THE INFLUENCE OF ABSTRACT THOUGHT--GREECE: ARISTOTLE
No sooner did the Greeks turn their attention to the sciences which had
originated in Egypt and Babylonia than the characteristic intellectual
quality of the Hellenic genius revealed itself. Thales (640-546 B.C.),
who is usually regarded as the first of the Greek philosophers, was the
founder of Greek geometry and astronomy. He was one of the seven "wise
men" of Greece, and might be called the Benjamin Franklin of antiquity,
for he was interested in commerce, famous for political sagacity, and
honored for his disinterested love of general truth. His birthplace was
Miletus, a Greek city on the coast of Asia Minor. There is evidence that
he acquired a knowledge of Babylonian astronomy. The pursuit of commerce
carried him to Egypt, and there he gained a knowledge of geometry. Not
only so, but he was able to advance this study by generalizing and
formulating its truths. For the Egyptians, geometry was concerned with
surfaces and dimensions, with areas and cubical contents; for the Greek,
with his powers of abstraction, it became a study of line and angle. For
example, Thales saw that the angles at the base of an isosceles triangle
are equal, and that when two straight lines cut one another the
vertically opposite angles are equal. However, after having established
general principles, he showed himself capable of applying them to the
solution of particular problems. In the presence of the Egyptian
priests, to which class he was solely indebted for instruction, Thales
demonstrated a method of measuring the height of a pyramid by reference
to its shadow. And again, on the basis of his knowledge of the relation
of the sides of a triangle to its angles, he developed a practical rule
for ascertaining the distance of a ship from the shore.
The philosophical mind of Thales laid hold, no doubt, of some of the
essentials of astronomical science. The particulars usually brought
forward to prove his originality tend rather to show his indebtedness to
the Babylonians. The number of days in the year, the length of the
synodic month, the relation of the sun's apparent diameter to the
ecliptic, the times of recurrence of eclipses, were matters that had
long been known to the Babylonians, as well as to the Chinese. However,
he aroused great interest in astronomy among the Greeks by the
prediction of a solar eclipse. This was probably the eclipse of 585
B.C., which interrupted a fierce battle between the Medes and the
Lydians. The advice of Thales to mariners to steer by the Lesser Bear,
as nearer the pole, rather than by the Great Bear, shows also that in
his astronomical studies as in his geometrical he was not indifferent to
the applications of scientific knowledge.
In fact, some writers maintain that Thales was not a philosopher at all,
but rather an astronomer and engineer. We know very little of his purely
speculative thought. We do know, however, that he arrived at a
generalization--fantastic to most minds--that all things are water.
Attempts have been made to add to this statement, and to explain it
away. Its great interest for the history of thought lies in the fact
that it is the result of seeking the constant in the variable, the
unitary principle in the multiple phenomena of nature. This abstract and
general view (though perhaps suggested by the Babylonian belief that the
world originated in a watery chaos, or by the teaching of Egyptian
priests) was preëminently Greek, and was the first of a series of
attempts to discover the basis or origin of all things. One of the
followers of Thales taught that air was the fundamental principle; while
Heraclitus, anticipating to some extent modern theories of the origin of
the cosmos, declared in favor of a fiery vapor subject to ceaseless
change. Empedocles, the great philosopher-physician, first set forth the
doctrine of the four _elements_--earth, air, fire, and water. For
Democritus indivisible particles or atoms are fundamental to all
phenomena. It is evident that the theory of Thales was a starting point
for Greek abstract thought, and that his inclination to seek out
principles and general laws accounts for his influence on the
development both of philosophy and the sciences.
Pythagoras, on the advice of Thales, visited Egypt in the pursuit of
mathematics. There is reason to believe that he also visited Babylonia.
