The Mathematics of The Quadrivium

by Brian K. Davis

Arithmetic, geometry, astronomy, and music are the four subjects that make up the quadrivium. A term first coined in the medieval period, it still carries weight today. Although it would appear that the quadrivium is made of two mathematical subjects and two non-mathematical subjects, astronomy and music are also based in math. Thus the quadrivium was solely based in the art of mathematics. Math has evolved over time and is still evolving today. The first known study of math came from Mesopotamia in 3,000 B.C.E. with the Babylonians and the Egyptians (Kline 3). However this math was basic and relied mostly upon counting. Math would not grow as a subject until the time of the Greeks in about 775 B.C.E. but would be lost to the world until the fifth century when Anicius Manlius Severinus Boethius (c480-524) began translating the Greek works (Kline 201). After Boethius’ translations of Greek math into Latin do we see the rise of math in Europe to help explain the universe. The use of the quadrivium would give scholars the mathematical ability to analyze the physical world around them, the first of these scholars being the Greeks and Plato’s Republic.

Plato’s book the Republic was centered on creating a utopian society for the people of Greece. Plato would also go on to describe a perfect school system to teach those who would eventually lead society. In his definition of education, comes the first inkling of the quadrivium, although not outright stated. When talking about education, Plato believes that the science of arithmetic is wholly concerned with numbers and the quality of numbers leads to truth (Plato 161).

Plato believes that by understanding numbers, people can better understand the truth and gain insight into the world. Plato would also go on to state that numbers are important for generals as well as philosopher, “For a soldier must learn them (arithmetic) in order to marshal his troops, and a philosopher, because he must rise out of the region of generation and lay hold on essence or he can never become a true reckoner, (Plato 161)” Plato believes that understanding arithmetic will better organize the troops in battle. However the nuance of truth keeps cropping up in Plato’s statements as well, “This branch of learning (arithmetic) should be prescribe by our law and that we should induce those who are to share the highest functions of state to enter upon that study of calculation and take hold of it, not amateurs, but to follow it up until they attain to the contemplation of the nature of number, by pure thought, not for the purpose of buying and selling, as if they were preparing to be merchants or hucksters, but for the uses of war and for facilitating the conversion of the soul itself from the world of generation to essence and truth, (Plato 163).” Plato likes the study of arithmetic because it is tangible, meaning it can be easily proven or disproven making people think about their arguments before making one (Plato 165).

After Plato’s discussion on arithmetic comes geometry. Once again he connects geometry to war, “So much of it (geometry),” he said, “as applies to the conduct of war is obviously suitable. For in dealing with encampments and the occupation of strong places and the bringing of troops into column and line and all the other formations of an army in actual battle and on the march, an officer who had studied geometry would be if he had not,” (Plato 167) and also stating, “Its (geometry) uses in war, and also we are aware that for the better reception of all studies there will be an immeasurable difference between the student who has been imbued with geometry and the one who has not,” (Plato 173). Plato also mentions how geometry compels the soul to contemplate essence, and that geometry forces the soul to turn its vision round to the region where dwells the most blessed part of reality (Plato 169), Plato believed that geometry would help people examine the physical shapes around them thus opening their eyes to truth, “For geometry is the knowledge of the eternally existent. Then, my good friend, it would tend to draw the soul to truth, and would be productive of a philosophic attitude of mind, directing upward the faculties that now wrongly are turned earthward,” (Plato 171).

After astronomy would follow geometry in which Plato was quick to point out its uses for telling the seasons, months, and navigation (Plato 171), all of these being important for the study of war. Astronomy also makes the soul look upward and leads it away from things here to those higher (Plato 181). Plato also believed that the study of the stars would lead towards reality, “We must use the blazonry of the Heavens as patterns to aid in the study of those realities, just as one would do who chanced upon diagrams drawn with special care and elaboration by Daedalus or some other craftsman or painter,” (Plato 185). Plato did not have much to say on music other than astronomy was for the eyes and harmonies for the ear (Plato 189). Instead he refers to the Pythagorean’s writings about music, “They (Pythagoreans) transfer it to hearing and measure audible concords and sounds against one another,” (Plato 191). Pythagoras was the first person to examine the physical science of music. Kline would state this about Pythagoreans, “Because the Pythagoreans “reduced” astronomy and music to number, these subjects came to be linked to arithmetic and geometry; these four were regarded as the mathematical subjects,” (Kline 149).

