Papist Orthodoxy

December 3, 2009

The Risk of Education

Filed under: Education — Antiochian-Thomist @ 5:40 pm

Excerpt from an article written by Fr. Dwight Longenecker.

The complete article can be found at InsideCatholic.com.

REASON & RESPONSIBILITY

If the educator accompanies the student as he verifies the truth, then a new perspective is opened up on the educational process. In a Catholic school, the mission becomes not simply to produce good examination results to get students into good colleges. Neither is the sole purpose simply to produce “good Catholics” who learn to “pray, pay, and obey.”

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Instead, every subject is taught with the critical instinct fully engaged. The reasonableness and necessity of every subject is verified, and the students are truly educated rather than simply given facts. When an entire school embraces the vision of “verifying the truth,” the students are given an overarching principle of education that enables them to draw together the different strands of education and experience in order to prepare them for life’s adventure.

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Engaging the critical instinct in education also brings teenagers into a higher level of responsibility. If he is simply learning facts, the student is not taking responsibility for his learning. But if he is engaging the critical instinct, he is automatically responsible for what he learns. As this becomes a habitual way of responding to his world, the student learns in a most natural way how to apply this critical instinct to every other aspect of life, and so learns to take responsibility for his thoughts, words, and actions.

November 30, 2009

Why Most High School Students Hate Math

Filed under: Education — Tags: , , — Antiochian-Thomist @ 6:45 pm

Also entitled: THE GROWING DIVIDE BETWEEN THE LINGUISTIC & MATHEMATICAL ARTS

The denial of axioms, those first principles that are either self evident or derived from a higher science, has led to an utter separation of the mathematical arts from the linguistic arts in the general liberal arts to the detriment of both general fields of study. This process began with force with the reformulation of the ancient order of the mathematical arts beginning with the reconsideration of the classical geometry of Euclid. Once the primacy of Euclid was destroyed and geometry seen in a new light of symbolic signs from which new and further abstractions could be gleaned, the mathematical arts further developed which gave rise to the new primacies of the algebras and calculus. Though the new primacies are not necessarily to be lamented in themselves, the preoccupation with the manipulation of numbers, variables, and other symbols abstracted from nearly all intelligible realities has led the mathematical arts into an isolated world with minimal contact and sharing with the world of the linguistic arts.

I. GEOMETRY OVERTHROWN

The classical geometry of Euclid had a multitude of benefits which contributed to its long reign as the basic mathematical art. Firstly, it proceeded from indemonstrable first principles which were (and are) self-evident, and, thus, common to many arts and sciences. Common notions such as “the whole is greater than the part” or “things which are equal to the same thing are also equal to each other”1 were the bedrock principles upon which Euclid’s geometry was based. Secondly, the fundamental geometric realities that were the considerations of classical geometry were and are immediately abstracted from the natural, material world. Thus the concepts of magnitude, square, circle, and triangle, once the varying qualities of matter were left behind, could be considered in their perfections. Thus this conceptual art was eminently intelligible to the intellect as its conceptual realties were immediately abstracted from nature and its proofs were based on arguments that proceeded from self-evident first principles.

While its intelligibility was without question, certain aspects of the classical geometry underwent further development especially in the realm of abstraction. The proofs, although well argued, possessed an inefficiency of expression that could be “streamlined” if further abstractions were performed. Further, with these additional abstractions, alternate considerations could be applied to the signified magnitudes that were not able to be performed previously, viz. arithmetic operations. Many, including the likes of Dr. Otto Bird, assert that René Descartes pioneered this consideration. In Descartes’ work, The Geometry, he asserts:

“Any problem in geometry can be reduced to such terms that a knowledge of the lengths of certain straight lines is sufficient for its construction. Just as arithmetic consists of only four or five operations, namely, addition, subtraction, multiplication, division, and the extraction of roots…so in geometry, to find required lines it is merely necessary to add or subtract other lines.”2

In short, Descartes takes a magnitude and reduces it to a unity which serves to be the measure of other magnitudes. Geometric magnitudes, then, are reduced to numbers. This is done by way of assigning letters to the magnitudes themselves and then performing an arithmetic operation. With this assertion, many claim, came the dawn of analytic geometry and the birth of the Cartesian coordinate system3 and the subordination of geometry to algebra as all geometric realities become a relation of numbers, with numbers themselves as expressed as variables, and not magnitudes, becoming the principle object of consideration. It is for this reason Dr. Bird says:

“Since all the variable letters in our equation represent numbers the geometric line is no longer anything that need be done geometrically; it can be done with numbers. So lines, curves, figures, solids and their relations can all be determined by equations which ultimately are but variable expressions for numbers. Thus Euclid’s Pythagorean Theorem4 proven as a relation between the sides of a triangle, and squares erected on them can now be stated, as we saw, much more simply as A2 + B2 = C2, where at issue is a matter of numbers even though they may also be taken as the lengths of the sides of the triangle. The arithmetical algebraic expression is admittedly more abstract than the corresponding geometric expressions, but it is simpler and easier to work with. Geometry has been arithmetized.”5

In addition to the additional abstraction applied to geometry further removing the signs from the original signification, mathematicians like Descartes established a new precedent by beginning their works not from axioms or any principle from a higher science but from postulates. Granted, Euclid worked from postulates as well, but not exclusively. Rather, he proceeded from postulates stemming from axioms and definitions thus rooting his art and argument in principles that require not blind ascent but common, rational experience. Further, Galileo and Newton also proceeded from axiomatic principles, but their era saw the dawn of arts that posited their own principles that defied scrutiny from other arts and sciences. Other developments in the mathematical arts certainly contributed to the replacement of geometry as the basic mathematical art, but non so much as the first introduction to numeric abstractions and the abandonment of axiomatic principles.

II. MATHEMATICAL STUDIES AFFECTED

With new primacies came new considerations. With old boundaries removed, so went many of the old obstacles. With the advent of variable numeric representation came the reconciliation, or rather the “ever approaching reconciliation”, of that which was formerly believed to be utterly irreconcilable: the curve with the straight and the discreet with the continuous. The efforts of Copernicus, Kepler, Brahe, Galileo, Descartes, Newton, Bonola, etc. allowed for curved realities to be given representation with discreet alphanumeric signification. Naturally, this called the necessity of the traditional mathematical arts as the principle mathematical arts of consideration into question, or, at least, called them into question insofar as how they were considered. Music and astronomy as the principle arts of ratios and mobile magnitudes respectively were replaced by more universal and abstract algebraic understanding of ratios and more universal applications of calculus to mobile beings in general. As stated before, these developments are not necessarily to be lamented insofar as they are productive of more profound knowledge of realities, whether they be concrete or conceptual. But the arts, or, rather, their proponents did not stop there.

