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Module 2: Medieval Sci/Tech

Medieval TechnologyChristianity and military warfare dominated the medieval world. This chapter discusses the

impact of military technology and the Christian monasteries on the making of medieval society

and examines the contribution of Christianity to the 12th century revival of learning.

Horses were used up to the 8th century for transportation and labor but never in combat. In the

early 8th century, however, the introduction of the stirrup, saddle, and cantle, according tohistorian of science Lynn White had a profound impact in the political reorganization of Europe.

First introduced by the Franks in the 8th century, the stirrup made the rider and the horse oneunit. This invention made mounted combat possible and implicitly cavalry not infantry became

the chief military force. The violence of mounted shock-combat, in its turn, invited thedevelopment of better armor, heavier horses, new types of shields, and the cross bow.

The Franks were the first to understand the military and political implications of mounted

combat. About 732 the Frankish leader Charles Martel sought to constitute an army of horsemen.He did not, however, have the necessary funds for the venture, and thus gave lands heconfiscated from the church to his officers upon the condition that they would generate enough

wealth in order to afford a horse of their own and be ready to fight at Martel's wish. Martel, thuscreated a social cast of feudal seniors. Martel's grandson, Charlemagne, enlarged the kingdom

under this system. In the 9th century, however, with the death of Charlemagne, the empiredisintegrated, and the cast of land owners-warriors established local political rule. This system

was later labeled Feudalism. The landlord supplied food, protection and assistance in exchangefor the work of the peasants. According to Lynn White, the revolution in military technology

introduced by the stirrup, was the seed of the medieval feudal system and thus also of the political reorganization of Europe. Along with these political developments, Western Europe was

also undergoing a second agricultural revolution.

In antiquity and early medieval society there was rarely agricultural surplus and thus most if not

all the population farmed the land. Several improvement, however, in farming generated an

agricultural revolution which in turn revolutionized society. By the mid of the 6th century theintroduction of a two-blade plow pushed by two animals enabled farmers to revolve the land

more efficiently. New land was reclaimed for agriculture thus significantly increasing productivity. The introduction of manure as a fertilizer related to improvements in cattle raising

and stock farming also increased land productivity. Other achievements included the rotation of fields and horse harnesses. The consequences of these technological innovations were such that

between 1000 and 1300 the population and the economy expanded significantly.

Increase in food production allowed people to concentrate on cities for no longer was agriculture

the only source of income. This demographic shift from the farm to the city required theimprovement of transportation because agricultural products had to be brought to the cities.

Nailed horse shoes and the horse harness were invented at this time thus providing better hauling. First introduced in Burges, Belgium, around 1236, inland navigation was significantly

improved. Another important innovation was in sea sailing. The Portuguese learned to build better boats and sail up wind. The center-board was perfected and the rudder introduced. The

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construction of better boats and deep sea navigation also brought the need for navigation tools.Originally a Chinese invention, the magnetic compass reached Europe in 1190 and within thirty

years its use was widespread.

Increase in productivity required a parallel increase in energy supply for there was more grain to

be grinned and more wood to be cut in order to build more boats and carriages. The water milltechnology grew larger and the wind mill introduced. First introduce in 1185 in the North Searegion, the wind mill soon became common throughout all of Europe.

Before the Medieval world would break its ties with the ancient world and the modern period

would be launched by the Renaissance, ancient and medieval attitudes towards work had tochange. The Greeks invented steam engines and the Romans built water wheels but they never

used this technology as sources of energy but rather as toys for entertainment. Slave or animal power fulfilled most if not all their energy needs. There were significant technological

achievements in antiquity only when there was a need. The Greeks, for example, developed pottery because they needed to store oil and wine; and the Romans were known for their roads

because they needed them for military purposes. But since slaves were cheap and plentiful therewas no need for machines. Such is the thesis of Benjamin Farrington. Slaves, however, were not

that plentiful neither cheap. They were human being who had to be fed, got sick and died. Whythen the Greeks and Romans did not develop alternative sources of energy?

The reason was that the ancients were prejudiced against manual labor. Plato, for example, placed artisans among the lowest ranks of the social ladder and Aristotle thought that they did

not deserve full citizenship. In short, ancient philosophers and the well educated, exactly thosewho could have applied their inventiveness, only distanced themselves from daily work and the

crafts.

According to Lewis Mumford, by the 12th century, however, Christianity, and the Benedictinemonasteries more specifically, radically changed this attitude towards work and technology. The

monasteries were organized along routines of prayer, study, and work. God had commanded sixdays of work and one day of rest. Labor and prayer were of equal value and a good act in the

eyes of God. The monks also sought to develop machines to ease their labor. In fact the monkswere instrumental in the shift from human and animal power to machines. Since antiquity most

of the heavy labor was slave labor. Christianity, however, had a problem with slavery and thusthe only reasonable alternative was to develop machines.

The Benedictine order established by St. Benedict of Nursia in the 6th century, was particularly

strict in labor matters. The key obligations of the order were, prayer, obedience to the superiors, poverty, and daily work as a Christian duty of no less than 5 hours a day. The Benedictine order

was internally organized to carry on the work twenty four hours per day non-stop. In doing so theBenedictine order theologically legitimated work. The Benedictine order was a source of discipline, rule, and sanction for labor. And as we shall see later, their routine of daily work was

the source of the notion of timing and centralized and automated control.

The Benedictines performed daily labor in shifts around the clock. This regularity and efficiency

of labor, according to Lewis Mumford, laid the ground for the moralization of labor. The

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literacy at a time when the number of literate persons was declining. Although the church didlittle to foster scientific and philosophic activities, it probably did more to assist in the

preservation of Greek knowledge than any other institution.

A better answer entails the realization that science, as an institution, had always been a very

precarious enterprise in the ancient world. It was a luxury to have talented people spend time in"non-productive" pursuits like science and philosophy. In a time of economic collapse such pursuits were the first to go. In a word, science and philosophy had nothing to offer society as a

whole (either Greek or Roman) that society could consider essential to its well-being. Sciencewas not yet allied with technology and could not thus promise new military hardware or miracle

cures. Science was basically useless. Societies generally support science only if it has some practical payoff. With the possible exception of the Library and Museum at Alexandria which

were supported by royal patronage, science never became institutionalized in Greece or theRoman Empire. Science prospered only so long as there was a large number of individuals who

were able to support themselves and willing to "swim against the stream." For often scientificnotions were seen to be disruptive to the dominant theology.

In any event, Roman society was hard pressed from many sides during its final years. Barbarian

invasions had forced a division of the Roman Empire into a Greek-speaking Eastern empire(Byzantium) and a Latin-speaking Western empire (with its capital in Rome). This political

division occurred around 395 A.D. Both domains continued to shrink under the pressures of theinvasions of barbarians.

Greek science did survive during this period, however. We know that it reappeared in the Westin the 12th century. How was Greek science recovered? How was it transmitted from Greece to

medieval Europe? How did it survive in the centuries separating Ptolemy from the 11-12thcenturies intellectual revival of the Latin West? It is important to keep in mind that there were

two types of transmission: a linguistic transmission which involved Greek, Syriac, Arabic,Hebrew, and Latin, and a geographical transmission which covered most of the Mediterranean

Sea (from the Greek mainland eastward across Asia Minor and into Persia, then south intonorthern Egypt, across North Africa, into Spain; and from Spain to northwestern Europe.

Beginning with the conquests of Alexander the Great (in the last quarter of the 4th century B.C.)

Greek learning and culture spread eastward. There were three main vehicles for this eastwardspread. First, the military conquests of Alexander (327-325 B.C.) and his establishment of

colonial cities throughout the conquered regions helped push Greek culture eastward. Greek culture survived in foreign lands all during this period. Second, trade with India, including

books, helped establish an Indian tradition in astronomy built on Greek foundations. And, third,religious persecutions forced several heretical sects to flee to non-Christian lands. These groups

often took with them a taste for Greek culture and learning. Christianity had become the statereligion in the 4th century. There ensued many doctrinal controversies and many persecutions of

sects seemed heretical.

