy

The Arabic word al-kīmyā may be derived from the Egyptian kemi (black), which might refer to

Egypt, sometimes called ‘the black land’, or to the black metal from which the alchemical

process begins. It may also be derived from the Greek chumeia = melting (of metals).

The most comprehensive series of books on alchemy in Arabic civilization is ascribed to

Jābir ibn Hayyān who is supposed to have lived in the 8th century. However, one assumes that

these books were actually composed by various scholars one century later. In the medieval West

a series of Latin alchemical works is also ascribed to Jābir (Lat.: Geber). However, they are nottranslations of the Arabic works ascribed to him. They were probably written in the 13th century

in the south of Italy.

As we have seen, the theory underlying alchemy is that the material basis of all

substances is the same and that substances differ by a different proportion of the qualities hot /

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cold and dry / wet. The most perfect proportion of these qualities exists in gold. In nature the

elementary qualities are combined over a long period to produce the various substances. The

alchemist tries to imitate this natural process and produce the same substances in a short time.

One treatise ascribed to Jābir sets forth the theory that the metals are formed in the earth

by a combination of mercury and sulphur (not the ordinary mercury and sulphur, but ‘pure

forms’ of them). Sulphur provides the hot and dry qualities, mercury the cold and wet ones.

When they are mixed in a perfect balance, the result is gold. The other metals result from a

mixture in a less perfect balance. When one is able to restitute the perfect balance and remove all

impurities, then again gold is produced. In this process elixirs play the role of catalyst. It is like

the medicine a doctor gives to the patient to restore the balance of his humours.

Distillation was an important part of the alchemical process and was much used in the

experiments of the alchemists. In that way they discovered new chemical substances, such as sal

ammoniac (NH4Cl).Another important alchemist was Abū Bakr al-Rāzī, who was also a famous physician

and philosopher (9th-10th century). He gave a classification of chemical substances that were

known in his time. They were divided into metals, spirits and mineral bodies. There were seven

metals (see above), but the seventh one was not mercury, but so-called ‘Chinese iron’ (a not

completely identified alloy). There were four spirits: sulphur, mercury, sal ammoniac and arsenic

sulphide; these were easily vaporized by heat. The rest of the substances were minerals. Al-Rāzī

contributed to chemistry by his description of a whole range of (al)chemical procedures, such as

distillation, solution, evaporation, sublimation, crystallization, amalgamation ( = alloy with

mercury), filtration, etc.

Arabic alchemical works were translated into Latin in the 12th century and were studied in

the medieval West. It developed into a mystical-magical worldview; for instance, transformation

of metals was associated with spirtitual transformation of the experimenter, and the elixir would

not only transform base metals into gold, but also give a long or even an eternal life to the

alchemist.

Not everyone believed that the goal of alchemy could be reached. Ibn Sīnā, for instance,denied the possibility of alchemy and he was followed by others such as Ibn Khaldūn (14th

century). Their argument was that what is produced in nature over a long time cannot be imitated

by an artificial process in a short time.

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Technology

There are two main written sources for our knowledge of Arabic technology: The Book of

Ingenious Devices of the Banū Mūsā (9th century), and The Book of Knowledge of Ingenious

Mechanical Devices of al-Jazarī (13th century).

Machines to raise water include shādūf, sāqiya, scoop-wheel and Archimedean screw.

Some of them date from ancient times. Al-Jazarī described several machines to raise water. He

also described water clocks and a fountain.

The Banū Mūsā described devices that were meant to amuse and to be enjoyed, such as a

self-replenishing vessel, a self-feeding, self-trimming oil-lamp. They made use of siphons and

conical valves to control the flow of liquids in their devices.

The Middle Ages

We have seen that in the early Middle Ages (500-1000) in the West there was a stagnation in the

development of natural philosophy and science. Most of the scholarly efforts was focused on

religious issues. Still, some of the ancient philosophy was preserved and transmitted by

translations and encyclopedic surveys. A revival occurred in the 8th century, during the reign of

Charles the Great (Charlemagne). His empire (Carolingian Empire) covered a large part of

Western Europe. He established schools connected with monasteries and cathedrals for better

education of the clergy. Here the seven liberal arts were taught, besides religious matters.

This educational revival produced a few scholars, among whom Gerbert of Aurillac (10th

century; he became Pope Sylvester II). He was educated at the monastery school in Aurillac

(central France), then studied in northern Spain. There he got acquainted with Arabic works on

mathematics and astronomy, translated into Latin. After his stay in Spain he further studied at the

cathedral school in Reims (northern France), and later taught there, especially Aristotelian logic

(which had been translated by Boethius), and probably the mathematics and astronomy he hadlearnt in Spain. He is considered to be the first scholar from the Latin West who came into

contact with the Arabic achievements in science such as they were known in Spain, and who

spread this knowledge further north into Europe.

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After the year 1000 there was more political stability; the economy was growing, and

with it the population grew as well. This led to further urbanization and the establishment of

schools in the city. These schools were not connected with a monastery; they could be connected

with a cathedral or they were public schools, not related to any religious institution. The

programs of these schools could be broader, depending on the demand of those who attended.

Logic, the quadrivial arts, law, medicine and theology were the subjects of the curriculum.

Famous schools became those in Chartres, Paris, Bologna and Oxford. Besides the doctrines of

Christian religion the classical Latin authors were studied, including Aristotelian logic and some

natural philosophy. Theological issues were appraoched by means of human reason

(rationalism): one tried to ‘prove’ religious doctrines (for instance, the existence of God) by

logical and philosophical methods. The use of logic and philosophy for discussing theological

matters was not approved by everyone in the church (conflict between reason and revelation).

As for natural philosophy in the 12th

century, Platonism dominated, since Plato’s ideas,for instance about he creation of the world by a Demiurg (Creator) and the rational order that

was thereby established in the world, could suitably be used for and adapted to the Christian

doctrines. Naturalism was a prominent feature in the natural philosophy of this period, that is,

one sought to explain natural phenomena with natural principles and rules. The creation of the

world was recognized as an act of God, but for the rest divine intervention was restricted as

much as possible. Those who criticized this view said that such a view would restrict the

omnipotence of God and make miracles impossible (see Lindberg pp. 200-201 for this

discussion).

Arabic books were translated into Latin starting from the 11th century, mostly in Spain.

Toledo was the most important center of Arabic learning in Spain. It was conquered by the

Christians in 1085. The most famous translator of the 12th century was Gerard of Cremona. He

came to Toledo and translated numerous works, such as the Almagest , the Elements, the Algebra

of al-Khwārizmī, many books of Aristotle, and medical works of Galen and Ibn Sīnā (Avicenna).

Translations from the Greek into Latin were made in the 12th and 13th centuries. The

Almagest and the Elements were translated in the 12th century; William of Moerberke (13th

century) translated the works of Aristotle and their commentators.

Starting from the 12th-13th century universities as centers of learning would play an

important part in the development of science. They gradually developed from the existing

schools where teachers and students came together and organized themselves as a kind of

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association or guild (universitas = association, corporation). The oldest universities in Western

Europe are Bologna, Paris and Oxford. The university of Paris, for example, had one

undergraduate faculty (liberal arts) and three graduate faculties (law, medicine, theology).

When the works of Aristotle became known in the West, they acquired a central position

in the curriculum of the arts faculty. Besides these, the translated works on medicine,

mathematics, astronomy, optics and other subjects were taught and studied.

The universities were quite independent from external authorities and masters were free

to teach whatever they wanted to teach. However, certain aspects of Aristotelian philosophy

were in conflict with Christian doctrine and at a certain moment this led to interference from the

Church authorities. One point of conflict was the eternity of the world, which is opposed to the

doctrine of creation. Another point was Aristotle’s ‘naturalism’: things in the world behave

according to their own nature and all events form a chain of cause and effect. Although the Prime

Mover is the first cause of motion and change, he does not further intervene in the world. Thisconflicts with the omnipotence and freedom of the Christian God. Also, according to Aristotle,

the individual human soul is the ‘form of the body’. Form cannot exist without matter. Therefore,

if the (material) body dies, the human form (= soul) ceases to exist. This conflicts with the

doctrine of the immortality of the soul.

In spite of such points of conflict, most scholars did not want to discard Aristotelian

natural philosophy, since it dealt with almost every topic of science and philosophy. The problem

was how to deal with the aspects that were in conflict with Christian doctrine. We mention some

scholars who were confronted with this problem.

Robert Grosseteste (d. 1253) was lecturer in Oxford. He was acquainted with much of

Aristotle’s work and wrote commentaries on some of them. His worldview was still influenced

by (Neo-) Platonic ideas.

Roger Bacon (13th century) lectured on Aristotelian natural philosophy in Paris. He

defended the importance of natural philosophy and sciences (mathematics, astronomy, optics,

alchemy, astrology, medicine) that had become available in the West. He stressed their utility

and pointed out that they may be used to prove and defend the doctrines of faith, to persuade thenon-believer, to explain the Bible, to establish the religious calender (astronomy), etc. Thus,

philosophy and science were essential ‘servants’ of theology. There is no real conflict between

faith and science, since philosophy and science are also a gift of God. Any apparent conflict is

the result of mistranslation or misinterpretation.

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Bonaventura (13th century) taught theology in Paris. He also recognized the useful

function of science and philosophy for theology and religion, but he was more conservative: he

rejected those points of Aristotelian philosophy that were opposed to the doctrines of faith.

Albert the Great (13th century) (Albertus Magnus; born in Germany; active in Cologne

and other German cities as member of the Dominican order) wrote commentaries on all books of

Aristotle known to him. They also include the results of his own investigations and thought. He

read many Greek and Arabic authors, such as Plato, Euclid, al-Kindī, Ibn Sīnā (Avicenna), Ibn

Rushd (Averroes), etc. He reported on plant and animal life from his personal observations. He

did not reject Aristotle’s ‘naturalism’, but accomodated it within his Christian worldview. He

acknowledged that God was the cause of everything, but he pointed out that God works through

natural causes. He makes a distinction between natural philosophy and theology, and says that

philosophy alone, without theology, can demonstrate many things about the world. He rejected

Aristotle’s view of the eternity of the world on purely philosophical grounds.Thomas Aquinas (13th century; born in Italy), was Albert’s pupil. He also makes a

distinction between science / natural philosophy and theology. Science uses sense experience and

reason to arrive at truths about the world insofar they can be reached in this way. Religion gives

us truths beyond those reached by science, by means of revelation. Theology provides the more

complete and perfect knowledge, and science / philosophy is still a ‘servant’ to theology.

However, both have their own fields of investigation and their own methods. Sometimes

philosophy and theology consider the same question, such as the existence of God. In such a case

no conflict can arise, since both our reason and revelation are from God.

As for the issue whether the world is created or eternal, he said that we know from

revelation that the world was created; philosophy (reason) on the other hand cannot decide the

matter one way or another. Therefore there is no real conflict.

Thomas’s philosophy is a “Christianized Aristotelianism” and at the same time an

“Aristotelianized Christianity”. It is the official position of the Catholic Church up to now.

The more independent role for natural philosophy in the harmonization of philosophy and

theology such as defended by Albert and Thomas induced some scholars to more radical views.They gave philosophical arguments without paying attention to religious doctrines. They

separated philosophy completely from theology; they claimed, for instance, that philosophy

cannot conclude to divine creation of the world, because that would introduce a supernatural

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principle in a philosophical argument. They accepted the idea of a ‘double truth’: the truth

reached by reason, and the truth from revelation.

This irritated the authorities of the Church, and the result was that such teaching was

condemned by the bishop of Paris, Etienne Tempier, in 1270 and again in 1277. An extensive list

of propositions was condemned, which all dealt with things that would be impossible in

Aristotle’s philosophy, and which consequently could not be done by God and thus would

restrict God’s onmipotence and freedom.

It seemed that theology was again master of philosophy and could determine what natural

philosophers should think and what not. On the other hand, one realized that certain things that

were thought to be impossible by Aristotle, could be possible after all, because with God

everything is possible. This led to a reconsidering, criticizing or even rejection of certain

principles of Aristotelian natural philosophy. For instance, if God could move the universe in a

straight line, then the universe would leave a void at the place from where it moved. Thus, a voidspace is possible, contrary to what Aristotle learnt.

The result of the condemnations was not that Aristotelianism was abandoned. It remained

an essential part of the curriculum in universities and the foundation of medieval world view,

with the exception of those issues that were contrary to faith. On the other hand, one became

more sceptical about the demonstrative power of philosophy if it concerned articles of faith, and

the scope of philosophy became smaller. Also, the omnipotence and free will of God became a

more important issue in considering natural phenomena. The order of cause and effect in nature

is not necessary any more, but dependent on God’s will: fire burns, not because it is the nature of

fire to burn, so that it is necessary that it burns, but because God chose to connect fire with

burning, and He also chose to maintain this connection most of the times. But He can also

choose to suspend this connection on special occasions, such as when Shadrach, Meshach and

Abednego were thrown in the furnace.

