The Frenzy of Philosophy

For the second semester in a row, I handed out copies of “What I Learn From Exams”. Last year, it led to intense in-class discussions about what grades mean to students, and about aspects of our college’s culture that inadvertently feed excessive anxiety about exams, nearly suffocating the real desire for learning we so carefully try to cultivate. This year, we did not discuss it in class, perhaps because I have mostly freshmen, who have yet to experience the frenzy of exam week. But at a lunch table Thursday, I asked one what she thought of it, which provoked a common discussion of the topic at the senior-dominated table, and provided myself and a fellow tutor a bully-pulpit for preaching against grade consciousness.

It also provided the opportunity for one senior to voice something that had been troubling her for some time. Senior year, she said, had caused serious crises for her. Reading some of the modern philosophers, and learning more of modern science and mathematics, had raised questions for her about things she thought she knew, and she karl-marxdidn’t know how to answer them. She wasn’t too challenged by Hegel, but Marx seemed to her scarily compelling. Dedekind and Lobachevsky have made her question her certainty about Euclid’s geometry, and Maxwell’s electromagnetic studies made her doubt she understood anything about the composition of the material universe.

The whole experience had depressed her. She felt her legs had been cut out from under her. This wasn’t what she thought would happen. She expected that her Catholic liberal education would give her an understanding of theology and philosophy together with the tools of the liberal arts that would allow her to answer the confusions of the modern world, and prepare her to save people from its deceits. Instead she has found she more profound questions than ever.

I felt for the girl, but I am afraid it also gladdened my heart. I had had this student when she was a freshman. Throughout the year, she revealed a beautiful soul. She was an important part of a most memorable conversation of Plato’s Symposium. I always like to start that seminar, which culminates the entire year, with this passage:

Now up to this point my tale could fairly be told to anybody; but from here onwards I would not have continued in your hearing were it not that…I share the plight of the man who was bitten by the snake: you know it is related of one in such a plight that he refused to describe his sensations to any but persons who had been bitten themselves, since they alone would understand him and stand up for him if he should give way to wild words and actions in his agony. Now I have been bitten by a more painful creature, in the most painful way that one can be bitten: in my heart, or my soul, or whatever one is to call it, I am stricken and stung by [Socrates’] philosophic discourses, which adhere more fiercely than any adder when once they lay hold of a young and not ungifted soul, and force it to do or say whatever they will….Every one of you has had his share of Bacchic frenzy of philosophy, so all of you shall hear. You shall stand up alike for what then was done and for what now is spoken. But the domestics, and all else profane and clownish, must clap the heaviest of doors upon their ears.

My question to the freshmen is this: Have we had a share in the “Bacchic frenzy of night-e1450465689181philosophy”? This is a question that I usually have to ask several times during the discussion, since my students have a difficult time even imagining the experience Alcibiades described. In this particular discussion, when the wildness of the claim about philosophy finally became clear, some eager conversationalist in the group said, “No! It’s not like you wake up in the morning thinking about this stuff.” To which the student of my tale replied, “Oh yes you do!” and proceeded to defend Plato’s presentation for the rest of the evening.

I often wondered whether she had continued to live the philosophic life with that intensity. Her quandary as a senior shows that she has indeed. It is a terrible thing to discover that the road to wisdom really does lead into valleys of darkness and doubt, but wisdom is a woman hardly to be gained without trying the depths of the soul. The education of the philosopher, as Plato saw it, should hopefully follow upon a healthy education of heart and imagination, but needs to proceed through mathematical studies, to test the student’s power of reasoning and the love of learning, but even more to discover whether he would be alive to wrestling with the most difficult questions about the foundations of mathematical thinking, which, since math promises to reveal the foundations of the material world, involves wonder about everything. Plato would have his overseers choose those young for further training (what he called “intellectual gymnastics”).

My own collegiate experience mirrored that of my student. The first two years, focused largely on Greeks, Romans, and Medievals, made me confident that there was beautiful and good truth that could be known, while the last two years presented modern challenges that I could not completely and satisfactorily answer. After graduation, this experience made me hesitant to strike back against those I thought presented wrong ideas, and more inclined to ask them questions to discover why they thought what they did. That was hard! I did not like being unsure of myself, especially when it concerned matters that were important to our faith. But, in the long run, I think that listening to those in error (an ability fostered by my liberal arts training) provided me with a deeper understanding of what was attractive about their error, and so an ability later in life, having incorporated what was worthwhile into my own view, to offer more satisfactory answers to those who were struggling with the same issues.

