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.



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


Socratic Education

by Danielle Brandli

There are many figures of educational importance throughout history. This essay will focus on the Greek philosopher Felix Socrates and his contributions to dynamic education, which are still prominent in educational systems today. Throughout this analysis Socrates’ background will be recounted and a thesis of his impact on education will be revealed. His concepts and theories will be declared and identified in multiple dialogues and those who furthered his theories will be noted. The reader will find that Socrates was the founder for present methods of philosophy and teaching as well as the founder for the present theory of knowledge. The philosopher Plato studied Socrates’ methods and Plato in-turn, taught Aristotle. All three of these dynamic philosophers play a large role in the knowledge underlying our education system today. To begin grasping Socrates’ impact on education, one must be knowledgeable about the life of Socrates.

It is important to know the background behind Felix Socrates in order to understand his philosophies. The Sophists, Socrates’ pupils, groups created from Socratic theories, the Peloponnesian War, the Democracy of Athens, and the trial and death of Socrates must all be known for any reader to gain a broad enough knowledge of Socrates’ background. Socrates was born in May of the year 468 BCE, as reported by C.C.W. Taylor in Socrates: A Very Short Introduction, published in 2000. It is believed that Socrates’ father was Sophroniscus, a sculptor, and his mother was a midwife named Phainarete who gave birth to Socrates in Athens (Taylor 4). He married Xanthippe who bore him three sons (Taylor 5). It was speculated that Socrates had a second wife named Mytro whom he was possibly wedded to at the same time as Xanthippe (Taylor 5). Little is known about the first part of Socrates’ life, but supposedly Socrates was a pupil of Archelaus who studied natural philosophy and ethics (Taylor 7). Complimentary to this belief, Archelaus’ studies can be noted as the probable foundation for many of Socrates’ analyses on human morale.

To our knowledge today, Socrates wrote no works of his own; therefore historians have only discovered Socrates through other philosophers’ writings as stated in The Cambridge Companion to Greek and Roman Philosophy (2003) by D.N. Sedley. In fact, there is no material proof that Socrates was even a living person. However based on other philosophers’ writings, it is very probable that Socrates lived. In this aspect Socrates parallels Jesus, for Jesus had no written works of his own but similarly, multiple people wrote him about. The written works philosophers left behind about Socrates give historians a look into the second half of Socrates’ life (Sedley 89). Plato, one of Socrates’ pupils, wrote numerous dialogues that exhibit conversations between Socrates and another person—who was usually a Sophist—about ethics and morals (Sedley 89). Some of these dialogues, the Laches, the Crito and the Apology, the Charmides, the Protagoras, the Gorgias, and the Hippias Major can be found in Trevor J. Saunders’ 2005 edited version of The Early Socratic Dialogues and will be discussed in latter portions of this paper. Xenophon (another student of Socrates) wrote a series of dialogues, called the Memoirs, which also depicted Socrates conversations with different Sophists (Sedley 89).

The Sophists, defined by W.C.K. Guthrie in the second volume of A History of Greek Philosophy printed in 1962, were a group that focused on customs and laws and started to develop universal moral principles as well as a theory of knowledge. Protagoras, a Sophist who converses with Socrates in one of Plato’s dialogues, developed the idea that every argument has an opposing argument and since each argument already has an opposite, one cannot argue by contradicting an argument but rather by questioning the knowledge behind the argument (Sedley 80). This thinking was adopted by Socrates and was eventually developed into the method of Socratic questioning as seen in education today. Others (some of whom were Sophists) also adopted this thinking and became students of Socrates. There were many followers of Socrates; however his most devoted disciples were Alcibiades, Critias, Charmides, Euclid, Aristippus, Antithenes, Xenophon, and Plato (Guthrie 47-48). Keep Alcibiades, Critias, and Charmides in mind for a later point. With his pupils, Socrates developed theories on knowledge, virtue, the psyche, and teaching. His most well known pupil, Plato, further developed Socratic education after Socrates’ death.