Long before anything was known of pitch numbers, or the means of counting them, Pythagoras had discovered that if a string be divided into two parts by a bridge, in such a way as to give two consonant musical tones when struck, the lengths of these parts must be in the ratio of these whole numbers. If the bridge is so placed that 2/3 of the string lie to the right, and 1/3 on the left, so that the two lengths are in the ratio of 2:1, they produce the interval of an octave, the greater length giving the deeper tone. Placing the bridge so that 3/5 of the string lie on the right and 2/5 on the left, the ratio of the two lengths is 3:2, and the interval is a fifth,” (Helmholtz 14). Pythagoras would later build a tuning scale based on fifths which was used until the creation of just intonation and tempered tuning. Plato would later state astronomy and music as a useless form of numbers; however this section of the Republic did set the stage for later works on the quadrivium.

Boethius was a medieval scholar that served a great purpose in the expansion of the quadrivium. Boethius would translate some of the Greek works on math and would create the term quadrivium in his own treatise on math. Boethius would get his idea for De Arithmetica from the Greek thinker’s liberal arts curriculum (Masi 83). Boethius would re-introduce the Greek works to the western part of Europe. In his book De Arithmetica Boethius would introduce the idea of proportionality, “He begins his discussion of proportionality with an extensive list of the types, drawn directly from the Boethian De Arithmetica. A ratio is a relation between two terms, as 1:2, or as expressed in a fraction, ½ and the relationship is called a rational number in its fractional form. A proportion is a ratio between ratios, as when 1 compared to 2, which is as 2 is to 4. Proportion may be set up in series, as a series of duplex, triple, or quadruple proportions. Bradwardine extracts the idea of proportionality from the Boethian conception of proportion. Bradwardine adapted, also from Boethius, the idea that the most important proportionalities are the arithmetic, geometric, and harmonic,” (Masi 91).

Boethius would also introduce irrational numbers as a way to explain geometry, like the sides of the triangles (Masi 91). Outside of translating the Greek works, Boethius’ works would become popular in the Middle Ages, “We must conclude that the Boethian mathematics enjoyed an extraordinary increase in popularity and influence between 1200 and 1600,” (Masi 81). His book would even become the text book during the middle ages, “Moreover, for the teaching of the first of the quadrivial arts, arithmetic, the Boethian De Institutione Arithmetica appears to have maintained its position as a basic text, and his was the case despite the fact that there were available for the study of arithmetic in the thirteenth century, in its various practical as well as other aspects, a wealth of materials both old and new,” (Kibre 72). Boethius’ works would go on unchallenged until Roger Bacon. However these two both believed that education needed a solid base of mathematics (Masi 92). Bacon would disagree with the order in which the quadrivium be placed, however he did agree with Boethius on the teaching of arithmetic, the species of numbers and the reasons for their operations (Kibre76). Boethius would also write a work on music.

Music was another sub-category of the quadrivium and was another topic Boethius would translate Greek works and write his own treatise on. During the Medieval and Middle Ages, chant was the source of music. Chant was only used by the Catholic Church and was in Latin, the chants were used to help the common people memorize scripture. The irony of this last statement is that most people could not speak Latin thus they did not know what they saying. The first part of Boethius’ book dealt with chant and how it should be organized. Boethius would organize the chants into tonaries, or the classifying of chants according to their tonal and melodic similarities (Bower 164). Boethius would place the chants based off their church modes which were: Lydian, Dorian, Myxolydian, Phrygian, Hypo-Phrygian, Hypo-Dorian, Hypo-Lydian, and Hypo-Myxolydian, church modes are based off which note they start on. After establishing the tonaries, Boethius would move on to compiling works into two categories, practical tonaries, those used by professional singers to check the tone of a chant, and didactic tonaries, those used to teach students the basic qualities of each tone (Bower 164). Boethius would treat music differently compared to his contemporaries. He took a more analytical approach whereas his peers believed in the mysticism of music. To Boethius, the main approach to musical pitch was qualitative rather than quantitative (Bower 165).