The most important group of heterodox Christian sects for our purposes was the Nestorians,

followers of Nestorius, a 4th century bishop of Constantinople. The doctrinal dispute centered onthe question of whether Mary was the mother of only the human nature of Christ, or of both his

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human and divine natures. In 431 the Council of Ephesus declared the Nestorian position (thatMary was the mother of only the human nature of Christ) heretical. Tensions, persecution, and

eventual exile brought the Nestorians eastward into Persia. There they established a school of theology. Over the next 100 years the Nestorians gradually came to exercise considerable

influence in the Persian court. The Nestorians became tutors to the royal children, and thus the

royal family received a Greek education. They developed a taste for Greek culture, and patronized Greek scholarship. In 530 the Nestorians established the equivalent of a Greek center of learning in the City of Jundishapur. Here, mathematics, astronomy, philosophy, and medicine

were taught at a high level. Thus, there was a dispersion of Greek culture and learning eastwardfor 850 years.

In 632 Mohammed, the founder of Islam, died. In the course of the next 100 years or so, Islamic

forces conquered Asia Minor, Persia, the north coast of Africa, and began to make inroads intoEurope itself. By the 10th century, they had settled Spain and Southern Italy. Muslims were

tolerant of other religions and often lived in peace with Christians and Jews.

The pocket of Nestorian Christians in Persia were able to survive--even thrive--under Islam. In749 a new dynasty came to power and established its capital in the new city of Baghdad. The

Khalifs (the rulers of the Islamic empire) in Baghdad came under the influence of the Greek learning patronized by the previous Persian lords. One Khalif, al-Mansur, was handicap and

sought medical help from the Nestorians at Jundishapur. This relationship becameinstitutionalized in the sense that the head of the medical school, usually a Nestorian Christian,

became the royal physician. Now the Khalifs patronized Greek learning.

Islamic culture flourished under this dynasty. The 8th and 9th centuries were an important period

for translation. In 850 the Khalif established a school of translation (the "House of Wisdom")with Hunain Ibn Ishaq as its head. Hunain himself was trilingual (Greek, Arabic, and Syriac) and

was responsible for an astonishing number of excellent translations of Greek writings. By 900almost the entire Greek intellectual heritage had been translated into Arabic, largely through the

efforts of those scholars working at this school of translation in Baghdad.

What did Islam do with this newly acquired knowledge? Very briefly we can list four important

characteristics of Islamic Science. First, science in Islam is carried on by a small intellectual

elite. Its interests focus upon Greek learning. Second, progress took place within the Greek framework. No radical alterations of the Greek structures took place. There were certainly

disagreements over details, but the fundamentals remained the same. For example, there weremodifications and alterations made to Ptolemy's planetary theory, but no new theoretical

advances. Third, somehow (the precise route and means are not understood) Islamic science becomes centered in Islamic Spain. Fourth, despite its significance, science never became deeply

integrated into Islamic culture. Why was this so? Greek science went against the basic strain of Islamic belief. Orthodox Islam does not encourage knowledge for its own sake. If it does not

conduce to spiritual salvation, then it is a waste of time. Greek science was seen as disruptive toIslamic society. It never became part of the educational program or its cultural values.

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By the 12th century, Islamic science was in serious decline. (The high period of medievalIslamic culture was from 900 to 1200). The second great wave of translation took place in the

12th century, and it was from Arabic into medieval Latin.

What was going on in the West during this time of preservation and transmission of Greek

learning? The Roman Empire suffered serious social and political decline during this time. TheEmpire was divided in half (Byzantium in the east and Rome in the west). There was economicand social decay. Literacy fell to very low levels. Cities shrank. There was a general loss of

affluence.

By the 11th century, for the reasons we have already discussed, the Latin West began to regain a

measure of political and economic stability. Population increased, agricultural production

increased (perhaps on account of climatic changes, greater rainfall, and milder temperatures).With political stability there comes increased size and complexity of governments. There was a

growing need from both the state and the church for a literate bureaucracy. Thus, there was aneed for educational institutions to meet these needs. The 11th century saw a dramatic increase

on the number and quality of educational institutions. As levels of learning increased, scholars became aware of the vast store of knowledge--much superior knowledge--in the Islamic cities of

Spain. Thus began an intensive period of translation in the 12th century. Facilitating these effortswas the military re-conquest of Islamic-held Iberia. Christians gradually regained political

control of the Iberian peninsula. Cordoba contained a library reputed to have had 400,000volumes. By the 12th century, this had fallen into Christian hands.

In summary the three important factors in the eastward transmission of Greek knowledge were:the military conquests of Alexander (4th century B.C.); trade with India (from circa 4th century

BC to 4th century AD); and the exile of heterodox Christian sects, especially the Nestorians (5thcentury AD and later). The Nestorians became teachers and physicians to the Persian royalty

and, later, to the Islamic rulers. In the 9th century, Hunain Ibn Ishaq headed an institute for translation founded by the Khalif. This institute became an important center of translation. By

900 almost the entire Greek heritage had been translated into Arabic. Islamic science flourished, but remained within the Greek framework. And, as in Greek culture, science failed to become

integrated into Islamic culture. With the recovery of economic, political, and social stability inthe Latin West, European scholars turned their attention to the wealth of knowledge in the

possession of Islamic scholars. A hundred-year period of translation ensued, and by 1200, almostall of the scientific accomplishments of Greek and Islamic thinkers had been translated into

Latin.The 12th century can well be considered an "age of translation" for the Latin West because

during this period Christian scholars in Europe actively sought out and translated Greek worksfrom Arabic into Latin. The question to ask now is: How did the Latin West respond to this

influx of "new" knowledge? We will next aim to answer this question. But first, there is the problem of the institutional setting, namely the medieval university.

Medieval UniversitiesUniversities were a medieval and European invention. They grew out of lower schools affiliated

with the major Cathedrals of Europe. For example, the Cathedral School of Notre Dame in Parisdeveloped into the University of Paris. This was a gradual process and it is, therefore, difficult to

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fix a precise date to the founding of a university. The beginnings of the University of Paris may be set between 1125 and 1150. The University of Bologna about the same time. The University

of Oxford (England) around 1150 to 1175. These were the three earliest universities in Europe,and they set the pattern for later universities. Perhaps 50 to 100 universities were modeled after

these institutions in medieval Europe.

What justification is there for maintaining that universities were a medieval invention? Why not

the Academy of Plato, or Aristotle's Lyceum, or the Museum and Library in Alexandria? What

did the medieval universities have that the others lacked?

There were two things. First, the medieval institutions were divided into undergraduate and

graduate faculties. Undergraduates studied the liberal arts, and this was a prerequisite for

admission to the graduate level. Second, the license to teach issued at one university wasrecognized and honored at other universities. Universities were a European system. The

acceptance of degrees from other universities facilitated a certain measure of standardization of curricula, texts, and administrative organization. This was lacking in ancient institutions. There

was rivalry between the Academy and the Lyceum; different views of philosophy were taught,and there was little exchange of ideas between them. Standardization also facilitated student and

faculty mobility. Consequently, there developed a body of professional scholars, using the samelanguage (Latin), discussing and debating the same set of intellectual problems, and committed

to the same world view who were busy educating the next generation in that view.

Initially there was not a great deal of organization to early universities. They were likely to be

simply groups of teachers and students located in towns that had acquired the reputation for being centers of education. With the proper credentials anyone was allowed to teach. There was

no campus and no physical plant. Teachers would simply "Hang out their shingles" to attractstudents rather like a physician licensed to practice medicine. The growing demand for educated

clerics to help administer the Catholic Church's secular business, and the need for an educated bureaucracy to work for the state increased the demand for teaching. Some cities became known

for the quality of teaching. This attracted students. The more students, the more teachers wouldcome to that city.