I shared much of this with my troubled senior, and I hope that it offered her comfort. At one point she exclaimed, “If it weren’t for the Faith, I don’t know what I would do!” I concurred, adding that our Faith in the One True, Good, and Beautiful allows us to face the real state of our knowledge. As Socrates said to Meno, in a passage that has dominated my intellectual life, “That knowledge differs from true opinion is no matter of christ-the-teacher-icon-550conjecture with me. There are not many things which I profess to know, but this is most certainly one of them.” Socrates and his philosophic frenzy enters into our heart, making us restlessly suspicious of what we think we know. This can lead to skeptical despair and even in our days a high rate of suicide. Thank God that we have the reliable authority Socrates lacked, so that we might be able to bear the realization of our own ignorance, and learn to be so patient and docile that we can gradually approach the gates of the house of wisdom.

I left the table grateful to be working with such a beautiful young soul, while praying for God to present to her with His rod and His staff. That night, my wife and I decided to Chrysostomosreturn to the College for Adoration. As we walked into the chapel, we were stunned to see it filled with well over 100 students, kneeling before the Lord in the monstrance, while student-led choirs filled the chapel with their pure voices raised in adoring song. This is the heart of Catholic liberal education.

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Human Exceptionalism Proven by Science!

A study released earlier this year of DNA strands from a large variety of species and millions of different individuals reveals that, while species genetically differ from one another markedly (there are no “blurred” lines among species), individuals within a species show very little genetic diversity. Scientists are drawing many fascinating ideas from this — e.g. 90% of animal species started off with a primary couple sometime within the last 200,000 years, suggesting a cataclysmic event, possibly a viral pandemic.  But the one stands out, as revealed by the title of the Phys.Org article:

Far from special: Humanity’s tiny DNA differences are ‘average’ in animal kingdom

One of the lead scientists suggests profound anthropological consequences:stoeckle-thaler_orig

Says Dr. Stoeckle: “Culture, life experience and other things can make people very different but in terms of basic biology, we’re like the birds. By determining the genetic variety within species of the animal kingdom, made possible only recently by the burgeoning number of DNA sequences, we’ve documented the absence of human exceptionalism.”

The director of the research institute overseeing the study draws ethical and sociological implications:

“At a time when humans place so much emphasis on individual and group differences, maybe we should spend more time on the ways in which we resemble one another and the rest of the animal kingdom.”
With a little more imagination and a lot better education, these scientists might have considered what stands out to me: The extraordinary diversity among human individuals and cultures has little to do with biological diversity. Being much less biologically diverse than other species, we completely blow them out of the water in terms of life diversity. Human exceptionalism was never more clear.
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Unexpected Classroom Enchantment

A few weeks ago, I was not looking forward to my morning class. Family health care issues had gotten me down, and I had little energy or inspiration for Sophomore Language. The translation assignment I had given them I did not think would take too long to go over, and I couldn’t count on it provoking interesting discussion. The passage they prepared was from the first chapter of St. Anselm’s Proslogion, which is a beautifulp00415 prayer arousing the mind to contemplation. I want to discuss it with students because it is one of the few places in our curriculum, which is ordered to contemplation, where they can see what contemplation really looks like. This is a topic I find fascinating, but I never know whether students will respond to it, whether they will see much of interest in it or not. So I had to have a backup plan for other things we might do with extra time. I really hate not knowing whether I will be able to generate conversation.

It turned out that we never got through more than one sentence, never got to the questions I might have wanted to discuss, and never had a lull in the conversation. I had asked them to compare a Latin paragraph with the English translation on the facing page of the edition they would use in their Theology class next semester. I wanted them to pay careful attention to the Latin forms, and be able to account for them syntactically. When I asked how it went, they were uneasy. They had had a difficulty with this sentence:

Fateor, Domine, et gratias ago, quia creasti in me hanc “imaginem tuam”, ut tui memor te cogitem, te amem.