Coupled with the abandonment of the scholastic understanding of the universe and its causes, including the disavowal of traditional metaphysics and theology, mathematics took on a new import which it previously did not enjoy and consequently affected its study insofar as its import was concerned. Theology and philosophy were no longer the highest sciences. With the sloughing of the scholastic world-view, the essence of things, natures as such, were no longer the most sought after knowledge for the means to know natures were abandoned. Instead, that which was most knowable to man became the most sublime to him: quantity. As a result, mathematics ascended to primacy among the sciences, a status it enjoys to this day. Let us return again to Descartes and his peers:

“Since the only known natural sciences with some degree of systematic coherence were astronomy and mechanics, and the key to the understanding of mechanics and astronomy was mathematics, mathematics became the most important means to understanding the universe. Moreover, mathematics with its convincing statements was itself the brilliant example that truth could be found in science. The mechanistic philosophy of this period thus came to a conclusion that was similar to that of the Platonists, but for a different reason. Platonists, believing in the harmony of the universe, and Cartesians, believing in a general method based on reason, both found in mathematics the queen of the sciences.”6

This new pedestal upon which mathematics was placed perpetuated infatuations that exacerbated its abstract nature and considerations. Abstractions and their manipulations themselves became the primary concern in many circles resulting in a “science of symbols” where often the symbols themselves were abstracted from any meaning whatsoever. Weber, Frege, and Peano were pioneers in this filed. As bizarre as this may sound its effects were far reaching, the evidence of which can be seen in most high school math textbooks to this day, much to the chagrin and consternation of many a high school student. Struik notes it well:

“…Algebra changed its ancient character. Instead of merely encompassing the theory of algebraic equations and the associated theory of invariants and covariants, it became the abstract doctrine of today with its rings, fields, ideals, and related concepts. One of the origins of the newer algebra was the development of group theory from Galois theory of algebraic equations into an abstract theory in its own right, especially in the theory of finite groups, thus setting a model for the transformation of algebra as a whole.”7

As history has shown, those arts which enjoyed primacy, if not in reality then by popular acclamation, subordinated others arts and often attempted to subsume them to themselves. Advocates of mathematics were no different. The venerable art of logic was the target for this attempted annexation with the most poignant attempts by the likes of Russel, Whitehead, Cantor, and Frege. Logic itself became the target of abstract symbols for its signification with the imposition of symbolic logic with its two subcategories, propositional and predicate. The attempt as noted by both Struik8 and Bird9 ultimately failed but the efforts persisted. The effects are still seen today in texts and graduate institutions that insist upon teaching symbolic logic in their philosophical programs.

III. THE GULF BETWEEN THE TRIVIUM & QUADRIVIUM WIDENED

Mathematics has abandoned the axiomatic system. This was the first and most fundamental break which has led to other divisions between the mathematical and linguistic arts. Without self-evident first principles, how can real knowledge be had? What relation then exists between the linguistic arts which are eminently grounded in reality and an art which seeks not sound and indemonstrable principles? Can mathematics now claim what it once could as expressed in the mouth of Dr. Bird?

“In fact it’s no exaggeration to claim that mathematics has provided the clearest and most explicit instance of reason, of reason itself at work, of reason reasoning, in its development of the axiomatic method. The earliest and most extensive use of this method is to be found in the thirteen books of Euclid’s Elements.

[…]

In denying that there aren’t any self-evident axioms these people are denying that there are any axioms in the old sense as principles distinct from postulates, with the result that the two words have come to be used interchangeably. In any case, an axiomatic system is one that begins from certain indemonstrable principles from which certain other propositions can be deduced as conclusions. “10

Ironically, the attempt to bridge the gap between the linguistic and mathematical arts by attempting a pure mathematics that could be propositionally inferred from earlier principles only served to broaden the chasm between the two general arts. The attempt at reducing logic to a branch of mathematics was intrinsically an attempt at reducing all sciences to the jurisdiction of mathematics –sciences that had concerns over and above that which was quantifiable. As a result, symbolic logic has been relatively ineffectual in the other arts (including philosophy in spite of its persistence) and has only enjoyed any real and lasting effects in mathematical logic. Instead of subsuming logic, mathematics, or rather mathematicians, developed its own language of logic apart from the linguistic arts. But this was not always the case with mathematics and logic. As Dr. Bird points out so well:

“…It is better to retain the old understanding of logic as the study of the principles that assure the validity of inference, and that its laws are those of the laws of the other sciences. Logic is thus the science of sciences, as Aristotle called it, or the art of arts, as Saint Thomas called it.

[…]

Mathematics since the time of its development by the ancient Greeks has always been prized for the power and beauty of its reasoning, and indeed for its ability to form and train the faculty of reasoning itself. As long as Euclid was studied as the basic introductory work to mathematics, Euclid’s geometry provided the basic training for the logic of argument. It provided the basic understanding of what a proof is and the means of constructing and establishing a proof. “11

The former complementarity enjoyed by the trivium and quadrivium through the cooperation of geometry and logic has died. If logic is found to be taught at all in schools, it is done so independent from geometry when this would never have been the case in ancient or medieval education. Hence we have one clear rift between the mathematical and linguistic arts.

Finally, a rift exists between mathematics and reality. Due to the aforementioned obsession with the manipulation of abstractions without any reference to that which is meant to be quantified, mathematics, at least in the general sense of the liberal arts as found in high school and undergraduate institutions, is practically divorced from all reality, concrete or conceptual, since it has become a “science of symbols” meant to arbitrarily signify anything in general or nothing in particular. The ancient considerations of mathematics, whether it was geometry, algebra, or calculus, though abstracted, abstracted from that which was real and considered that which was real. This was true for Euclid’s Elements, Apollonius’s Conic Sections, Ptolemy’s Almagest, Galileo’s Two New Sciences, Descartes’ Geometry, or Newton’s Principia. Now, reference to the real which was once found in the ancient quadrivium can often be more readily found in the more advanced and specialized mathematics proper to certain vocations –not to education in general. The linguistic arts have not suffered this problem; thus the widening between the linguistic and mathematical arts.

BIBLIOGRAPHY

1. Bird, Otto, Ph. D. “The Mathematical Arts of the Quadrivium II”, a lecture given for the International Catholic University and Holy Apostles College & Seminary for the course, “Liberal Arts: Their History & Philosophy”, 2005.