Such growth led to the need for regulation and organization. The teaching profession adopted a

guild system. A guild was a legal entity designed to afford legal protection for the interests of acommon trade or craft. A guild was capable of suing and being sued, of forming monopolies,

raising wages, and enforcing standards. In this respect, teaching guilds were quite like craftguilds, e.g., stone masons' guilds, carpentry guilds, etc. In fact the Latin word "universitas"

means nothing more than guild (the same is true of the word "collegium"). The students alsoadopted the guild system when they organized. In Southern Europe, most notably in Bologna,

students banded together in order to protect themselves against the abuses of townspeople andteachers. The student guild enforced teaching standards, tried to hold down rents and food prices,

issued degrees, etc. At the University of Bologna the student guild ran the university: theyorganized the lecture schedule, fined teachers for being late or giving bad lectures, set classroom

standards, and regulated food and rent prices. The chief executive officer of the university was astudent (usually a graduate student). The University at Bologna became the model for a number

of southern European universities. In the universities of northern Europe, the faculty were the

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ones to gain control. But often students and faculty would unite to protect their common interestsagainst an occasionally exploitative townspeople. And not uncommonly the entire "universitas"

(the students and teachers) would simply pack their bags and move to a different town. Theuniversity, after all, was not a physical thing; it was a corporate body of scholars bound together

in a guild.

In order to get into a university one had to know Latin for that was the language of scholarship.

To prepare a student for entrance to the university there existed grammar schools where the

student learned Latin (the student would have learned the vernacular at home; medieval Englishin England, medieval French in Paris, etc.) The student then matriculated at age 13-14 in the

faculty of arts where he (usually only boys went to the university) studied for about two years.He could then present himself for the baccalaureate's degree. If he passed, he could become a

member of the faculty of arts. He would then perform Teaching Assistant-like duties whileworking toward the master's degree. After this degree, which usually took 3-4 years, he would be

obliged to teach in the faculty of arts for two years. The master's degree allowed him to teachanything in the faculty of arts curriculum. This follows the master-apprentice system of most

guilds. After a certain number of years of apprenticeship, and after the skills of the craft were"mastered," the student is accepted into the ranks of the profession. The length of the

apprenticeship depended on the "craft;" the master's (or doctorate) degree in law or medicinetook 5-6 years, in theology it took from 8-16 years.

Students usually came from the affluent middle classes, merchants, etc, and only rarely from the

nobility. Because of the rather young age at which students matriculated, delinquency was oftena problem. Records of instances of rowdy, even riotous, behavior can be found. But as members

of church-run universities (all students and faculty were clerics, i.e., members of the church)student-offenders were tried in church, and not civil, courts. Church courts were comparatively

lenient. There was no capital punishment in church courts, and first-offenders often got off withvery light sentences. Students could--but rarely did--marry while attending the universities. The

faculty were not allowed to marry.

What is called the seven liberal arts dates back to the Roman educational system. They were

called "liberal arts" because they were the skills needed by free men; slaves would learn only themanual arts and crafts. The seven liberal arts were divided into two parts: the trivium (grammar,

rhetoric, and logic), and the quadrivium (arithmetic, geometry, astronomy, and music). Asimpressive as the latter division may sound, it tended to be taught at a very elementary level.

Arithmetic generally consisted of nothing more than what we might call "business arithmetic;"addition, subtraction, multiplication, and division. Geometry was required for only about six

weeks in the student's career. The student learned the rudiments of Euclid's geometry, and eventhis was geared toward the practical. Astronomy was often nothing more than learning the

techniques necessary to calculate the date of Easter. This required little theoretical knowledge,and clearly was motivated by the practical concerns of the church calendar. Music treated the

mathematical aspects of harmony; the "science of the scale."

Until the translations of the 12th century, most knowledge could easily be placed under these

headings. However, with the great influx of Greek knowledge these categories no longer

sufficed. Thus, in addition to the seven liberal arts there were the three philosophies: natural

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philosophy under which most of what we could call "science" fell, moral philosophy, andmetaphysics. Furthermore, there emerged in the university curriculum specialized faculties in

medicine, law, and theology. Medicine would have been the one faculty in which what we wouldconsider "science" was taught. Occasionally certain universities would place special emphasis on

one or another part of the quadrivium. There were instances where one could get an excellent

education in Ptolemaic astronomy or geometry. But it was a mixed picture, and for the most part,the scientific aspects of the curricula were not emphasized.

In the 13th century, after the period of translation (from Arabic and Greek to Latin) Aristotle's

philosophy came to dominate the university curriculum. A student at the University of Paris was

required to master (i.e., to have read) all of Aristotle for the master's degree.

Medieval universities greatly facilitated the introduction and assimilation of Greek and Islamic

science in the 12th and 13th centuries. This contrasts markedly with the situation in the Muslim

world. European universities helped to institutionalize Greek learning in medieval Christendom.It was within universities that professors and students debated and argued, accepted and modified

ancient Greek philosophy. The Greek and Islamic intellectual heritage was largely assimilatedinto Western European culture through the agency of the medieval university. The Greek

learning of Plato, Aristotle, Ptolemy, and many others became a part of European intellectualculture in a way that it did not in medieval Islamic culture.

In conclusion, Medieval European universities were unlike anything that came before them, because they were organized into both an undergraduate and graduate faculty and there was a

large measure of standardization among the various universities: there was a common language(Latin), a shared curriculum, a universally-recognized license to teach which greatly facilitated

student and faculty mobility, and there was a shared world view. The major universities of Europe emerge from church-run cathedral schools (the University of Paris, for example). The

increasing demand for an educated clergy and civil bureaucracy attending the economic and political revival of the Latin West motivated much of the growth of medieval universities.

Universities were originally nothing more than a corporate body of students and teachersorganized as guilds for legal protection, and to unite in defense of common concerns and

interests. In southern European universities the student guilds gained control of theadministrative power. In northern European universities the faculty guilds won out. University

lectures were always in Latin; students taking notes as teachers read (with commentary) standardtexts. Degrees were awarded at the completion of certain levels: 2-3 years for the baccalaureate,

3-4 years for the master's (or doctorate). There were also advanced degrees in the specializedfaculties; law, medicine, and theology. The seven liberal arts formed the backbone of

undergraduate education, and science was generally only lightly treated and geared toward practical ends. After the period of intensive translation in the 12th century, Aristotle came todominate what we would call the "scientific" curriculum. The medieval universities played a

crucial role in the introduction and eventual assimilation of Greek learning into WesternEuropean culture.

Christian Reception of Pagan LearningAs we have mentioned before, science in the Greek and Islamic cultures never was seen as

having filled a social need. It thus never became institutionalized. This helps to explain whyscience disappeared during times of economic hardship. In the Latin West, the university

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supplied this learning with an institutional home. Greek learning did, in fact, become part of Western cultural life, but not without a struggle. Much of this struggle centered around

Aristotle's philosophy. Most Greek scientific and philosophical thought as accepted by medievalscholars without problem. It filled an intellectual vacuum. It was not in competition with any

entrenched systems of knowledge. The technical fields like optics, mathematics, astronomy, etc.,

were eagerly received. There was nothing volatile about Euclid and Ptolemy.

This was not the case with Aristotle's philosophy. Parts of Aristotle's natural philosophy directly

contradicted accepted Christian doctrines and assumptions. Aristotle, in places, came into directconflict with established Christian theology. Aristotle's philosophy was not filling a vacuum, but

rather coming into direct competition with certain tenets of Christian faith. It also competed withPlatonic philosophy, which was already entrenched in Western thought.

Christianity had already made its peace with Plato. There existed a greater degree of

compatibility between Plato's ideas and those of Christianity. Plato's Timaeus (his myth of creation) had been known throughout the Middle Ages. And it bears some striking similarities to

the creation story told in Genesis. The reconciliation between Christian faith and Platonicthought was easier. For example, Plato, in the Timaeus, claimed that a divine being, a

"demiurge," crafted the material world out of the preexisting chaos. And this demiurge fashionedthe world in accordance with "patterns" from the world of forms. This is easily reconciled with

the Christian conception of the God of Genesis. In the same dialogue Plato explicitly stated thatthe human soul was immortal.