Socrates’ philosophies were at the root of multiple groups meaning that his knowledge was a large influence on other philosophers. Antithenes, who built off of Socrates’ theories and Sophist ideas, founded a group called the Cynics who explored the concept of morals (Guthrie 96). Cynics theorized that happiness was the sole goal of a moral life (Guthrie 115). Similarly, Euclid led the Megarics who explored the concepts of possibility, motion, chance, and annihilation while Aristippus led the Cyrenaics (Guthrie 93, 118). The Cynics and the Cyrenaics directly opposed the Platonic theory of reality being composed of Forms, which is intriguing because Platonism and the theories of the Cynics and Cyrenaics all stemmed from Socrates.

Next, information about the Peloponnesian War comes from Henry J. Perkinson’s work Since Socrates: Studies in the History of Western Educational Thought that was published in 1980. The Peloponnesian War occurred from 431 to 404 BCE, during the second half of Socrates’ life (Perkinson 2). The war ended in 404 BCE when a group called the Thirty Tyrants overthrew the democracy of Athens; three of these tyrants were Alcibiades, Critias, and Charmides (Perkinson 2). Shortly thereafter—in 401 BCE—the Tyrants fell and the democracy was restored (Sedley 91). Following the democracy’s restoration, three men filed a claim against Socrates in 399 BCE for worshipping unknown gods and for corrupting the youth (Taylor 14). Although the claim was that he had corrupted the youth through his teachings, it has been speculated that part of the reason a case was brought against him was due to his connection to Alcibiades, Critias, and Charmides (Perkinson 2). Since these tyrants were taught by Socrates and also involved themselves in the overthrow of the Athenian democracy, the Athenian government concluded that Socrates must have taught them that democracy was a bad form of government and therefore Socrates was responsible for their actions (Perkinson 2).

Plato’s dialogues show that Socrates did in fact dislike democracy. However, the laws of the Athenian democracy, deduced by Richard Kraut in his 1984 novel of Socrates and State, pleased Socrates because they were designed for improvement of the youth and they provided correct standards for behavior. Even still though, Socrates disagreed with the idea of democracy because he believed it gave power to the majority (Kraut 196). He thought that the majority—what he called the many—was corrupt because their morals were false and because the many could not give children an appropriate education (Kraut 196). Socrates concluded that democracy was not the ideal way to govern and he suggested that a board of experts could rule. Yet he questioned who was even qualified to be an expert for this proposal, and thus Socrates eventually recognized that there were no better options than democracy (Kraut 208).

Returning to Socrates’ trial— Socrates was tried in the spring of 399 BCE; the jury convicted him of corrupting the youth and sentenced him to death by hemlock poisoning (Taylor 12). Before his execution in late spring, Socrates spent a period of time in jail and while in jail Socrates had the chance to escape, but he chose not to (Taylor 14). Socrates stayed to be executed due to personal morals and he inevitably became a martyr to prove a key point: it is wrong to silence critics (Perkinson 13). Teaching society through action and sacrificing himself was what he considered to be the greatest act of teaching (Perkinson 13).

Socrates’ pupil Plato wrote two dialogues that accounted Socrates’ trial and personal motivations behind drinking the hemlock poison. The Crito and the Apology dialogues explain Socrates’ justification for his life and his reasoning for the necessary continuation of dynamic education. The Apology explains how Socrates teaches and that his life has been spent philosophizing which is essential to teaching; therefore Socrates concludes that his life is a just cause. The Crito explicates that Socrates must obey the law unless that law requires him to do an injustice. In this dialogue, Crito presents an argument for Socrates to escape from jail after he has been convicted, but Socrates refuses to do so. Socrates argues that he must stay and be executed for the well being of his psyche. Socrates believes that his psyche will no longer be able to philosophize if he commits the injustice of escape. Socrates deems that he may be able to continue to philosophize in heaven so his educational task will not be stopped by his execution (Teloh 98-128). After Socrates’ death, Plato continues to progress Socrates’ dynamic teaching.

Now that Socrates’ background is established, the nature of Ionian science must be explained before beginning to explore the theories Socrates created. As explained in Before and After Socrates written by Francis Cornford in 1958, Ionian science first began in an Ionian colony in the sixth century. Ionian science was the change to a science of impersonal nature from mythology with personal sacrifices to the gods (Cornford 17). Very few had claimed this point of view and most Greeks still carried on with their mythology for thousands of years to come (Cornford 17). This forward view of Ionian science is also called pre-Socratic science; moreover it is the science of “how,” which is asked before the “why” (Cornford 1-2). Socrates also pioneers this concept of asking the “why”.