2. Euclid. The Elements of Geometry, Thomas Health (translator), Dover Publications, New York. 1956.

3. Descartes, Rene. The Geometry, David Smith & Marcia Latham (translators), Dover Publications, New York. 1954.

4. Struik, Dirk J. A Concise History of Mathematics, fourth edition, Dover Publications, New York. 1987.

1Euclid. Elements of Geometry, Book I, Common Notions 1 and 5.

2Descartes, René. The Geometry, Book I

3Struik, D. A Concise History of Mathematics, pp. 96-99. Struik points out that many others that preceded Descartes used what could be considered a numeric coordinate system, including the likes of Apollonius of Perga, Ptolemy, and Oresme. Nonetheless, he does not deny that Descartes work was of the greatest influence on coordinate systems and analytic geometry.

4Euclid. Elements of Geometry, Book I, Proposition 47

5Bird, Otto, Ph. D. “The Mathematical Arts of the Quadrivium II”, a lecture given for the International Catholic University and Holy Apostles College & Seminary, 2005.

6Struik, D. A Concise History of Mathematics, Chapter VI, Section 3

7ibid. Chapter IX, Section 6

8ibid. Chapter IX, Section 7

9Bird, Otto, Ph. D. “The Mathematical Arts of the Quadrivium II”

10 ibid.

11 ibid.

November 4, 2009

The Great Adventure

Filed under: Education, Sacred Scripture and Theology — Tags: — Antiochian-Thomist @ 9:14 pm

This post does not necessarily constitute an endorsement of the featured product. I am just calling it to the attention of those who wish to potentially profit more from the study of Sacred Scripture. I invite those who read this blog to review the product and offer their opinions in the comment box for this blog-post. Thank you and I look forward to reading your opinions. There is potential for interesting discussion.

–Antiochian-Thomist


From the website for “The Great Adventure”

The Great Adventure is a Catholic Bible learning system that makes the complex simple by teaching the story (the narrative) of the Bible. Every day, more and more people are encountering God’s Word through the methods taught in The Great Adventure.
Jeff Cavins developed The Great Adventure in 1984 when he realized that most people, despite their strong faith, did not grasp the big picture of the Bible. Though they knew selected stories, they were not able to connect them into a full narrative. His answer was to identify the books of the Bible that tell the story from beginning to end. By reading just these 14 narrative books, a chronological story emerges.
From this idea grew the immensely popular Bible Timeline program, which teaches the story in a way that is easy to remember and helps people to continue reading Scripture on their own. Hundreds of thousands of Catholics have learned to read the Bible through this system, which provides a solid foundation for all other reading and study.
Since the creation of The Bible Timeline, The Great Adventure has grown into a remarkable system designed to give the average Catholic a solid foundation for a lifetime of Bible reading. Parishes around the world are finding renewed faith and increased involvement among parishioners whose lives have been changed by this exciting study series.

Testimonials:

“I am impressed with the methodology and growth of The Great Adventure: A Journey Through the Bible. The canonical approach that The Great Adventure employs is a marvelous way to introduce the faithful to salvation history. When Sacred Scripture, Sacred Tradition, and the Magisterium are all brought together in study the result is a clearer picture of God’s will, resulting in a road map for living. The Great Adventure, being faithful to Dei Verbum (the Second Vatican Council’s Constitution on Divine Revelation), is bearing much fruit in the Church today and contributing to a stronger, more informed laity.”

–Francis Cardinal George, O.M.I., Archbishop of Chicago

“I have seen real change in many of my parishioners. They have not only learned about the ‘big picture’ that contextualizes salvation history, but they’ve gained practical insights into walking with the Lord and learning to trust Him. If every parish did this program, we’d see a true revolution in the Church.”

–Rev. Tomi Thomas, St. Matthew Catholic Church, Norwalk, CT

“Wondering whether a twenty-four week course would work, I started The Bible Timeline in the parish. A solid group of about twenty-five stayed with it for the whole time. I myself got a great deal from it; for the first time I have a grasp of the chronological aspect of the story of salvation. The same group followed through with Matthew. This was a more in-depth, probing study that touched everyone’s heart. We are looking forward to the study of Acts and Revelation next year. I consider The Great Adventure to be one of the most important contributions I have made to the parish, a legacy I leave my successor after my retirement soon.”

–Msgr. Charles Quinn, St. Stanislaus, Pleasant Valley, NY

October 29, 2009

YOUR CHILDREN ARE NOT EDUCATED (PART 1): WHY IT IS SO

Filed under: Education, Philosophy — Tags: — Antiochian-Thomist @ 9:48 pm

The following article, though not very scholarly itself,  is on the current model of education used as the standard in public and private school systems at the primary, grammar, and secondary levels. If you are parents of children that are enrolled in a school, unless that school explicitly states that it operates with some sort of alternative method (e.g. “classical liberal arts”, “trivium & quadrivium”, “montessori” [no, I am not necessarily endorsing montessori], etc.) then your child, more likely than not, is involved with the Horace Mann/John Dewey method of education which was modeled on the Prussian and Soviet systems for the purpose of producing compliant, dumbed-down, soldiers and “citizens”. Even private schools, Catholic or otherwise, employ this system, just with a Catholic or Christian varnish, albeit without malice. This is why even in private high schools, students might graduate with piety but also with an inability to think themselves out of a paper bag.

–Antiochian-Thomist

The Public School Nightmare:

Why fix a system designed to destroy individual thought?

by John Taylor Gatto  [Two time New York State “Teacher of the Year”]

I want you to consider the frightening possibility that we are spending far too much money on schooling, not too little. I want you to consider that we have too many people employed in interfering with the way children grow up — and that all this money and all these people, all the time we take out of children’s lives and away from their homes and families and neighborhoods and private explorations — gets in the way of education.

That seems radical, I know.  Surely in modern technological society it is the quantity of schooling and the amount of money you spend on it that buys value.

And yet last year in St. Louis, I heard a vice-president of IBM tell an audience of people assembled to redesign the process of teacher certification that in his opinion this country became computer-literate by self-teaching, not through any action of schools.  He said 45 million people were comfortable with computers who had learned through dozens of non-systematic strategies, none of them very formal; if schools had pre-empted the right to teach computer use we would be in a horrible mess right now instead of leading the world in this literacy.

Now think about Sweden, a beautiful, healthy, prosperous and up-to-date country with a spectacular reputation for quality in everything it produces.  It makes sense to think their schools must have something to do with that.