When I asked one of them to translate it, he did it correctly: “I speak, O Lord, and I give thanks, because you created this your image in me, so that, mindful of you, I might think of you, I might love you.” I said that was fine. But the uneasiness persisted. The English translator had rendered the last part of the sentence, “so that I might remember you, think of you, love you.” What puzzled them was that they thought “memor” is an adjective in Latin, but “remember” in English is a verb. At first, they thought they must have misunderstood what part of speech “memor” is. Having confirmed their knowledge, I then asked whether the Latin expression is significantly different from the English. One of the students pointed out that, while the English presented the three acts as on the same level, the Latin suggested that “being mindful” is a condition for thinking and loving the Lord.

Now this was getting interesting; I thought we might start exploring Trinitarian implications in St. Anselm’s description of the image. But then one of the students blurted out, partly in astonishment, partly in indignation, “But that’s against the rules!” It latin-noun-mastery-chartswas an ingenuous expression of the feeling of a student who had been trained for some years of her young life to memorize all the rules for correct translation, and had often lost points on quizzes and tests for making the very mistake that this published translator was making. How could he dare to translate an adjective by verb? Or was he so bad that he didn’t realize he was making a mistake?

This question determined the rest of the conversation. We started to explore what translating really is. We discussed what language, especially in the hands of a masterful author like St. Anselm, is able to convey, and the students saw, seemingly for the first time, how many difficult choices a translator faces. As the conversation developed, I was delightfully surprised at the students’ genuine, intense, even invested interest in the question. Perhaps it struck them so because translating has formed a prominent part of their education, and they were realizing for the first time that they had never really understood what they were doing. Several of the students lit up as they were able to voice their appreciation for the contextual and emotional aspects of language, which most often had to be pushed aside to achieve technically correct translations.

At some point, I noticed that my own temporal anxieties had vanished; for just a little while I myself was enchanted with the question, and with witnessing my students’ minds open onto a small but not insignificant stream leading into the ocean of wisdom.

 

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Esolen Describes Beautiful Schools

https://www.thecatholicthing.org/2018/11/24/unplanned-the-fresh-air-comes/

Anthony Esolen shares his delight in being a part of a small, fully intentional Catholic educational community in ways that many of us have been blessed to recognize:

Yesterday as I was walking to class, two of my students, an alto and a bass, were singing “White Christmas” out of the window, in harmony, hailing the arrival of the first snow.  They sometimes hiccoughed in their harmony for laughing.  I sat at lunch next to a student and a colleague, the former carving up the latter over a chessboard.  Every day I see things I have not seen before.  They are ordinary things, in order, and not the result of a committee.

There is an intellectual and artistic liveliness among them too.  One of them, perhaps the quietest of all, spent fifteen minutes asking me questions about free verse, blank verse, why stress was the most prominent feature of English verse, whether that was so in other languages, and where he could learn more about the matter.  I gave him a book to read.

 

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Five Definitions of Man

Five Definitions of Man

Am I a monster more complicated and swollen with passion than the serpent Typho, or a creature of a gentler and simpler sort, to whom Nature has given a diviner and lowlier destiny? Socrates, Phaedo

I have long wondered why Aristotle never really defined man, and why no one seems to have noticed. At our institution, freshmen read Porphyry before anything of Aristotle, and thereafter wittingly or unwittingly follow St. Thomas’s habit of using “rational animal” as the preeminent example of a definition. (That St. Thomas seems to inform this practice, though they have not read him, is suggested through how quickly Porphyry’s actual definition, “rational and mortal animal”, is forgotten.) The strength of the practice is seen in the seemingly total unawareness that Aristotle never uses the expression in his logical works we read, preferring “two-footed featherless animal” when he needs a non-mathematical definition. In fact, suspecting a wild goose chase but not certain because I have not read all of his extant works, I have challenged students and fellow faculty members to find anywhere that Aristotle uses the expression. So far the goose remains as elusive as the loon.

Thanks to working with a very diligent, studious and inquiring senior a few years ago, I have come to the conclusion that, if he ever considered it, Aristotle likely never used the expression in a logical work because it would lead his readers and students to think that the magical expression solved the greatest mystery in the sub-lunar universe, “What is man?” My student’s thesis work was driven by her strong intuition that only God’s revealed words have offered the best definition of man, “Let us make man to our Image and Likeness.” In the course of our discussions and re-readings of the Posterior Analytics, I have come to think that Aristotelean/Thomistic principles suggest five definitions of man, divided according to the different kinds of study that might think about man. Without going into too much argumentation, I offer them for consideration and discussion.