On the other hand, Aristotle asserted that the world is eternal and uncreated; it can never bealtered in how it operates. Though Aristotle believed in a divine being, it was not concerned with

the lives and sufferings of people. His was an indifferent god who had no hand in determininghuman destiny. This situation was made worse by the means through which the Latin West

gained their first knowledge of Aristotle's complete philosophy. Aristotle's works entered Europeaccompanied by Arabic commentaries. Aristotle is tough going. Writing commentaries was a

very common way of assisting the reader's understanding. The most extensive commentator wasAverroes, a 12th century Spanish Muslim (d. 1198).

The translations of Aristotle were also translations of Averroes' commentary on, andinterpretation of, Aristotle. And some of Averroes' interpretations went considerably beyond

Aristotle's intended ideas. Thus a number of problems arose for the acceptance of Aristotle byLatin scholars because of Averroes' enthusiasm. These problems were:

1. The only source of truth is reason. This rules out revelation or faith as a means of finding

truth.2. The particular philosophical system that embodies rational truth is that of Aristotle.

Aristotle's doctrines (for Averroes) are the summit of truth. Aristotle was created and givento us so that we might know what it is possible to know. Or so thought Averroes. This sort of

arrogance only antagonized Christian scholars.3. There is no divine providence. There is a god, but that god did not create the world and

does not concern himself with human existence. Christians rather believed in a personal,caring god.

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4. The universe is eternal; uncreated and unperishing. Moreover, the laws by which the worldoperates are unchanging and unchangeable. There can be no such thing as divine

intervention.5. The world, in a word, operates deterministically. Thus there can be no free will, no

freedom of choice. But if Christians allow no freedom of choice, then it is meaningless to

speak of responsibility, sin, or salvation.6. There is no personal immortality. For Averroes there were two arts to the human soul or mind (these can be used interchangeably): an active soul that is immortal and universal, and a

passive soul that is individual and mortal.

Clearly, deep divisions existed between traditional Christian theology and AverroisticAristotelianism. A serious conflict arose, and this conflict centered on the question of

subordination. How does one rank philosophy (reason) and theology (faith)? Are they equals? If they come into disagreement over some point, which one is right? Which one is authoritative?

This was the central problem for medieval intellectuals; the problem of faith vs. reason.

Three choices characterize the spectrum of the 13th century responses to the problem of faithversus reason. Either ultimate authority lies in the providence of theology, or it lies in

philosophy, or there can be a shared authority with both having their domains of expertise. Thefollowing groups represent each of these positions: the Augustinians, the Thomists and the

Averroists.

The Augustinians tended to be the conservatives, theology was the central authority and

philosophy was thought to be potentially dangerous. Theology provides us with all that we need

to know. Philosophy is not an autonomous system of knowledge but dependent on the truths of revelation. Of course, there was a spectrum of Augustinians. Moderates might well argue that

philosophy, within bounds, was harmless, etc. That is, philosophy could be employed as aservant to theology, but never anything more than that. The Thomists can be considered the

"moderates." They thought that there should be a place for both philosophy and theology, andthat each had its own field of authority. To ask a theologian about the number of spheres in the

heavens would be as inappropriate as asking the philosopher about the meaning of a difficult passage in the Bible. But what if there are questions that touch on both fields--and there certainly

are such? There are areas where the two do overlap. For example, the question of the eternity of the world concerns both the natural philosopher and the theologian. The Thomist claims that in

those areas of overlap there must be perfect agreement between philosophy and theology. Godgave us both the faculty of reason and the faculty of revelation. Thus there can be no real conflict

between them. If there is conflict it is because we have either not done our philosophy well or our theology well. Both come from God, and He cannot contradict Himself. Such conflicts areapparent, not real.

The Averroists position is easy to understand. Their allegiance lies with philosophy. Specifically,

Aristotle's philosophy. Reason is the sole source of truth. For Christians teaching as members of the clergy in church-run universities such a position could well be problematic.

In summary, the Augustinians placed ultimate authority in the teachings of Christian theology

based on revelation. Philosophy is thus subordinate to theology. At best, philosophy can serve as

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a secondary aid to theological truth. Truth rests fundamentally on revelation (faith). TheThomists argue that both philosophy and theology can lead to truth, and more importantly, that

truth is one. God gave us reason and faith. God cannot be self-contradictory. Therefore, philosophical truths cannot conflict theological truths. If there appears to be such a conflict, this

means that one is doing either one's philosophy or one's theology poorly. The Averroists,

however, are less optimistic. Their sentiments clearly lie with rational philosophy. They wouldlike to argue that philosophy (alone) leads to truth, but they must accept the truths of theChristian faith--truths which sometimes contradict their philosophical conclusions.

So far we have considered the Christian response to Aristotelianism in the abstract. We will now

turn to the historical details. It took time for the dangers of Aristotelianism to orthodoxChristianity to be recognized. By 1200 there were lectures in the universities about Aristotle's

philosophy. Aristotle's complete works had only recently been translated into Latin. And thesetranslations of Aristotle were accompanied by translations of Averroes' commentary on Aristotle.

Western scholars recognized the superior nature of his philosophy; it was more sophisticated,more comprehensive, and more systematic than anything they had ever encountered. It took time

to fully assess the implications of his works. In 1210 the provincial Synod of Sens (a council of regional bishops) issued a decree which stated that Aristotle and his commentators should not be

read, neither privately nor publicly, on pain of excommunication. Clearly, church authorities had become aware of the dangers of Aristotle. In 1215 the decree was renewed. Keep in mind that

this evidence is drawn only from Paris. It is a local affair. But the University of Paris was the biggest and most prestigious university in all of Europe. So these decrees are not trivial.

There was no rigid uniformity throughout Christendom. In fact, in Toulouse the recently

established university actively advertised its lectures on Aristotelianism! In 1231 Pope GregoryIX issued a papal bull calling for an edited version of Aristotle. There is no evidence that such a

council ever met. Nor has there been discovered an edited version of Aristotle. The Pope'sdecree, however, demonstrates the profound ambivalence of church leaders. On the one hand,

there is a great attraction in Aristotle's works--he should be read. But, on the other, not all of hisworks are fit to read. He should be edited, censored. There is simultaneously the recognition of

Aristotle's worth and fear of his unorthodoxy. Yet by 1255 the University of Paris required all itsmaster's students to have read all the works of Aristotle. Aristotle has gradually made his way

into the curriculum, and he even comes to dominate it.

Clearly, against the background of ambivalence, there has been a gradual liberalization since

1200. Aristotle has come to be the most important part of the (13th century) university scene.The task is now to reconcile Aristotelianism with the teachings of the Christian Church.

How does one go about working out the details of such a reconciliation? It is not simply a

reconciliation; it is also a restructuring of Christian theology in accordance with Aristoteliancategories of thought. It was an enormous task. Many persons contributed to this effort, but two

especially stand out: Albertus Magnus and his important student, Thomas Aquinas. Not onlymust the areas of apparent conflict be identified and evaluated, but the precise means by which

either Aristotelian philosophy is modified or rejected as well as the modifications andadjustments to Christian theology must be delineated. This work took place roughly between

1250 and 1270. And it was the "moderates" (who eventually took their name from Thomas

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Aquinas himself) who emerged as the leaders in this endeavor. The upshot of this was that by the16th century, Aristotle had the appearance of a Christian saint; he became the official church

philosopher.

However, the progressive liberalization that culminated in the Thomist reconciliation of Aristotle

and Christian theology had other consequences as well. The tolerant atmosphere of mid-centuryencourages the more radical Averroists to adopt an extreme position. Siger of Brabant was theleader of this faction and he and his followers were charged with teaching heresies in the name

of (Aristotelian) philosophy. For example, it was claimed that they taught the eternity of theworld. This outraged the more conservative Augustinians. The Averroists' extremism provoked

an equally extreme conservative (Augustinian) reaction. The Augustinians go to StephenTempier, the Bishop of Paris, and complain to him of the Averroist excesses.