As for medieval cosmology, in the 13th century Platonic ideas gave way to Aristotelian ones,

with some additions taken from a literal interpretation of the Bible. The Aristotelian division of the universe between the celestial and terrestrial regions, each characterized by their own

properties, is adopted. Some scholars, under the influence of the condemnation of 1277, assumed

that outside the universe there was a void space; others were content to admit the possibility of a

void space.

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The celestial sphere contained the spheres of the seven planets and the sphere of the fixed

stars. Some scholars assumed two more spheres: a crystalline, transparent heaven, consisting of

water in some form, and an invisible and motionless empyreum, the dwelling place of the angels.

These ninth and tenth spheres were added since the story of the creation in the Bible says that on

the first day God created the heaven and on the second day the ‘firmament’ (the fixed stars), and

that the firmament separates the waters beneath it from the waters above it. These spheres also

got astronomical functions.

The Unmoved Mover of Aristotle was usually identified with the Christian God. He

moved the outer movable sphere. The other spheres were moved by angels or ‘separated

intelligences’ (minds without body). Or it was supposed that they moved due to a kind of motive

force (impetus, see below), imposed on them by God at the creation.

Those who wished to take into account the observed irregularities of the planetary

motions adopted Ptolemy’s system. Each of the planetary spheres was given a certain thickness,so that the eccentrics and epicycles could fit within this thickness.

Below the sphere of the moon followed the spheres of the four elements in their proper

places, with the spherical earth as the center of the whole universe.

The possibility that the Earth would move around its axis in 24 hours has been discussed

since ancient times. Aristotle had shown that the Earth is stationary, and this was adopted by all

medieval scholars, although they were aware that a rotating Earth had the advantage that each

celestial sphere could do without its daily motion; this supposed motion involves tremendous

speeds, especially for the outer spheres. The possibility of a rotating Earth was again discussed in

the Middle Ages, but eventually rejected. Nicole Oresme (14th century) pointed out that by

observation of the heaven one cannot decide whether it is the Earth that is rotating or the

heavens. He refuted all arguments of those who denied the possibility of a rotating Earth. For

instance, if the Earth was rotating, a stone thrown upward would come down at a different place,

since the Earth would have moved under it while it was in the air; this does not happen, and

therefore the Earth is stationary. Oresme argued that if the Earth rotates, the stone will also

partake in the rotational motion while it is the air, and therefore it will come down at the same place. In the end he adhered to the traditional opinion of a stationary Earth on the basis of a text

in the Bible. In fact he wanted to show that rational argument is not completely conclusive and

that when it deals with a doctrine of faith, one should be skeptical about it.

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Astronomy in the Middle Ages followed the model of Ptolemy. Textbooks were written

for use at universities and astronomical tables were used, first the ‘Toledan tables’, based on

tables of Ptolemy and Arabic tables, then the ‘Alfonsine tables’, based on new observations in a

school founded by king Alfonso X (Spain) in the second half of the 13th century.

Astrology was a standard part of the medieval world view. Its basic idea is that the

phenomena in the heavenly region influence what happens on Earth. Examples of such an

influence are obvious from observation: the seasons which are related to the yearly motion of the

Sun; the tides which are influenced by the Moon. Moreover, heavenly bodies were traditionally

associated with gods who have an influence on the terrestrial region. Aristotle argued that the

changes in the terrestrial world are eventually caused by the motions of the celestial spheres.

In Islam and early Christianity there was some opposition against astrology; it was

argued that if the stars and planets determine what happens on Earth, this would imply a

determinism which is in opposition to the free will and omnipotence of God. Ibn Sīnā alsooffered philosophical arguments against astrology.

When in the 12th century Greek and Arabic astrological works were translated, the

interest in astrology revived, although the deterministic aspect was still rejected. It became also

associated with the practice of medicine.

The Aristotelian theory of matter and form was adopted by medieval scholars. What we call

chemical combination was described by them as the complete mixture of the elements into a

homogenous compound, such that the original forms of the elements are replaced by the new

form of the compound (see above in the section on ancient chemistry and alchemy). But in some

way the original forms of the elements should still be present in the compound, since it is

possible that the compound is again dissolved into its elemental constituents. How this was

possible was a subject of debate among the medieval natural philosophers.

Matter was thought not to be atomistic, but continuous, that is, infinitely divisible.

However, a mixture could not be divided infinitely without losing its specific form. It was

supposed that there were minima naturalia. They were the smallest quantities of a substance thatstill preserved their specific form. If one would divide them further the quantities would be too

small to preserve their form and they would lose their identity. We remark that the theory of

minima naturalia is fundamentally different from atomism. (What are the differences? See

Lindberg p. 287).

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Motion was a topic that provoked a number of discussions among the medieval natural

philosophers which led to some new concepts and ideas. First, the question ‘What is the nature of

motion?’ was addressed. Two points of view were developed. (1) Motion is just the moving body

and its sucessive places; it is not something that exists apart from the moving body; it is a

process that consists in occupying successive places. This view was called forma fluens (flowing

form). It was defended by Willian of Ockham (14th century) with the argument that if one

restricts the number of existing things in the world as much as possible, the description of the

world will be more economical. (2) Motion is a kind of quality (such as green, hot, etc. are

qualities) that is added to a body when it moves. This view was called fluxus formae (flow of a

form). It was defended by John Buridan (14th century). His argument was as follows: suppose the

universe as a whole, including the Earth, has a rotational motion (it is within God’s power to

accomplish this). Then, if motion were nothing but the process of occupying successive places,

then this rotation would not be a motion, since this rotating universe is not in a place at all. Weremark that the place of a body, according to Aristotle, is the inner surface of the surrounding

body; since nothing surrounds the universe as a whole it is not in a place. Thus, motion must be

some attribute which a body acquires when it is set into motion.

A mathematical description of motion (kinematics) was developed in the 14th century by

a number of scholars connected with Merton College, Oxford (Thomas Bradwardine, William

Heytesbury, Richard Swineshead). They were able to define the velocity of a motion. Of course

people before them were aware that things can move with various velocities. This was expressed

by saying that a distance could be covered in various times, or that in a certain time various

distances could be covered. However, velocity was never defined as a quantity. In the 14 th

century one arrived at the concept and definition of velocity by a philosophical analysis of

qualities. A quality, such as warmth, wetness, colour can have various degrees or intensities, and

the degree of a quality can increase or decrease (intensio, remissio). If one considers motion as a

kind of quality, then the intensity of this quality may be identified as velocity.

Moreover, besides the intensity of a quality, one has to consider its extensity, that is, the

quantity of it that is present in a body: two bodies of the same substance, but of different sizehaving the same temperature (‘intensity of heat’) contain different quantities (‘extensities’) of

heat. Oresme put this in a graphical representation. For instance, in the case of a rod which is

heated such that one end is hotter than the other, the temperature is set out vertically against the

distance on the rod horizontally. Analogously, if a rod is rotating around a fixed end, one may set

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out the velocities of the different parts of the rod against the distance of those parts from the

fixed end. If one has a body that moves as a whole, such that all parts have the same velocity, but

this velocity changes with time, then one may take time as the horizontal axis, and velocity may

be plotted as a function of time. The quantity of motion is identified with the distance covered,

and Oresme showed that it is represented by the area of the figure in the velocity-time diagram.

One special case was that of the uniformly accelerated motion. The Merton scholars had found

that in this case the distance covered in a certain time is equal to the distance covered by a body

moving during the same time with a uniform velocity equal to the average (mean) velocity of the

accelerated motion (mean-speed theorem, or Merton rule). The proof can easily be seen from

Oresme’s graphical representation of motions (Lindberg, pp. 297-300).

The 14th century also saw developments in dynamics, that is, the description of the

relation between motion and its cause. The Aristotelian principle that every moving body is

moved by something else that is in contact with it offered a problem for cases such as when astone is thrown upward. Such a motion is not natural for a stone: its natural motion is downwards

(falling). When the stone has left the hand that threw it and is moving upward through the air, by

what is it moved? Aristotle himself thought that it was the surrounding air that propels it. John

Buridan proposed an alternative answer. He said that the thrower transfers into the stone a kind

of quality, whose nature it is to move the stone. This quality was called ‘impetus’. The strength

of this impetus was proportional to the velocity and the quantity of matter of the body. It retains

its original strength when there is no resistance against the motion. A resistance or opposition

weakens the impetus. The heavenly spheres also move by an impetus, which was given to them

by God at their creation; since there is no resistance to their motion they will continue to move

eternally.

In the 12th century the works on optics by the ancient Greek authors, the sections about

optics in the work of Aristotle, al-Kindī, Ibn Sīnā and Ibn Rushd, and Ibn al-Haytham’s Optics

became available in Latin. The results of Ibn al-Haytham (Alhazen) were adopted by the

medieval scholars. Roger Bacon adopted Alhazen’s approach, but also tried to incorporate the

views of Aristotle and the visual ray theory of Euclid, Ptolemy and al-Kindī. For instance, hesaid that vision occurs by intromission of light rays into the eye, but at the same time visual rays

also play a role. They ‘prepare’ the medium so that it becomes suitable to transfer the light rays.

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The word Renaissance ( = rebirth) refers to certain cultural changes that began in Italy in the 14th

century and spread to the rest of Europe in the 15th century. It is usually said that it represents the

end of the Middle Ages and the beginning of the ‘modern age’. As we have seen above, many

works of the classical (Greek and Latin) authors were known in the Middle Ages. However,

study of them was usually done ‘in the service of’ religious education. Now there arose an

interest in the classical authors as inspiration for new conceptions, mainly concerning morality,

literature and art. There arose an interest in man as a free individual, in nature and its beauty. The

culture of the ancient Greeks and Romans was taken as an example for a new culture in Europe.

The ‘rebirth’ of the Renaissance refers to this new interest in classical culture and to the

supposed revitalization of culture in Europe based on classical culture.

Although printing was known in China in the 7th century, it was introduced in Europe

around 1440 by Gutenberg, of Mainz (Germany). It caused a wide diffusion of the classical

philosophical and scientific works.Aristotelian ideas continued to be taught at universities in the 15th and 16th centuries, for

instance in Padua (northern Italy). The study of Aristotle was now more ‘secularized’, less ‘in

the service of’ religion. The main faculty in Padua was the faculty of medicine.

At the same time also a new approach to the study of nature developed that would

eventually lead to the abandonment of the Aristotelian world view. Characteristics of this ‘new’

science were the use of observation and experiment, and the use of mathematics. These made

possible a better classification of experience and the discovery of new causal laws. Then, new

measuring instruments were invented (telescope, microscope, thermometer) which became

indispensable for observation and experiment. An interest in the processes of technics and

manufacture may have contributed to the development of the ‘new’ science. This new approach

will become evident in the further development of the various disciplines, as we shall see below.

Developments in astronomy

CopernicusThe change from the geocentric, Aristotelian picture of the universe to the heliocentric picture

occurred in the 16th century; it was brought about by Copernicus (born in Poland, d. 1543). He

explained his theory in the book De Revolutionibus Orbium Coelestium (On the Rotations of the

Celestial Spheres). He claimed that (1) the Earth rotates around its own axis in 24 hours; it is not

43



the celestial spheres that rotate around the Earth; and that (2) the Earth moves around the Sun in

one year; it is not the Sun that moves around the Earth. Furthermore, the Moon moves around the

Earth along an epicycle, and the other planets move around the Sun, not around the Earth. All

motions are uniform, circular motions, as before.

Copernicus proposed these new ideas not because of observational data: these had hardly

been improved since the days of Ptolemy; telescopes did not yet exist; Copernicus mainly used

the data from the Almagest . His motivation was that the system of Ptolemy did not fulfill the

requirements of a proper explanation of the motion of the celestial bodies, namely that all

motions should be uniform rotations around the center of a sphere. Ptolemy’s introduction of the

equant point was not in agreement with this requirement. Thus, Copernicus wanted a model

without an equant point. He put the Sun in the center of the universe, since it is ‘the spirit, ruler

and visible god of the universe’. He still needed epicycles and eccentrics to explain the observed

data; for instance, the center of the Earth’s motion around the Sun was not the Sun itself, but itwas located at a certain distance from it. His system was more simple, in the sense that the

irregular motions of the planets with their retrogradations were now explained as apparent

motions seen from the moving Earth; the number of epicycles needed by Copernicus was less

than in Ptolemy’s system. Also, it seemed more ‘natural’ to let the earth rotate around its axis

than the whole heaven perform a revolution in 24 hours.

Copernicus did his own observations in order to confirm his model. Although his system

was non-Aristotelian in various respects, he still adhered to the idea of a finite spherical universe

in which the planets moved in circles, carried by wheels.

The heliocentric system was not accepted by most of Copernicus’ contemporaries.

Church authorities opposed the system because it contradicted several passages from the Bible,

but physical objections seemed to be at least equally important; they were the same objections as

already discussed by Oresme in the 14th century (see above).

Giordano Bruno (d. 1600) was more a theologian and philosopher than an astronomer. He

defended the Copernican system, and moreover held that the universe was infinite, that there was

no essential difference between the celestial and terrestrial regions, and that the Earth, nor theSun had a privileged position in the universe; the Sun was just a star among the many stars.