Boethius believed that one could mathematically analyze music in order to learn how to better write music; in essence he created the first step towards music theory. Boethius affirms that one holds immutable truths concerning music when one knows the related mathematical quantity in the proportions of consonances (Bower 166), in Boethius’ time this would be the examination of one tone to another. For example when one strikes a string and touches it in the middle the octave is sounded thus the relationship between a note and an octave must be 1:2. Boethius would base his math off of Pythagoras. Boethius also argues that the practicing artist is separated from musical science, and thus is not worthy to be named a musician (Bower 166), in other words if a musician does not understand the theory behind it they do not fully grasp it and in fact are missing an element to music. Boethius’ works would begin the study of music theory, however like his other works, failed to advance the study of math as a whole.

The problem with the quadrivium was that it was translated into Latin but never expanded upon. In the Middle Ages the quadrivium was arithmetic, considered as the science of pure numbers; music, regarded as an application of numbers; geometry, or the study of magnitudes such as length, area and volumes at rest; and astronomy, the study of magnitudes in motion (Kline 202), and did not really evolve past that definition. According to Kline, “the introduction of some of the Greek words retarded the awakening of Europe for a couple of centuries. By 1200 or so the extensive writings of Aristotle became reasonably well known. The European intellectuals were pleased and impressed by his vast store of facts, his acute distinctions, his cogent arguments, and his logical arrangement of knowledge,” (Kline 207).However the quadrivium would have an effect on the Church. Once established, the clergy was expected to defend and explain the theology and rebut arguments by reasoning, and mathematics (Kline 202). Today the quadrivium is still used; however it is not referred to as such.

Math is now taught to every child in the United States. Most kids will start their training in mathematics in elementary school. Arithmetic is still the first subject taught with addition and subtraction, followed by the basics of geometry. What is interesting is that education today combines basic arithmetic and geometry with multiplication. Astronomy is rarely taught and the basic of music, mainly how to play an instrument, is taught. If one is lucky they will receive a little music theory, however most students do not. Education today however, has grown beyond the quadrivium. Today students are taught trigonometry, an upper level math of geometry, and advanced algebra, upper level arithmetic, and calculus. With the advancement of technology, there is less need for the average person to know astronomy, however for those who go on to study astronomy as their profession will rely on calculus. The study of music has advanced beyond comparison of tones.

Scientists have figured out that music is a disturbance of air in a wave like pattern. Hermann Helmholtz would crack many mysteries behind musical sound. Helmholtz was able to prove that musical sounds were actually complex sine waves, “Where two condensations are added we obtain increased condensation, where two rarefactions are added we have increased rarefaction; while a concurrence of condensation and rarefaction mutually, in whole or in part, destroy or neutralize each other,” (Helmholtz 28), in other words, sounds are created by multiple sine waves that are added together. Helmholtz proved there were multiple sine waves with his invention the Helmholtz resonator which is a bottle that will resonate only one sound, one sine wave, which is part of the complex sine wave (Helmholtz 43). However, this is a more advanced analysis of music. Most students will not learn this unless they go into music as a profession, even then they may not receive this knowledge. Professional musicians, however, will get a healthy dose of music theory. Students today no longer learn only the quadrivium; in fact, students now learn more math and its applications than at any other point in history.

The quadrivium was first discussed by Plato in what he believed was necessary to be a philosophical person. Boethius would later translate the Greek works of Plato, Aristotle, Euclid, and many others into Latin and introduce the quadrivium to the school system of Western Europe. Boethius’ quadrivium would be the platform for which the study of math would stand on for centuries and would later become the first step in expanding the concepts of math. Today the quadrivium is no longer directly taught but its subject matter still is. Students get a great deal of arithmetic and geometry and some will focus their studies on astronomy and music. The quadrivium served an important purpose in the advancement of European education and its affects should not be overlooked.

Bibliography

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Adams, Herbert B. Circulars of Information of the Bureau of Education. Washington D.C.: Washington: Government Printing, 1887. Print.

Blackburn, Joyce. George Wythe of Williamsburg. New York: Harper & Row, 1975. Print.

Hellenbrand, Harold. The Unfinished Revolution: Education and Politics in the Thought of Thomas Jefferson. Newark: University of Delaware, 1990. Print.

Hoeveler, J. David. Creating the American Mind: Intellect and Politics in the Colonial Colleges. Lanham, MD: Rowman & Littlefield, 2002. Print.

Robarge, David Scott. A Chief Justice’s Progress: John Marshall from Revolutionary Virginia to the Supreme Court. Westport, CT: Greenwood, 2000. Print.

Servies, James A. Vital Facts: A William and Mary Chronology, 1693-1963. Williamsburg: College Library, 1963. Print.