They get him to issue, in 1270, a condemnation of about 13 "Averroist" propositions allegedlytaught at the University of Paris by the Averroists. In 1277, Tempier extends the list of

condemned propositions to 219, including several from Thomas Aquinas. Here the conservativereaction had gone too far. Even the moderate propositions of Aquinas were condemned as

heresies. Those who continued to teach the condemned propositions were threatened withexcommunication. What sort of things were condemned? The following ten are illustrative.

1. The doctrine of the double truth (i.e., that there are two independent truths, the truth of

philosophy and the truth of theology).2. Theology is built on myth.

3. Religion is an obstacle to enlighten education.4. Happiness can be found only in this life.

5. The world is eternal.6. There is no divine providence.

7. There is no personal immortality.8. Certain astrological doctrines concerning the repetition of history in accordance with the

repetition of astrological (i.e., planetary) configurations (the argument here is that thestars in some way control natural and human events on the earth, thus a repetition of

celestial phenomena--thought to occur in 36,000-year cycles--would necessitate therepetition of human history; this does not fit well with the Christian view of the unique

mission of Christ).9. Even if He wanted to, God could not move the entire cosmos in a straight line (for this

would violate Aristotle's assertion that there can be no void space).10. God could not make more than one world (Aristotle had argued that logically there can

be only one world).The last two propositions especially irritated Christian theologians because they explicitly

limited God's freedom and omnipotence. This, they could not abide. As an omnipotentand omniscient God--the God of creation--no human system of thought could dare to

place logical or natural limitations on God's freedom of action.

What were the consequences of the condemnations? Clearly theological concerns now threatenedto interfere with the philosopher's enterprise. Philosophers were no longer free to follow where

logic led them. The fear of theological censure restricted their philosophical activities. Scholarswould have to tread carefully on ground that theologians might claim as their own; e.g., in 1350

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Jean Buridan, a philosopher at the University of Paris, addressed himself to the question of whatforces caused the celestial spheres to rotate. He excluded the probability of angelic movers. But

(he claimed) "Do not assert this, but tentatively suggest it and seek the advice of the learnedchurch officials." He must be careful what he asserts for fear of invoking theological censure.

Most of the condemned propositions were Aristotelian. This had the effect of weakening thedominance of Aristotelian philosophy and encouraging alternative philosophical positions. Issuesthat were understood as "closed" in the Aristotelian system were opened up to fresh speculation

as a consequence of the Condemnations. The Condemnations can be seen as having guaranteedthe omnipotence and freedom of God. He is free to do anything he wishes short of self-

contradiction. This theological position comes to be used by philosophers in arguing non- or even anti-Aristotelian lines of speculation. It implicitly encouraged philosophers to seek paths

which diverged from "orthodox" Aristotelianism. That is about 100 years after theCondemnations, Nicole Oresme argues that there is an infinite void space surrounding our

cosmos, and that our world could be moved through this void region in a straight line. Then headds that if anyone objected to his line of reasoning, they stood in danger of contradicting the

Condemnations of 1270 and 1277. Oresme was explicitly using the Condemnations to justify hisnon-Aristotelian speculations.

The Condemnations were certainly a temporary setback for Aristotelian philosophy. But the

more important point is that Greek rational philosophy had come to stay. In the long run, areconciliation was achieved (through the efforts of Aquinas, Albertus, and others). Greek

philosophy and science do become a part of Western intellectual culture. It became firmlyintegrated into Christian culture. This can be viewed as one of the crucial formative events in

Western culture. Aquinas' arguments prevailed in the long run. By the end of the 16th century,Aristotle was the official Church philosopher. Contrast this with the situations in ancient Greece

and medieval Islam. Science never became fully integrated into the cultural and societal structureof values. In Islam it remained "foreign learning."

In conclusion, the great bulk of Greek knowledge introduced into the Latin West in the 12thcentury presented little problem. It filled an intellectual vacuum. Aristotelian philosophy,

however, ran into direct competition with the already entrenched Platonic philosophy (which initself was more amenable to a Christian interpretation than was Aristotle's philosophy). There

were also a number of Aristotelian tenets that ran directly counter to established Christiandoctrine (the eternity of the world, denial of personal immortality, etc). This problem was

accentuated by the biased commentary of Averroes which accompanied the earliest translationsof Aristotle. The Christian response to Aristotle can be characterized by the conservative

Augustinians (philosophy subordinate to theology), the moderate Thomists (there can be nogenuine conflict between philosophy and theology), and the radical Averroists (philosophy has

its own independent realm of validity). The Averroist position was difficult to maintain in a(Christian) theological society.

From the time of the introduction of Aristotle's works into the West (c. 1200) until the mid-13thcentury there was evidence of progressive liberalization in the acceptance of Aristotelianism, but

always against a background of theological tension. Aristotle's works were officially banned for undergraduates at Paris but they continued to be read. The Pope calls for a purged version of

Aristotle, but this was never carried out. Finally, by mid-century, the University of Paris requires

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all of Aristotle to be read for the master's degree. The excesses of the Averroists provoked anAugustinian reaction; many Aristotelian propositions are condemned. This has both a restrictive

and liberating effect on philosophy. In the long run, Greek learning was integrated into Westernculture.

Chronology of Greek LearningI. Greek Learning to Islam 325 B.C. - Eastward spread of Greek culture begins.

431 A.D. - Council of Ephesus; Nestorians declare heretics.529 " - Scholars from Plato's Academy (closed by Justinian)

invited to Jundi-Shapur.632 " - Death of Mohammed; spread of Islam.

749 " - New Muslim dynasty (Abbasids) patronize translation.850 " - Humain Ibn Ishaq heads an institute of translation.

900 " - Islamic science begins to flourish in its own right.1100 " - Translation from Arabic to Latin begins.

1200 " - Islamic science is in serious decline.II. Islamic Learning to Medieval Christendom 400-600 - Barbarian destruction of the Roman Empire.

800 - Carolinian Renaissance under Charlemagne.1100 - 12th century revival of learning revives interest in

learning; translation from Greek and Arabic begins.1200 - The full legacy of Greek and Muslim learning is

available in Latin and is incorporated intoUniversity curriculum.

1277 - Condemnations by Bishop of Paris represent thechurch's reaction against Aristotelian and other

Greek and Muslim Learning.

Medieval Cosmology and AstronomyPtolemaic astronomy has been translated into Arabic. Arabic astronomy was both observational

and theoretical. There were perhaps twenty "observatories" in the medieval Islamic world. Someof these observatories were equipped with large, naked-eye instruments, which supplied new and

better data. A number of these achievements were transmitted to the Latin West in the 12thcentury. In 1170, Gerard of Cremona set out to find and translate Ptolemy's Almagest. Hetraveled to Spain, learned Arabic, and translated Ptolemy. This and other efforts formed the

foundations for the Latin tradition in astronomy.

Ptolemaic astronomy was understood in the Latin West soon after Gerald's translation. In anygeneration during this time perhaps as many as two or three dozen scholars had thoroughly

mastered the technical intricacies of Ptolemaic astronomy. On a less sophisticated level,knowledge of Ptolemy was quite widespread. The Theoretica Planetarium was a standard text on

Ptolemaic astronomy which provided medieval students with about as much knowledge of Ptolemy as has been presented in this course. This was a standard work. It was not only copied a

number of times in manuscript, but with the advent of printing in the 15th century, was publishedin numerous editions thereafter.

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There were also the Alphonsine Tables compiled under the patronage of Alphonso the Wise (amid-13th century Spanish king). These planetary tables remained in use over three hundred

years.

Thus the astronomical tradition of the West had its beginnings in the 12th Century and continued

all through the Middle Ages. Medieval astronomers had a solid grasp of the technical details of Ptolemaic astronomy. When Copernicus went to the University of Cracow in 1491 heencountered this medieval astronomical tradition. He was working within the medieval tradition.

