The Success of Euclid’s ‘Elements’

Scuola_di_atene_07In a survey of books used for education throughout the history of Western civilization two books stand out: the Bible and Euclid’s Elements (Carl B. Boyer and Uta C. Merzbach, A History of Mathematics, 119). Poet and schoolmaster Edna St. Vincent Millay says of the Elements that “Euclid alone has looked on Beauty bare.” And Euclid earned a spot amongst Raphael’s School of Athens painting alongside Plato and Aristotle. What can account for such high praise and popularity? Is it that Euclid has laid the foundations for all mathematics? If so, why has Euclid been left behind in the modern classroom? Is there any value in a return to Euclid? What value might there be in studying Euclid today?

It may be too strong a claim to say that the Elements provide the foundation for all mathematics. Nevertheless, the basic principles or axioms of many of the branches of mathematics can, in fact, be seen in Euclid. In the classical mathematical Quadrivium of Arithmetic, Geometry, Music, and Astronomy, we see that Geometry is but one of the fundamental subjects of mathematics. Yet, in Euclid’s Elements there are applications and axioms for the other branches. For example, his earliest axioms like, “If equals be added to equals, the wholes are equal” have clear implications for the axioms (if not being identical) in Arithmetic. The proofs for relationships of ratios throughout Book X (and elsewhere) have clear implications for the science of Music which deal in harmonies and patterns. And certainly the principles of trigonometry that are laid down by Euclid have far reaching application from Astronomy to sea-faring to engineering.

200px-EuclidStatueOxfordYet Euclid does not specifically set forth the axioms of those other branches. However, to the student who is attentive, the Elements does teach an important principle concerning the nature of learning and of certain disciplines. In demonstrative sciences one always begins with axioms and definitions and then begins to reason from those assumptions. They are the grounds or conditions of the reasoning that follows. In this sense they are indemonstrable. To ask for such demonstrations is to misunderstand the nature of the science. For example, Aristotle in the Metaphysics, sets forth to show that the Principle of Non-Contradiction (the foundations of Logic itself) cannot and should not be demonstrated. To attempt a proof is to misunderstand the nature of proof, for one cannot prove it without assuming it. The best Aristotle can do in this case is show that it is impossible to deny, because to deny it, one must assume it.  In Geometry it would be improper for Euclid to attempt to prove that “a proportion in three terms is the least possible.” Rather, this definition functions as an assumption from which the proofs proceed.

As indicated from the example from Aristotle, Geometry is not the only science that proceeds in this fashion. The student who is attentive in his studies of the Elements should see parallels in other disciplines as well, such as the philosophical and theological sciences. Just as there are axioms of Geometry, so too are there axioms of philosophy and theology that are not subject to proof, but are the grounds from which reasoning proceeds. This may be one of the mistakes of Descartes in Epistemology: he attempted to assume nothing and prove everything. A task which is impossible, for all disciplines requires axioms. Even Moral Philosophy, of which Thomas Aquinas asserts the axiom of all action is: “good is to be done and pursued, and evil is to be avoided” (Summa Theologica, II-I, Q. 92, A. 1).

This may partially account for the staying-power of the Elements throughout history, the implicit lesson about the nature and procedure of demonstrative sciences. In addition to this, the one who studies Euclid does not just study Geometry. For the Elements is also a lesson in the Trivium of Grammar, Logic, and Rhetoric. That is, Euclid bridges the gap between the Trivium and the Quadrivium. This is also why Euclid may appeal to those persons who find mathematics difficult or intimidating. For as a modern student peruses the Elements they may be struck with how “unmathematical” it appears. There are no numbers, no Cartesian coordinate planes, no formulas. It is as much a book of literature as it is of geometry. This may account for the testimony throughout history of its elegance and beauty. For each of Euclid’s proofs begin with an assertion followed by the elegant “for if not” reductio ad absurdum and ending with pointed “the very thing which was to be shown” (Q.E.D.) or “the very thing which was to be done” (Q.E.F.). Thus, in the process of learning Geometry, the student also learns Grammar and Logic, as well as certain principles of persuasive argumentation (Rhetoric). This may also account for the popularity of the Elements in education.