Swindler, William F. “William and Mary Marks Bicentennial of Its First Chair Of Law.” American Bar Association Journal/64.12 (1978): 1872. Academic Search Complete. Web. 4 Feb. 2012

 

This paper was originally created for Steve Jackson’s History of Higher Education course.

 

The Relationship of Christianity and Scholasticism During The Middle Ages

by Elizabeth Anne Rathburn

The era of Scholasticism was not merely the narrow-minded and constricting form of education many modern scholars had deemed rank with intellectual stagnation. The overall concept of Scholasticism cannot be understood outside of its historical context. The Scholastic movement began as a response to the bitter turmoil of the Dark Ages, and at its peak in the twelfth and thirteenth centuries culminated into a well-refined method of critical thought. Scholasticism can be thought of as the intellectual refinement of the knowledge available to scholars of the Middle Ages. While the Middle Ages were not a time of great intellectual growth, it ensured that Europe would never again see a time of complete intellectual stand still. In relation to scholasticism’s historical context, the Middle Ages cannot be understood without the recognition of the dominating force of Christianity through out all of European society. The scholastic movement was seeded within, and grew with the progression of the Roman Catholic Church: its primary cultivators. The Fathers of the Roman Catholic Church became the initial authors of scholastic thought by creating harmony between the contrasting viewpoints of philosophy and theology. The works of saints became the texts, which the schoolmen of the monastic and cathedral schools committed to memory. As a result, the growth of Christianity and Education coincided with one another through out the span of Medieval Europe. The intellectual thought of the Middle Ages was highlighted by the symbiotic relationship formed between Scholasticism and Christianity, resulting in a fixed and formal system of education, and the preservation of religious, classical and antiquity works, which together, carved the intellectual path into the European Renaissance.

While the scholastic movement did not consist of new intellectual developments, it did serve the purpose of an intellectual awakening. This period of education and intellectual thought would serve as the foreground for the development of higher education. Scholasticism began in the Christian monasteries with the accumulation of knowledge, these monasteries would later transform into universities. The rise of universities however, began towards the end of scholasticism’s reign; as so, this discussion will stay within the confines of the development of the monastic and cathedral schools. In its broadest framework, scholasticism developed within the Church. Due to the meager intellectual material available, “the limited learning of the times arranged into a systemized form largely on the deductive basis of the Aristotelian logic” (Graves 51). Because of the power wielded by the Church, all subject matter, whether religious or secular, was approached through a highly theological perspective. Medieval thought from the ninth to the twelfth and thirteenth centuries was dominated by this ideal, and thus was taught within the schools of the Church, thereby solidifying the methods of scholasticism. Scholasticism was indeed, “the peculiar methods and tendencies of philosophic speculation that arose within the Church”. The term scholasticism was derived from ‘doctor scholasticus’, the term used for the authorized teachers in the monastic schools (Graves 50). From the very beginning of monastic education in the Middle Ages, scholasticism and Christianity were intertwined, influencing those who sought higher intellect within its schools. Both the Christian religion and scholastic method were the basis of a schoolman’s learning. It became a young scholar’s goal through scholastic deduction and argumentation, to show how doctrines, “were consistent with each other and in accordance with reason” (Graves 51). Even with its apparent flaws, such as its characteristic narrowed scope, the greatest aim of scholasticism was to equip a student with the dialectic and intellectual discipline that enabled an individual to be keen and well versed in knowledge of the time.

Medieval education in Europe began with the development of the monastic and episcopal schools, and thus is where the origin of scholasticism is found. The establishment of monasteries, “rose from a protest against vice and corruption, and pointed the way to a deeper religion and nobler life” (Graves 21). Based upon the Benedictine code, the primary purpose of monastic education was the discipline and repression of the body, and gave great prominence to doctrines of labor and systematic reading. It was through the daily devotion of reading that literacy began its revival in Europe (Graves 10). Small isolated communities formed around monasteries, creating a reserved educated culture, whose knowledge would soon spread with the growing influence and strength of the Church. Monks within these communities created the demand for manuscripts and the reproductions of the text. As a result monasteries became precious depositories, providing the preservation of ancient literature and learning. As monastic life grew, so did the interest and care of ancient manuscripts increase, and the demand for duplicates of the sacred writings resulted in the addition of the scriptorium, a room reserved for the copying of texts. Thus the preservation of texts became the primary source of labor in monastic life.