For him and his followers mathematics became a philosophy--almost a
religion. They had discovered (by experimenting with the monochord, the
first piece of physical-laboratory apparatus, consisting of a tense
harpstring with a movable bridge) the effect on the tone of the string
of a musical instrument when the length is reduced by one half, and also
that strings of like thickness and under equal tension yield harmonious
tones when their lengths are related as 1:2, 2:3, 3:4, 4:5. The
Pythagoreans drew from this the extravagant inference that the heavenly
bodies would be in distance from the earth as 1, 2, 3, 4, 5, etc. Much
of their theory must seem to the modern mind merely fanciful and
unsupported speculation. At the same time it is only just to this school
of philosophers to recognize that their assumption that simple
mathematical relationships govern the phenomena of nature has had an
immense influence on the advance of the sciences. Whether their
fanaticism for number was owing to the influence of Egyptian priests or
had an Oriental origin, it gave to the Pythagoreans an enthusiasm for
pure mathematics. They disregarded the bearing of their science on the
practical needs of life. Old problems like squaring the circle,
trisecting the angle, and doubling the cube, were now attempted in a new
spirit and with fresh vigor. The first, second, and fourth books of
Euclid are largely of Pythagorean origin. For solid geometry as a
science we are also indebted to this sect of number-worshipers. One of
them (Archytas, 428-347 B.C., a friend of Plato) was the first to apply
geometry to mechanics. We see again here, as in the case of Thales, that
the love of abstract thought, the pursuit of science as science, did not
interfere with ultimate practical applications.
Plato (429-347 B.C.), like many other Greek philosophers, traveled
extensively, visiting Asia Minor, Egypt, and Lower Italy, where
Pythagorean influence was particularly strong. His chief interest lay in
speculation. For him there were two worlds, the world of sense and the
world of ideas. The senses deceive us; therefore, the philosopher should
turn his back upon the world of sensible impressions, and develop the
reason. In his _Dialogues_ he outlined a course of training and study,
the professed object of which was to educate a class of philosophers.
(Strange to say, Plato's curriculum, planned originally for the
intellectual _élite_, still dictates in our schools the education of
millions of boys and girls whose careers do not call for a training
merely of the reason.)
Over the porch of his school, the Academy at Athens, were inscribed the
words, "Let no one who is unacquainted with geometry enter here." It was
not because it was useful in everyday life that Plato laid such
insistence on this study, but because it increased the students' powers
of abstraction and trained the mind to correct and vigorous thinking.
From his point of view the chief good of geometry is lost unless we can
through it withdraw the mind from the particular and the material. He
delighted in clearness of conception. His main scientific interest was
in astronomy and mathematics. We owe to him the definition of a line as
"length without breadth," and the formulation of the axiom, "Equals
subtracted from equals leave equals."
Plato had an immediate influence in stimulating mathematical studies,
and has been called a maker of mathematicians. Euclid, who was active at
Alexandria toward the end of the fourth century B.C., was not one of
Plato's immediate disciples but shared the great philosopher's point of
view. The story is told that one of his pupils, arrived perhaps at the
_pons asinorum_, asked, "What do I get by learning these things?"
Euclid, calling his servant, said, "Give him sixpence, since he must
make gain out of what he learns." Adults were also found, even among the
nimble-witted Greeks, to whom abstract reasoning was not altogether
congenial. This is attested by the familiar story of Ptolemy, King of
Egypt, who once asked Euclid whether geometry could not be learned in
some easier way than by studying the geometer's book, _The Elements_. To
this the schoolmaster replied, "There is no royal road to geometry." For
the academic intelligence abstract and abstruse mathematics are tonic
and an end in themselves. As already stated, their ultimate practical
value is also immense. One of Plato's associates, working under his
direction, investigated the curves produced by cutting cones of
different kinds in a certain plane. These curves--the ellipse, the
parabola, the hyperbola--play a large part in the subsequent history of
astronomy and mechanics. Another Platonist made the first measurement of
the earth's circumference.
Aristotle, the greatest pupil of Plato, was born at Stagira in 384 B.C.