Bruno was convicted by the Church and burnt in Rome because of his heretical theological ideas;

it is unsure whether his defense of Copernicus also played a role.

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Tycho Brahe

A great advance in observation of the stars and planets was made by the Danish astronomer

Tycho Brahe (d. 1601). He improved the instruments of observation, so that a greater accuracy

was achieved. He did not accept the rotation of the Earth, nor its motion around the Sun. Against

the rotation of the Earth he argued that projectiles fired from a cannon towards the west and

towards the east cover the same distance. If the Earth were to rotate from west to east, then a

projectile fired towards the west would reach further than one fired towards the east.

He proposed a model in which the Earth is stationary at the center of the universe, with

the Sun, Moon and fixed stars revolving around it, while the planets are revolving around the

Sun. This system is geometrically equivalent to that of Copernicus.

Kepler

The improved observations of Tycho Brahe and further calculations in the Copernican modelmade Kepler (from Germany; d. 1630) conclude that the planets cannot move uniformly in

circular orbits. Instead, he formulated three laws that would explain the motions of the planets:

(1) Planets move in ellipses with the Sun in one focus.

(2) They do not move uniformly, but their speeds are such that a line joining the planet and the

Sun sweeps out equal areas in equal times.

(3) When one compares any two planets, then the squares of the periods of revolution are

proportional to the cubes of the mean distances from the Sun.

These ‘laws of Kepler’ provided the solution of the ancient problem of how to describe the

observed motions of the celestial bodies. It meant giving up the uniformly moving spheres that

were considered to be necessary for such a description since Plato until Copernicus.

Galileo

The telescope was invented in the beginning of the 17th century. It was used by Galileo Galilei

(born in Florence, lived in Pisa, then in Padua; d. 1642), who made a number of new discoveries

in the celestial sky. He observed that Venus had phases just like the Moon, which confirmed thatits orbit was inside that of the Earth, in agreement with Copernicus’ model. (In the model of

Ptolemy Venus is always more or less between the Sun and the Earth, never in opposition to the

Sun, so that it would never be seen as ‘full’). He observed the rings of Saturn, the moons of

45



Jupiter, spots on the sun and mountains on the moon. He adhered to the theory of Copernicus,

not Kepler.

Galileo’s defense of the Copernican system brought him into conflict with authorities of

the Church who were mostly Aristotelians and who saw a conflict with the text of the Bible in its

literal interpretation. Although many churchmen had no problem with the Copernican system if it

was presented as a hypothesis to explain the observational data and some of them even said that

astronomical questions should not be decided from the Bible, Galileo was reproached for

defending Copernicus and told to give up his opinion that the Earth was actually moving.

Developments in mechanics

Galileo

The characteristics of the ‘new’ science mentioned above are displayed in the work onmechanics by Galileo. Aristotelian natural philosophy was based on the common sense-

experience of daily life. For instance, having noticed that bodies only move when they are

pushed or pulled by something else, and that when they are no longer pushed or pulled they stop

and come to rest, Aristotle concluded that everything that moves requires something else that

causes the motion. He stated that the speed of a moving body was proportional to the force

something else applied to it and inversely proportional to the resistance, in this case the

resistance against motion, that is, the mass (Note that we use here the terms ‘force’ and ‘mass’

anachronistically; before Newton people had intuitive ideas about force and mass, but these

concepts were not exactly defined). In the case of a freely falling stone, which seemed to move

‘by itself’, the cause of the motion was supposed to be its nature: it belonged to the stone’s

nature to be in its natural place, which is down, where the earth is. Aristotle supposed that the

speed of a falling body was proportional to its weight and inversely proportional to the resistance

from the medium through which it fell.

Now Galileo looked at the facts of experience in a new way. Firstly, he explained that

cause and effect are just phenomena that regularly occur together and that science should try toestablish such regularities, and should not look for ‘essential natures’ as causes for phenomena.

Words such as ‘weight’,‘gravity’ are just names for certain observed regularities. Secondly, he

abstracted from the phenomena of direct, daily experience the non-essential aspects and then

tries to express the regularities between the abstracted phenomena by means of mathematical

46



relations. These relations between the abstracted phenomena cannot be observed themselves, but

observations can be derived from them. This made possible the investigation of phenomena by

specially arranged experiments, in which irrelevant conditions were excluded so that the

phenomena could be studied in their most ‘pure’ forms. Of course, such conditions can never be

completely excluded in real experiments; therefore one can never expect that the result of an

experiment will exactly confirm the mathematical relation it is supposed to test.

The main works of Galileo in which the ‘new’ science is set forth are Dialogo sopra i

due massimi sistemi del mondo, tolemaico e copernicano (1632) and Discorsi e dimostrazioni

matematiche intorno à due nuove scienze (1638). We refer below to these works in the English

translation by Stillman Drake ( Dialogue Concerning the Two Chief World Systems, Ptolemaic

and Copernican, University of California Press, Berkeley and Los Angeles, 1953, rev. ed. 1967)

and Henry Crew and Alfonso de Salvio ( Dialogues Concerning Two New Sciences, Dover

Publications, New York, 1914) as The Two Chief World Systems and Two New Sciences,respectively.

As for the case of freely falling bodies, it was already known that Aristotle’s rule that the

(average) speed of a falling body is proportional to its weight was not correct. Philoponus (6th

century) had remarked that when one observes different bodies falling from a height, then the

heavier one arrives before the lighter one, but the time difference is only small, and certainly not

in agreement with Aristotle’s rule. In the time of Galileo it was the Dutch mathematician and

physicist Simon Stevin who had dropped bodies of the same material but different weight and

found that they arrived at the earth almost at the same time. Moreover, Aristotle’s rule implies

that the speed of the fall will approach infinity when the density of the medium becomer thinner

and thinner; this seemed quite implausible, as already noted by Philoponus.

When Galileo discusses the motion of freely falling bodies, he takes into account that

they do not only have a downward inclination, but are also influenced by the surrounding

medium and get an upward inclination by the Archimedean upward force. This means that

bodies of different density will be subject to different forces, and therefore acquire different

speeds.

Galileo refutes Aristotle’s rule for falling bodies as a part of the discussions in Two New

Sciences (First Day). He first mentions that experiments have shown that a leaden ball of two

hundred pounds dropped from a height in air will reach the ground only slightly earlier than a

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medium opposes this tendency by offering a resistance which is proportional to the speed of the

body. Therefore the acceleration is diminished until the increasing speed reaches such a point

that the resistance balances the downward tendency; then there is no further acceleration and the

body continues with constant speed. Now the resistance of the air to the small weight of the

bladder will be relatively much more than the resistance to the large weight of the lead.

Therefore, if the air would be removed, the bladder will move much faster than in air, so that its

speed will become equal to that of the lead, which will not move much faster. (Two New

Sciences pp. 73-77).

Note that Galileo here discusses the retardation of a moving body due to friction with the

medium, this friction being proportional to the speed. The effect of friction also depends on the

material, shape and size of the body. Bodies of the same material and shape, but of different size

will experience different friction: the one with the larger surface will be more retarded (Two New

Sciences pp. 88-89). The retardation by friction is different from that which is due to the upwardArchimedean force. Due to the Archimedean force falling bodies of different density get

different speeds, but the ratio of their speeds remains constant. Due to friction the ratio of the

speeds initially increases and after a sufficient long time the speeds become constant,

proportional to the mass. Galileo extrapolates from both kinds of retardation to the case of a fall

in vacuum and in both cases concludes that all bodies fall equally fast in vacuum, irrespective of

weight and density. The retardation due to the medium is again discussed in the Fourth Day,

when Galileo deals with the motion of projectiles (Two New Sciences pp. 252-255).

Also note that Galileo here implicitly states that a force is the cause of acceleration, not

of velocity as Aristotle thought. As we saw above, he assumed that a heavy body (of constant

weight) falls with a constant acceleration and that bodies of different (constant) density fall with

a constant proportion of speeds. He also stated that if forces on a body balance each other, then

the velocity is constant.

Galileo wanted further experiments to test his assumption that bodies of different weight

fall with equal speed. In order to diminish as much a possible the retarding effect of the medium

by friction he reduces the speed by letting bodies move along an inclined plane instead of lettingthem fall freely. And to get rid of the retardation caused by the friction between the moving body

and the inclined plane he used the pendulum. He attached a ball of cork and one of lead to two

threads of the same length and let them swing. He found that the period of the swing was equal

for the heavy and the light body. If the balls on the pendulums are released from the same height

49



at the same time, then they move with the same speed. This speed will gradually decrease due to

the resistance of the air, but both balls will continue to have the same speed (Two New Sciences

pp. 84-87). Without further proof or comment Galileo states that the period of a pendulum is

proportional to the square root of the length of the thread (Two New Sciences p. 96).

Two New Sciences (Third Day) is a discussion of motion, especially the accelerated motion of

bodies under the influence of gravity. He first makes certain suppositions about these motions

and then confirms these suppositions by experiments. Starting with the observation that a falling

stone continually increases its speed, he assumes that this increase occurs in the most simple

way, namely that in equal times the speed increases an equal amount. This is the definition of a

uniformly accelerated motion. It means that the increase in speed is proportional to the increase

in time (Two New Sciences pp. 161-162). Galileo remarks that in the context of this discussion it

is not worth while to try to discover the cause of the acceleration, whether is attraction by theearth, or anything else. He is going to find the properties of accelerated motion and when these

properties are found to be realized in falling bodies, then we may conclude that falling bodies

have such a motion (Two New Sciences pp. 166-167).

He derives that for such a uniformly accelerated motion the distance travelled is

proportional to the square of the time, in a way similar to that of the Mertonians (Two New

Sciences pp. 173-175). Then he confirmed this with experiments in which balls were rolling

down an inclined plane. Speeds of bodies on an inclined plane are much smaller than those of

freely falling bodies; therefore the effect of air resistance is smaller. He took care that the balls

and the surface of the plane were very smooth, so that the influence of friction was excluded as

much as possible. The items to be measured were the distance and the time. He found that the

results of his experiments agreed with the mathematical law he had derived (Two New Sciences

pp. 178-179).

The rest of the Third day of Two New Sciences is taken up by all kinds of propositions

about motion along inclined planes. For example: if a body falls along planes inclined at

different angles but of the same height, the speeds with which it reaches the bottom are the same.And: if a body falls along planes inclined at different angles but of the same height, the times of

descent are proportional to the lengths of the planes.

He remarks that the tendency of a body to move down towards the centre (of the earth) is

at its maximum when a body is on a vertical plane; this tendency of the body (or impelling force

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on the body) becomes less and less when the plane inclines more and more towards the

horizontal. When the body is on a horizontal plane, by which he means a surface every point of

which has the same distance to the centre of the earth (so this horizontal plane is in fact a sphere

with its center at the center of the earth), then it has no downward tendency any more. He shows

that the ratio of the impelling force acting on a body in descent along an inclined plane and the

force acting on it when it descends along the vertical is the inverse of the ratio of the length of

the inclined plane and its height (We would say that the force that causes a body to move along

an inclined plane is equal to its weight times the sinus of the angle between the inclined plane

and the horizontal plane) (Two New Sciences p. 181-183).

One of the propositions from the Third Day is that if a body falls a certain distance along

a vertical line and then continues its motion in a horizontal plane, then the distance covered on

the horizontal plane in a time equal to that of the fall along the vertical line is twice the distance

of the fall. This can easily be proved geometrically by plotting the velocity against the time.(This proof is given also in The Two Chief World Systems, pp. 228-229). Then Galileo remarks

that any velocity once imparted to a moving body will be rigidly maintained as long as external

causes of acceleration or retardation are removed. This condition is found only on horizontal

planes, for in planes sloping downward there is always a cause of acceleration and in planes

sloping upward there is always a cause of retardation. Thus, on a horizontal plane motion is

uniform and perpetual. Furthermore, if a body after descent on a downward plane is deflected to

a plane inclined upward, then the velocity is has acquired in the descent is maintained, but

subtracted from is the velocity resulting from the natural downward acceleration. Galileo then

shows that in such a situation the body will ascend up the second inclined plane to the same

height as from where it descended (from rest) on the first inclined plane, irrespective of the angle

of the inclined planes with the horizontal (Two New Sciences p. 214-218).

We see here that Galileo knows a kind of principle of inertia: a body maintains its

uniform velocity as long as it is not subject to external forces. The difference with Newton’s

formulation is that, since Galileo uses this principle for heavy bodies under the influence of

gravity, he says that the condition of not being subject to external forces applies to bodies on ahorizontal plane, which is then a spherical surface, parallel to the surface of the earth.

As we saw above, if a body arrives on a horizontal plane with a certain speed, this speed

will always be maintained; that means that the motion which occurs in the absence of external

forces is a uniform, circular motion. Indeed, in The Two Chief World Systems, Galileo says that

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we look only at terrestrial objects, since we partake in the same motion. Motion is relative: it

only exists in relation to things that do not move. If we look to the heaven we see it moving in

relation to the earth, completing one rotation in twenty-four hours. This effect is the same

whether the earth performs this rotation while the heaven is at rest or the earth is at rest while the

heaven is rotating. Now it seems more plausible and more simple to let a single body, namely the

earth, rotate with a moderate speed than this immense number of large bodies with extremely

large speeds (The Two Chief World Systems, pp. 114-117).