Socrates had a few concepts that asked “why,” which were publicized in the dialogues of his pupils. His theories and concepts that will be introduced are the psyche, “know thyself,” a theory of knowledge, the concept of virtue, and the Socratic Method. With these concepts, Socrates created a basis for dynamic learning that was further developed by both Plato and Aristotle. Although Socrates had no written works of his own, his theories can be seen in the dialogues of Plato. Yet, was the purpose of these dialogues to educate people about Socrates’ dynamic theories? The immediate use of Plato’s dialogues is unknown but the philosophical purpose was to create something concrete that others could not argue with. Plato claims no original thought and credits the theories in his dialogues to Socrates, thus one can conclude that Plato constructed his dialogues to be a tangible and unarguable assembly of Socratic theories. The dialogues examined in this essay are the Charmides, the Protagoras, the Laches, the Gorgias, and the Hippias Major. Through the investigation of these dialogues, Socrates’ theories and his dynamic teaching style will be discovered and deemed as largely important to philosophy and education today.

First, Socrates’ concept of the psyche will be defined. Judged in Ellen M. Wood’s work Class Ideology and Ancient Political Theory: Socrates, Plato, And Aristotle in Social Context (published in 1978,) the psyche, or the soul, was an important concept to Socrates (Wood 107). He believed that the psyche was more superior to the body, and thusly that the body was simply a tool to be used by the psyche (Wood 107). Socrates observed that most men were too infatuated with the physical aspects of life and that people needed to pay more care to their psyche (Wood 107). Socrates believed that caring for your psyche correctly was the path to goodness and the first step on this path was critical self-examination: one must “know thyself’ (Wood 107). Socrates created a hierarchical system based on the purity of psyches (Wood 108). This system is ordered from the most pure to the least pure psyche:

-Authentic Philosophers

-Warrior Rulers

-Law Abiding Kings

-Physicians, Athletic Trainers, and Athletes

-Prophets and Priests

-Poets and Artists

-Artisans and Farmers

-Sophists and Demagogues


It is ironic that Socrates listed Tyrants as having the most impure psyches considering that three of his pupils later became Tyrant Rulers. If Alcibiades, Critias, and Charmides followed Socrates’ teachings truly, then they would have known that their act of tyranny made them impure.

Next, Socrates’ greatest commandment was “know thyself” (Guthrie 65). He believed that if one knew oneself (defined as improving the psyche) then that person’s knowledge would greatly increase (Perkinson 9). In his 1979 work, Socrates: Philosophy in Plato’s Early Dialogues, Gerasimos X. Santas reports that Socrates theorized that virtue is the knowledge of goodness and that the knowledge of good and evil is the foundation for teaching and defining the world around us. If virtue—also known as moral—is the knowledge of goodness, then what is the definition of “goodness?” Socrates likely pondered this question and then defined what was useful and beneficial to mankind as “good” (Guthrie 68). If a man was knowledgeable in what was beneficial to other men, then they were virtuous. This type of thinking led Socrates to conclude that virtue was wisdom and success (Guthrie 70). Socrates also believed that being aware of one’s ignorance made one wise. These concepts are Socrates’ theory of knowledge and virtue, which he stayed firmly fastened to throughout his lifetime as seen during his trial and execution.

Plato’s dialogue the Charmides displays Socrates’ theory of virtue. In the dialogue, Charmides, Critias and Socrates discuss the aspects of temperance: self-control and modesty. Charmides says that temperance is doing one’s own business, which Socrates concludes to be immodest thinking, and therefore wrong. Thus, Socrates seeks to change Charmides thinking. Socrates decides to improve Critias’ thinking who, in-turn will improve Charmides’. Critias defines temperance as self-knowledge, which causes Socrates to deem Critias ignorant. Critias will not admit his ignorance but Charmides did and also asks Socrates to teach him more of virtue and help increase his wisdom. This brings up the earlier topic of Socrates’ accountability for the overthrow of the Athenian democracy by Alcibiades, Charmides, and Critias. Is Socrates to blame for Charmides role in the Thirty Tyrants? The last line of the dialogue, “You [Socrates] must expect me [Charmides] to use force…since he [Critias] gives me the command: take counsel…” clearly shows that Charmides becomes Critias’ pupil and thus, Charmides is made into a tyrant by Critias, not Socrates (Teloh 57-68).