He came of a family of physicians, was trained for the medical
profession, and had his attention early directed to natural phenomena.
He entered the Academy at Athens about 367 B.C., and studied there till
the death of Plato twenty years later. He was a diligent but, as was
natural, considering the character of his early education, by no means a
passive student. Plato said that Aristotle reacted against his
instructor as a vigorous colt kicks the mother that nourishes it. The
physician's son did not accept without modification the view that the
philosopher should turn his back upon the things of sense. He had been
trained in the physical science of the time, and believed in the reality
of concrete things. At the same time he absorbed what he found of value
in his master's teachings. He thought that science did not consist in a
mere study of individual things, but that we must pass on to a
formulation of general principles and then return to a study of the
concrete. His was a great systematizing intellect, which has left its
imprint on nearly every department of knowledge. Physical astronomy,
physical geography, meteorology, physics, chemistry, geology, botany,
anatomy, physiology, embryology, and zoölogy were enriched by his
teaching. It was through him that logic, ethics, psychology, rhetoric,
æsthetics, political science, zoölogy (especially ichthyology), first
received systematic treatment. As a great modern philosopher has said,
Aristotle pressed his way through the mass of things knowable, and
subjected its diversity to the power of his thought. No wonder that for
ages he was known as "The Philosopher," master of those who know. His
purpose was to comprehend, to define, to classify the phenomena of
organic and inorganic nature, to systematize the knowledge of his own
time.
Twenty years' apprenticeship in the school of Plato had sharpened his
logical powers and added to his stock of general ideas, but had not
taught him to distrust his senses. When we say that our eyes deceive us,
we really confess that we have misinterpreted the data that our sight
has furnished. Properly to know involves the right use of the senses as
well as the right use of reason. The advance of science depends on the
development both of speculation and observation. Aristotle advised
investigators to make sure of the facts before seeking the explanation
of the facts. Where preconceived theory was at variance with observed
facts, the former must of course give way. Though it has been said that
while Plato was a dreamer, Aristotle was a thinker, yet it must be
acknowledged in qualification that Plato often showed genuine knowledge
of natural phenomena in anatomy and other departments of study, and that
Aristotle was carried away at times by his own presuppositions, or
failed to bring his theories to the test of observation. The Stagirite
held that the velocity of falling bodies is proportional to their
weight, that the function of the diaphragm is to divide the region of
the nobler from that of the animal passions, and that the brain is
intended to act in opposition to the heart, the brain being formed of
earthy and watery material, which brings about a cooling effect. The
theory of the four elements--the hot, the cold, the moist, the dry--led
to dogmatic statements with little attempt at verification. From the
standpoint of modern studies it is easy to point out the mistakes of
Aristotle even. Science is progressive, not infallible.
In his own time he was rather reproached for what was considered an
undignified and sordid familiarity with observed facts. His critics said
that having squandered his patrimony, he had served in the army, and,
failing there, had become a _seller of drugs_. His observations on the
effects of heat seem to have been drawn from the common processes of the
home and the workshop. Even in the ripening of fruits heat appears to
him to have a cooking effect. Heat distorts articles made of potters'
clay after they have been hardened by cold. Again we find him describing
the manufacture of potash and of steel. He is not disdainful of the
study of the lower animals, but invites us to investigate all forms in
the expectancy of discovering something natural and beautiful. In a
similar spirit of scientific curiosity the Aristotelian work _The
Problems_ studies the principle of the lever, the rudder, the wheel and
axle, the forceps, the balance, the beam, the wedge, as well as other
mechanical principles.
In Aristotle, in fact, we find a mind exceptionally able to form clear
ideas, and at the same time to observe the rich variety of nature. He
paid homage both to the multiplicity and the uniformity of nature, the
wealth of the phenomena and the simplicity of the law explaining the
phenomena. Many general and abstract ideas (category, energy,
entomology, essence, mean between extremes, metaphysics, meteorology,
motive, natural history, principle, syllogism) have through the
influence of Aristotle become the common property of educated people the
world over.