Logical – “Rational Animal” – Logic offers ways to define all things based on our common conceptions of them, apart from any specialized inquiry. This begins with categorization and proceeds through difference. With regard to substances, commonly accepted differences for each genus should be determined, and all those that apply to a particular being are its definition, when arranged according to priority and posteriority. Porphyry follows this when he determines that the differences of animals are rational/irrational, mortal/immortal. Since we no longer believe in the gods and their horses, we should only use the one division.

Political – “Political Animal Capable of Speech to Express the Useful and Unuseful (and consequently the Just and Unjust”) – In Politics I.1, Aristotle comes as close as he ever does to offering a formal definition of man (as in Ethics I.12 he comes as close as he ever does to the expression “rational animal”). This follows the logical pattern in identifying a genus (Political Animal includes herd and colonial animals, as cattle and bees) and a difference, adapting the pattern to the concern of the kind of knowledge he is seeking, identifying the whole of which man is a part, and suggesting something of his preeminent activity and final cause (speaking about the just, for the sake of the whole, potentially eternal city). Strikingly, Aristotle has already concluded near the end of the Ethics that the political life, while offering properly human happiness, is not a life of the individual as such, nor does it attain the highest happiness of which the individual is capable.

Natural – “Intelligent soul that gives life to a body capable of the imaginations suitable for thought.” The natural philosopher seeks the material and formal principles of each being and defines accordingly. Aristotle’s study of soul reveals that the highest soul has the power of intelligence and needs a body that makes understanding possible. Strikingly, Aristotle shows that the activity and the existence of the intellectual soul transcends the body which it informs.

Metaphysical – “A Purely Potential Intelligence that Must Share its Existence with a Body” – This is suggested by St. Thomas’s On Being and Essence, and follows naturally from the considerations found in the Political and Natural studies. Considered with respect to all being, man is not best seen as a composition of body and soul that is part of a temporal community, but against the backdrop of all the possibilities of intelligent (angelic) existence, whose differences are grasped according to degree of act and possibility in their existence. Our intellect is the lowest possible, beginning being with no actual understanding at all, and needing a body substantially united to it in order to come to know.

Theological – “A Creature Made by God to His Image and Likeness as the Culmination of His Material Creation” – This definition includes formal, material, efficient and final causes.

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Questions, Opinions, and the Philosophic Life I, with Quotations from Authorities

I gave a talk this week at our college (Thomas Aquinas College) which I entitled, “Questions, Opinions, and the Philosophic Life”. In it, after sharing something of my experience as a sometimes joyfully, sometimes painfully driven questioner, I tried to argue that the natural, normal, and even highest mode of the philosophic life for most of us  is that of questioning.Below I share quotations from some authorities (mostly Plato) on this topic.

In the talk, I drew on Plato’s Socrates as both a model of the philosophic life, and as one who gives the best accounts of what the philosophic life is like. I distinguished the philosophic life from the teachings that are called philosophy and become objects of study. Socrates’ life, as exteriorly manifested, is dominated by relentless, exacting, formalized questioning during which opinions, questioner, and answerer are subjected to examination. Questions aim to determine the consequences that follow from an opinion, and to reveal the more comprehensive ideas which underlie opinions. Socrates strongly believed that this life of continual testing is the proper way to live if one cares for his soul above all, and so he strove to arouse it in anyone who would listen, especially the most promising young men of his day. He believed that in doing so he was fulfilling God’s will, acting as a divinely appointed gad fly to the great city of Athens. He looked forward to death as the great opportunity to question, test, and examine the heroes who had gone before him.

Socrates believed this because he thought that our thought as expressed in words is always in a state of opinion, rather than knowledge. Though right opinion is as good a guide as knowledge, he said, a life content with opinion without pursuing knowledge ardently is “not worth living”, even though it might lead to a form of virtuous living.