Technical astronomy, however, was for the few. It was never a large number those who mastered

its details. Cosmology, on the other hand, enjoyed both a widespread appreciation and a largemeasure of consensus. By cosmology we mean the basic structure of the universe, its

fundamental architecture. The medieval cosmos was Aristotelian in its essence. In a word, it was believed that God created a finite spherical world that contains all material substance. Everything

that is material is contained within this sphere. Beyond that sphere there was nothing--not evenspace. Medieval scholars--in true Aristotelian fashion--believed in the materiality of space;

without "stuff" there can be no space and without space there can be no "stuff." The outermostsphere in this scheme is the Empyreum, the abode of the angels. Next is the crystalline or

aqueous sphere. After this comes the stellar sphere. As one continues to travel inward, the worldis arranged almost exactly as Aristotle had pictured it.

The modifications of his scheme occur with the addition of the last two spheres; the crystallinesphere and the Empyreum. These were added in order to make the scheme consistent with the

story of creation told in Genesis in which God is described as having "separated the waters abovethe firmament from the waters below the firmament." (This is an excellent example of how

Christian theology impinged on Aristotelian natural philosophy). The crystalline sphere was thus pictured as a watery sphere in a solid or "crystalline" state. Inward from the stellar sphere the

sophisticated would adopt Aristotle's argument that claimed there were 55 or so spheresaccounting for the movements of the planets.

The less sophisticated would simply assume that there was one sphere per planet. Hence, when

one speaks of the "eighth sphere" it is understood as the stellar sphere. As one descends belowthe orbit of the moon one passes from the realm of changelessness and perfection--the celestial

region--to the realm of change and corruption--the terrestrial region. But this is not to say thatmedieval people thought that the earth was in some way evil. The earth was, after all, the

creation of God, and He had pronounced it "good." The earth was the stage for the great humandrama of redemption. God was concerned about the earth. It could not be fundamentally evil.

The shape of the earth was known to be spherical. No one in the Middle Ages who was educated

had any doubt about this. John of Sacrobosco (also called John of Hollywood) had set fortharguments for the sphericity of the earth in his 13th-century astronomical handbook called TheSphere. It was a very well-known text, and in it, was argued that since the times of the setting

and rising of various heavenly bodies varied depending on one's eastward or westward location,then the earth must be spherical. Indeed, the circumference of the earth as calculated by

Aristosthenes was known in the Middle Ages: 252,000 stadiums. There was even a calculation

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for the size of the entire universe. Roger Bacon (13th century) had calculated the surface area of the Empyreum to be approximately 10

12square miles.

Often modern historians portray the medieval cosmos as small, cozy, and comfortable. This can

be misleading. The earth was thought of as point, like in comparison to the sphere of the stars,

there was no ratio between the size of the earth and the size of the cosmos. The cosmos wasthought to be vastly bigger than the earth. If the medieval cosmos was cozy, it was because itwas designed by a loving God. And humans were at the center-stage; they were the main focus

of God; all creation was given to human beings. The universe was also cozy in the sense that itwas seen to be hierarchically structured, unified and coherent in its order.

There was thought to exist a thorough-going interrelatedness among its various parts, almost like

an organism. Astrological forces tied the universe together in an immediate way. The connection between the motion of the Sun and moon and tides was undeniable. Planets were thought to be

responsible for the production of certain metals in the earth and for certain dispositions inhumans. Saturn, for example, controlled the growth of lead, produced melancholy moods in

people, and was generally held to be responsible for sicknesses and disasters. Jupiter influencedthe production of tin, caused cheerful dispositions in people and brought happiness and good

times to the kingdom. Planets were connected with various diseases and various parts of the body. Hence, physicians and healers were often much concerned to know the position of the

planets before undertaking cures or operations. The Great Plague of the 14th Century wasthought to have been brought about by an unusually unhappy arrangement of planets.

Astrological influences could affect the body, but not the will. Christian doctrine required personal responsibility in order to make sense of notions like sin and salvation. The Church

tolerated astrology insofar as it restricted itself to natural and bodily influences.

The creatures in God's universe were arranged in a hierarchical system of decreasing orders of

perfection. At the very top of course was God Himself (perhaps "Herself"?) The sophisticatedmedieval person would know that God does not exist in any one place. He is not a physical

being. He is omnipresent. He is everywhere and nowhere. Below God are the angels; spiritual beings devoid of body, existing as minds or souls, and employed by God as agents of His will (as

messengers to humans on the earth, for example). Their abode was the Empyreum. The angelswere placed in three hierarchies of three species each. Below the angels were the inhabitants of

the airy region just below the orbit of the moon. These beings were corporeal (or at least capableof assuming corporeal form), intermediate between angels and humans, but neither good nor bad

in essence. (The connotation of "evil" associated with the word "demon" is a later development).On the earth there were semi-human creatures like elves, fairies, nymphs, etc., which were

generally thought to be small, playful, elusive, annoying, capricious creatures of the woods andmountains. They seldom interfered in human affairs. Then comes human beings. Below humans

were the animals and plants with which we are familiar. In addition to these creatures were anumber of exotic mythical beasts like unicorns, griffins, and satyrs.

There was never any doubt about the centrality of the earth. No one ever questioned Aristotle's

geocentric picture. However, there were questions raised concerning the possibility of the earth'srotation. How do we know that the earth isn't rotating and the stellar sphere fixed? This very

problem was taken up at the University of Paris in the mid-14th century by Jean Buridan. He

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argued that if the earth was rotating (once a day) then the stars and planets would not have to.This would be a simpler, more economical universe. There are no astronomical objections to

such a situation. All celestial phenomena would appear just the same. But there is a physicalobjection. Suppose an arrow were shot vertically upward. If there is no wind then the arrow

would fall to the west of the archer for the earth must have carried the archer to the east. That is,

the rotation of the earth would move the archer eastward away from the spot from which thearrow was shot. Hence the arrow should fall to the west of the archer. This is not observed, sotherefore, the earth must not be rotating.

Nicole Oresme takes up the same problem. He wishes to present an argument in favor of a

rotating earth, but he first begins by refuting a number of standard objections to the notion of arotating earth. He then lays out a few positive reasons for the rotation of the earth. First, his

refutations of objections to a rotating earth:

Objection: Our senses tell us that the earth is at rest; we cannot feel any motion.

Refutation: All we can perceive is relative motion and as long as we all share the same motionwe cannot perceive it. Any argument from observation, therefore, is no argument at all.

Objection: If the earth is rotating from west to east, then there should be a constant breeze from

east to west.

Refutation: The water and air on the earth are moved along with the earth. The tall mountains

push the air before them. Thus, there is no wind.

Objection: Astrology would be in shambles if the earth were rotating.

Refutation: Astrology depends only on the relative motions of the heavens and earth; putting theearth in motion has no effect on celestial influences.

Objection: The Bible teaches that the earth is fixed: there are clear references in the Bible to the

sun rising, not the earth rotating; Joshua commanded the sun to stand still, not the earth to stop

rotating.

Refutation: The Bible employs popular speech and popular concepts of nature in order to

communicate with all people. The Bible is not attempting to describe scientifically natural phenomena. The language of the Bible is figurative and not literal (from Oresmes' Le Livre du

Ciel et du Monde).

Now in positive support of the argument for a rotating earth, Oresme presents the following: it

would be much simpler to have the earth rotate once a day on its axis than to have the enormous

stellar sphere and all the planetary spheres whirl about once a day. God would be wasteful of Hisenergy had He would not thus let the earth rotate. God would be doing it the hard way and not

the simple way. Here we have a very cogent argument advanced in the 14th century for therotation of the earth. One hundred fifty years later, Nicolaus Copernicus will use similar

arguments in defense of a rotating earth. But Oresme is not done. In the final paragraph of his

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argument, he claims that, the above arguments notwithstanding, he supports the traditional viewafter all, e.g., the earth does not rotate. What are we to make of this surprising ending? Why

would he abandon a beautifully constructed argument at the very end? The stereotypic view of the medieval scholar would have Oresme attempting to save his skin by giving in to oppressive

church authority. But this wouldn't do. Oresme was the church authority. He was the most

powerful bishop in all of France; he was advisor to the King of France. People had to answer tohim on matters of theology and philosophy. He had little to fear from the church.