The Aristotelians defended their position by the argument that a stone dropped from a

tower falls vertically and reaches the ground at the foot of the tower (see above); a similar

argument was that a projectile fired from a cannnon towards the west would reach further than

one fired towards the east (see above under Tycho Brahe) (The Two Chief World Systems, pp.

126-127).

The reply to these arguments is that the tower and the stone partake in the motion of theearth; when the stone is released it maintains this motion and added to it is a vertical accelerated

motion. In relation to the tower only the vertical motion exists, and so the stone arrives at the

foot of the tower. The situation is similar to that of a stone dropped from the top of the mast of a

uniformly moving ship. Thus, the observation of a vertically falling stone is not decisive against

nor for the case of a moving earth (The Two Chief World Systems, 138-149, 171-173).

From the above discussions it has become clear that all natural phenomena are the same,

irrespective of whether they occur within a system that is at rest as a whole or a system that is

moving with a uniform motion (in modern terms: equivalence of inertial systems). Galileo says

that everything happens in the same way within a ship at rest as within a ship that moves

uniformly (The Two Chief World Systems, pp. 186-188).

Another argument of the Aristotelians against the rotation of the earth was that

everything that partakes in a circular motion acquires an impetus to move away from the center,

so that everything on the earth would be thrown off from it. Galileo explains that indeed a

projectile which is rotated by someone who wants to throw it, when it is thrown and is separated

from the thrower, keeps the impetus it has at that moment and continues its motion along thestraight line that is the tangent of the circle at the point of separation. However, this impetus is

overcome by the tendency towards the center of the earth; therefore things on earth are not

thrown off (The Two Chief World Systems, pp. 188-196). Galileo goes at some lengths to show

quantitively that indeed gravity is always stronger than the tendency to be thrown off.

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In the course of the discussion of this issue the question arises what the resistance is of a

body against motion. He observes that in the case of a balance with unequal arms a large weight

placed at the end of the short arm is in equilibrium with a small weight placed at the long arm; if

the balance is set in motion, then the small weight is able to move the large one while the large

one moves only a small distance and the small one moves a large distance. The large weight gets

a small speed and the small one a large speed. Thus, the resistance against motion depends not

only on the weight of the body, but also on the speed it obtains. The resistance against motion of

a body of one pound moving with a speed of one hundred units is equal to the resistance of a

body of one hundred pounds moving with a speed of one unit (The Two Chief World Systems, pp.

213-215). It appears that Galileo had an idea of the importance of the concept of momentum (=

mass times velocity), although its explicit definition was given only later by Newton.

From the passages summarized above from Galileo’s main works we conclude that he starts withthe observation that every body has a natural tendency to move to the center of the earth; this

tendency is called weight or gravity. He does not ask what gravity is, he does not look into the

cause of this tendency. He does not assume an external force, such as attraction by the earth,

although he mentions the possibility. It is this tendency which is the source of (accelerated)

motion.

Galileo established a kind of principle of inertia, but it was not the correct principle such

as would be formulated by Descartes and Newton. The correct principle of inertia states that a

body, left to itself, remains in a state of rest or uniform rectilinear motion as long as nothing

intervenes to change this state. This implies that motion and rest are states of the body, and that

the body is unaffected by which of these two states it is in. Neither of these states brings about

any change in the body and the transition from one of these states to the other is of no

consequence for the body. It follows that one can only attribute the state of motion (or rest) to a

body in relation to another body, which is taken to be at rest (or in motion) and it is completely

arbitrary which of the states is attributed to which of the bodies. This is the principle of relativity

of motions.The principle of inertia that states the perpetuity of uniform rectilinear motion as long as

nothing intervenes was not the principle formulated by Galileo. For him, a body is always heavy

and its motion is due to its natural tendency to fall to the earth, and this motion is always

accelerated; it is retarded when the body has an initial speed and is moving up. It is only on a

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horizontal plane that this tendency does not have an effect, because then any motion does not

bring it closer to or further from the earth; then the motion is not accelerated nor retarded, but

uniform. However, if a body would move rectilinearly on a plane that is horizontal in the

geometrical sense, that is, a plane tangential to the earth’s surface, it would approach the earth or

move away from it, so it would be accelerated or retarded, and a uniform rectilinear motion is

not possible there. Thus, the horizontal plane in which bodies can move uniformly is in fact a

spherical surface concentric with the earth, and the motion is a uniform circular motion. Thus,

Galileo’s principle of inertia states the perpetuity of uniform circular motion on a spherical

surface concentric with the earth. A perpetual rectilinear motion is impossible for Galileo, since

he cannot abstract from gravity: a body is always heavy, it is one its constitutive properties, so

the only possible perpetual motion is a circular motion around the earth. This agrees with his

view that a perpetual rectilinear motion is impossible since the universe is finite and it would

disturb its order; only circular motion is ‘natural’. He could not perform the mathematization of dynamics such as he had done for kinematics.

The obstacles that impeded Galileo to adopt the correct principle of inertia were (1) his

ignorance about the cause of weight and therefore his inability to abstract from the heaviness of

bodies; (2) his believe in the finiteness of the universe. The classical mechanics explained by

Newton makes clear that weight is caused by an external attraction, that it is not a constitutive

property of a body. Moreover, the universe was considered to be infinitely extended. Within this

framework the correct principle of inertia could be formulated.

Galileo’s circular principle of inertia implies the relativity of motion for physical systems

that move uniformly along a horizontal (= circular) line. Physical phenomena on a ship are the

same for an observer on that ship, no matter whether the ship moves uniformly or is at rest.

Similarly, physical phenomena on earth are the same for an observer on earth, no matter whether

the earth is rotating or at rest. We cannot perceive motion in which we ourselves participate.

Descartes

Descartes (d. 1650) carried to the extreme the idea that the only objective aspect of nature is

what can be expressed mathematically. Matter is extension. Motion is not a process for which a

cause is needed, as the Aristotelians thought, but it is a state of the matter, just as rest is a state.

At the creation God created matter together with the motion and rest of its parts, and he keeps the

amount of motion and rest constant. One of the rules imposed by God on nature is that every

particle of matter remains in the same state as long as contact with others do not compel it to

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change it; this means that when it is at rest it will remain at the place where it is, unless other

particles push it away from its place, and when it is in motion it will continue to move always in

the same way, unless other particles stop it, slow it down or make it change direction. Descartes

further states that all motion is, of itself, along straight lines. We see that Descartes has

formulated the princple of inertia, that each body persists in a state of rest or uniform rectilinear

motion, unless it is acted upon by other particles. The principle follows as self-evident from

Descartes’ concept of motion as a state.

From the rule that all motions is of itself along straight lines Descartes concludes that

bodies which are moving in a circle always tend to move away from the center of the circle

which they are describing. Here he recognizes (but incorrectly formulated) the centrufugal effect

of circular motion.

Something else that is also kept constant by God during any process is the total

momentum ( = the product of mass and velocity mv). This especially applies to collision.Descartes states that for every collision the total momentum is conserved, that is, the total

momentum before the collision is equal to the total momentum after the collision. From this ‘law

of collision’ he deduced seven rules for collision processes, but only one of them was correct.

This was due to the fact that he interpreted the total momentum as a scalar number, not as a (sum

of) vectors.

Descartes adhered to the Aristotelian principle that there cannot be a void, since the

attribute extension can only exist if it inheres in some substance; thus, the infinite space is a

plenum (full). He rejected action at a distance, such as gravitational attraction, so the force that

would cause deflection from rectilinear motion can only work by contact. In order to explain

curvilinear motion, such as the motion of the planets, he assumed vortices in the plenum: each

particle of (infinitely divisible) matter can only move by replacing the next, and thus producing a

vortex, that is, a closed circuit of moving matter. These vortices carry the heavenly bodies round

and also cause the propagation of light and magnetism.

The acceleration of falling bodies is explained by means of pressure: the earth is

surrounded by a cloud of subtle matter (see below) swirling around it in a vortex; this swirlingmatter pushes bodies toward the earth. The impact from the subtle matter on the body gives it a

certain increase of speed; so if every instant the body receives a new impact the speed will

increase proportionally with the time. But the speed will not increase indefinitely; after some

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time it will have become equal to the speed of the subtle matter itself, so that the latter does not

exert a pressure any longer; then the speed remains constant.

Descartes did not try to discover experimentally the laws of nature, such as Galileo did;

he imposed on nature the laws which he deduced from his abstract principles. More about

Descartes, especially his theory of the structure of matter, will be discussed below.

The system of classical mechanics that was established in the 17th century was developed by

Huygens and Newton from the principles of Galileo, not of Descartes. It involved the precise

definition of the concepts mass and force. Then it could be explained why bodies of different

weight fall with the same acceleration: weight is the force that causes the accelerated falling

motion and mass is the ‘resistance’ against this motion. The theory of universal gravitation

implies that weight and mass are proportional, their proportion being the acceleration. This

theory of gravitation also explained the motion of the heavens, such as described by Kepler, andthis meant the final destruction of Aristotle’s distinction between the celestial and the terrestrial

world.

Magnetism: Gilbert

William Gilbert (d. 1603) studied magnetism. It was already known in Thales’ time that some

pieces of iron ore, called lodestone, attract iron. The Chinese and later the Arabs knew that such

lodestone orientated itself in the north-south direction, and used this for the invention of the

compass. The use of the compass was known in the Western world since the 13 th century. A

treatise on the magnetism of the lodestone, with a description of many of its properties deduced

from experiments, was writen by Petrus Peregrinus in the 13th century. He supposed that the

orientation of the lodestone was towards the poles of the celestial heavens. The magnetic

attraction at a distance was explained in an Aristotelian way: the lodestone changes the condition

of the medium (air, water,…) next to it, which changes the condition of the parts next to it, etc.

until this change reaches the iron and gives it a power to move towards the lodestone.

Gilbert extended the work of Peregrinus. He showed that the orientation of the lodestonewas caused by the earth itself, which was a huge magnet, with poles near the geographical poles.

His explanation of magnetic attraction was not more advanced than that Peregrinus: the

lodestone has a kind of efficient principle, comparable to the soul; when a piece of iron is in its

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neighbourhood the lodestone excites a similar power that was dormant in the iron. Because of the

affinity of these powers in lodestone and iron, they mutually attract each other.

The work of Gilbert inspired Kepler to use magnetic forces as the cause for the motion of

the moon around the earth and of the planets around the sun. He adhered to the current

Aristotelian concept of motion as a process requiring the continuous operation of a motive

power. He assumed that magnetic ‘lines of force’ are extended radially from the earth, which

carry around the moon, the atmosphere and everything that is thrown upward. Similarly,

magnetic lines of forces extending from the sun carry around the planets.

Electricity

The phenomenon that amber (a fossil resin found in the earth) attracts small things when it is

rubbed was known since the time of Thales. (The Greek word for amber is ēlektron). Gilbert

discovered that also other materials such as glass and sulphur and have this property. Otto vonGuericke (from Magdeburg, Germany, d. 1686, see below for his vacuum pomp) invented an

electrical machine, consisting of a sulphur globe, the size of a child’s head, which could be

rotated and rubbed by the hand until sparks came off.

The 18th century saw some further developments in showing the effect of electrical

charge, but the theoretical explanation did not advance much. It was discovered that there were

two kinds of electricity, the one that existed in rubbed glass, the other that existed in resinous

bodies when rubbed, such as amber. Bodies with different kinds of electricity attract each other,

those with the same kind repel each other. Bodies which are not electrical may acquire either of

these two kinds.

Ewald von Kleist and Pieter van Musschenbroek independently invented an instrument to

collect and store electrical charge, the Leyden jar (so called since van Musschenbroek was

professor at Leyden University in the Netherlands). It was a glass jar coated on the outside with

metal foil and containing (accidentally) impure water that acts as a conductor, connected by a

chain or wire to an external sphere. The outside of the jar was connected to the pole of an

electrical machine. The charge will be collected on the sphere and very strong sparks may be produced. The charge is actually stored on facing surfaces of the conducting elements separated

by the glass, which forms a dielectric. The water can be replaced with a foil lining, with which is

connected a rod that passes through the lid of the jar and ends in a metal ball. The inner and outer

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http://en.wikipedia.org/wiki/Dielectric

http://en.wikipedia.org/wiki/Dielectric



and animal bodies and at the same time falsified the concept of Galen that blood was

continuously produced by the liver from food, and ebbed and flowed in the heart and vessels. For

instance, he calculated that the quantity of blood pumped through the heart each hour is about

three times the weight of the body. Such a quantity could not have been produced from the food.

Harvey did not know how the blood passed from the arteries to the veins. Some years

after his death Malpighi discovered with the microscope that this passage occurs in the capillary

vessels.