Will Euclid ever be used again to the same degree as he was in the past? This seems unlikely for a number of reasons. First, there is a need for certain modern concepts in geometry like the Cartesian coordinate plane. Second, textbook companies have no incentive in publishing Euclid since the Elements is in the public domain. Third, the modern student (for a variety of reasons beyond the scope of this essay) may no longer have the capability to read Euclid as an introductory text on Geometry. Yet, for the student who struggles with mathematics, Euclid may be a way to bridge the gap between the humanities and mathematics. And maybe, these students too may come to see that: “Euclid alone has looked on Beauty bare.”

The Necessity of Gratuitous Education

As we look over the plethora of options for education available to us, how we to decide what education is best? There is “on the job training,” vocational schools, technical schools, nursing schools, and the list goes on and on. Among this array of choices is “liberal arts education.” Looking over a truly liberal arts education, we might be struck to see the lack of similarity among the classes. We find classes in literature, philosophy, history, mathematics, speech, possibly theology, and the sciences. What exactly is the point of all this? Why would anyone pursue this kind of education? A liberal arts education will not train us to be bricklayers, it will not make us into doctors or lawyers, and it will not enable us to buy a home. It seems entirely gratuitous—something a rich person might indulge in until forced (if ever) to get a “real job.”

First, what exactly is meant by a “liberal arts education”? Many programs today which call themselves “liberal arts” would be unrecognizable as such fifty or more years ago. Today, many “liberal arts” programs have been reduced to “general studies” which contain little to no common core and an abundance of elective choices. Instead, a liberal arts education is one which has no electives whatsoever, for to allow the student to choose his own course of study is to turn over the process of education to the one who is in the least position to know what needs to be known: the student. As Mortimer J. Adler points out, “it is the student who is the master under the elective system … the relatively ignorant and incompetent, choose their own road to learning, according to the fickle interests of their immaturity.” In a liberal arts education, all students receive the same education because the end of liberal arts education is the cultivation of the human mind, not the training for a productive career. Since all are human, all require the same education.

250px-Grigorii_chudotvoretzIt is the end of liberal arts education itself which is the greatest argument for its pursuit. We should pursue the liberal arts because we are human. No one can choose not to be a human being, one can only choose whether or not to be a good one. To become fully what we are means the cultivation of the mind. James V. Schall states that within each of us is a “longing to know … [this is] the very heart of what we are as rational beings.” Most importantly, and yet often least known, is the need and desire to know “ourselves”—who we are, where we come from, where we are going. Liberal arts education aims to reveal the student to themselves. Gregory Thaumaturgus claims that this was one of the highest things that Origen taught his students: “teaching us to be at home with ourselves, and to desire and endeavor to know ourselves, which indeed is the most excellent achievement of philosophy, the thing that is ascribed also to the most prophetic of spirits as the highest argument of wisdom—the precept, Know thyself.” This indeed is the beginning of knowledge. For without knowledge of ourselves, no amount of our struggling will bring us closer to what we truly need.

So no, the liberal arts will not help you get a bigger boat, a better job, or a beautiful spouse. It will, however, teach you why none of those things, in themselves, will make you happy. Instead, the liberal arts will enable you (no matter what possessions you have, no matter what career you choose, no matter whether you are married or single) to be more human, more of what you were intended to be, and consequently, happier.

Adler, Mortimer Jerome. Reforming Education: The Opening of the American Mind. Edited by Geraldine Van Doren. New York: Macmillan, 1988.

Schall, James V. On the Unseriousness of Human Affairs: Teaching, Writing, Playing, Believing, Lecturing, Philosophizing, Singing, Dancing. Wilmington, DE: ISI Books, 2001.

Gregory Thaumaturgus. “Oration and Panegyric Addressed to Origen.” In The Great Tradition: Classic Readings on What It Means to Be an Educated Human Being, edited by Richard M. Gamble, 179-80. Wilmington, DE: ISI Books, 2009.


In Over My Head?

I’m taking a course next semester: “Mathematical and Scientific Reasoning.” After looking over the reading list, for the first time in a long time, I fear I might be in over my head:

Plato, Meno
Euclid, The Elements
Archimedes, On the Equilibrium of Planes
Nicomachus, Introduction to Arithmetic
Sir Thomas L. Heath, Greek Astronomy
Kepler, Epitome of Copernican Astronomy
Galileo, Two New Sciences
Bacon, Novum Organum and The Sphinx
Newton, Mathematical Principles of Natural Philosophy
Huygens, Treatise on Light
Lavoisier, Elements of Chemistry
Gilson, From Aristotle to Darwin and Back Again

It will be a challenging few months – to say the least! My plan is to invent a new form of calculus, that ought to be enough to pass the class!