Oresme's purpose was simply this: to show the absurd conclusions one could reach by relying

solely on reason. Reason could not lead to certain knowledge, only revelation could do that.

Oresme has learned the lessons of the Condemnations of 1270 and 1277 well. No philosopher and no philosophical argument can bind God to a single course of action. God is not obliged to

make the earth rotate simply because mere human rational philosophy claims that would be theeasier way to do things. Human reason cannot be used to limit the freedom of God. Reason

cannot be trusted to lead to truth. Oresme's argument concerning the rotation of the earth provesthat. The argument is rationally sound, but the point is that rationality itself is not "sound." It can

lead one astray. Here we have a theological discussion yielding one of the most significantcosmological arguments of the Middle Ages.

In conclusion, the astronomical writings of Ptolemy entered the Latin West in the 12th and 13th

centuries along with most of the Greek and Islamic heritage. This becomes the foundation for theWestern tradition in mathematical astronomy of which Copernicus was a part. The medieval

world picture was geocentric, finite, spherical, and closed; the entire material world wascontained within the last celestial sphere. Although vast, the medieval cosmos was the creation

of a loving, caring God whose chief concern was the human drama unfolding on the earth. Thecosmos was causally interrelated through astrological forces and influences. The animate

creation was arranged in a descending hierarchy of beings ranging from God and the angelsthrough demons to semi-human creatures of the woods and mountains to human beings, the

mythical and "natural" beasts, etc. The geocentricity of Aristotle's universe was never questionedthough the notion of a rotating earth was examined. A number of arguments against the rotation

of the earth were refuted by Nicole Oresme.

Medieval Science of MotionThere is clearly a difference between the theories of motion of early modern (e.g., 17th century

Newtonian) and the Aristotelian ancient and medieval world view. While material bodies in themodern view material are indifferent to motion or rest, in the Aristotelian view the natural state

of a body is at rest. Concerning the relation between force and motion, in the modern view

acceleration is proportional to the force applied and the mass of the object (a w F/m); in the

Aristotelian view velocity is proportional to the force applied and the resistance of the medium(V w F/R. The modern mathematical description of accelerated motion is v w t, and s w t

2(where

"v" is velocity, "t" time and "s" the total distance traversed). There was no such conception of

acceleration and analysis of uniform accelerated motion in Aristotelian physics.

The question we will address here are the contributions of the Middle Ages to the science of

motion. A most significant contribution made by medieval scholars was their distinction between

dynamics and kinematics. Kinematics is the attempt to provide a mathematical description of

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motion without trying to explain the forces causing the motion. Dynamics is the attempt to dealwith the causes of the motion. Aristotle had thought that dynamics was the heart of any study of

motion. (Indeed, we have seen this sort of distinction before in astronomy. We could label whatEuxodus was doing as "kinematic astronomy" and what Aristotle was doing as "dynamic

astronomy"). But without an explicit division of the problem into kinematics and dynamics the

science of motion becomes overwhelmingly difficult. It was a group of scholars working the14th century who first made the distinction between kinematics and dynamics.

Before we ask what these medieval scholars accomplished in kinematics we must first

understand the nature of the endeavor. Is kinematics simply a matter of measurement? In modern

kinematics we take s (distance), t (time), v (velocity), and a (acceleration) and measure these parameters with metersticks and clocks. We know that it is these quantities that are important in

understanding motion and we know how to measure them. But it is not all that easy to measurethese quantities; not while the object is in motion. Certainly no one in the Middle Ages would

have had the necessary technology simply to go out and measure the distances, times andvelocities of a thrown stone. More fundamentally, is it obvious that s, t, v, and a are the proper

quantities to measure? Perhaps distance and time suggest themselves the very nature of motion.But "velocity" and "acceleration" are not so obvious. One cannot "see" velocity and acceleration.

They do not jump up and label themselves as crucial parameters in motion. The point is this: theterms by which a scientific concept are described have to be created by the investigator. They are

not simply given to the investigator. This is the most difficult part of the scientific enterprise,namely, the creation of a conceptual framework to be imposed on the phenomena by the

investigator. Another way of saying this is to realize that finding what the problem is and statingit in such a way that is conceptually clear is the most important step toward the solution. Until

medieval scholars established a conceptual vocabulary with which to discuss the problems of motion there could be no science of motion.

Concerning the problems of velocity and acceleration, there was no scientific conception of both

notions in Aristotle. The ancients described motion not in terms of the ratio of distance to time,as we would, but solely in terms of the total distance traversed. The only descriptive terms that

entered their discussions of motion were distances and times. Why was this? Why not take theratio of distance over time? This was not done in antiquity because it was thought that one

should not take the ratio of unlike things. Mixed ratios made no sense. A ratio is a comparison.To compare distance-to-distance, or time-to-time made sense; but not distance-to-time. Thus,

there was no concept of velocity in antiquity comparable to the modern notion. The idea of velocity originated in the medieval period and it emerged from a philosophical context.

Remember we labeled Aristotle's philosophy "qualitative" not because it ignored numbers but because qualities were thought to be really real. As Aristotelians medieval scholars wereconcerned with an analysis of how qualities changed; how they increased and diminished.

They concluded that qualities can alter in two ways, by quantity and by intensity. Take the

quality of "heat." The intensity of heat we can measure with say a thermometer. The quantity of heat would be the object's heat capacity. If we consider weight, then the quantity would simply

be its weight (on a scale) and its intensity would be its density. This two-fold characterization of qualities is true for any quality; intelligence, charity, even the quality of motion. Here the

quantity of motion was taken to be the total distance traversed and the intensity of motion--the

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velocity. The concept of velocity enters their vocabulary through their analysis of intensity of qualities. It now becomes possible to speak of ratios of velocities just as before one could speak

of ratios of time and ratios of distances. Moreover, velocity becomes a concept to which numberscan be applied. But remember, this arose in the analysis of abstract philosophical concepts and

not through measurement. (It was not until the 17th century that the "mixed ratio" v = s/t came

about). Medieval scholars also possessed the notion of instantaneous velocity. A similar processaccounts for the origin of the idea of acceleration. The question was, how to describe a qualitychange? Medieval scholars developed a classification of motions. One could have "uniform

motion" which is simply, motion without a change in velocity, motion at a constant speed. Onecould have "non-uniform motion." But this could be of two types--uniformly non-uniform

motion and non-uniformly non-uniform motion. The former is what we call uniformlyaccelerated motion and the latter non-uniformly accelerated motion. This sort of binary

classificatory system can be extended indefinitely. But for all practical purposes the only cases of motion that medieval scholars considered were uniform motion and uniformly non-uniform

motion. These were the simplest cases of motion.

One now had the basic building block, the fundamental conceptual vocabulary with which to proceed toward a successful kinematics. The creation of these concepts, velocity, acceleration,

etc., were the most difficult and most important parts of the construction of a coherentkinematics. Much of this work was done at Merton College, Oxford, between 1325 and 1350.

The most important members of this group were Heytesbury, Swineshead, Dumbleton, andBradwardine. All of these concepts were embodied in the odd-numbers law, also called the

mean-speed theorem, the item we turn to next.

Both the mean-speed theorem and the odd-numbers law apply only to uniformly accelerated

motion. Motions of more complicated nature (e.g., non-uniformly non-uniform motion) were not

treated. As in antiquity, any calculations done in the medieval period were comparisons. In fact,this is true of Galileo's work in the 17th century. We are not talking about absolute

measurements of velocities or accelerations.