Then what do you make of the fact that you can’t go to school in Sweden until you are 7 years old?  The reason the unsentimental Swedes have wiped out what would be first and seconds grades here is that they don’t want to pay the large social bill that quickly comes due when boys and girls are ripped away from their best teachers at home too early.  It just isn’t worth the price, say the Swedes, to provide jobs for teachers and therapists if the result is sick, incomplete kids who can’t be put back together again very easily. [Sweden is considered to have the best educated populace in the developed world. –Antiochian-Thomist]

The entire Swedish school sequence isn’t 12 years, either — it’s nine.  Less schooling, not more.  The direct savings of such a step in the US would be $75-100 billion, a lot of unforeclosed home mortgages, a lot of time freed up with which to seek an education.

Who was it that decided to force your attention onto Japan instead of Sweden?  Japan with its long school year and state compulsion, instead of Sweden with its short school year, short school sequence, and free choice where your kid is schooled?   Who decided you should know about Japan and not Hong Kong, an Asian neighbor with a short school year that outperforms [emphasis added] Japan across the board in math and science?  Whose interests are served by hiding that from you? [not yours, let me tell you…]

One of the principal reasons we got into the mess we’re in is that we allowed schooling to become a very profitable monopoly, guaranteed its customers by the police power of the state.  Systematic schooling attracts increased investment only when it does poorly, and since there are no penalties at all for such performance, the temptation not to do well is overwhelming.  That’s because school staffs, both line and management, are involved in a guild system.  And in that ancient form of association no single member is allowed to outperform any other member, none are allowed to advertise or to introduce new technology or improvise without the advance consent of the guild.  Violation of these precepts is severely sanctioned–as Marva Collins, Jaime Escalante and a large number of once-brilliant teachers found out.

The guild reality cannot be broken without returning primary decision-making to parents, letting them buy what they want to buy in schooling, and encouraging the entrepreneurial reality that existed until 1852. That is why I urge any business to think twice before entering a cooperative relationship with the schools we currently have.  Cooperating with these places will only make them worse.

The structure of American schooling, 20th century style, began in 1806 when Napoleon’s amateur soldiers beat the professional soldiers of Prussia at the battle of Jena.  When your business is selling soldiers, losing a battle like that is serious. Almost immediately afterwards a German philosopher named Fichte delivered his famous “Address to the German Nation” which became one of the most influential documents in modern history.

In effect he told the Prussian people that the party was over, that the nation would have to shape up through a new Utopian institution of forced schooling in which everyone would learn to take orders. [emphases added]

So the world got compulsion schooling at the end of a state bayonet for the first time in human history; modern forced schooling started in Prussia in 1819 with a clear vision of what centralized schools could deliver: [yes, make the comparisons]

1. Obedient soldiers to the army;

2. Obedient workers to the mines;

3. Well subordinated civil servants to government;

4. Well subordinated clerks to industry

5. Citizens who thought alike about major issues.

Schools should create an artificial national consensus on matters that had been worked out in advance by leading German families and the head of institutions.  Schools should create unity among all the German states, eventually unifying them into Greater Prussia.

Prussian industry boomed from the beginning.  She was successful in warfare and her reputation in international affairs was very high.  Twenty-six years after this form of schooling began, the King of Prussia was invited to North America to determine the boundary between the United States and Canada.  Thirty-three years after that fateful invention of the central school institution, at the behest of Horace Mann and many other leading citizens, we borrowed the style of Prussian schooling as our own. [emphases added]

You need to know this because over the first 50 years, our school’s Prussian design — which was to create a form of state socialism — gradually forced out our traditional American design, which in most minds was to prepare the individual to be self-reliant.

In Prussia the purpose of the Volksshule [work school], which educated 92 percent of the children, was not intellectual development at all, but socialization in obedience and subordination [emphasis added]. Thinking was left to the Real Schulen, [Real School] in which 8 percent of the kids participated.  But for the great mass, intellectual development was regarded with managerial horror, as something that caused armies to lose battles.

Prussia concocted a method based on complex fragmentation to ensure that its school products would fit the grand social design.  Some of this method involved dividing whole ideas into school subjects, each further divisible, some of it involved short periods punctuated by a horn so that self-motivation in study would be muted by ceaseless interruptions. [I knew there was a reason I hated those darn school horns/buzzers.]

There were many more techniques of training, but all were built around the premise that isolation from first-hand information, and fragmentation of the abstract information presented by teachers, would result in obedient and subordinate graduates, properly respectful of arbitrary orders.

“Lesser” men would be unable to interfere with policy makers because, while they could still complain, they could not manage sustained or comprehensive thought.  Well-schooled children cannot think critically, cannot argue effectively. [Oh boy, is this ever true.]

One of the most interesting by-products of Prussian schooling turned out to be the two most devastating wars of modern history.

Erich Maria Ramarque, in his classic, All Quiet on the Western Front, tells us that the First World War was caused by the tricks of schoolmasters, and the famous Protestant theologian Dietrich Bonhoeffer said that the Second World War was the inevitable product of good schooling.

It’s important to underline that Bonhoeffer meant that literally, not metaphorically — schooling after the Prussian fashion removes the ability of the mind to think for itself.   It teaches people to wait for a teacher to tell them what to do and if what they have done is good or bad.  Prussian teaching paralyses the moral will as well as the intellect.  It’s true that sometimes well-schooled students sound smart, because they memorize many opinions of great thinkers, but they actually are badly damaged because their own ability to think is left rudimentary and undeveloped.

We got from the United States to Prussia and back because a small number of very passionate ideological leaders visited Prussia in the first half of the 19th century, and fell in love with the order, obedience and efficiency of its system and relentlessly proselytized for a translation of Prussian vision onto these shores.

If Prussia’s ultimate goal was the unification of Germany, our major goal, so these men thought, was the unification of hordes of immigrant Catholics into a national consensus based on a northern European cultural model.  To do that children would have to be removed from their parents and from inappropriate cultural influence.

In this fashion, compulsion schooling, a bad idea that had been around at least since Plato’s Republic, a bad idea that New England had tried to enforce in 1650 without any success, was finally rammed through the Massachusetts legislature in 1852.

It was, of course, the famous “Know-Nothing” [which was one of the most anti-Catholic political parties in America] legislature that passed this law, a legislature that was the leading edge of a famous secret society which flourished at that time known as “The Order of the Star Spangled Banner,” whose password was the simple sentence, “I know nothing” — hence the popular label attached to the secret society’s political arm, “The American Party.”

Over the next 50 years state after state followed suit, ending schools of choice and ceding the field to a new government monopoly.  There was one powerful exception to this — the children who could afford to be privately educated. (Although it may be relevant that not ALL private schools are geared to a “real” education, but are simply more of the same as the public schools, but are promoted as being for the elite.)