While the copying of sacred texts were in primary regard to the neatness of lines and careful ornamentation, monks gained both intellectual and moral influences from the content of their work. Not only did the text strengthen an understanding of language, reading, and writing, but also monks began to make their own personal connections to the religious topics. As a result monks became authors concerning mainly religious topics such as, “commentaries upon the Scriptures or the Christian Fathers, The Lives of Saints, and the sermons or moral tales” (Graves 12). These writings indicated the first instances of the rudimentary characteristics of scholastic thought/education. The monks and schoolmen of the monasteries began what would be a strong emphasis on the extension of knowledge through dialectical reasoning. What began in the writings of monks was the method of critical thought that would dominate the teachings of Medieval Europe.

A greater understanding of the relations between the Christian faith and the scholastic method can be seen within the influential writings of medieval monks. Their works solidified both the understanding of the doctrines of Christianity and the growth of the critical intellectual thinking characteristic of scholasticism. One such Benedictine monk was St. Anselm of Bec (1033-1109), whose writings, consistent with the methods of scholasticism, contributed greatly to the understanding of the intricacies of the Christian faith. Remember that scholasticism combined, “philosophy, seen as the autonomous operation of reason, and theology, where certitude of the conclusions is based on the principles of faith” (Vignaux 35). This concept was considered an idea under the generalized term of philosophical theology. With the growing influence of secular works through out the middle ages, monks such as Anselm supported the Christian dogma through the elimination of contradictions by intense dialectical analysis. Anselm believed in the accord of reason with dogma, but held that faith must precede knowledge as he once said, “The Christian ought to advance to knowledge through faith, not come to faith through knowledge” (Graves 51). Anselm spent much time in making clear various Christian dogmas such as the Trinity, becoming the most influential/famous to future scholars in his ‘ontological’ argument for the existence of God (Graves 51-52). Adhering to scholasticism, Anselm didn’t seek to discover new truth, but sought to define a clearer concept of his existing beliefs through reason. Reason came through the comparison of works such as his De veritate, what would be considered philosophical, to the Holy Scripture (Vignaux 35). Luscombe supports this idea, for in his perspective Anselm, “sought to explore his existing beliefs with the instrument of reason – and not with this alone for prayer was used as well – and with the aim of bringing out and elucidating the meaning, the implications, and also the truth and the plausibility of Scripture and of revealed truth” (44). Anselm’s work, like many other scholastics, furthered the complex understanding of traditional doctrines. The most significant characteristics of Anselm’s arguments were that while they were purely arguments of Christian faith, they also proceeded as arguments of logic and reason.

While the monastic schools established small communities of education, it was not until the establishment of Abbey and Cathedral schools that learning became widespread. It was through the relationship between education and the Roman Catholic Church that scholasticism became well established during the Middle Ages. This progression took form during a short period within the Middle Ages called the Carolingian Renaissance. The Carolingian dynasty arose out of a period of time reflecting political disintegration. One of the more prominent figures of this era known as Charles the Great, or Charlemagne (742-814), who utilized his power given to him by the Pope over the united Frankish state to ensure a genuine unity of his people (Pedersen 72). Charlemagne, having been taught by monks and thus receiving some formal education recognized that the unity of his people, “could be brought about only through the inner life by means of a common language, culture, and ideas”, and so a revival of learning was deemed necessary (Graves 27). Historically during the end of the eighth century, there existed a lack in education found within not only the officials of the Church, but also the ‘secular’ clergy and nobility. The monastic and cathedral schools had become sadly stagnant in manuscript and intellect production. This case was proven through Charlemagne’s letter to the Abbot of Fulda, in which he states,

We have frequently received letters from monks and in them have recognized correct sentiments, but an uncouth style and language. The sentiments inspired in them by their devotion to us they could not express correctly, because they had neglected the study of language. Therefore, we have begun to fear lest, just as the monks appear to have lost the art of writing, so also they may have lost the ability to understand the Holy Scriptures; and we all know that, though mistakes in words are dangerous, mistakes in understanding are still more so (Graves 27).