The odd-numbers law and the mean-speed theorem provide techniques of comparison, and this

comparison is always between uniformly non-uniform motion and simple uniform motion. Theyallow one to reduce complex motion to simple motion. The mean-speed theorem states that if an

object travels for a given time with a uniformly accelerated motion, it travels the same distanceas it would had traveled with the mean speed of the accelerated motion for the same length of

time. One is reducing the non-uniformity of (uniformly) accelerated motion to the simplicity of uniform motion. Consider the following example: suppose you take a short bike trip starting with

a beginning velocity of zero and can manage to accelerate the bike uniformly until, at the end of three seconds, you are going ten feet per second. How much distance have you covered? The

mean-theorem claims that had you instead traveled with the mean (average) speed of your accelerated trip (you started out at 0 ft/sec and ended at 10 ft/sec, therefore your average speed

was 5 ft/sec) for the same length of time (3 seconds) you would have traveled the same distance,e.g., 3 sec x 5 ft/sec = 15 ft. The mean-speed theorem thus allows one to treat uniformly

accelerated motion as uniform motion.

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The mean-speed theorem and the odd-numbers law are kinematic descriptions of uniformlyaccelerated motion. The former states that a body undergoing uniformly accelerated motion

covers the same distance in the same time as it would had it moved with its mean, or averagespeed. Clearly this is simply a description of accelerated motion without any attempt to explain

the cause of the acceleration. Around the middle of the 14th century at the University of Paris,

Jean Buridan and his student, Nicole Oresme developed a graphical demonstration of the mean-speed theorem.

Let a vertical axis represent the intensity of motion (the velocity) and an horizontal axis the

extent or duration of the motion (the time) as illustrated below. The vertical line represents the

velocity at that particular point in the object's journey. A line sloping upward to the right can betaken to represent the history of the velocity of the object during its trip. Now Buridan and

Oresme argued that the area under the sloping line represents the total distance traveled by theobject. The graphical demonstration simply states that the area under the sloping line

(representing uniformly accelerated motion) is equal to the area under the level line (representingthe hypothetical "mean-speed" journey). Since the two areas are clearly equal, the distances

traveled in each case must be the same.

As stated above, the odd-numbers law also concerns uniformly accelerated motion. This law

states that an object moving with uniformly accelerated motion travels in each successive

interval of time a distance that increases as the odd numbers. That is, if in the first interval of time, the object travels one unit of distance, then in the second interval of time the object will

travel three units of distance, in the next, five units of distance and so on. The graphicaldemonstration of the odd-numbers law rests on the same framework as the one for the mean-

speed theorem. If, for the uniformly-accelerated motion one divides the successive time intervalsinto similar triangles, it becomes obvious by inspection that the additional distances traveled in

successive intervals of time increase as the odd numbers.

As we shall see, Galileo's "new" mechanics rested directly on the kinematics developed in the

14th century. Galileo will employ the same kinematic laws and the same constructions in the17th century. He will use the odd-numbers law in his analysis of free fall motion and in his

experiments with the inclined plane. He will work with the 14th-century tradition of kinematics.However, one must keep in mind that the medieval scholars were working with abstract notions.

They never identified an actual example of uniform acceleration in the natural world. No one inthe Middle Ages sought to experimentally confirm the odd-numbers law. Their work was done

entirely in the abstract.

In summary the attempt to describe uniformly accelerated (or uniformly difform) motion,

medieval scholars compared it to uniform motion (that is, motion of constant speed). One result

of this comparison was the "mean-speed theorem" or "Merton rule," which stated that a body possessing uniformly accelerated motion traverses the same distance in a given time as another

body that moves for the same length of time at a constant speed equal to the mean (or average)speed of the accelerated body.

Medieval dynamics, on the other hand, studied projectile motion and free fall. Concerning projectile motion, Aristotle gave what we now consider an unsatisfactory explanation of

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projectile motion. Remember, he argued, that what keeps a projectile in motion after it leavesone's hand is the disturbed air behind the projectile. Note the crucial assumption here: there must

be an agent in order for there to be motion. Without a pusher, there can be no motion. Here it isthe air that allegedly acts as the "pusher." In the 6th century A.D., John Philoponus, an

Alexandrian Greek, strongly objected to Aristotle's explanation.

He argued that if you put a stone on a very smooth surface it would not move regardless of how

violently you stirred up the air behind it. The air, he concluded, cannot act as an agent of motion

for a projectile. What does move the rock then? It seems he could have had two options. Hecould have argued that the motion does not need an agent. He could simply deny the Aristotelian

assertion that every motion requires a mover. Had he done this, the modern notion of inertiawould have been very close at hand. He didn't argue this, however. The only other choice he had

was to find an alternative agent, a mover other than the air.

This he did argue and thus remained, in the broad sense of the word, an Aristotelian. Philoponus

claimed that when you throw a rock you deposit in the rock a force that continues to act after it

leaves your hand. It is this force that continues the motion of the rock. He is arguing here ananalogy with living things. Animals are capable of moving themselves. The cause of the animal's

motion is internal to the animal. Similarly, for a projectile the cause of the stone's continuedmotion must be something internal to the stone. That something is the force or "impetus"

deposited in it by the thrower's arm. An internally impressed force maintains the stone's motionafter it leaves the hand. The notion of an "internal impressed force," or impetus becomes the

standard explanation of projectile motion in the 14th century. Indeed, the theory of impetus livedon into the 17th century.

Concerning free fall, Aristotle and his successors said that an object in free fall is responding toits weight as a force causing it to return to its natural place. The speed of fall of a stone in free

fall should, therefore, be proportional to the stone's weight. If a second stone is twice the weightof the first, then it should fall with twice the speed. And the object should continue to fall at the

same rate (assuming the resistance remains constant).

Nicole Oresme thought differently. He claimed that if you throw a stone upwards it first starts

out moving rapidly, gradually slow until it comes to a stop, then gradually accelerates. He sought

to give a dynamical explanation of this behavior in terms of a dissipating impetus, in other words, in terms of an impetus that gradually used itself up. Dissipative impetus "dissipates" with

time, like heat. Consider the case of tossing a stone upward. How did Oresme explain its motion.For the stone to fly up, out of one's hand, the impetus impressed on the stone must be greater

than the weight of the stone. After the stone leaves one's hand the impetus begins to dissipate. Asthis happens the relative balance of upward impetus and downward weight is changing in favor

of the weight. Thus the stone's upward motion slows. Soon the impetus has decreased to the point where it is just equal to the weight. Now, as the impetus continues to decrease, the weight

becomes greater than the impetus and the stone begins to slowly fall. Finally, when all theimpetus has dissipated only the weight remains and the stone should now proceed downward

with a constant velocity. This is Oresme's dynamical explanation of free fall. This too becomes astandard explanation and survives into the 17th century. When Galileo first tries to deal with

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motion he uses Oresme's impetus theory. He eventually gives up the impetus theory but does notgive an alternative.

As to the laws of dynamics, a dynamical law must relate velocity (or acceleration) and force. It

must connect the velocity achieved with the force applied. As we have seen, Aristotle's

dynamical notions can be conveniently summarized in the short-hand expression

v w f/r,

where v is velocity, f is force, and r is resistance. The problem here is that if the force is just

equal to the resistance, this expression claims that there will be a net positive motion, whereas

common sense tells us that there should be no motion at all. In addition to his above-mentionedcriticism, Philoponus also was critical of Aristotle's law of dynamics. As an alternative,

Philoponus suggested the following:

v w f-r.

For Aristotle, the notion of R=0 was absurd, for this would be a motion in a void. In his

expression, it leads to the absurd infinite velocity. Philoponus, on the other hand, wanted toconsider motion in the void without the absurd consequence of infinite velocity. Thus, in his law

of dynamics, R=0, leads to a finite velocity.

John Bradwardine, leader of the 14th century group of scholars at Merton College, didn't like

either formulation. He wished to preserve Aristotle's rejection of the void, and he wished toovercome the problem that arose for Aristotle when f=r. How can he get around these problems?

Bradwardine wants a relationship between force and velocity, something like v w f, and

something like v w 1/r for resistance. His solution (one that meets all these demands) can beexpressed in a number of ways. One is to say that v increases arithmetically as f/r increasesgeometrically. That is, to double v one must square f/r, to triple v one must cube f/r, etc. Another

way of expressing Bradwardine's relation requires familiarity with logarithms. This

(anachronistic) expression looks like this: v w log f/r.

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