Classical Education the Key to Scientific Progress

From E. Christian Kopff’s Greek to Us: The Death of Classical Education and Its Consequences

The decades on either side of WWI witnessed brilliant work in Physics: the concept of quanta, the theories of special and general relativity and the development of quantum mechanics. One might expect that the most important work in these fields would be done by graduates of the technical school system. Nearly the opposite is true. Max Planck, Werner Heisenberg, Erwin Schrödinger, Niels Bohr were classically educated. Einstein attended a Swiss technical high school, but he had spent his first six years at a classical school, where his sister remembered his best subjects as Mathematics and Latin: “Latin’s clear, strictly logical structure fit his mindset.” Heisenberg wrote: “I believe that in the work of Max Planck, for instance, we can clearly see that his thought was influenced and made fruitful by his classical schooling.” Heisenberg insisted that his own insights into nature came from his classical education. Its combination of math and physics with language instruction led him to read Plato’s Timaeus in Greek. He was impressed by Plato’s rational appeals to understand nature mathematically rather than as a purely physical reality: “I was gaining the growing conviction that one could hardly make progress in modern atomic physics without a knowledge of Greek natural philosophy.”

An Apologia for the Study of Logic

In the never ending world of education reform, from “No Child Left Behind” to “Common Core Standards,” we are continually told of the need for “critical thinking,” reading, and writing skills—along with technical skills for future employment. A survey of the reforms and initiatives put into law and practice, however, all have a similar defect: a failure to teach Logic. When, exactly, Logic was dropped from the curriculum, I do not know, but it’s reintroduction does not seem to be a goal of any reformers of public education.

metalogicon250One of the most cogent and eloquent defenses of the teaching of Logic comes from the 12th century thinker John of Salisbury. In his book, The Metalogicon, John argues persuasively that a study and knowledge of Logic is necessary for myriad reasons. The title, while admittedly daunting, means simply “on behalf of Logic,” and in the book John sets forth to refute those thinkers of his own time (who he refers to collectively as Cornificius) who were adversaries of the teaching of Logic (or the trivium more generally). Cornificius, says John, is the “ignorant and malevolent foes of studies pertaining to eloquence, attacks not merely one, or even a few persons, but all civilization and political organization” (11-12). Bold words indeed, for as John sees it, to oppose the teaching of Logic, is to oppose civilization. John’s apologia includes more than just a defense of Logic, undeniably it is a robust defense of the whole of liberal arts education, but I will restrict my discussion here to the focus on Logic.

What exactly is “Logic” as a field of study? For John, Logic has a twofold meaning: “the science of verbal expression and reasoning” (32). That is, Logic (in the narrow sense) covers the rules of rational thinking and (in the broad sense) knowledge and skill of how to express reason with speech—or, as John puts it, “all instruction relative to words” (32). This broader sense, Augustine referred to as, “the science of argumentation” (80). Thus, John suggests that the traditional trivium of Grammar, Logic, and Rhetoric, is what he has in mind by “Logic.”

This seems to go beyond the traditional definition of Logic which was restrictive to the art and science of reasoning, with Rhetoric taking up the ability to express ideas eloquently and winsomely and Grammar the science of words. The reason John extends the use of Logic to encompass all of the art of argumentation seems to be due to the nature of Logic itself as the hinge to both proper Grammar and effective Rhetoric. Grammar, affirms John, “is the science of speaking and writing correctly—the starting point of all liberal studies” (37). Rhetoric is the art of expresses those words eloquently, or as John puts it, “Rhetoric, where persuasion is in order, supplies the silvery luster of its resplendent eloquence” (67). In order to show why Logic is the “linchpin,” so to speak, of the verbal arts, it’s nature and purpose must first be explored.

The kind of Logic, in the narrower sense, John has in mind is that formalized by Aristotle. Aristotelian Logic, certainly at the time of John, was the only game in town. Aristotle, being its one and only founder, dominated Logic studies and John did not depart from this tradition.