Plato was a mathematician and an astronomer. Aristotle was first and
foremost a biologist. His books treated the history of animals, the
parts of animals, the locomotion of animals, the generation of animals,
respiration, life and death, length and shortness of life, youth and old
age. His psychology is, like that of the present day, a biological
psychology. In his contributions to biological science is manifested
his characteristic inclination to be at once abstract and concrete. His
works display a knowledge of over five hundred living forms. He
dissected specimens of fifty different species of animals. One might
mention especially his minute knowledge of the sea-urchin, of the murex
(source of the famous Tyrian dye), of the chameleon, of the habits of
the torpedo, the so-called fishing-frog, and nest-making fishes, as well
as of the manner of reproduction of whales and certain species of
sharks. One of his chief contributions to anatomy is the description of
the heart and of the arrangement of the blood-vessels. A repugnance to
the dissection of the human body seems to have checked to some extent
his curiosity in reference to the anatomy of man, but he was acquainted
with the structure of the internal ear, the passage leading from the
pharynx to the middle ear, and the two outer membranes of the brain of
man. Aristotle's genius did not permit him to get lost in the mere
details of observed phenomena. He recognized resemblances and
differences between the various species, classified animals as belonging
to two large groups, distinguished whales and dolphins from fishes,
recognized the family likeness of the domestic pigeon, the wood pigeon,
the rock pigeon, and the turtle dove. He laid down the characteristics
of the class of invertebrates to which octopus and sepia belong. Man
takes a place in Aristotle's system of nature as a social animal, the
highest type of the whole series of living beings, characterized by
certain powers of recall, reason, deliberation. Of course it was not to
be expected that Aristotle should work out a fully satisfactory
classification of all the varieties of plants and animals known to him.
Yet his purpose and method mark him as the father of natural science. He
had the eye to observe and the mind to grasp the relationships and the
import of what he observed. His attempt to classify animals according to
the nature of their teeth (dentition) has been criticized as
unsuccessful, but this principle of classification is still of use,
and may be regarded as typical of his mind, at once careful and
comprehensive.
One instance of Aristotle's combining philosophical speculation with
acute observation of natural phenomena is afforded by his work on
generation and development. He knew that the transmission of life
deserves special study as the predominant function of the various
species of plants and animals. Deformed parents may have well-formed
offspring. Children may resemble grandparents rather than parents. It is
only toward the close of its development that the embryo exhibits the
characteristics of its parent species. Aristotle traced with some care
the embryological development of the chick from the fourth day of
incubation. His knowledge of the propagation of animals was, however,
not sufficient to make him reject the belief in spontaneous generation
from mud, sand, foam, and dew. His errors are readily comprehensible,
as, for example, in attributing spontaneous generation to eels, the
habits and mode of reproduction of which only recent studies have made
fully known. In regard to generation, as in other scientific fields, the
philosophic mind of Aristotle anticipated modern theories, and also
raised general questions only to be solved by later investigation of the
facts.
Only one indication need be given of the practical results that flowed
from Aristotle's scientific work. In one of his writings he has stated
that the sphericity of the earth can be observed from the fact that its
shadow on the moon at the time of eclipse is an arc. That it is both
spherical and small in comparison with the heavenly bodies appears,
moreover, from this, that stars visible in Egypt are invisible in
countries farther north; while stars always above the horizon in
northern countries are seen to set from countries to the south.
Consequently the earth is not only spherical but also not large;
otherwise this phenomenon would not present itself on so limited a
change of position on the part of the observer. "It seems, therefore,
not incredible that the region about the Pillars of Hercules [Gibraltar]
is connected with that of India, and that there is thus only one ocean."
It is known that this passage from _The Philosopher_ influenced Columbus
in his undertaking to reach the Orient by sailing west from the coast of
Spain.