It’s important to note that the underlying premise of Prussian schooling is that the government is the true parent of children — the State is sovereign over the family.  At the most extreme pole of this notion is the idea that biological parents are really the enemies of their own children, not to be trusted.

How did a Prussian system of dumbing children down take hold in American schools?

Thousands and thousands of young men from prominent American families journeyed to Prussia and other parts of Germany during the 19th century and brought home the Ph. D. degree to a nation in which such a credential was unknown.   These men pre-empted the top positions in the academic world, in corporate research, and in government, to the point where opportunity was almost closed to those who had not studied in Germany, or who were not the direct disciples of a German PhD, as John Dewey was the disciple of G. Stanley Hall at Johns Hopkins.  Virtually every single one of the founders of American schooling had made the pilgrimage to Germany, and many of these men wrote widely circulated reports praising the Teutonic methods.  Horace Mann‘s [the father of the American public school system] famous 7th Report of 1844, still available in large libraries, was perhaps the most important of these.

By 1889, a little more than 100 years ago, the crop was ready for harvest.  It that year the US Commissioner of Education, William Torrey Harris, assured a railroad magnate, Collis Huntington, that American schools were “scientifically designed” to prevent “over-education” from happening.   The average American would be content with his humble role in life, said the commissioner, because he would not be tempted to think about any other role. [emphases added]

My guess is that Harris meant he would not be able to think about any other role.

In 1896 the famous John Dewey, then at the University of Chicago, said that independent, self-reliant people were a counter-productive anachronism in the collective society of the future.   In modern society, said Dewey, people would be defined by their associations –not by their own individual accomplishments.  In such a world people who read too well or too early are dangerous because they become privately empowered, they know too much, and know how to find out what they don’t know by themselves, without consulting experts. [emphases added]

Dewey said the great mistake of traditional pedagogy was to make reading and writing constitute the bulk of early schoolwork.  He advocated the phonics method of teaching reading be abandoned and replaced by the whole word method, not because the latter was more efficient (he admitted that it was less efficient), but because independent thinkers were produced by hard books, thinkers who cannot be socialized very easily.

By socialization Dewey meant a program of social objectives administered by the best social thinkers in government.  This was a giant step on the road to state socialism, the form pioneered in Prussia, and it is a vision radically disconnected with the American past, its historic hopes and dreams.

Dewey’s former professor and close friend, G. Stanley Hall, said this at about the same time, “Reading should no longer be a fetish.  Little attention should be paid to reading.”

Hall was one of the three men most responsible for building a gigantic administrative infrastructure over the classroom.  How enormous that structure really became can only be understood by comparisons: New York State, for instance, employs more school administrators than all of the European Economic Community nations combined.

Once you think that the control of conduct is what schools are about, the word “reform” takes on a very particular meaning.  It means making adjustments to the machine so that young subjects will not twist and turn so, while their minds and bodies are being scientifically controlled.  Helping kids to use their minds better is beside the point. [emphases added]

Bertrand Russell once said that American schooling was among the most radical experiments in human history, that America was deliberately denying its children the tools of critical thinking.

When you want to teach children to think, you begin by treating them seriously when they are little, giving them responsibilities, talking to them candidly, providing privacy and solitude for them, and making them readers and thinkers of significant thoughts from the beginning.  That’s if you want to teach them to think.  There is no evidence that this has been a State purpose since the start of compulsion schooling.

When Frederich Froebel, the inventor of kindergarten in 19th century Germany, fashioned his idea he did not have a “garden for children” in mind, but a metaphor of teachers as gardeners and children as the vegetables.

Kindergarten was created to be a way to break the influence of mothers on their children [Take note of this]. I note with interest the growth of daycare in the US and the repeated urgings to extend school downward to include 4-year-olds.  The movement toward state socialism is not some historical curiosity, but a powerful dynamic force in the world around us.

The state socialism movement is fighting for its life against those forces which would, through vouchers or tax credits, deprive it of financial lifeblood, and it has countered this thrust with a demand for even more control over children’s lives, and even more money to pay for the extended school day and year that this control requires.  A movement as visibly destructive to individuality, family and community as government-system schooling has been, might be expected to collapse in the face of its dismal record, coupled with an increasingly aggressive shake down of the taxpayer, but this has not happened.

The explanation is largely found in the transformation of schooling from a simple service to families and towns to an enormous, centralized corporate enterprise.  While this development has had a markedly adverse effect on people and on our democratic traditions, it has made schooling the single largest employer in the United States, and the largest grantor of contracts next to the Defense Department.

Both of these low-visibility phenomena provide monopoly schooling with powerful political friends, publicists, advocates and other useful allies.  This is a large part of the explanation why no amount of failure ever changes things in schools, or changes them for very long.  School people are in a position to outlast any storm and to keep short-attention-span public scrutiny thoroughly confused.

An overview of the short history of this institution reveals a pattern marked by intervals of public outrage, followed by enlargement of the monopoly in every case.  After nearly 30 years spent inside a number of public schools, some considered good, some bad, I feel certain that management cannot clean its own house.  It relentlessly marginalizes all significant change.

There are no incentives for the “owners” of the structure to reform it, nor can there be without outside competition.  What is needed for several decades is the kind of wildly-swinging free market we had at the beginning of our national history.

It cannot be overemphasized that no body of theory exists to accurately define the way children learn, or which learning is of most worth.  By pretending the existence of such we have cut ourselves off from the information and innovation that only a real market can provide.  Fortunately our national situation has been so favorable, so dominant through most of our history, that the margin of error afforded has been vast.

But the future is not so clear. Violence, narcotic addictions, divorce, alcoholism, loneliness… all these are but tangible measures of a poverty in education.   Surely schools, as the institutions monopolizing the daytimes of childhood, can be called to account for this.  In a democracy the final judges cannot be experts, but only the people.

Trust the people, give them choices, and the school nightmare will vanish in a generation.

THE SEVEN LIBERAL ARTS

Filed under: Education, Philosophy — Tags: , , — Antiochian-Thomist @ 8:36 pm

From the Original Catholic Encyclopedia.