So, why study Aristotelian Logic? John gives several reasons. First, logic provides the groundwork or rules which give birth to Prudence. Says John, “Of all things most desirable is wisdom, whose fruit consists in the love of what is good and the practice of virtue” (74). Could we considered anyone wise who reasons illogically? In fact, is that not a true oxymoron, to “reason illogically”? Logic provides the tools for the mind to operate and enable it to judge (if not to act) wisely. In order to act Prudently, one’s mind must operate along the rules of logic, which guide the mind to the proper course of action. This, of course, is not a perfect road map, but without it, one could only follow the proper course by accident. With all the roads that we would take, who could navigate without the ability to read the map?

In an age which is tempted to worship science, it is a wonder that training in Logic is not mandatory, given that the presumed object of science is truth and logic is the mind’s aid to discover truth. As John says, “Prudence consists entirely in insight into the truth, together with a certain skill in investigating the latter; whereas justice embraces the truth and fortitude defends it, while temperance moderates the activities of the aforesaid virtues” (74). That is, at the center of the Cardinal Virtues is Truth and Logic provides the means to attain the Truth.

Given all of this, we can now see why Logic is the linchpin of the verbal arts, and why John calls the whole of the trivium “Logic.” Logic is what connects the grammar of the word with the eloquence of expression. Without Logic, Rhetoric becomes Sophistry. Logic aids in judging propositions, it is what guides the mind in the discovery of Truth. If the mind is not aimed at Truth, Rhetoric is merely aimed at power, overcoming one’s opponent. As John puts it, Rhetoric “unenlightened by reason, is rash and blind” (10). The uniting of the trivium John explains poetically:

If we may resort to a fable, antiquity considered that Prudence, the sister of Truth, was not sterile, but bore a wonderful daughter [Philology], whom she committed to the chaste embrace of Mercury [Eloquence]. In other words, Prudence, the sister of Truth, arranged that [her daughter], the Love of [Logical] Reasoning and Knowledge, would acquire fertility and luster from Eloquence. Such is the union of Philology and Mercury. (78-79)

It may be that the modern educator’s failure to teach and instruct in the art and science of Logic is an implicit rejection of Truth. For if there is no Truth, Logic is irrelevant. So too is reason, knowledge, and science. If, however, Truth is deemed possible, to ignore the study of Logic is to handicap the mind. It is to lead the student in the study of truth but not to give the student the tools to discover it. A recovery of the study of Logic, therefore, is one of the truly necessary areas of “reform” for modern education, even if it is not on the agenda of any modern school boards or legislators.


John of Salisbury, The Metalogicon: A Twelfth-Century Defense of the Verbal and Logical Arts of the Trivium, translated by Daniel D. McGarry, Philadelphia: Paul Dry Books, 2009.

Stretched Out Towards Knowing: Human Wonder and Knowledge

The wonder in a child’s eyes as they encounter the world for the first time is as exhilarating as it is unmistakable. It is the exuberance, delight, and astonishment of a young mind dazzled by creation. The dazzled young mind does not remain dazzled though, it is drawn out to know that which dazzles it. The child asks “why” incessantly, struggling to know this world in which he lives, this world which dazzles him so. This experience reveals something profound about human nature and the process of education.

St. Thomas Aquinas from  by Carlo CrivelliAt the center of the child’s experience is wonder. Thomas Aquinas defined wonder as “a kind of desire for knowledge, a desire which comes to man when he sees an effect of which the cause either is unknown to him, or surpasses his knowledge or power of understanding” (Summa Theologica, I-II, Q. 32, A. 8). As we see the fireworks, we might wonder as to how the pyro-technician is able to produce explosions of different colors, shapes, or sizes. When we hear a strange sound at night, we might wonder what kind of goblin is roaming our house. As we reflect on ourselves, we might wonder why we exist at all! This experience of wonder reveals an essentially human characteristic, for of all creatures, humans alone wonder. These feelings of wonder are an essentially human phenomenon. As Philip Melanchthon muses, “Who is so hard-hearted…that he does not sometimes, looking up at the sky and beholding the most beautiful stars in it, wonder at these varied alternations…and desire to know the traces…of their motions?” (Orations on Philosophy and Education, 106)