Is he right? Do we who pursue wisdom live in a state of opinion that demands continual questioning and examining? Certainly Aristotle and St. Thomas agree (as evidenced by the dialectical practice of beginning every topic by a thorough going-over of difficulty after difficulty after difficulty) that knowledge is only going to be acquired through a consideration of many of the opinions that men have held on a given topic. But they also present answers to questions and resolutions of difficulties that seem assertions of knowledge, not opinion.

[more to follow]

 

John Milton Gregory, The Seven Laws of Teaching

The most important stimuli used by nature to stir the minds of men have already been noted. They might all be described as the silent but ceaseless questions which the world and the universe are always addressing to man. The eternal questions of childhood are really the echoes of these greater questions. The object or the event that excites no question will provoke no thought. Questioning is not, therefore, merely one of the devices of teaching, it is really the whole of teaching. It is the excitation of the self-activities to their work of discovering truth. Nature always teaches thus….

An explanation may be so given as to raise new questions while it answers old ones. The explanation that settles everything and ends all questions, usually ends all thinking also.

After a truth is clearly understood, or a fact or principle established, there still remain its consequences, applications, and uses. Each fact and truth thoroughly studied leads to other facts which renew the questioning and demand fresh investigation. The alert and scientific mind is one that never ceases to ask questions and seek answers. The scientific spirit is the spirit of tireless inquiry and research.

As with the world, so with the child. His education begins as soon as he begins to ask questions. It is only when the questioning spirit has been fully awakened, and the habit of raising questions has been largely developed, that the teaching process may embody the lecture plan. The truth asks its own questions as soon as the mind is sufficiently awake. The falling apple had the question of gravitation in it for the mind of Newton; and the boiling teakettle propounded to Watt the problem of a steam engine.

Plato, The Theaetetus

Socrates, I often wonder like mad what those things can mean; sometimes when I’m looking at them I begin to feel quite giddy….It seems that Theodorus was not far from the truth when he guessed what kind of person you are. For this is an experience which is characteristic of a philosopher, this wondering. This is where philosophy begins and nowhere else.

Plato, The Symposium

Something much more painful than a snake has bitten me in my most sensitive part – I mean my heart, or my soul, or whatever you want to call it, which has been struck and bitten by philosophy, whose grip on young and eager souls is much more vicious than a viper’s and makes them do the most amazing things. Now, all you people here have all shared in the madness, the Bacchic frenzy of philosophy. (Symposium)

Plato, The Meno

I certainly do not think I am guessing that right opinion is a different thing from knowledge. If I claim to know anything else – and I would claim that about few things – I would down as one of the things I know.

There if it not through knowledge, the only alternative is that it is through right opinion that statesmen follow the right course for their cities. As regards knowledge, they are no different from soothsayers and prophets.

Plato, The Phaedo

The happiest of these [who are choosing to return to a body] are those who have practiced popular and social virtue, which they call moderation and justice and which was developed by habit and practice, without philosophy or understanding….no one may join the company of the gods who has not practiced philosophy and is not completely pure when he departs from this life, no one but the lover of learning.

Plato, The Apology

The greatest good for a man [is] to discuss virtue every day and those other things about which you hear me conversing and testing myself and others for the unexamined life is not worth living for men.

Plato, The Phaedo

Taking as my hypothesis in each case the theory that seemed to me the most compelling, I would consider as true…and as untrue whatever did not agree….If someone then attacked your hypothesis, you would ignore him and would not answer until you had examined whether the consequences that follow from it agree with one another or contradict one another. And when you must give an account your hypothesis itself…you will assume another hypothesis, the one which seems to you best of the higher ones until you come to something acceptable….

Plato, The Republic

(This happens) when many gathered together sit down in assemblies, courts, theaters, army camps, or any other common meeting of a multitude, and, with a great deal of uproar, blame some of the things done, and praise others, both in excess, shouting and clapping; and besides the rocks and the very place surrounding them echo and redouble the roar of blame and praise. Now in such circumstances, as the saying goes, what do you suppose is the state of the young man’s heart? Or what kind of private education will hold out for him and not be swept away by such blame and praise and go, borne by the flood, wherever it tends so that he’ll say the same things are noble and base as they do, practice what they practice, and be such as they are?