We must pass over Aristotle's observation of a relationship (homology)
between the arms of man, the forelegs of quadrupeds, the wings of birds,
and the pectoral fins of fishes, as well as many other truths to which
his genius for generalization led him.
In the field of botany Aristotle had a wide knowledge of natural
phenomena, and raised general questions as to mode of propagation,
nourishment, relation of plants to animals, etc. His pupil and lifelong
friend, and successor as leader of the Peripatetic school of philosophy,
Theophrastus, combined a knowledge of mathematics, astronomy, botany,
and mineralogy. His _History of Plants_ describes about five hundred
species. At the same time he treats the general principles of botany,
the distribution of plants, the nourishment of the plant through leaf as
well as root, the sexuality of date palm and terebinth. He lays great
stress on the uses of plants. His classification of plants is inferior
to Aristotle's classification of animals. His views in reference to
spontaneous generation are more guarded than those of his master. His
work _On Stones_ is dominated by the practical rather than the
generalizing spirit. It is evidently inspired by a knowledge of mines,
such as the celebrated Laurium, from which Athens drew its supply of
silver, and the wealth from which enabled the Athenians to develop a
sea-power that overmatched that of the Persians. Even to-day enough
remains of the galleries, shafts, scoria, mine-lamps, and other utensils
to give a clear idea of this scene of ancient industry. Theophrastus
considered the medicinal uses of minerals as well as of plants.
We have failed to mention Hippocrates (460-370 B.C.), the Father of
Medicine, in whom is found an intimate union of practical science and
speculative philosophy. We must also pass over such later Greek
scientists as Aristarchus and Hipparchus who confuted the theories of
Pythagoras and Plato in reference to the relative distances of the
heavenly bodies from the earth. Archimedes of Syracuse demands, however,
particular consideration. He lived in the third century B.C., and has
been called the greatest mathematician of antiquity. In him we find the
devotion to the abstract that marked the Greek intelligence. He went so
far as to say that every kind of art is ignoble if connected with daily
needs. His interest lay in abstruse mathematical problems. His special
pride was in having determined the relative dimensions of the sphere and
the enclosing cylinder. He worked out the principle of the lever. "Give
me," he said, "a place on which to stand and I will move the earth." He
approximated more closely than the Egyptians the solution of the problem
of the relation between the area of a circle and the radius. His work
had practical value in spite of himself. At the request of his friend
the King of Sicily, he applied his ingenuity to discover whether a
certain crown were pure gold or alloyed with silver, and he hit upon a
method which has found many applications in the industries. His name is
associated with the endless screw. In fact, his practical contrivances
won such repute that it is not easy to separate the historical facts
from the legends that enshroud his name. He aided in the defense of his
native city against the Romans in 212 B.C., and devised war-engines with
which to repel the besiegers. After the enemy had entered the city, says
tradition, he stood absorbed in a mathematical problem which he had
diagrammed on the sand. As a rude Roman soldier approached, Archimedes
cried, "Don't spoil my circles," and was instantly killed. The
victorious general, however, buried him with honor, and on the tomb of
the mathematician caused to be inscribed the sphere with its enclosing
cylinder. The triumphs of Greek abstract thought teach the lesson that
practical men should pay homage to speculation even when they fail to
comprehend a fraction of it.
REFERENCES
Aristotle, _Historia Animalium_; translated by D'A. W. Thompson. (Vol.
IV of the _Works of Aristotle Translated into English_. Oxford:
Clarendon Press.)
A. B. Buckley (Mrs. Buckley Fisher), _A Short History of Natural
Science_.
G. H. Lewes, _Aristotle; A Chapter in the History of Science_.
T. E. Lones, _Aristotle's Researches in Natural Science_.
D'A. W. Thompson, _On Aristotle as a Biologist_.
William Whewell, _History of the Inductive Sciences_.
Alfred Weber, _History of Philosophy_.