As Thomas’ definition suggests, humans can wonder, because they can know. Aristotle opens his Metaphysics with the claim that “All men by nature desire to know” (980a22). This translation hides an interesting dimension to Aristotle’s claim. For the word here translated as “desire” is the word ὀρέγω (orego), which does not simply mean “desire” but “stretch out, extend” and in this context could be rendered: “All men by nature are stretched out towards knowing.” Humans are stretched out but also must stretch themselves out to live in according with this nature. As Aristotle says, humans “must, so far as we can…strain every nerve to live in accordance with the best thing in us” (Nicomachean Ethics, 177b33-34). The mind is, as James V. Schall says, capax omnium—capable of knowing all things (On the Unseriousness of Human Affairs, 15). It is in human nature to be pulled towards and to strain towards truth, for only truth can be known. Both Plato and Aristotle cite wonder as the cause of or the beginning of all philosophy (wisdom): “This feeling of wonder shows that you are a philosopher, since wonder is the only beginning of philosophy” (Theaetetus, 155D) “For it is owing to their wonder that men both now begin and at first began to philosophize” (Metaphysics, 982b12-13).

At this point, we are still missing an important part of wonder. The Latin word for wonder, admirare, comes into English as “admire” or “admiration.” Yet, wonder is not admiration, for admiration suggests a distanced response to something worthy of respect. Wonder, on the other hand, involves the wonderer. The wonderer is not a distance observer, but a participator with those wonders. As involved in the process, the wonderer experiences a great pleasure. This pleasure is not simply that of amusement (far from it!), but a hope that that which causes awe in us due to our ignorance can come to be known. Again, says Thomas, “wonder is a cause of pleasure in so far as it includes a hope of getting the knowledge one desires to have. … Wonder gives pleasure … in so far as it includes the desire of learning the cause, and in so far as the wonderer learns something new.” Wonder, therefore, is intimately linked with hope. For, if there is no hope that the wonderer will come to know the object of his wonder, the only result is despair. Consequently, any belief system which denies that knowledge is possible, or that truth is attainable by the human mind, must be a system of despair; and must chastise the child that wonders.

If this desire to wonder and to know is innate in human nature, why then do many people stop wondering as they grow? A full treatment of the decline in our wonder is beyond the scope of this essay, but I would like to suggest one possibility. As we grow, we sin, and as we sin, we violate our very nature. The effects of this will vary as individuals vary, but one of the effects is often the diminished desire for our very nature to develop. We lose what G.K. Chesterton calls, “the eternal appetite of infancy” (Orthodoxy, 58) The world becomes a wearisome and tiresome place, because we are wearied and tired of ourselves. We are born, as Wordsworth puts, “trailing clouds of glory … [and] Heaven lies about us in our infancy.” But as we grow up, we grow old and can no longer see Heaven around us.

The question now becomes, what is to be done? How are we to recover this eternal infancy? How are we to grow up, without growing old? The answer must partly come from education. Education of the kind that does not dull the mind into submission, but which liberates it from opinion and ignorance, and feeds it on truth, goodness, and beauty. Then, and only then, is the mind freed to continue wondering, knowing, and delighting in the process as it matures. Furthermore, as the mind matures, it’s capacity to wonder also matures and so too does the delight in knowing. In short, we become more human, more of what we are, more of what we were intended to be.

Would Aristotle Send His Son to a Public School?


[ Disclaimer: please understand that I am not, in this post disparaging those people who work in public education. My criticisms are leveled against the Philosophy of Education which is driving modern Progressivist Education. I wholeheartedly support those people who are working hard in public schools, in spite of the philosophy which drives it.]


Aristotle stands in between two giants of history: his teacher, Plato, and his student, Alexander the Great. As both a student of a great teacher and a teacher of a great leader, one wonders just what Aristotle thought of education. Today there are several strains of educational theory which each offer their own views on the means and ends of education. Aristotle himself had an insatiable thirst for knowledge, so one wonders just what kind of education he thought best? A brief analysis of his Nicomachean Ethics reveals that Aristotle would likely reject modern theories of education.