Bacon, The New Organon

The syllogism consists of propositions, the propositions of words, and words are tokens and symbols of notions. If therefore the very notions of the mind (which are, as it were, the soul of words, and the basis of the whole system and structure) are badly and carelessly derived from things, and vague, inadequately defined and circumscribed, in short, if they are defective in many ways, then everything collapses.

Aristotle, The Metaphysics

WE must, with a view to the science which we are seeking, first recount the subjects that should be first discussed. These include both the other opinions that some have held on the first principles, and any point besides these that happens to have been overlooked. For those who wish to get clear of difficulties it is advantageous to discuss the difficulties well; for the subsequent free play of thought implies the solution of the previous difficulties, and it is not possible to untie a knot of which one does not know. Now those who wish to succeed in arriving at answers will find it profitable to go over the difficulties well; for answers successfully arrived at are solutions to difficulties previously discussed and one cannot unite a knot if he is ignorant of it. But the difficulty of our thinking points to a ‘knot’ in the object; for in so far as our thought is in difficulties, it is in like case with those who are bound; for in either case it is impossible to go forward. Hence one should have surveyed all the difficulties beforehand, both for the purposes we have stated and because people who inquire without first stating the difficulties are like those who do not know where they have to go; besides, a man does not otherwise know even whether he has at any given time found what he is looking for or not; for the end is not clear to such a man, while to him who has first discussed the difficulties it is clear. Further, he who has heard all the contending arguments, as if they were the parties to a case, must be in a better position for judging.

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Sacra Doctrina Project

John Brungardt informs us of a promising new initiative that ‘aims to contribute to the Church’s longstanding tradition of seeking a knowledge through causes that is certain and evident about the source of our salvation that is still, at its height, a speculative form of knowledge, a knowledge that “aims both at the clarity needed to properly evaluate theological claims and at the fulfillment of the natural desire to know intimately that which one loves.”’

via Sacra Doctrina Project

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Discussing Elijah

I had a wonderful discussion of Elijah’s journey to Mt. Carmel (1 Kings 19) with St. Augustine Academy students. You never know where discussions will lead, and what students will come up with, if you can get students to talk, if you can stand letting them talk, if you follow up what interests them while not losing sight of the central parts of the reading. 
elijah-broom-treeWhile having them recount the episode (which can often be discouraging, since you find how many of them either didn’t read the assignment, or did it with little attention), one student asked, “Is it right for Elijah to ask God to let him die?” Debating that for awhile drew our attention to Elijah’s intense discouragement (well expressed in this homily by a Malaysian priest who knows about broom trees — which another student asked about, but I didn’t know the answer to at the time). This opened up the question, “How did God respond to Elijah’s prayer to die?”
The lesson we learned: If you find yourself at 50 or 60 years old, having spent your life being jealous for the Lord and His Church, seeing the complete failure of all you tried to do, alone in the wilderness starving, pray to God to die. And He will send an angel to feed elijah1660you, and tell you, “Your journey has only begun,” and will send you to His holy mountain, where He will reveal His inner nature to you, and give you a whole new mission, to prepare for something greater than you ever dreamed.
Along the way, one student had us start to compare Elijah’s experience on the mountain with Moses’ at Sinai (Exodus 19), and another student pointed out something I think may be crammed with mystical significance, “The Lord only passed by in the wind and the earthquake and the fire, but he was found in the still, small voice.”
I wonder what our next discussion will bring.
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Towards Reforming High School Math and Science

…If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education. Paul Lockhart, “A Mathematician’s Lament

This weekend, I was privileged to gather at the Catholic University of America with fellow educators who feel the force of Lockhart’s now-famous Lament and who have taken steps over the years to do something about it. They are part of the classical liberal arts revival that is gaining momentum among Catholic schools, and recognize that many of these schools have found it difficult to integrate mathematics and the sciences into the liberal arts curriculum. These branches of knowledge, whose hold on the privileged place in education seems to grow with each passing year, pose particular difficulties for the classical liberal arts schools.