Arts, the SEVEN LIBERAL. —The expression artes liberales, chiefly used during the Middle Ages, does not mean arts as we understand the word at the present day, but those branches of knowledge which were taught in the schools of that time. They are called liberal (Lat. liter, free), because they serve the purpose of training the free man, in contrast with the artes illiberales, which are pursued for economic purposes; their aim is to prepare the student not for gaining a livelihood, but for the pursuit of science in the strict sense of the term, i.e. the combination of philosophy and theology known as scholasticism. They are seven in number and may be arranged in two groups, the first embracing grammar, rhetoric, and dialectic, in other words, the sciences of language, of oratory, and of logic, better known as the artes sermocinales, or language studies; the second group comprises arithmetic, geometry, astronomy, and music, i.e. the mathematico-physical disciplines, known as the artes reales, or physiccs. The first group is considered to be the elementary group, whence these branches are also called artes triviales, or trivium, i.e. a well-beaten ground like the junction of three roads, or a crossroads open to all. Contrasted with them we find the mathematical disciplines as artes quadriviales, or quadrivium, or a road with four branches. The seven liberal arts are thus the members of a system of studies which embraces language branches as the lower, the mathematical branches as the intermediate, and science properly so called as the uppermost and terminal grade. Though this system did not receive the distinct development connoted by its name until the Middle Ages, still it extends in the history of pedagogy both backwards and forwards; for while, on the one hand, we meet with it among the classical nations, the Greeks and Romans, and even discover analogous forms as forerunners in the educational system of the ancient Orientals, its influence, on the other hand, has lasted far beyond the Middle Ages, up to the present time.

It is desirable, for several reasons, to treat the system of the seven liberal arts from this point of view, and this we propose to do in the present article. The subject possesses a special interest for the historian, because an evolution, extending through more than two thousand years and still in active operation, here challenges our attention as surpassing both in its duration and its local ramifications all other phases of pedagogy. But it is equally instructive for the philosopher because thinkers like Pythagoras, Plato, and St. Augustine collaborated in the framing of the system, and because in general much thought and, we may say, much pedagogical wisdom have been embodied in it. Hence, also, it is of importance to the practical teacher, because among the comments of so many schoolmen on this subject may be found many suggestions which are of the greatest utility.

The Oriental system of study, which exhibits an instructive analogy with the one here treated, is that of the ancient Hindus still in vogue among the Brahmins. In this, the highest object is the study of the Veda, i.e. the science or doctrine of divine things, the summary of their speculative and religious writings for the understanding of which ten auxiliary sciences were pressed into service, four of which, viz. phonology, grammar, exegesis, and logic, are of a linguistico-logical nature, and can thus be compared with the Trivium; while two, viz. astronomy and metrics, belong to the domain of mathematics, and therefore to the Quadrivium. The remainder, viz. law, ceremonial lore, legendary lore, and dogma, belong to theology. Among the Greeks the place of the Veda is taken by philosophy, i.e. the study of wisdom, the science of ultimate causes which in one point of view is identical with theology. “Natural Theology”, i.e. the doctrine of the nature of the Godhead and of Divine things, was considered as the domain of the philosopher, just as “political theology” was that of the priest; and “mystical theology” of the poet. [See O. Willmann, Geschichte des Idealismus (Brunswick, 1894), I, -§ 10.] Pythagoras (who flourished between 540 B.C. and 510 B.C.) first called himself a philosopher, but was also esteemed as the greatest Greek theologian. The curriculum which he arranged for his pupils led up to the ieros logos, i.e. the sacred teaching, the preparation for which the students received as mathematikoi, i.e. learners, or persons occupied with the—mathemata, the “science of learning”—that, in fact, now known as mathematics. The preparation for this was that which the disciples underwent as akousmatikoi, “hearers”, after which preparation they were introduced to what was then current among the Greeks as mousike paideia, “musical education”, consisting of reading, writing, lessons from the poets, exercises in memorizing, and the technique of music. The intermediate position of mathematics is attested by the ancient expression of the Pythagoreans metaichmon, i, e. “spear-distance”; properly, the space between the combatants; in this case, between the elementary and the strictly scientific education. Pythagoras is more over renowned for having converted geometrical, i.e. mathematical, investigation into a form of education for freemen. (Proclus, Commentary on Euclid, I, p. 19, ten peri ten geometrian pholosophianeis schema paideias eleutherou metestesen.) “He discovered a mean or intermediate stage between the mathematics of the temple and the mathematics of practical life, such as that used by surveyors and business people; he preserves the high aims of the former, at the same time making it the palaestra of intellect; he presses a religious discipline into the’ service of secular life without, however, robbing it of its sacred character, just as he previously transformed physical theology into natural philosophy without alienating it from its hallowed origin” (Geschichte des Idealismus, I, 19 at the end). An extension of the elementary studies was brought about by the active, though somewhat unsettled, mental life which developed after the Persian wars in the fifth century B.C. From the plain study of reading and writing they advanced to the art of speaking and its theory (rhetoric), with which was combined dialectic, properly the art of alternate discourse, or the discussion of the pro and con. This change was brought about by the sophists, particularly by Gorgias of Leontium. They also attached much importance to manysidedness in their theoretical and practical knowledge. Of Hippias of Elis it is related that he boasted of having made his mantle, his tunic, and his footgear (Cicero, De Oratore, iii, 32, 127). In this way, current language gradually began to designate the whole body of educational knowledge as encyclical, i.e. as universal, or all-embracing (egkuklia paideumata, or mathemata; egkuklios paideia). The expression indicated originally the current knowledge common to all, but later assumed the above-mentioned meaning, which has also passed into our word encyclopedia.