Because of this lack of sustained knowledge, Charlemagne utilized his power over the monasteries and bishoprics as the foundation of a revised organized system of education. It was Charlemagne who wished to therefore link public education with the already established education of monks (Pedersen 74, 78). In 787 an educational capitulary was issued to the abbots of all the monasteries, to reprove the clerics of their literacy, and for the schools to offer at least a complete elementary course of education. By using the Church as a vessel of learning, the floodgates of knowledge began to open enabling the scholastic movement to reach a wider pool of intellects. Teachings that were once reserved for the ‘regular’ clergy of the monastic community were brought forth to the general European society.

The schools established within the churches served significant roles to the growth of intellectual awakening during the Middle Ages. Granted, these schools began as institutions of fundamental knowledge in which, “the word school almost invariably mean a grammar school: its chief function was to supply the Church with clergy” (Lawson 8). The schools initially began teaching reading, writing, computation, singing, and Scriptures, which would later lead to the trivium (grammar, rhetoric, and dialectic) (Graves 34). Eventually, through the work of Alciun of York, the educational advisor of Charlemagne, was encouraged the adoption by the Carolingian Franks a program of education in the liberal arts (Luscombe 29), a conjunction of both the trivium and quadrivium (arithmetic, geometry, astronomy, and music). As the Middle Ages progressed, scholasticism began to involve more areas of study as opposed purely to the realm of theology. However, throughout all education, the Church held great influence and control over knowledge, and schoolmen were affected through the direct association with their teachers. The Fathers were the first interpreters of the sacred texts; “it was they who gave inspiration and direction to the achievements of the Schoolmen with the importance of philosophy and theology so that the science of God became the monument of medieval learning” (Cassidy iii). It was not until the decline of scholasticism that the Church began to lose power over the intellectual knowledge of European schools, thus proving the close relationship between scholasticism and Christianity.

In regards to the scholastic movement, it cannot be judged fairly apart from the historical context in which it took place. Scholasticism developed within confines of the Roman Catholic Church, and thus like all aspects of European society of the time, submitted to its power of Divine revelation. The range of knowledge the scholastics of the time were able to investigate, served as both an advantage and disadvantage. Unfortunately, only the subjects deemed orthodox by the Church could be defended, lest the men wished to endure persecution. The Middle Ages presented the great thinkers with a fine line between secular knowledge deemed useful and acceptable, and that which threatened the foundation and power of the Church. Counter to this regard, the limited knowledge forced the schoolmen to reduced knowledge into an extreme and logical system, and therefore, “obliged to exercise their keen analytic minds most intensively, and so divided, subdivided, and systemized their material beyond all measure” (Graves 59). Scholasticism allowed these schoolmen to sift through centuries of traditional and rather irrational doctrines, and culminate their findings into a rational system of intellect. Not only did scholasticism equip its subjects with the skills necessary to be keen in what was considered ‘modern’ knowledge, but also it forced the highest accuracy in thinking, refined by careful analytical argumentation. Scholasticism therefore fostered the intellectual development necessary for the beginning of the Renaissance. As Cassidy stated, “whatever is learned that is new must be learned in terms of what is already known (27). Scholasticism, through the preservation of knowledge, as well as the refinement of intellectual thought, became the foundation for new thought to occur.

Bibliography

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Angeles, Moses Aaron T. “St. Anselm on the Being of God.” Philippiniana Sacra. 64.130 (2009): 5-20. Print.

Cassidy Ph.D, Rev. Frank P. Molders of the Medieval Mind. Binghamton: B. Herder Book Co. , 1944. Print.

Graves, Frank Pierrepont. A History of Education During the Middle Ages and the Transition to Modern times. Norwood: The Macmillan Company, 1910. Print.

Pedersen, Olaf. The First Universities studium Generale and the Origins of University Education in Europe. New York: Cambridge University Press, 1997. Print.

Vignaux, Paul. Philosophy In The Middle Ages. London: Burns & Oates, 1959. Print.

 

The Trivium Through The Ages

by Alexander Rumann

Liberal Arts have been the basis for education since ancient Greece and are still used to this day. The Trivium has been long standing as the foundation for education. The trivium makes up the first tier of the liberal arts and consists of Grammar, rhetoric, and dialectic. Learning the first three liberal arts is the starting point for the rest of learning that would consist of the quadrivium and then higher learning in research. The three parts to the trivium all feed off each other and one must learn each subject thoroughly before moving on. The starting point of the trivium is grammar for obvious reasons. Students must learn to read and write their letters and make complete coherent sentences. After grammar students move on to the more difficult subjects of rhetoric and dialectic. The last two that are mentioned are argument, also known as public speaking, and logic respectively. These three subjects are to prepare students for the other half of the liberal arts, the quadrivium. The trivium was an instrumental tool for education in ancient Greece and is still used in the world to this day.