Based on the early modern developments of algebra and mathematical approaches to the study of the natural world by which men like Descartes, Galileo, and Newton transformed our understanding the world around us and the very way the human mind should hope to achieve knowledge of what is real, contemporary math and science arose outside of the traditional liberal arts curriculum, rejected its presuppositions, forced their way into education through battles in the nineteenth and early twentieth centuries, and always followed their own ways, even imposing those ways upon the properly humane studies. In these days of “teaching to the test”, even math and science have suffered a loss of coherence and meaning, leaving mathematicians and scientists like Lockhart, himself no classicist, mourning and weeping.

Today’s situation forces difficult questions on those trying to teach within the classical liberal arts tradition. Should the ancient Quadrivium – Euclidean geometry, the contemplative study of  integral numbers, astronomy as a discipline distinguished from physics, and the numerical analysis of music — be revived in the upper school curriculum? To what extent? How are the modern developments in these areas to be  resuscitated and integrated with both the ancient Quadrivium and the rest of the liberal arts curriculum, and, more importantly, to contribute to the formation of the young in the true, good, and beautiful?

All those gathered agreed that the study of mathematics and the natural world provides important opportunities for accomplishing central goals of a liberal arts education:

  • the development of wonder
  • the confidence that comes from arriving at knowledge of what is real through ordered investigation and thought
  • the ability to judge well the character, extent, and limitations of that knowledge
  • that students will be best prepared to take full advantage of collegiate courses in these areas if they have learned how to ask the right questions and measure the worth of the answers given
  • That natural philosophy should play some important role in helping students integrate these branches of knowledge into a complete vision of the world that is, and in fortifying them against the reductionist mentality formed by cultural scientific indoctrination.

Michael Moynihan, Head of Upper School at The Heights in Washington, D.C., emphasized the threat posed by the philosophical presuppositions underlying contemporary relativism and explicitly contained in the framing sections of most high school science textbooks. Michael identified four profound errors that today’s young drink in with their mother’s milk [my metaphor] and find reinforced in ordinary education (which he is elaborating in his Bring Back Reason series).

  • Everything is composed of little particles.
  • There really are not such things as substances in the classical sense of something as a whole entity having a unified substantial existence.
  • There are really no such things as natures.
  • Living things are machines.

To combat these errors and prepare their students to be able to give reasonable witness to natural truth, The Heights is introducing a robust Philosophy program into its college-prep curriculum. For a number of years, Freshmen have spent a semester learning formal and (more recently) material logic (drawing on Martin Cothran’s Memoria Press texts). Beginning this year, Sophomores and Juniors are being introduced to concepts central to traditional Aristotelian and Thomistic natural philosophy and metaphysics. This sequence will help them see that the human mind has more, more fundamental, and more certain ways of knowing the real world than simply through contemporary science. Seniors will find their history class devoted to the intellectual revolutions that have characterized Western thought and provide an understanding of today’s cultural foundations which, together with an Apologetics course that culminates the theology sequence, will bring out the profound significance of the ideas studied in previous years.

Peter Orlowski, teacher at the recently formed Summit Academy in Fredericksburg, Virginia, expressed his conviction that teachers of math and science should first be teachers of human beings, seeing themselves as having the same fundamental goals as teachers involved in the humanities and arts. He witnessed  to the creativity shown by teachers committed to these ends and given freedom to work. He tells students and parents that the best preparation for collegiate courses is often not found in learning parts of those courses ahead of time, but in learning what scientific thinking is about and how it proceeds.

Peter believes that the ancient quadrivium should continue to be a curricular foundation, with algebra, calculus and higher mathematics providing a higher level wisdom about these same subjects. Although as an individual teacher, he has not been able to incorporate much arithmetic or musical mathematics, Peter shared with us his approaches to astronomy, Euclidean geometry, and natural philosophy. In each of these areas, Peter consciously aims to foster student questioning, activity, satisfaction in knowing, and caution in judgment. Astronomy focuses students’ attention on celestial bodies, opening them to becoming fascinated about objects that can’t be produced by human beings. Peter’s students spend significant amounts of time observing and charting the movements of the sun, moon, and stars, learning to tell time by the positions of stars in the night sky, and experiencing trigonometric functions through carefully noting the annual changes in the shadows cast by gnomons. They think through the problems involved with determining the lengths of the month as determined by moon and stars, activities which culminate in a field trip to observe a lunar eclipse, which they can compare with their predictions.