The Protagoras dialogue also explores the teaching of virtue. In the Protagoras, Protagoras and Socrates start their conversation with different views on both teaching and virtue; Socrates thought that it was impossible to teach high demotic virtue while Protagoras believed low demotic virtue could be taught. After discussing Socrates decides that all virtue is the knowledge of good and evil which can be taught, while Protagoras changes his view to deny that any virtue can be taught. This dialogue does not show that Socrates successfully educated Protagoras and yet it does not recommend Protagoras’ teaching methods either. Plato could have written this dialogue while questioning Socrates’ teaching techniques (Teloh 164-175).

Another key concept that Socrates held was that what was “good” or “evil” could not be decided by society (Santas 139). He viewed society as a corrupt mass—as examined earlier—and thought that one should not look for societal approval but rather seek answers from experts on the subject. Socrates suggested consulting experts for help to decide what was “good” or “evil.” Furthermore, he emphasized that one must also learn these things from within (Perkinson 10).

Socrates aimed to change the thoughts of everyone, not just of the upper class and Sophists (Kraut 200). He wanted to spread his theories and educate people using his teaching techniques. These techniques, also known as the Socratic Method, were used to educate others and can be defined as “extorting a common truth from the loose and contradictory statements of different individuals” (Guthrie 47). This method is successful because it is based on the fact that man is fallible and that man does not know all. One must make mistakes when conceiving their morals and Socrates points out these faults through questioning arguments and creating counter-arguments (Perkinson 11). If a person admitted his ignorance during an argument with Socrates, then Socrates believed he would be able to successfully educate them. Socrates taught by not telling his pupils what was good, true, better, or desirable but rather by directing his pupil to see what was evil (Perkinson 11). This kind of teaching—as stated by Henry Teloh in his 1986 work Socratic Education in Plato’s Early Dialogues—was new for the time period and many of the people who would converse with Socrates would in turn become irritated with his techniques (Teloh 46). People were obviously unaccustomed to the Socratic way of thinking. Most Sophists still thought of philosophy as having an external nature while Socrates philosophized about the study of man and human action.

The Socratic Method, which we use today, is defined as the extraction of a common truth of “good” from loose and contradictory statements that are “bad” or “wrong” (Guthrie 47). Socrates theorized that wisdom came from virtue—the knowledge of what was “good” through personal thought—and that the better a person knew themselves, the more pure one’s psyche was, the more knowledgeable one could be. Socrates was a teacher who did not directly teach these theories but rather he educated his pupils by questioning them until they discovered the truth for themselves (Perkinson 11).

In the Laches dialogue, two fathers Lysimachus and Melesias have both been failures and they want their children to turn out better than they did. These fathers ask two generals, Nicias and Laches, if their children will be better off if they fight. The generals give contradictory speeches about fighting which leads to a discussion between Socrates and the generals about psyche and courage. Socrates questions the generals about what makes a man courageous and when the generals start to tire of Socrates’ questions he simply admits his ignorance. Socrates states that the generals have been more courageous than him; therefore they are wiser than him on the topic at hand. Socrates’ humility persuades the generals to answer his questions and the conversation ends with the conclusion that internal psychic is the cause of courageous actions. Two different definitions of courage come from both general; courage is the knowledge of good and evil or courage is endurance. This dialogue shows Socrates’ teaching methods and his success in educating both Nicias and Laches through guiding them to extract their own true meaning of courage (Teloh 41-56).

Now that we have discussed Socrates’ concepts in Plato’s dialogues, we will briefly look at how his pupil Plato further developed his philosophies. Platonism was developed with the Socratic Method as its foundation. Platonism in fact follows the Socratic Method so strongly that the separation of one method from the other is unclear (Cornford 55). However, Plato’s dialogues the Gorgias and the Hippias Major show that the Socratic Method of teaching needed to be expanded.