Optics

The refraction of light in lenses was studied geometrically. With the spread of spectacles a lens-

grinding industry developed. This led at the beginning of the 17th century to the invention of the

telescope and microscope by empirical combination of lenses. The law of refraction was

established experimentally by Snell (Snellius), a Dutch astronomer and mathematician (d. 1626).(remember that the law was already used by Ibn Sahl in the 10th century, although he did not

formulate it explicitly). Descartes gave a theoretical derivation of the law, based on wrong

premisses; the usual derivation is the one given by the wave theory of Huygens (see below).

Kepler gave a new theory of vision. He started from Ibn al-Haytham’s principle that each

point of the surface of a visible object is a light source that emits rays in straight lines into all

directions. Thus, there are cones of light rays with have a point of the object as their tops and the

pupil of the eye as their bases. The lens of the eye focuses the rays within each cone to a single

point on the retina at the back of the eye. In this way an image is formed of each point of the

object at a point of the retina.

According to Aristotelian natural philosophy, colours were different from (white) light.

Colour was a property of the surface of the visible object, and this property was transmitted

through a transparent medium to our eye. As for the colours of the rainbow, that was a different

matter; they were explained as a weakening of (white) light when it passed through or was

reflected by a dark medium. Descartes dismissed colour as a property of the visibe object. He

thought that light is a kind of pressure transmitted from the light source to our eye by means thespherical particles that fill the whole space (see below). These particles also have a rotation

around their own axes; different speeds of rotation give the impression of different colours.

When light falls on the surface of an object, or is refracted through a prism, these speeds are

changed and thus give the impression of various colours.

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A new theory of colours was proposed by Newton. He said that (white) light is composed

of different rays which each give the impression a different colour and that each colour is

differently refracted; he verified this assumption with experiments with prisms, disproving the

theory that colour was a modification of white light. He also supposed that rays of different

colour are reflected differently, in this way explaining the colours of an object’s surface: for

instance, a surface appearing red reflects mainly red rays, not blue ones.

Descartes’ theory that light is a pressure transmitted though a material medium developed

into the ‘wave theory’ of Huygens (see below). Newton’s theory of light was different: he

thought that light was a stream of particles moving with immense speed.

Descartes

As we have seen above, Descartes carried to the extreme the idea that the only objective aspect

of nature is what can be expressed mathematically. He was in the first place mathematician; his philosophy and scientific ideas were inspired by mathematics. The deductive method of

geometry was for him the example for all philosophy and science: everything should be deduced

from certain basic propositions that need no further proof, since they are obvious.

Matter is completely determined by the geometric characteristic of extension, so that one

may say that matter is extension. All qualitative properties such as hardness, bitterness, etc.,

should be explained from the primary, quantitative properties form, size and order of the material

particles. All change is to be explained by direct contact of particles, that is, by collision or

pushing.

Space extends infinitely; since the attribute extension can only exist if it inheres in some

substance, the infinite space is a plenum (full of matter). As space is completely full, motion

causes vortices (turbulences or whirls). Action at a distance, such as gravitational attraction is

impossible. Everything, including animals, works as a machine, the parts of which move by

direct contact.

As for the theory of matter, Descartes assumed that the infinite space (which is

completely filled with matter) is divided into parts by surfaces. These parts are brought intomotion by God at the creation of the world. When the parts move they grind away from each

other their edges and acquire a spherical shape. These spherical particles (which he called the

‘second element’) partly cohere into larger, coarser parts of matter (the ‘third element’). The

grindings are subtle matter (the ‘first element’ or ‘aether’) that fills the space between the other

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matter of the second and third elements. The spherical particles form whirls (vortices) and drive

subtle matter to the center, where they form the Sun and the fixed stars. Thus, the Sun and the

stars are surrounded by the spherical particles; the spherical particles together with the subtle

matter between them is called celestial matter; this celestial matter moves in whirls around the

Sun and the stars. The whirl of celestial matter around the Sun drags along the planets. The

infinite universe consists of an infinite number or whirls.

The coarser matter forms the Earth, the planets and all earthly bodies. The space between

them is filled with celestial matter. The quantity of matter (mass) of an earthly body is

determined by the volume of coarse matter it contains. The actual volume equals the volume of

coarse matter plus the volume of celestial matter between the coarse parts. Expansion of a body

means that more celestial matter fills the space between the coarser matter.

Light and gravity are also explained by means of the vortices (whirls). Since the celestial

matter in a vortex is moving in a circular way, it has a centrifugal tendency to escape from itsorbit. Therefore each layer of moving matter at a certain distance from the center of the vortex

exerts a pressure on the layer that is further from the center. This pressure is transmitted through

the space to our eye and is observed as the light of the Sun and the stars. Thus, light is not

something emitted by the Sun and stars themselves, but it is an effect of the whirls around these

celestial bodies. The transmission of the pressure may be compared with the way a blind man

may ‘see’ and object by using his stick: when the stick hits a stone a pressure is transmitted to

the man’s hand, and he becomes aware of the stone. Since pressure is a tendency to motion, one

may compare a ray of light to a moving bullet and in this way Descartes derives the laws of

reflection and refraction.

The earth has a whirl of celestial matter around itself and is dragged along by this whirl

in a daily rotation. Gravity is the effect that bodies with less centrifugal tendency are forced

down by bodies with a greater centrifugal tendency, which rise. For instance, a stone contains

less celestial matter than an equal volume of air. Therefore the air under the stone has a stronger

centrifugal tendency than the stone, and wants to replace the stone, which is pushed down. A

body will always move to the place where the centrifugal tendency of its celestial matter is equalto that of the surroundings.

Descartes was not interested in experiments to verify his physical theories; he thought he

had explained everything with his deductions from ‘reasonable’ premisses. When it was pointed

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out to him that his rules of collision did not describe actual collisions he did not believe

experience.

The ancient and medieval worldview was ‘organic’, the explaining principles of things

were the immutable essences (the Aristotelian forms); these forms or essences were the

organizing principles of each substance, similar to the soul which is the organizing principle of

living beings. The whole world was conceived as a living organism, in which one should not

interfere with experiments. This view changed with the recognition of experiment and

technology. The worldview became mechanistic: the world is like a machine. Man is allowed to

interfere with the operation of such a machine. The world is God’s creation, and so we have to

respect is as such; but it is not God itself, and so we are allowed to interfere in it with

experiments and control it with technology. A machine is something that has been made with a

plan or design; thus, the mechanistic worldview implies that the world is made according to a

design (of God). This is opposed to the mechanistic worldview of the atomists Leucippus,Democritus and Epicurus: according to them, the atoms out of which the world is composed

move about by chance, without any plan or purpose.

The idea that matter is composed of particles or corpuscules that combine and separate to

form the various material substances became more popular in the 17th century. As we saw,

Descartes adopted a theory of corpuscules, which are infinitely divisible; space is completely

filled with them; there is no void.space. This is implied by his view that matter equals extension.

His contemporary Gassendi (d. 1655) also adopted a corpuscular theory, but he was an

atomist such as Democritus: the world is a collection of indivisible particles moving about in a

void space. Gassendi ‘christianized’ this view by stating that the atoms are created by God, and

that they do not move arbitrarily, but according to a plan: the world is like a machine of atoms.

However, to us it seems as if the atoms move arbitrarily.

The physics of Descartes may truly be called mechanistic: all explanations are made with

concepts from mechanics: form, size and motions of material parts or particles that compose the

bodies we observe. No mention is made of Aristotelian concepts such as form, nature, essence,

purpose. This view implies that sensible qualities such as colour, taste, temperature are notqualities of the body themselves, but are the result of the way material bodies influence our

senses.

The word ‘mechanistic’ as applied to natural processes also means that these processes

are similar to the processes that occur in man-made machines: there is no basic difference

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between the functioning of an animal and a watch. Therefore Descartes was interested in the

work of craftsmen and in experimental research of nature, although at first sight one might think

that his rationalistic-deductive method had little use for it.

Descartes says that his theories of nature are presented as hypothesis, that it is possiible

that they are wrong, and that he will adhere to the doctrines of religion if his physical theory

would to contradict them. However, he trusts in God who does not deceive those who use their

reason; therefore he believes that what he has derived by reason will not be false.

The 16th and 17th centuries also saw the further development of measuring instruments, such as

clock, thermometer, barometer, telescope, microscope, that were necessary for experiments. The

first thermometers were versions of a device described earlier by Philo of Byzantium (2nd century

B.C): a tube was fixed in a globe containing air; the other end of the tube was immersed under

water in a vessel. When the globe was heated air was expelled and could be seen to escapethrough the water. When the globe was cooled the contracting air drew the water up in the tube.

The explanation of this phenomenon was based on the Aristotelian doctrine of the impossibility

of the vacuum: if the air contracts, water must remain into contact with it, otherwise a void

would come into existence. The same explanation is given for the fact that if one fills an open

vertical tube with water, the water does not flow out from the lower end if the top is closed off

(this explanation is known as horror vacui: ‘nature abhors vacuum’).

Exsitence of the vacuum: Torricelli, Pascal, Boyle

The Italian physicist and mathematician Torricelli (d. 1647) filled a tube having one end closed

with mercury and inverted it with its open end under mercury in a vessel. Then the column of

mercury standing in the tube reached until a certain height (around 76 cm); the space above the

mercury must be empty; it became known as the vacuum of Torricelli. He explained the effect as

due to the pressure of the atmosphere; this pressure, that works outside the tube on the surface of

the mercury, is in equlibrium with the pressure of the column of mercury inside the tube. Thus,

this device works as a barometer. The correctness of Torricelli’s hypothesis was confirmed whenthe French mathematician/physicist/philosopher Pascal (d. 1662) took such a barometer up a

mountain and found that the height of the mercury decreased. Indeed the pressure of the air

should be less, since the height of the atmosphere above the mountain is less than that above sea

level.

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These experiments were a final refutation of Aristotle’s arguments against the existence

of the void. In fact, they showed that the Torricellian vacuum contained no air or other matter.

Some physicists, following Descartes’ view that an absolutely empty space cannot exist, found it

necessary to postulate a plenum of some sort, something that filled the whole space, including

vacuum spaces such as those of Torricelli. This space-filling medium, called aether, was then

supposed to be responsible for the transmission of influences such as gravity, magnetism and

light. For instance, we saw that Descartes thought that light consisted of particles of the plenum

and that it was transmitted instantaneously by pressure from one particle to the next.

Descartes thought that the vacuum of Torricelli still contained subtle matter. When the

mercury in the tube descends until around 76 cm, the space above it is filled by subtle matter,

which moves in from outside through the glass. Since the mercury in the tube descends, it rises

in the vessel; this pushes air upwards which arrives in the area of subtle matter outside the

atmosphere. The arriving air pushes away subtle matter from that area and this displacement istransmitted through the subtle matter in the atmosphere and finally causes the entering of subtle

matter into the space above the mercury.

The vacuum pump was invented by Otto von Guericke (from Magdeburg, Germany, d.

1686). Experiments with this pump made him adhere to the notion of air pressure and reject the

horror vacui. His well known hemispheres could not be drawn apart by 24 horses (in two teams

of 12).

The British physicist and chemist Robert Boyle (d. 1691) continued the experiments with

the vacuum pump together with Hooke and Papin. He found that air in a cylinder that is closed

by a piston expands when surrounding air is pumped away. This was due to what he called the

‘spring’ (elastic power) of air: air may be compressed by an external force; when the force ceases

to work, the air takes its original volume again, just like a spring (he did not think of the air

pressure being caused by moving air molecules).

He further did experiments with a U-tube, with a long open side and a short closed side.

The tube is filled with mercury, such that above the mercury in the closed side there is air of

atmospheric pressure; then the mercury at the open side is at the same level as at the closed side.When mercury is added at the open side it will rise at the closed side as well, and the mercury at

the open side will stand higher than at the closed side. This means that when the volume of the

enclosed air decreased, its pressure increased. Then he found the ‘law of Boyle’ that volume and

pressure of this enclosed air are inversely proportional.

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Boyle remained sceptical about the vacuum. He said that the spaces he evacuates in his

experiments do not contain air, but they may contain some kind of aetherial matter, since light

and magnetic influences are transmitted through such spaces. However, it has not been shown

experimentally that such matter indeed fills these spaces.

Huygens

The mechanistic view is applied most extensively by Christiaan Huygens, a Dutch

mathematician and physicist (d. 1695). Particles of matter are moved by direct contact with other

moving particles (impact). Particles are characterized only by form, size and motion, and they

are absolutely hard. When they collide the collision is perfectly elastic. Huygens adopts the

Cartesian view that particles exist in different grades of coarseness and fineness.

Huygens’ most famous achievement is his theory of light. He supposes that space is filled

with very subtle matter, called aether. A light source emits fastly moving particles. These particles collide with the particles of the aether, and the effect of these collisions extends

spherically around the source of light. This is analogous to the circular extension of waves in

water when one has thrown a stone in the water. Therefore he talks about spherical light waves.