In Book I of the Nicomachean Ethics, Aristotle begins his discussion of ethics with the observation that whenever a person acts, they always act with some end in mind, some purpose, goal, or good. Further, he observes that the ends we have in mind are mostly means to other ends. For example, I brush my teeth. This is not done, however, without purpose. Clearly there is a good I have in mind for the action, for otherwise I would not brush my teeth. People may brush their teeth with different goods in mind. For example, one person may do it in order to avoid gingivitis, others to have a “clean” feeling in their mouths. Either way, the end in mind is a means to another end. In the former case the end is health and in the later it is pleasure.

Aristotle links the chain of means and ends and asks, is there something towards which all actions aim? That is, is there a “last end” or a “highest good” that we have in mind when we act? Aristotle asserts that the end we all have in mind is “happiness.” (See Note at end of post) That is, whatever we do, we do because we think it will make us happy. All people, says Aristotle, agree on this, but that is as far as the agreement goes. Just what is meant by “happiness” is highly disputed. Some might say that happiness is found in wealth, some that it is found in pleasure, others that it is found in honors. Is there any way to settle this dispute? Aristotle thinks so.

The question of “what is human flourishing or human happiness” must be defined in terms of what it means “to be human.” For, to find the “good” of anything, we must know its function. For example, the good of the computer rests in its functioning as it was designed to function (compute) and it reaches its “good” when it functions (computes) according to the way it was designed to function. The guitarist is a “good” guitarist when he plays the guitar in the way it was designed to function. So, if a human being has a function, the human being’s ultimate “good” will be functioning according to its nature (i.e., we will find fulfillment (our good) when we function according to our essence). Yet, how might we determine the human function?

To determine an object’s function one needs to discover what distinguishes it from all other objects. What is it that makes it, it? What is it, within humans, which makes them “human” and not “whales” or something else? Aristotle claims that the human function is “the soul’s activity that expresses reason [as itself having reason] or requires reason [as obeying reason]” (Nicomachean Ethics 1098a7-8). That is, it is the ability to think or to know that is unique and the principle element that makes a human, a human.  However, it is not merely “thinking” but rather reasoning and acting in accordance with reason. Furthermore, it is not just thinking and acting, but thinking and acting well; that is, excellently or virtuously. Aristotle concludes, “each function is completed well when its completion expresses the proper virtue.  Therefore the human good turns out to be the soul’s activity that expresses virtue” (1098a15-17). Happiness, therefore, “is an activity of the soul expressing complete virtue” (1102a5).

So, what has all of this to do with education? Education itself is an action and therefore may be analyzed with regards to its means and ends. The central dispute in contention is two different theories as to the end of education, and how these relate to the end of human “happiness.” (Here and throughout, I will not assess the means (i.e., methods and materials) by which the two views on education attempt to reach their ends, but only the ends themselves.)

On the “Progressivist” view of education, the primary purpose of education is vocational in nature. For example, the United States Department of Education’s stated purpose is “to promote student achievement and preparation for global competitiveness by fostering educational excellence and ensuring equal access.” No doubt, the competition to which this statement refers is “jobs” or “careers.” The consistent message from politicians with regard to education is that students need to be prepared to enter the “workforce,” and that we must be more “competitive” in math and sciences so that Americans will not be displaced by foreign competition in the job market. So, when the question is put forth as to the end of education, the answer is, “to secure a career.”

On the “Classical” view of education, the primary purpose of education is to rear children into adults. Education on this view has the whole of the person in mind, to train boys to become men and to train girls to become women. It is not taken for granted that as children grow they will naturally mature into adults. This begs the question of what we mean by “adult”. There are a range of answers to this question, but invariably the Classicist will answer along the lines of Aristotle outlined above. The Classicist holds that the end of education is to train the child to think and act well in accordance with virtue. Says Aristotle, “excellence, then, being of two kinds, intellectual and moral, intellectual excellence in the main owes both its birth and its growth to teaching (for which reason it requires experience and time), while moral excellence come about as a result of habit…” (1103a14). Habits themselves are trainable and we must, through education, come to learn “to enjoy the things we ought and to hate the things we ought” (1172a22).

So, which of these two views of education is most consistent with the end of “human happiness?” The Progressivist view of education, while it may prepare a student for a job, has confused the means with the end. For if it is asked, “why do we want people to have careers,” the answer, most assuredly would be, so that they can be “happy.” How exactly having a career ipso facto makes one happy or just what “happiness” is, is never quite addressed, especially given how unhappy so many people are in their careers. It isolates a single part of life and leaves the children to fend for themselves in all other things. Furthermore, it eliminates even the possibility of educating for “happiness” precisely because it attempts to remain neutral with regard to the definition of “humanity.” Thus, Progressive education is reductive by its very nature, treating children not as humans who need to be nurtured, but as animals that need to be trained.