As a young child in Greece you would have three teachers. One teacher would be for physical training, a music teacher and one who would teach you letters. The teacher of letters would teach you the basics of reading and writing (Barrow 62). The belief was that a student could not continue on to other parts of the trivium until they had a solid foundation in grammar. The goal of education was to generate sociable and happy citizenry. Education of the Athenians in the fifth century B.C.E. was a form of training in a very strict sense that was more a system of instruction. It consisted of two main parts: the training of the mind and training of the body (Walden 10). Due to the strict sense of education the Greeks used physical was the only way they knew how to deal with unruly students and a child’s resistance to learning to read which they found incomprehensible. The reason for having such a strict system was for the purpose of trying to create a civic spirit, a pride in belonging to a free city, and having loyalty to a political community (Finley 186, 188).

Education in ancient Greece was heavily influenced by the sophists. The sophists especially were the ones who promoted grammar (Walden 20). In the ancient civilization of Greece the trivium was started around the age of twelve, much older than a child in today’s world would start education. In Greece a child would start grammar school at twelve and typically stay there till the age of fifteen where they would then move on to the next stage of the trivium. According to an ancient writer grammar is an ancient discipline that we are exposed to from a very early age. This is true that in grammar there is a concern with the written word and literate societies were concerned with an education that had a large role in the mastery of words (Clarke 11, 12). Before reaching the age to attend grammar school, boys were to be taught by their father or guardian. Fathers were to provide some sort of training to their children so they could obtain some profession or trade when they are older (Walden 60).

The ultimate goal of teaching grammar was to assist student in becoming proficient and effective language users (Glenn 10). Grammar was taught by a specialist called the grammatikos. The basic function of the grammatikos was most revealed in times of decadence when the program was reduced to the bare essentials. Even to this day our vocabulary bears witness to the irreducible nucleus of grammar. The grammatikos would teach very elementary exercises in composition. He would also do some preparatory work with students in the areas of the other parts of the trivium. He would give the basic instruction of the theory behind the art of oratory and the elementary principles of logic (Marrou 192). This early instruction would lead into the area that would be taught by the rhetorician. Grammarians would have boy citizens from the ages twelve to fifteen and then the children would move to the rhetorician. The grammatikos would provide what would now be considered preparatory school (Clarke 12).

Today we still have what we would consider preparatory and grammar schools. Even though in today’s life children are sent to school at the ages of five to seven depending on the parents. Grammar schools are still the first step in a person’s education that must be mastered before they can move on just like in Greek culture. Without grammar a student would be completely helpless in higher education and would have no hope of obtaining the necessary tools to knowledge. The use of grammar is important throughout a person’s life no matter what profession they enter in to. Without the ability to read and write there is little that one can do in society today and causes a great hindrance on them as a functioning role in society. Grammar is of the upmost importance and is the major stepping stone for education.

The second part of the trivium is known as rhetoric, also known as oratory or argument. Boys would start rhetoric school after completing grammar school at the age of fifteen and remain there until the age of eighteen (Walden 33). Rhetoric or public speaking was considered a way of employing various oratorical tropes or ‘tricks of the trade’. Scholars like Plato and Aristotle didn’t initially agree with the art of rhetoric because it was not based on objective facts that could be backed up, it was all about presenting your side in a fair light. Oratory was mainly used to appeal to a person’s emotions rather than present facts (Fuller 296). The main goal of an orator is to express his appealing personality to his audience. It is of the utmost importance to impress that he is a man of common sense, upstanding moral character, and of good will. The orator must be able to read the various emotions of the audience any play to their sympathies and use their feelings to his advantage, in a sense he must excite them. In rhetoric a man must be an expert in controlling the emotions of his audience. He should be able to cause a rise in anger or quickly turn away the wrath of a crowd; or possibly implant a feeling of friendliness or hatred. He cultivates fears in his listeners or inspires them to make a motion. In the same ways he should make the audience feel shame or shamelessness or he must impress on them how kind he is and the unkindness of his opponent and by doing that appeal to their pity. Needless to say the orator must use various methods to excitants not with any respect to the merits of his cause but only to ensure victory. A great rhetorician is one who has the power to impress his own personality onto the audience. He uses this art to manipulate what he says into something that seems credible so as to win the assent of his spectators. It makes no difference if he uses this power of influence for good or falsehood. Orators’ who skillfully choose or invent maxims that express the beliefs of his listeners gets a reputation of being a man of good reputation. The gist of oratory is to string together maxims properly and apply them to the situation at hand. In order to be a great rhetorician one must be familiar with the subject they are presenting whether it is history, finance, or law. Athenian society was constituted on the fact that every citizen should be both their own congressman and lawyer if they were ever convicted of a crime but also to function in society. Most political arguments largely consist of discrediting the opponent as making the other persons argument seem unjust, unimportant or useless (Fuller 294, 296-7, 301).