In Plato’s dialogue the Gorgias, Gorgias, Socrates, Polus, and Calicles discuss the teaching methods of rhetorical and dialectical teaching. Socrates believes that the ultimate goal of dialectic is to gain knowledge. Socrates and Gorgias contrast rhetoric and dialectic until Socrates concludes that dialectic is the ideal way of educating and Gorgias, Polus, and Calicles use the wrong method of rhetoric. Socrates however does not change these men into dialecticians. The dialogue shows Socrates’ failure was due to the fact that these men had already established their values. Also in this dialogue, Plato notes that Socrates’ teaching methods needed to be advanced, which becomes his reasoning for the necessity of pre-dialectic teaching in the Republic dialogue (Teloh 129-150).

The Hippias Major dialogue displays a conversation between Socrates and Hippias about beauty. Socrates rejects Hippias’ definitions and Socrates unsuccessfully attempts to change Hippias’ thinking. Socrates uses all of his usual teaching methods, yet they do not seem to have any impact on Hippias. In this dialogue Plato highlights that Socrates fails his educational mission and proposes his own answer: people need basic education in music and gymnastics (Teloh 176-194).

Plato’s dialogues illustrate how Socrates taught others. Every dialogue discussed shows Socrates using the Socratic Method while trying to guide the student towards finding the truth in Socrates’ theories. However, the Gorgias and the Hippias Major dialogues show Socrates’ failure to educate the other conversers, which Plato spends his life trying to progress. Plato took Socrates’ theories and advanced them into a system of the world. Plato’s system embraced both the nature of man and external Nature, whereas Socrates was only concerned with the nature of man (Cornford 56). Plato created the Republic dialogue as a program (based on the philosophies of Socrates) for the reform of Athens, dedicated to restore a moral life to society (Cornford 58). Plato’s main theory of Forms, or ideas, was that the vision of a Form was knowledge. He expanded on Socrates use of definitions and created a universal definition for Forms called absolute meaning: Forms are fixed within Nature and are unchangeable (Cornford 61). Plato believed that a world of perfect Forms contains the truth of all things, which further developed the Socratic Method of seeking the truth (Cornford 64). Plato’s work led to the establishment of the Pythagorean doctrine as well as the theory of reminiscence (Cornford 70).

Plato’s teachings also led to the establishment of Aristotle as a philosopher, whom migrated to Athens specifically to become a pupil of Plato’s (Cornford 85). For the first part of his life, Aristotle followed Plato’s teachings and created dialogues in imitation of his teacher. During the second part of his life, Aristotle moved away from Plato’s theories. Like a true dynamic learner, he questioned Plato’s idea of Forms and shifted from Platonism towards philosophy of the common sense (Cornford 88). Aristotle’s philosophy that “knowledge lies within Nature as revealed by the senses” was rooted in the Socratic idea of seeking the truth (Cornford 90). With his students, Aristotle began researching the nature of things through observation (Cornford 92). This Aristotelian system led to the development of biological science that broadly included physics and metaphysics (Cornford 106). Through research, Aristotle believed that one could find a universal answer to every question because everything is rational (Cornford 106). This theory of a universal answer completes Socrates’ search for the truth. Aristotle’s expansion of Socratic concepts may not have had an impact on our present educational system today if Aristotle had not taught Alexander the Great. Alexander the Great spread the Socratic knowledge he gained from Aristotle throughout the Roman Empire.

To conclude this analysis of Socrates’ educational influence, we will return to a few key points. Felix Socrates was a highly influential philosopher in the field of education. He was the foundation for philosophy as a study of mankind, teaching methods, and the theory of knowledge that were all continually developed by others and are prominent in our educational system today. Without Socrates’ theories, Plato and Aristotle may have never created their own philosophies. Without Plato, Aristotle, and Alexander the Great, Socrates’ dynamic teaching methods may not have been taught. Without the spread of the Socratic Method, our education system might not be what it is today. There is no doubt that Socrates’ life dedication to the study of the philosophy was very impactful in the education of man.



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This paper was originally presented in Steve Jackson’s History of Higher Education course.