Socrates having already strongly emphasized the moral aims of education, Plato (429-347 B.C.) protested against its degeneration from an effort to acquire culture into a heaping-up of multifarious information (polupragmosune). In the “Republic” he proposes a course of education which appears to be the Pythagorean course perfected. It begins with musico-gymnastic culture, by means of which he aims to impress upon the senses the fundamental forms of the beautiful and the good, i.e. rhythm and form (aisthesis). The intermediate course embraces the mathematical branches, viz. arithmetic, geometry, astronomy, and music, which are calculated to put into action the powers of reflection (dianoia), and to enable the student to progress by degrees from sensuous to intellectual perception, as he successively masters the theory of numbers, of forms, of the kinetic laws of bodies, and of the laws of (musical) sounds. This leads to the highest grade of the educational system, its pinnacle (thrigkos) so to speak, i.e. philosophy, which Plato calls dialectic, thereby elevating the word from its current meaning to signify the science of the Eternal as ground and prototype of the world of sense. This progress to dialectic (dialektike poreia) is the work of our highest cognitive faculty, the intuitive intellect (nous). In this manner Plato secures a psychological, or noetic, basis for the sequence in his studies, namely: sense-perception, reflection, and intellectual insight. During the Alexandrine period, which begins with the closing years of the fourth century before Christ, the encyclical studies assume scholastic forms. Grammar, as the science of language (technical grammar) and explanation of the classics (exegetical grammar), takes the lead; rhetoric becomes an elementary course in speaking and writing. By dialectic they understood, in accordance with the teaching of Aristotle, directions enabling the student to present acceptable and valid views on a given subect; thus dialectic became elementary practical logic. The mathematical studies retained their Platonic order; by means of astronomical poems, the science of the stars, and by means of works on geography, the science of the globe became parts of popular education (Strabo, Geographica, I, 1, 21-23). Philosophy remained the culmination of the encyclical studies, which bore to it the relation interfere with the search for the truth which they contain. The choicest gift of bright minds is the love of truth, not of the words expressing it. “For what avails a golden key if it cannot give access to the object which we wish to reach, and why find first to obtain a firm foothold; culture was by them identified with eloquence, as the art of speaking and the mastery of the spoken word based upon a manifold knowledge of things. In his “Institutiones Oratorise” Quintilian, the first professor eloquentue at Rome in Vespasian’s time, begins his instruction with grammar, or, to speak precisely, with Latin and Greek Grammar, proceeds to mathematics and music, and concludes with rhetoric, which comprises not only elocution and a knowledge of literature, but also logical—in other words dialectical—instruction. However, the encyclical system as the system of the liberal arts, or Artes Bonce, i.e. the learning of the vir bonus, or patriot, was also represented in special handbooks. The “Libri IX Disciplinarum” of the learned M. Terentius Varro of Reate, an earlier contemporary of Cicero, treats of the seven liberal arts adding to them medicine and architectonics. How the latter science came to be connected with the general studies is shown in the book “De Architecture.”, by M. Vitruvius Pollio, a writer of the time of Augustus, in which excellent remarks are made on the organic connection existing between all studies. “The inexperienced”, he says, “may wonder at the fact that so many various things can be retained in the memory; but as soon as they observe that all branches of learning have a real connection with, and a reciprocal action upon, each other, the matter will seem very simple; for universal science (egkuklios, disciplina) is composed of the special sciences as a body is composed of members, and those who from their earliest youth have been instructed in the different branches of knowledge (variis eruditionibus) recognize in all the same fundamental features (notas) and the mutual relations of all branches, and therefore grasp everything more easily” (Vitr., De Architecture, I, 1, 12). In these views the Platonic conception is still operative, and the Romans always retained the conviction that in philosophy alone was to be found the perfection of education. Cicero enumerates the following as the elements of a liberal education: geometry, literature, poetry, natural science, ethics, and politics. (Artes quibus liberales doctrins atque ingenuse continentur; geometria, litterarum cognitio et poetarum, atque ills quae de naturis rerum, quae de hominum moribus, quae de rebus publicis dicuntur.)

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October 4, 2009

Nature and Convention in the Linguistic Arts

Filed under: Education, Philosophy — Tags: , , — Antiochian-Thomist @ 10:25 am

by Antiochian-Thomist

With language, as with society, we have to hold that there is both a natural and a conventional aspect to it. It is not without significance that Adam’s naming of the beasts follows immediately upon the notice of the social nature of man. “And the Lord God said, It is not good for man to be alone.”i What Aristotle noted about the state holds also for language. Man is social by nature, and yet he who founded the state was the greatest of benefactors. Man is a talking animal as much if not more so than he is a breathing and walking animal. And in this sense language is natural to him.ii

-Otto Bird, PhD.

Sacred Scripture, Aristotleiii, St. Thomas Aquinasiv, the above-quoted Dr. Bird, and a plethora of other intellects of worthy reputation assert that man is a social creature. Let us accept that as an established fact. It is also therefore the case that man with his natural tendency to seek out and live in a societal environment must have necessary and corollary natural gifts if that social nature is to be properly fulfilled. But what are these “natural gifts” to which we allude? In ways not entirely dissimilar to man, we see brutes who, to use the term loosely, live in “society” such as herds, prides, packs, flocks, and so forth. What does experience show us these creatures –man and beast alike– have in common in regards to the successful functioning of their “society”? Communication or the ability to communicate should be an obvious answer. However, man’s primary mode of communication is language, and that is learned. Further, the reality that there are a multiplicity of languages gives evidence to the fact that languages are themselves conventional. Did we men forsake our natural mode of communication for the sake of an artifice? Hardly. Rather, it was the nature of man to verbally communicate and to contrive that caused him to fashion the particular, conventional languages –the linguistic arts– so that he may fulfill his societal nature.

Society requires a cooperation among its members for it to be called society at all. Thus, whatever the framework of that society, its ordering necessitates the communication of its members. Therefore, as the end is a cause, the end of society is the cause of communication in general for society.

Though animals communicate, and do so vocally, man alone among the composite creatures is rational and has the capacity to formulate and communicate both concrete and abstract concepts. This he does in various and sundry modes, but history shows his preference for the spoken word and later the written word, which is nothing more than the visual symbols of the spoken wordv. Why this preference? Why does he not prefer to normatively use flags and standards, drum beats, or interpretive dance instead of language? St. Augustine gives us a glimpse of a possible explanation:

The signs that address themselves to the ear are, as I have said, more numerous, and for the most part consist of words. For though the bugle and the flute and the lyre frequently give not only a sweet but significant sound, yet all theses signs are very few in number compared with words [emphasis added]. For among men words have obtained far and away the chief place in indicating the thoughts of the mind.vi

Augustine argues for the sheer number of auditory possibilities that the spoken word offers above and beyond the noise-making devices than man can contrive. Here we implicitly see an argument for efficiency of expression that can more completely communicate the nigh-to-innumerable experiences, concepts, imaginings, and desires of man. Further, it can be noted, that since nature acts for an endvii, and since nature has supplied man with vocal chords with the possibility of a greater or more subtle sound variety which is more proportionate to his multitudinous experiences, it is proper than man employ his voice and the use of words for communication.