However, the particles of aether do not oscillate and there is no periodicity in their motion; they

just get an impact which they transmit to the adjacent particles. The way in which the impact on

the particles of aether is propagated is explained by means of the Principle of Huygens: every

particle of aether that is hit by a particle of light becomes itself a kind of light source, in the

sense that it transmits the impact in all directions and thus becomes the center of new spherical

‘wave’. The surface that envelops all these partial waves is the new front of the wave.

Then Huygens derives the laws of reflection and refraction using his theory. As for the

propagation of light through a transparent medium, he assumes that the mass of a body is

determined by the quantity of coarse matter, and that the space between the parts of coarse

matter is filled with aether. The volume of this space is much more than the volume of the coarse

matter itself, otherwise it could not be explained that, for instance, a volume of mercury is

fourteen times as heavy as the same volume of water.(Apparently it is assumed that there is onekind of coarse matter). When light reaches a transparent medium, then it is again propagated by

the aether that exists between the coarse matter, but its velocity is diminished by the presence of

the coarse matter, since this matter forces it to make roundabout ways. He is then able to derive

the law of refraction using his theory. The proportion of the speeds of light in air and in a

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medium appears to be equal to the proportion of the sines of the angles of incidence and

refraction.

Huygens’ theory of light is opposed to Newton’s theory (see above), which stated that

light is a stream of moving particles. A crucial distinction between both theories is that if light

passes into a medium in which it moves slower, it is refracted toward the normal in Huygens’

theory, but away from the normal in Newton’s (and Descartes’) theory. An experiment to decide

between the two theories by measuring the speed of light is different media was not possible in

their time (this was done only in the 19th century). However, at the beginning of the 19th century

experiments showed that light should be considered as a periodic oscillation giving rise to waves.

Newton, nor Huygens referred to such oscillations in their theories.

Huygens also explained gravity in mechanistic terms. He did not accept the possibility of

action at a distance, such as is assumed in the theory of Newton. He assumed that the earth is

surrounded by certain subtle or fluid particles of matter which revolve together with the dailyrotation of the earth. Due to their rotation these particles move radially outwards in relation to

the moving earth (centrifugal effect). A piece of coarse matter that is placed among these fluid

particles at a certain distance from the earth is not able to follow their centrifugal motion and will

be pushed towards the center of the earth.

The theory may be illustrated by the following experiment: a cylindrical vessel filled with

water is brought in rotational motion around its axis. Some small solid particles, such as ashes,

are brought into the water. During the rotation these particles will move outward to the edge of

the cylinder. When the rotation of the vessel is stopped, the water continues to rotate for a while,

and the particles of ash collect in the middle of the vessel.

Newton

The English mathematician and physicist Newton (d. 1727) brought order in the confusion of

terms and concepts related to mechanics. One had used terms such as force, mass, gravity,

resistance in a way based on daily experience, but one never had given an exact definition of

them. Moreover, force was always seen as the cause of a motion, but in the mechanisticworldview of the 17th century it became an effect of motion: the centrifugal force was the force

due to which a body that is swung around tries to move away from the centre of its circular

motion; the gravity of a body is the effect of the motions of rotating fluid matter; due to its

motion a body is able to exert a force, and this force was seen to depend on the speed. Newton

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certain time is proportional to the total force that acts during that time. With this addition

Newton’s second axiom follows from F = m .a, but it is also possible that the latter does not

hold, while the second axiom does hold. Moreover, mass is not mentioned the second axiom. It is

in the explanation of the third axiom that Newton mentions that when motions are equally

changed, the changes of the velocities are inversely proportional to (the masses of the) bodies.

Nowadays it is usual to formulate the second axiom as that the rate of change of the momentum

is proportional to the total force, is in the same direction as the force, and is inversely

proportional to the mass.

Nowhere in his work did Newton formulate the relation F = m .a. It is probable that he

knew that this relation was valid, but that he did not took the trouble to formulate it explicitly as

he may have found it obvious.

It is possible to derive classical mechanics by defining force as the product of mass and

acceleration. Then it is not considered to be an independent phenomenon, but just a shortenedway of saying that a body is subject to an acceleration, and its magnitude is measured by the

amount of change of momentum. That was not Newton’s approach; he defined force as an

independent phenomenon, which may be of different kinds, either an attraction to a central point,

or an impact, or a pressure. The magnitude of a force may be measured, independently of the

change of momentum it may cause, by static means, such as the expansion of a spring, or a

weight that keeps the body in equilibrium via a pulley while the force is acting.

The third axiom (Third Law of Motion ) states that all forces occur in pairs, and these two

forces are equal in magnitude and opposite in direction; in other words, with every action there is

a reaction which is equal in strength and in opposite direction.

In what follows in his Principia Newton applies his definitions and axioms to special

instances in nature. First, he proves that for all motions that occur due to the action of a central

(‘centripetal’) force (irrespective of how the magnitude of the force depends on the distance from

the centre) the speed is such that a line joining the body to the center sweeps out equal areas in

equal times (Kepler’s second law), and conversely that if a motion follows this law, it occurs due

to a central force. Then he shows that if a body moves along an ellips under the influence of aforce which is directed towards one of the focuses, the magnitude of the force is inversely

proportional to the square of the distance to the center. From these results and the findings of

Kepler he concluded that the planets are attracted by the sun with such a force, and that

according to his Third Law the planets attract the sun with an equal force in opposite direction.

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Then he generalizes this result and states that all material bodies attract each other with forces

the magnitude of which is inversely proportional to the square of their distance and directly

proportional to each of their masses. Now all motions in the universe may be calculated

mathematically and the cases of stones falling on the earth or thrown upward, ebb and flood, the

moon moving around the earth and the planets moving around the sun are treated on equal

footing as effects of one type of of force: the universal gravitational force F = g . m1 . m2 / r 2.

The notion of action at a distance introduced here by Newton was opposed by those who

defended the mechanistic view, such as Descartes and Leibniz. In order to see to what extent

Newton deviated from the mechanistic picture of the world, we have to look into his

philosophical ideas about science. He states that the forces he introduces to explain the various

motions, such as the gravitational force, are just mathematical concepts. He does not claim to

know the nature of gravity or the physical cause of gravity. He does not ‘frame hypotheses’.

Only what can be derived from observed phenomena belongs to natural science. It is sufficient toknow that gravity exists and that it is able to explain the motions of the celestial bodies and the

things on earth. Thus, he does not assume the existence of particles that supposedly are

responsible for the action of a force, such as the mechanists had assumed, as long as the

existence of such particles is not proved from experience. He does not deny that one may find (in

the future) a further explanation of what gravity is, and that it may be derived from other, deeper

principles, provided that these principles are not ‘hypotheses’, but can be derived from

experience.

On the other hand, as we have seen above, Newton does not go so far as saying that the

concepts of force and gravity are in fact superfluous, and that one only can say that two material

bodies in each other’s presence are accelerated along the line that connects them.

According to Newton, science is never opposed to religious faith, and even supports and

promotes it. When we always try to find the causes from the effects, without ‘framing

hypotheses’, we will eventually arrive at the primary Cause. If one considers nature and its order,

and the purposeful way the organs of a living being work together, one has to conclude that there

must be an immaterial, living, intelligent Being who has originated all things and knows andunderstands them completely.

Even though contemporary scholars criticized Newton because he did not adhere to the

principles of the mechanistic worldview, one may also say that he extended the mechanistic

worldview with the concept of forces that act at a distance. This extended mechanistic approach

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would prove to be very fruitful in the science of the 18th and 19th centuries, and one finally

formulated the mechanistic principle as that all phenomena should be explained with forces that

are acted upon material bodies by one another, the magnitude of these forces being dependent

only on the distance of the bodies.

The successful further development of the mechanistic worldview did not lead to what

Newton wished and hoped for, namely that it would support and promote religion. On the

contrary, the more one succeeded in explaining nature by means of forces that operate according

to fixed laws, the less place there was for a God who maintains and provides for the world. After

his act of creation He could retire while the universe provided for its own continuation. This

meant that science and religion became separated, each with their own way of getting knowledge

of the world.

ChemistryAlchemy/chemistry was given an impulse for further development at the beginning of the 16th

century by Paracelsus. He did not deny the possibility of transmutation of metals, but his main

business was to prepare and purify chemical substances for use as drugs. Chemistry became an

essential part of medical training. In fact, this was a revival of a tradition that had started in the

time of the ancient Egyptian and Babylonians. In Hellenistic times Dioscurides (1st century A.D.)

wrote the book Materia Medica in which he described drugs made from plants, animals and

minerals. The book was translated into Arabic. In Muslim Spain it was Abulcasis (al-Zahrawī)

who wrote a book on how to prepare drugs, mostly by destillation and sublimation.

According to Paracelsus, all material substances are composed of sulphur, mercury and

salt. They represent the fiery, inflammable principle, the fusible and volatile principle and the

incombustible, non-volatile principle respectively. These three primary substances are in their

turn composed of the four Aristotelian elements.

Chemical experiments were done by the Flemish scholar van Helmont (beginning 17th

century, born in Brussels). Using the balance he showed that matter is conserved in chemical

reactions. He thought that water was the main element of material substances; with the help of aseminal spirit water could transform into metals, wood, etc. (a tree grows from its seed when it is

regularly provided with water). He especially studied gases; he introduced the word ‘gas’, from

Greek chaos. He mentioned different kinds of gas that arose from certain chemical reactions,

such as gas carbonum (from burning charcoal; CO2 or CO), gas sylvester (when aqua fortis

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HNO3 acts on metals such as silver or copper; nitric oxide NO; 8HNO3 + 3Cu → 3Cu(NO3)2 +

4H2O + 2NO). Air was not considered as a gas, since it cannot be converted into, or produced

from water and therefore plays no role in the constitution of matter.

Combustion, according to the theory accepted in the 17th century, was the decomposition

of a compound substance, in which the ‘oily’ principle present in the ‘sulphur’ was lost. It was

this ‘oily’ principle that was held responsible for the cohesion of a substance. Thus, combustion

will imply a decrease in weight. However, experiments done with combustion showed that the

total weight of the matter before and after the process was conserved. The correct theory of

combustion ( = oxidation) came at the end of the 18th century, initiated by the research of

Lavoisier.

Boyle as a chemist

The theory of the structure of matter got a further impulse by the work of Robert Boyle. In hiswork The Sceptical Chymist he criticizes both the Aristotelian theory of the four elements and

the theory of Paracelsus of the three basic substances salt, sulphur and mercury. He said that the

products into which one may analyze a chemical compound by heating are not always three in

number and that they do not always have the properties of the three basic substances.

In his work The Origin of Forms and Qualities According to the Corpuscular Philosophy

Boyle adopts the mechanistic, corpuscular view of matter: everything is composed of small

particles of different form and size which move about in various ways. These particles are

created by God and their motions are regulated by Him. Thus, the whole world including the

complicated bodies of the living beings are designed and realized by God. His view was a

christianized atomism, like that of Gassendi. There is an order in nature which is imposed by

God and which we call the laws of nature.

Boyle states that compound substances are composed of elements (not the four elements

or the three of Paracelsus), which he defines as those substances which cannot be further

analyzed into other substances. The elements are composed of conglomerations of atoms that are

only seldom split up by nature. These conglomerations are called primary concretions. The properties of each element are determined by the form, size, motion, position and order of the

atoms in the primary concretion. Compound substances arise when primary concretions combine

and form a body. This view of the structure of matter is completely theoretical. Indeed he says

that he does not know how many elements there are and which they are, and he does not try to

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http://en.wikipedia.org/wiki/Copper


http://en.wikipedia.org/wiki/Copper



find out what exactly the pattern of atoms is for the primary concretions of a certain chemical

substance.

The mechanistic-corpuscular theory of matter still leaves room for alchemical

transformation: since the properties of a substance are determined by the pattern of atoms of its

primary concretion, it must be possible to obtain another substance by modifying the pattern of

atoms. Indeed Boyle occupied himself with alchemy.

Boyle took great pains to show that his mechanistic-corpuscular worldview did not clash

with the doctrines of Christianity. He stated that God has revealed Himself also in nature;

therefore a Christian should study nature in order to discover that it is ordered according to laws

designed by God. The mechanistic worldview, which implies the purposefulness of nature, helps

to understand that there must be a Designer who has created the world and maintains it.

He was aware that the research of nature had its own method, namely the experimental

method, and that it should be separated from religion and philosophy. He founded the ‘InvisibleCollege’, in which a goup of scholars devoted themselves to scientific reasearch. This later

became the Royal Society (of London for the Improvement of Natural Knowledge). Its

commitment was to establish the truth of scientific matters through experiment rather than

through citation of authority.