Contrariwise, the Classicist has in view an education that creates, not young adults who are prepared for a specific career, but adults who are prepared to live well no matter what their career. For “career” is not an end itself, but a means to an end. Occupation is but one part of life and unless the child is taught to think and act well, even with an occupation, the child can never be fully “happy.” Furthermore, Classical education allows the student to stand before and judge all things, thus preparing the child for whatever may come. The carpenter, who has received only training in carpentry, may be able to judge what is or is not a good wardrobe, but not what is or is not a just society. Such judgments, however, are necessary for the fully formed human.  For, to know, to judge, and to act well is what it means “to be human.” As Aristotle says,

“Now each man judges well the things he knows, and of these he is a good judge. And so the man who has been educated in a subject is a good judge of that subject, and the man who has received an all-round education is a good judge in general” (1094b27-95a1).

Given this, it seems unlikely that Aristotle would have entrusted the education of his son to the modern public school system. The education which Aristotle endorsed was one which conforms to the purpose of human beings, contributes to their proper functioning, and enables the child to grow into adulthood. An education that only equips the student to accomplish a single task is not meant for the free, liberated man. Without the ability to stand before all things and judge, the child is at the mercy of those who can. What needs to be assessed now are the best means by which to accomplish this end.


Aristotle uses the word “eudaimonia” which is misleadingly translated as “happiness,” and notoriously difficult to define. Etymologically, “eudaimonia” means “well-spirited” but may best be translated as “flourishing,” “blessed,” or “fulfilled.” The English word “happiness” is derived from the Old Norse “happ,” which means “chance” or “luck.” Clearly this cannot be what Aristotle has in mind. See, Aristotle Nicomachean Ethics 1099b9-17.

Why Scientists Need Classical Education

What has science to do with Classical Education?  After all, we need scientists, not people who dawdle around in dead languages.  Yet, E. Christian Kopff argues persuasively that many of the greatest modern scientific achievements were made by scientists who were classically educated.  Further, that it was because of that classical education, not in spite of it, that they made the advancements they did.  Says Kopff,

The decades on either side of WWI witnessed brilliant work in Physics: the concept of quanta, the theories of special and general relativity and the development of quantum mechanics. One might expect that the most important work in these fields would be done by graduates of the technical school system. Nearly the opposite is true. Max Planck, Werner Heisenberg, Erwin Schrödinger, Niels Bohr were classically educated. Einstein attended a Swiss technical high school, but he had spent his first six years at a classical school, where his sister remembered his best subjects as Mathematics and Latin: “Latin’s clear, strictly logical structure fit his mindset.” Heisenberg wrote: “I believe that in the work of Max Planck, for instance, we can clearly see that his thought was influenced and made fruitful by his classical schooling.” Heisenberg insisted that his own insights into nature came from his classical education. Its combination of math and physics with language instruction led him to read Plato’s Timaeus in Greek. He was impressed by Plato’s rational appeals to understand nature mathematically rather than as a purely physical reality: “I was gaining the growing conviction that one could hardly make progress in modern atomic physics without a knowledge of Greek natural philosophy.”

You can find the full text of Kopff’s essay here.

The American Founders and Education

E. Christian Kopff has an excellent piece on the influence of classical education on the American founders in The Imaginative Conservative.

For centuries Americans understood that their free and creative way of life was founded on virtue, instructed by a curriculum that balanced the study of language and mathematics and fostered by reading ancient authors like the Bible, Virgil and Cicero, Livy and Tacitus. The old classical curriculum by balancing education in language and mathematics avoided the alternating crises that are endemic in contemporary education. Students were thoroughly grounded in grammar before studying critical thinking (dialectic) and persuasive writing (rhetoric). Classical education balanced instruction in mathematics and language and made sure students had mastered basic subjects before proceeding to more challenging ones. It was not expensive, but it was demanding. But then so is freedom.

You can read the rest here.

I also highly recommend Kopff’s book, The Devil Knows Latin.