Particular language, however, is still an art and thus conventional. But art is produced from reason as the likes of Aristotle and St. Thomas Aquinas assert frequently; and reason specifically differentiates man from brute. Thus, art comes not from nature generally, but from rational nature specifically, for “the human race lives also by art and reasonings.”viii More particularly, art is produced from the reasoned considerations of experiences and is thus a universal in man, not to be lost upon any one exercise of the art. This is why Aristotle says, “art arises when from many notions gained by experience one universal judgement about a class of objects is produced.”ix Moreover, man is expected to make reasoned judgments from his gathered experiences for it is in his nature as rational to do so. Art, then, resides primarily in the intellect, and that part of the intellect which is “productive”.x

But neither art nor Aristotle stop there. The Philosopher also says:

…art is identical with a state of capacity to make, involving a true course of reasoning. All art is concerned with coming into being, i.e. with contriving and considering how something may come into being which is capable of either being or not being, and whose origin is in the maker and not the thing made […].xi

This “state of capacity” of which Aristotle speaks is discussed in the context of the treatment of the intellectual virtues in his sixth book of the Nicomachean Ethics. In short, art is a rational, productive habit, an acquired disposition, which resides in the man himself and not the thing produced. But man is not born with this art. Rather, he is born (under normal circumstances) with the ability or potentiality of acquiring this art or habit. This forces the conclusion that this capacity in man comes from at least two principles: one which is intrinsic to the man –which is natural, and one which is extrinsic to him –which is learned or acquired. Otherwise, if this capacity was entirely intrinsic, and all men were born with the acquired habit of language, it would stand to reason that all men would speak the same language. Of course, experience shows that there are more languages than there are nations in the world. This notion of the two-fold principle is clearly drawn out by St. Thomas Aquinas:

There are, therefore, in man certain natural habits, owing their existence, partly to nature, and partly to some extrinsic principle: in one way, indeed, in the apprehensive powers; in another way, in the appetitive powers. For in the apprehensive powers there may be a natural habit by way of a beginning, both in respect of the specific nature, and in respect of the individual nature. This happens with regard to the specific nature, on the part of the soul itself: thus the understanding of first principles is called a natural habit. For it is owing to the very nature of the intellectual soul that man, having once grasped what is a whole and what is a part, should at once perceive that every whole is larger than its part: and in like manner with regard to other such principles. Yet what is a whole, and what is a part–this he cannot know except through the intelligible species which he has received from phantasms: and for this reason, the Philosopher at the end of the Posterior Analytics shows that knowledge of principles comes to us from the senses.xii

This explanation bears out with man’s capacity for language. For it is owing to the very nature of the productive part of the intellect, which is common to the species, that man has by nature the inclination towards and the general ability to acquire and produce language. This potentiality and potency resides in the man, and is thus of his specific nature, though it might admit of degree in the individual natures, and is therefore an intrinsic principle. The experiences men encounter, such as hearing parents, friends, and teachers speaking, which are external to the man, form the extrinsic principles and are taken in via the senses, ruminated upon by the intellect, and are subsequently judged and acted upon. The latter portion of this process, i.e. the judgment and action, can only occur if the intrinsic principle is in place. With both present, the conventional art of language is produced and resides in the soul. Therefore, the intrinsic principle is universal and common to all men, but of itself not productive of language or the linguistic arts. The variety of languages, then, comes from the extrinsic principle, for those experiences and customs are varied depending upon where the individual man finds himself. Thus we see the truth in Dr. Bird’s statement:

Through usage and customs certain sounds have come to be selected out of a whole range of human sounds and organized in certain significant patterns. The resulting conventional construct is a specific language, English or Chinese. Conventional as so used to characterize a language can be opposed to natural. It then describes not the origin of the language but the modality and signification between the pattern of sounds and the experience they are associated with. How, for example, the expression “man” in English means “a man”.xiii

We have been told that originally all men spoke one language, and that multiplicity of languages owes its existence “to the sin of discord among men, which springs from every man trying to snatch the chief place for himself”xiv when we in the earlier part of our history tried to build that infamous tower.xv This we do not dispute. Nor, however, does it weaken our claim for what was imprinted on us originally now must be gained through nature and convention.

Nature, therefore, under a certain aspect, is a cause of convention insofar as convention is art. For man has by his nature those organs requisite for spoken language which give the material cause for the linguistic arts. Man is a social animal by nature, and society provides the final cause of his communicative abilities. Further, man is by nature rational, and reasoned intent provides the efficient cause for his linguistic artxvi which works in conjunction with and serves the final cause. Man’s nature receives the intelligible forms of things via the senses and his intellectual nature formulates concepts which together provide the formal cause of language. The linguistic arts, though conventional, are habits which find their seat in the soul of a man and arise from an intrinsic principle which is found in all men of sound and whole nature, and when combined with the extrinsic principles of experience give rise to the celebrated and necessary convention by which we have all benefited and will continue to benefit.

___________________________________________________________________________________________

iGenesis, 2:18

ii“Learning and the Liberal Arts”, Dr. Otto Bird, first lecture for the course, Liberal Arts: Their History and Philosophy, given by the International Catholic University through Holy Apostles College and Seminary, Cromwell, CT.

iii Politics, 1253a; Nicomachean Ethics, VII, 1155a5

ivSumma Theologiae, I-II, 72.4

vAristotle, On Interpretation, 16a 5

viDe Doctrina Christiana, Book II, Chapter 3

viiSt. Thomas Aquinas, Commentary on Aristotle’s Physics, Lecture 13 [198b34-199a33]

viiiAristotle, Metaphysics, 980b25

ixibid., 981a5

xNicomachean Ethics, VI,1139b

xiibid., VI, 1040a10-13

xiiSumma Theologiae, I-II, 51.1

xiii“Learning and the Liberal Arts”, Dr. Otto Bird, first lecture for the course, Liberal Arts: Their History and Philosophy, given by the International Catholic University through Holy Apostles College and Seminary, Cromwell, CT.

xivSt. Augustine, De Doctrina Christiana, Book II, Chapter 4

xvGenesis, 11

xviAristotle, Nicomachean Ethics, VI 1139a31-32

BIBLIOGRAPHY

Aquinas, St. Thomas. Commentary on Aristotle’s Physics. Notre Dame, Indiana: Dumb Ox Books, 1999.

_______. Summa Theologica (in English, 5 vols., Notre Dame, Indiana: Christian Classics, 1981)

Aristotle. Nicomachean Ethics (Richard McKeon, ed., The Basic Works of Aristotle, New York: Random House, 1941).

_______. Metaphysics (McKeon, Basic Works of Aristotle)

_______. On Interpretation (McKeon, Basic Works of Aristotle)

_______. Politics (McKeon, Basic Works of Aristotle)

_______. Physics (McKeon, Basic Works of Aristotle)

Augustine, St. De Doctrina Christiana (Philip Schaff, ed., The Nicene and Post-Nicene Fathers of the Christian Church, Volume II, Grand Rapids, Michigan: WM. B. Eeardmans, 1993).

Bird, Otto, Ph.D. “Learning and the Liberal Arts”, International Catholic University, 1996/2005.

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