Phlogiston theory

The 17th century theory of combustion (see above) developed into the phlogiston theory. This

theory is associated with the name of Georg Stahl (d. 1734), a professor of medicine and

chemistry in Halle (Germany). According to this theory, all combustible substances, such as

sulphur, carbon, oil, etc. contain phlogiston (Greek phlogistos = flammable), a substance without

color, odor, taste or weight. During combustion phlogiston escapes from the combustible

substance, thus changing their properties. Metals also contain phlogiston; when metals are

converted into their calces (metal oxides), phlogiston escapes. The calx is the ‘dephlogisticated’

substance, which was supposed to be the ‘true’ form of the substance. ‘Perfect’ metals contain

very little or no phlogiston. Air is essential for combustion; Boyle had shown that combustionceases when air is withdrawn from a closed vessel and that a glowing splint was rekindled when

air was readmitted. The explanation was that air stirs up the phlogiston particles and causes them

to escape. Metals may also be converted into calces by dissolving them in sulphuric acid (H2SO4)

or nitric acid (HNO3). Then the metal gives up its phlogiston to the acid which lacks it.

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The known experimental fact that metals increase in weight when they are converted into

calces seemed to contradict the phlogiston theory. Stahl replied that the escape of phlogiston

produces empty spaces in metals, and that air will rush into those spaces, replacing the

weightless phlogiston.

Stahl later extended the theory of phlogiston beyond combustion; phlogiston became a

universal principle governing all chemical processes.

The gas hydrogen H2 was identified by the British scientist Henry Cavendish (d. 1810),

although the gas had already been produced before by Paracelsus. Cavendish produced it by

mixing mercury with an acid, giving the reaction Hg + 2 H+ → Hg2+ + H2. He found that is was

highly flammable and called it ‘flammable air’; he also found that it produced water when it was

burned. The name hydrogen was given to it by Lavoisier (see below).

The discovery of oxygen O2 is usually ascribed to Joseph Priestley (d. 1804), a British

chemist and clergyman. It had also been discovered about a year earlier by the Swedish pharmacist Scheele, but Priestley’s result was published before that of Scheele. They both

produced it by heating mercuric oxide HgO. Priestley called it ’dephlogisticated air’, since it had

supposedly surrendered its phlogiston to the metal oxide and consequently it had a great capacity

to take up phlogiston. Indeed, he noticed that it greatly supported the burning of a candle and

respiration (breathing was considered to be a kind of combustion, so the burning of a candle and

respiration were the same kind of processes, giving off phlogiston). The name oxygen was given

by Lavoisier.

The gas nitrogen N2 was discovered by the Scottish chemist David Rutherford (d. 1819).

He burned a candle in a closed quantity of air until it went out. In the remaining gas a mouse

died and nothing could burn in it. He called this gas noxious air or phlogisticated air. It was later

called nitrogen. The burning candle had given off phlogiston, until the air was saturated with it

and could not take more. Therefore nothing could burn in it and no respiration was possible.

Priestley and most chemists of his time still thought that air was an element, not

composed of other substances. Also, they adhered to the phlogiston theory. That is why oxygen

and nitrogen were called dephlogisticated air and phlogisticated air respectvely: oxygen was air that had given up its phlogiston to the metal oxide; therefore it had a capacity to take up more

phlogiston than ordinary air, and so it could support combustion to a greater extent; and nitrogen

was air that was saturated with phlogiston, therefore it did not support combustion.

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Lavoisier

The French scientist Lavoisier (d. 1794) is called the ‘father of modern chemistry’. He showed

by his experiments that calcination of metals is in fact the combination of the metal with oxygen.

He first combined a measered quantity of oxygen with mercury and thus obtained mercuric

oxide; when he then heated the oxide he recovered the same quantity of gas. This made the

phlogiston theory superfluous.

He also showed that water was composed of hydrogen and oxygen: when hydrogen was

ignited and burnt the result was water. In fact, Cavendish had done this experiment before, but he

explained it in terms of the phlogiston theory: flammable air (hydrogen) surrenders its phlogiston

to dephlogisticated air (oxygen) and becomes water.

Lavoisier also formulated the law of conservation of matter: in a chemical reaction, the

sum of the mass of the reactants equals the sum of the mass of the products.

He clarified the concept of an element as a simple substance that could not be brokendown by any known method of chemical analysis; he drew up a list containing 33 elements,

which included hydrogen, nitrogen, oxygen, phosphorus, mercury, zinc, and sulphur . It forms the

basis for the modern list of elements.

Although Lavoisier abandoned the phlogiston theory of combustion, he introduced

another theory, the caloric theory, according to which heat consists of a subtle fluid called

‘caloric’ that flows from hotter to colder bodies. Gases such as oxygen were supposed to be rich

in caloric. The quantity of this substance is constant during all processes throughout the universe.

In the 17th century chemists explained chemical reactions with the concept of affinity: one body

would expel a second one from its union with a third because the first one had more affinity with

the third than the second. For instance, acids have more affinity to iron than to copper, more to

copper than to silver. Tables were set up that showed the affinity of chemical substances for each

other. For instance, one could compare the affinity between a metal and acids, by putting a

identical metal cylinders in various acids and then determine their loss of weight after one hour.

The theory of affinities prepared the field for the atomic theory of Dalton.The British chemist and physicist Dalton (d. 1844) discovered the law of multiple

proportions, which says that if two elements form more than one compound between them, then

the ratios of the masses of the second element which combine with a fixed mass of the first

element will be ratios of small whole numbers. For example, if 100 grams of carbon reacts with

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133 grams of oxygen to produce carbon monoxide CO, then with 266 grams of oxygen it will

produce carbon dioxide CO2. This could be explained by the atomic theory, the main points of

which were: (1) Elements consist of tiny particles called atoms. (2) The atoms of a given element

are identical. (3) The atoms of a given element are different from those of any other element. (4)

Atoms of one element can combine with atoms of other elements to form compounds. A given

compound always has the same relative numbers of types of atoms. (5) Atoms cannot be created,

divided into smaller particles, nor destroyed in the chemical process. A chemical reaction simply

changes the way atoms are grouped together. Dalton then gave a table of atomic weights.

Mathematics

Descartes

The importance of Descartes lies in mathematics, more than in physics. He developed analyticgeometry. The idea of analytic geometry is that each equation of the form f(x,y) = 0 corresponds

to a curve in two-dimensional space. In order to draw the curve one needs a system of

coordinates. In fact, the system of ‘Cartesian coordinates’ was not much developed in Descartes’

work.

His work was not just the application of algebra to geometry; he also solved algebraic

problems in a geometrical way such as the Greeks had done. We consider parameters and

unknowns in an equation as numbers; Descartes considered them as line segments. In contrast to

the Greeks, he interpreted x2, for example, not as a square, but also as a line. He described the

solution of a quadratic equation x2 + ax = b2 by constructing a line AB of length b, a

perpendicular AC of length a/2 erected at A and a circle of radius a/2 with center C. If BC

intersects the circle at D and E, then DB is the required length x.

Fermat

Besides Descartes the French lawyer Fermat (d. 1665) was the other main figure of mathematics

in his time. He founded the modern theory of numbers. For instance, he showed that every primenumber of the form 4 n + 1 can be written in one and only one way as the sum of two squares.

He also stated that for every integer n greater than two there are no positive integers x, y and z

such that xn + yn = z n. This remained unproved until 1995, when Andrew Wiles found a proof

using advanced modern methods.

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PHILOSOPHY OF SCIENCE

Aristotle

Aristotle distinguished between knowledge of the fact and knowledge of the reason why. The

former starts from an observed fact or event and concludes to a prior or more general principle

that supposedly explains the fact; the latter starts from a prior or more general principle from

which the fact is deduced. For instance:

(a) The moon is eclipsed, therefore there is a body between the moon and the sun.

(b) There is a body between the moon and the sun, therefore the moon is eclipsed.

Or:

(a) This wood is being burned, therefore it is affected by fire.

(b) This wood is affected by fire, therefore this wood is being burned

Arguments (a) discover the cause from knowledge of the effect, arguments (b) deduce the effectfrom a prior known principle or cause. We say that the cause of the wood is being burned is that

it is affected by fire, not that the cause of being affected by fire is that it is burned.

The first process is induction, the second one is deduction. Induction is proceeding from what is

observed and what is ‘more knowable to us’ to principles that are prior ‘in the order of nature’

but at first ‘less knowable’ to us. This involves finding a statement or definition of the principle

that causes the observed phenomenon.

Grosseteste

Grosseteste (13th century) explains how to arrive at such a definition of the principles causing

observed phenomenon (see Crombie pp. 219 ff.). First, one has to use the process of ‘resolution

and composition’ (analysis and synthesis). Resolution is the process in which one collects

instances of the phenomenon, noting the properties they have in common, and suggesting a

causal connection when these properties are found to be frequently associated with other

phenomena or with the suggested cause. Then follows the procees of composition, in which it is

shown that the phenomenon can indeed be deduced from the suggested cause and that they arerelated as cause and effect.

Furthermore, it is also possible that from repeatedly observed facts one arrives at an

explaining principle by a sudden intuition or scientific imgination.

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In natural science one cannot arrive at a complete definition or an absolutely certain

knowledge of the cause from which an effect follows, in contrast to what is the case in

mathematics, where objects are completely defined and all other properties may be deduced from

these definitions. In nature it is possible that the same effect follows from more than one cause

and one can never know all possibilities. One gets closer to a true knowledge of the causal

principles when a theory is confirmed by certain experiments (verification) and when one

eliminates theories which are contradicted by experience (falsification).

Grosseteste also recognized that the process of induction is based on the assumption that

nature is uniform: the same kind of things will produce the same kind of effects, always and

everywhere. Another principle was the principle of economy: a demonstration is better when it

requires a smaller number of suppositions or premisses from which it proceeeds (Crombie

p. 222).

In the time of the Renaissance this method of scientific research was explicitly statedagain, for instance, in Padua and other universities in northern Italy in the 15th and 16th century

(see Dijksterhuis pp. 259-260, Crombie pp. 228-229). The method of resolution and composition

was taken up by the doctors in the medical school of Padua in finding the cause of a disease and

the effectiveness of a drug.

Ockham

Induction was discussed in the 14th century by William of Ockham. He adhered to two principles:

(a) Only the individual sensible substances are real and only propositions about individual things

apprehended by the senses are ‘real science’. All explaining theories use names which stand

merely for concepts, not for anything really existing. (b) The principle of economy, already

stated earlier (see above). He formulated it as ‘A plurality must not be asserted without

necessity’. The slogan Entia non sunt multiplicanda praeter necessitatem was introduced in the

17th century (Ockam’s razor).

He defined cause as something that when it is present the effect follows and when it is

not present, all other conditions being the same, the effect does not follow (cf. Mill’s method of Agreement and Difference). He recognized that the same effect may have different causes, so

that it is necessary to eliminate other suggested causes. If one observes (repeatedly) that someone

is cured from fever after eating a certain herb, and all other possibe causes of his cure are

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removed, then one knows that this herb was the cause of recovery and one has experimental

knowledge of this particular connection.

In fact, Ockham attacked the Aristotelian concept of necessary causation. We can observe

only individual objects and events, and we can establish that certain facts are occurring together

with certain others, but we cannot demonstrate that there is a necessary causal connection

between them. This led to his concept of motion as something having no reality apart from the

moving bodies. A moving body is just a body existing successively in different places; motion is

not an attribute that is added to a body when it starts moving.

Francis Bacon

According to the British philosopher Francis Bacon (d. 1626), we should not only get to know

Nature, but also control it by technology. This control of Nature may be achieved by ‘obeying’

it, that is, our technological action should be ‘in conformity with’ Nature. One has to startcollecting facts and data. Then one has to order them and, for instance, look into the cases where

two phenomena occur together and where they do not occur together. Then one has to look for

rules that explain these cases and these rules have to be verified with experiments.

Bacon’s ideas may be connected with the ideas of the Reformation. Man is God’s

governor in the world, therefore man should get knowledge of Nature and control it. This will

also serve the improvement of the condition of man.

Galileo

As we have seen above, Galileo did not look for essential natures as the cause of natural

phenomena. The goal of physical research is just to establish regularities in nature and to

describe them in mathematical terms. In this respect his ideas were similar to those of Ockham.

The method to be followed is the method of resolution and composition: by induction from

experience one may find a general theory and this theory should be verified or falsified by

experiments. What Galileo added to this method is that one needs to abstract from the experience

of daily life in order to isolate the ‘pure’ phenomenon, which then can be described inmathematical terms (show how Galileo followed this method in his discovery of the relation

between distance and time for a uniformly accelerated motion).

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Descartes

Descartes belongs to those who adopt a rationalist philosophy: everything is deduced from

certain primary principles that are obvious for human reason and nature behaves according to

what we have deduced. This is in opposition to the empiricist approach of, for instance, Bacon,

Galilei, Huygens and Newton. The empiricist does not impose his way of thinking to nature, but

starts to investigate nature itself and adapts his way of thinking to what he has found. A

rationalist approach is not suitable for the progress of science.

The philosophy of Descartes can be characterized as dualism: there are two substances:

matter, which is characterized by extension, and spirit or mind, which is characterized by

thinking. These two substances are rigidly separated: thinking has no property characteristic of

matter and matter has no property characteristic of spirit: matter has no active, organizing

principles comparable to Aristotelian forms.