Rhetoric has two sides to it. When someone uses the art of oratory for good everyone loves it but when it is used for evil we find rhetoric to be terrible. Modern day rhetoricians that we know are Roosevelt and Churchill and also Hitler (Barrow 25). As in ancient Greece as it is today public speaking is extremely important whether it is used for good or evil. Speaking clearly or marshalling an argument can determine whether anyone will listen to or follow you. In today’s world rhetoric is still in use to the same extent it was in ancient Greece. Lawyers and congressmen today use the art of oratory every day to defend clients or rally people to their cause. Without rhetoric there would be a different world than the one we live in. The United States justice system is based on rhetoric; condemning or clearing accused of charges is the way our courts run.

The third part of the trivium is dialectic or also known as logic. Dialectic is literally translated means ‘discussion by question and answer’. Plato argued that discussion between individuals is a much better way of seeking knowledge. Through this discussion one can develop understanding which Plato saw as the essence of education. Dialectic plays off of rhetoric in the sense that it is a form of conversation that is built from the basics of grammar and also a part of rhetoric. The original purpose of dialectic was to understand mathematics. “The metaphor of the line introduced four modes of perception, the final two of which are thinking focused on mathematical objects and true intellect or knowledge focused on the Forms. Mathematical thinking is inferior to dialectic in two respects: it makes use of models, diagrams and so forth and it takes its own concepts for granted or does not question its own hypothesis”, this was not the case later on (Barrow 87, 96, 105-6). What Plato defined dialectic as was “not thinking applied to this or that field but pure thinking, proceeded by independently by sensuous perception”. Dialectic was and is a very abstract study. One devotes themselves to the analysis and clarification of concepts, leading to their arrangement in the interrelated systems which follow the laws of classification and decision and make technical definition possible (Lodge 97, 106).

Logic is still a topic that is used in education today. There is no set curriculum for logic in today’s school system but it is still used. At a young age children usually learn by question and answer even before they are enrolled in school. Anyone who has been around a four year old can attest to that. This style of learning has been used since ancient Greece. There are classes in the college level that are logic based but this is a subject that has been eradicated from early education.

The trivium has come a long way since ancient Greece but it is still a vital part in our educational system. The use of grammar, rhetoric and dialectic has continually been a part of the education that a young person receives. The main pieces are in place still to this day even if how they are taught is completely different. The quadrivium was abandoned during parts of the Middle Ages but the trivium has been constant. There have been changes to the teaching method and presentation of the trivium but it has ever been there in education. The trivium as the foundation of the liberal arts is still the same today as it was back in ancient Greece.

Bibliography
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Clarke, M.L. Higher education in the ancient world. Albuquerque: University of New Mexico Press, 1971. 11-2, 33. Print.

Marrou, H.-I. The Legacy of Greece. Oxford: Clarendon Press, 1981. 186-192. Print.

Glenn, Cheryl. The Place of Grammar in Writing Instruction. Portsmouth, NH: Boyton/Cook Publishers, 1995. 9-11. Print.

Fuller, B.A.G. History of Greek Philosophy. New York: Greenwood Press, Publishers, 1968. 294-301. Print.

Barrow, Robin. Plato. Great Britain: Biddles Ltd, 1988. 5, 25, 62, 87, 96, 105-6. Print.

Walden, John. The Universities of Ancient Greece. New York: Charles Scribner’s Sons, 1909. 10, 20-21. Print.

Barrow, Robin. Plato, utilitarianism and education. London and Boston: Routledge & Kegan Paul, 1975. 179-180. Print.

 

This paper was originally created for Steve Jackson’s History of Higher Education course.