Descartes first explains his method of philosophy: He says: “I will never accept anythingas true if I did not have evident knowledge of its truth; that is, to include nothing more in my

judgements than what presented itself to my mind so clearly and distinctly that I had no occasion

to doubt it”. These ‘clear and distinct’ ideas are the simplest components or principles of a

subject matter that can be directly grasped by intuition.

In order to arrive at a fundamental set of principles that one can know as true without any

doubt, Descrate starts with doubting any idea that can be doubted. For instance, when we dream

we perceive things that seem real, but do not actually exist. Thus, one cannot be sure that the

data of sense experience correspond with things that really exist. Also, perhaps there is an ‘evil

demon’: a powerful and cunning being who tries to deceive us from knowing the true nature of

reality. Therefore, nothing can be known for certain, except one thing: if I am being deceived,

then surely ‘I’ must exist. Descartes expressed this as cogito ergo sum (I think, therefore I am).

Thus, Descartes concludes that he can be certain that he exists.

Then he argues that he perceives his body through the use of the senses which have

previously been proven unreliable. Thus, the only undoubtable knowledge is that he is a thinking

thing . Descartes defines ‘thinking’ (cogitatio) as ‘what happens in me such that I amimmediately conscious of it, insofar as I am conscious of it’. Thinking is every activity of a

person of which he is immeditately conscious.

Descartes further shows the unreliabilty of sense perception with the example of wax.

When he looks at a piece of wax: His senses inform him that it has certain characteristics, such

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bodies themselves but only exist in the mind of the observer, as a result of the relation between

the body, the sense organs and the mind (primary and secondary qualities). Thus, the whole

visible world is 'as if it were a machine in which there was nothing at all to consider except the

figures and motions of its parts'.

In the human being the thinking substance and the material substance are intimately

united, bnt still remain distinct. The essence of the mind is thinking; this does not involve the

body. The ideas of imagination, sensation, purposeful movement of body, appetites and most

emotions involve some relation to the body and therefore do not belong to the essence of the

mind. On the other hand, imagination, sensation, etc., which are produced by the body, are not

possible without the mind. The human body considered in itself is part of the external material

world that works a machine. But from the point of view of the self, the presence of the soul in the

body makes it different from other matter. Thus, the ideas we have of the body and mind in

union are different from, and irreducible to, the ideas we have of either extended matter, or of thinking substance.

Descartes believes that the union of body and mind only occurs in humans. Animals have

only bodies and are essentially automata or biological robots which behave according to their

internal biological/mechanical makeup. Thus, they do not think, but they do have life and

sensations. The characteristic that distinguishes humans from animals is their ability to

communicate by means of a language.

The ideas in the mind that do not involve the body are innate ideas. According to

Descartes, our minds come stocked with a variety of intellectual concepts—ideas whose content

derives solely from the nature of the mind. These ideas includes concepts in mathematics (e.g.,

number, line, triangle), logic (e.g., contradiction, necessity), and metaphysics (e.g., identity,

substance, causality). Since bodies do not have properties corresponding to our ideas of colors,

sounds, tastes, etc., also these ideas are innate in the mind itself. However, the formation of these

sensory ideas depends on sensory stimulation.

Descartes’s dualism poses a problem insofar as an explanation is needed as to how our

minds and bodies interact. This problem is not solved just by their close union, for they are stillessentially different kinds of things. He suggests that it is the pineal gland in the brain which is

the gateway between the two realms. With sensory perception, information is transferred to the

pineal gland through animal spirits, blood, and nerves. With motor commands, the gland is

moved by the soul, and thrusts the animal spirits towards the pores of the brain, and onto the

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nerves. Suggesting the pinal gland as the site of interaction between mind and body is not meant

as an explanation of this interaction. The notions we have of mind and of body are primary, that

is, they cannot be explained in other terms, and similarly the notion of their union must be taken

as primary.

Pascal

For a long time Pascal has remained sceptical about the correctness of the explanation of the

barometer by means of the pressure of the air. He considered this explanation as a hypothesis,

but he also looked into other current hypotheses, such as the notion of the horror vacui.

According to him, a scientific statement should be accepted as true only either if it is obvious to

one’s senses or reason, or if it is a logical conclusion from one or more of such obvious

principles. Any other statement is a hypothesis the truth of which is doubtful. In fact, there are

three possibilities for a hypothesis: (1) From its denial a contradiction or impossibility follows;then the hypothesis is true. (2) From its assertion a contradiction or impossibility follows; then

the hypothesis is false. (3) In other cases the hypothesis remains doubtful. Especially, if all

known phenomena are explained by the hypothesis and may be derived from it, its truth is not

established. Thus, the truth of the theory of air pressure is not established by the phenomena of

the barometer. Pascal also says that the truth of the Copernican system is not established by the

astronomical observations; the systems of Ptolemy and Tycho Brahe also explain the planetary

motion, and therefore are of equal value.

Pascal was convinced of the truth of the hypothesis of the air pressure by the experiment

with the barometer on the top of the mountain. Then he rejected the hypothesis of the horror

vacui. In fact, this decision was not in agreement with his own requirements for the truth or

falsity of a hypothesis. The hypothesis of horror vacui did not lead to a contradiction with the

experiment and the fact that the result of the experiment may be derived from the hypothesis of

air pressure does not establish the truth of the latter.

Indeed, Pascal’s criteria for the truth of a hypothesis apply for mathematics, but for

science they are too severe. This implies that science does not arrive at the same certainty of knowledge as mathematics.

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Scientific method

We have discussed the experiments Galileo did to refute the Aristotle’s theory of motion and to

test his own theory. The question arises which conclusion we are justified to draw: that Galileo’s

theory is correct and Aristotle’s theory is wrong? Or that Galileo’s theory is correct under certain

circumstances but may be wrong under others? Or that Aristotle’s theory is correct under certain

circumstances but may be wrong under others? Or that Galileo’s theory is more likely to be

correct than Aristotle’s? Assuming that Galileo was honest, maybe there was something wrong

with his experiments without him knowing it. If so, what would be the consequences for the

answer on the preceding questions? Why do scholars generally think that Galileo’s theory is

better than Aristotle’s? Trying to find an answer on such questions is part of the philosophy of

science. One question which arises in relation to this is: how is science supposed to proceed,

what is the method of science? Not surprisingly, philosophers have replied to this question indifferent ways.

As we have seen above, Bacon supposed that the way for science to proceed is to collect

as much data as possible and to infer general theories from them. This is the method of

induction. It is in this way that, for instance, Snellius found the law of refraction. One problem

with this method is that even when we have collected many data and found a theory that explains

them, we will never be able to collect all data relevant to the theory. (Perhaps there is an infinite

number of them, some of them lying in the future). Thus, it always remains possible that there is

a fact or phenomenon that contradicts the theory. Suppose we see a sheep and it is white. We see

another sheep and it is also white. How many white sheep do we have to see before we are

allowed to conclude that all sheep are white? Even if we have seen a million of white sheep it

remains possible that the next one we see is black (problem of induction).

The method of induction is not the method of Galileo. He did not start with balls rolling

down an inclined plane and then found the relation between the distance travelled and the time.

He had already derived the relation between distance and time from his theory and then used the

experiment to verify it. This is called the hypothetico-deductive method. One starts with an ideaor theory (the hypothesis), we deduce from it certain consequences that can be tested by an

experiment or observation, and then verify the theory with the experiment. This is the method

also used by Newton.

Stated in logical form this method proceeds as follows:

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P1: If theory T is correct, then we expect to observe certain facts F.

P2: We observe F.

C: Thus, T is correct.

This argument is logically not valid. From the premisses P1 and P2 one the conclusion C does

not follow.

Another method was defended by Popper (born in Vienna, later worked in London,

d. 1994). He tried to avoid the problem of induction, by suggesting that scientists should propose

theories and then try to falsify them with experiments and observations (critical rationalism). If

we see just one black sheep, then the theory that all sheep are black is refuted. A good theory is a

theory that has survived many attempts at falsification. Every further white sheep we see is a

confirmation of the theory that all sheep are white. But is is not a verification: still it is possible

that it is wrong. It means that we never can be sure whether a theory is correct or not; everytheory remains a hypothesis, some being better than others. A theory that is constructed in such a

way that it is impossible for it to be falsified is not scientific.

This method of falsification proved to be problematic as well. Sometimes a theory is

falsified, but still scientists remain to consider it correct. Maybe there was an error made in the

experiment or observation, or maybe it was possible to explain the result by expanding the

theory. The phlogiston theory, for instance, continued to be defended despite the fact that metals

increased in weight at oxidation. When the motion of the planet Uranus showed discrepancies

with the motion calculated for it with the laws of Newton, these laws were not considered to be

refuted. Instead, one proposed the existence of another planet, which was subsequently found

(Neptune). Popper considered this discovery as a strong confirmation for the theory of Newton.

However, Lakatos (born in Hungary, later worked in London, pupil of Popper, d. 1974) asked

what would have happened when Neptune had not been found. Would Newton’s theory have

been refuted, and abandoned? No, another explanation would have been found, maybe an error

in the telescope, influence of the earh’s atmosphere, etc.

The American historian and philosopher of science Thomas Kuhn (d. 1996) claimed thatthe history of science shows that scientists seldom proceed according to the method of

falsification alone. He proposed another model for the development of science: he described

science as consisting of periods of normal science in which scientists continue to hold their

theories in the face of anomalies, interspersed with periods of great conceptual change ( scientific

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revolutions), when one paradigm is replaced by another. For instance, Aristotelian natural

philosophy is one paradigm. Scholars worked within that paradigm during a long period of time

without putting its fundamental principles into doubt. The work of Galileo and Newton may be

considered as the overthrow of this paradigm and its replacement by a new paradigm, that of

classical mechanics. Kuhn holds that two different paradigms are incommensurable, that is, that

it is not possible to understand one paradigm through the conceptual framework and terminology

of another rival paradigm, since the terms and concepts of different paradigms mean different

things, even if the same word is used in both paradigms (for instance: the term ‘mass’ in

Newtonian mechanics and in Einstein’s theory of relativity).

It is now recognized that there not one unique method for science. Different disciplines

(biology, physics, etc.) use different methods and within one discipline methods have varied in

different periods of history.

Philosophers of science have tried to find criteria to decide what is science and what not,for instance, to distinguish between astronomy and astrology, theory of evolution and

creationism, etc. (demarcation problem). Several of such criteria were proposed, but they were

all subject to critique. Many philosophers have decided that there is not a unique set of criteria

that would solve the demarcation problem. Instead, they set up a list of characteristics that would

describe science. For instance, a scientific theory is such that (a) it makes testable predictions;

(b) it is falsifiable; (c) it explains known facts; (d) it predicts new facts; etc. It is possible that a

theory does not satisfy all criteria of such a list, while it is still a good or useul theory.

Lakatos explained that scientists work according a scientific research programme. He

looked for the factors that made scientists decide when it is appropriate to discard a theory and

when it is preferable to adhere to it. For instance, atomism was proposed as a theory in ancient

Greece. Since then the theroy has been verified and falsified, supported and rejected on several

occasions, and two thousand years later it was accepted as a theory fulfilling sufficient criteria to

be called scientific. Thus, how can we be sure that if we discard a theory we are not making a

mistake? If we cannot be sure, it means we should give a chance even to ‘crazy’ theories that do

not seem to be strongly supported. This is the idea of pluralism. It was proposed in an extremeform by Feyerabend (born in Vienna, a pupil of Popper, worked at universities all over the

world, d. 1994).

Lakatos analysed scientific research programmes and concluded that a scientific theory

consists of parts which form its core and which we are reluctant to give up (for instance, the

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laws of Newton), and additional or auxiliary ideas that are used to defend the theory when

anomalies (apparent contradictions) and new information come up (for instance, in the time that

it was assumed that there were seven planets, the hypothesis that an eighth planet exists). He

suggested that a progressive research programme (that is, research that makes science advance)

is such that it makes new predictions or discovers new facts, in contrast to a degenerative resarch

programme, which does not.

The problem of realism.

An important issue in the philosophy of science is the problem of realism. Consider the theory of

gravity explaining the fall of an apple, or the theory of electrons explaining the emission of light.

In view of the fact that no one has ever seen gravity itself or electrons themselves, but only

experienced the consequences of their alleged existence, one may ask whether gravity, or electrons really exist . Previously people have used phlogiston, aether, etc. in their theories, but

these theories were abandoned and these stuffs were declared not to exist.

The question of real existence may be asked not only for unobservable concepts, objects

and events occurring in scientific theories, but for all things in the world, including those which

are directly experienced by our senses. How do we know that something exists outside ourselves

that corresponds to our sense experience? We have seen that Descartes claimed that indeed

things exist in the external world, namely matter with its primary properties of size, shape, order

and motion, but that secondary properties, such as color and heat, do not really exist outside

ourselves, but are induced in our mind by the material objects.

There are several possibilities for one who denies the real existence of concepts used in

scientific theories. One may say that a theory is an instrument that is used to explain or predict,

and that when a theory is successful in this, it does not say anything about what really exists or

does not exist (instrumentalism). Or one may say that a theory represents a model of the world,

hist phil sci

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