Peter prepares students for the study of Euclid through weeks of discussions about where the study of shapes should begin. After debating the relative merits of the Pythagorean theorem, coordinate systems, what is most interesting, they inevitably move towards the simplest objects, culminating in the partless point. After this, they move carefully through demonstrations of Euclid’s first book, which culminates in the demonstration of the Pythagorean theorem. The training in demonstration has a profound impact on all of their studies, such as literature discussions, as students become accustomed to expecting that opinions will be held based on clear, evidenced-based reasoning.

Peter introduces students to natural philosophy through a sequenced reading of Greek philosophers, beginning with Thales and culminating in reading (with assisting commentary) the first two books of Aristotle’s work On Nature. For each thinker, students are required first to present the best arguments they can think of to support a philosopher’s view (such as Thales’ view that everything is made out of water), and then to argue against it. Often they anticipate the critiques and advances made by subsequent thinkers. This sequence includes a complete reading of Plato’s Timaeus, which they find challenging but deeply formative.

Edward Trudeau, one of the co-authors of the influential Educational Plan of St. Jerome Academy, is now deeply involved with forming the St. Jerome Institute high school, which will open its doors next fall. SJI intends to fully integrate the math and science sequences into its overall curriculum. By doing this, they hope to avoid forming in students the belief that those disciplines provide the only objectively right answers to questions, while giving them a deep understanding of how advances in these areas have profoundly affected human affairs. The carefully-sequenced modules will help students to live adult lives filled with the true, good, and beautiful, and also prepare them well for collegiate learning and fruitful careers.

Their four year program, which they call Natural Philosophy rather than Science, situates learning techniques within narratives that raise historical problems leading to the need to develop more sophisticated tools for problem-solving. Each year, problems are presented that relate to a common school-wide theme. The first year’s theme of “Exodus and Odyssey” invites such problems as those involved in discovering means of determining longitude, crucial for learning to  navigate the globe, or the logistical failures in the provision system for Napoleon’s army as it moved through Russia. The second year turns to observing and understanding whole beings and systems, such as animal life and eco-systems, while the third year (“God and the Human Person”) follows the humanist-led turning inward through dissection and analytical reasoning. The fourth year draws upon all the previous years to address larger social problems.

The SJI approach always begins with what amount to elaborate, significant word problems which not only increase interest in learning techniques of solution but also provide iterative training in what is considered the hardest part of equation-based reasoning. Narrative context provides a motivating question, and an occasion to discuss preliminary ideas on how to approach it. Historical readings (such as Columbus’s logs) and activities deepen understanding of the narrative context. Students are then taught simpler and more complex tools (e.g. vector multiplication or matrix transformation) that they can use to address the problem. Higher level word problems train them in using the tools, which are finally applied back to arrive at more satisfactory solutions to the original narrative. Students are expected to engage in research and investigative thinking for homework.

Each of the presenters emphasized that they are only in the initial stages of enacting their ideas, and affirmed their intention to adapt in the light of experience. But their work promises to help students experience the power and beauty of math and science, intelligently and critically appropriate their riches, assess the evidence for questions of contemporary importance (e.g. biological and cosmological evotution, bioethical challenges, the value of sociological research), and be aware of the contingent character of scientific theory as well as its impact on human culture and history.

 

Posted in Math and Science, Quadrivium, Secondary Education | 1 Comment

Turning the Whole Soul: The Moral Journey of the Philosophic Nature in Plato’s Republic

I forgot that we were playing and spoke rather intensely. For, as I was talking I looked at Philosophy and, seeing her undeservingly spattered with mud, I seem to have been vexed and said what I had to say too seriously as though my spiritedness were aroused against those who are responsible. (VII.536c)

Socratic dialogues are always dramatic, and the Republic is no exception. Opinions are revealed by the characters who hold them. Thrasymachus frightens Socrates by the forcefulness with he expresses his opinion that justice is the rule of the stronger. So when we see something as unusual as Socrates admitting to being upset, we should pay careful attention. This hardly ever happens. Even when Socrates attended a performance of Aristophanes’s Clouds, he didn’t erupt or storm out; instead he stood so the crowd display-1337could see how like him was the comic mask worn by the stage Socrates. But at the end of Book VII of The Republic, in the privacy of a group of friends, Socrates’ love of Philosophy makes his blood boil at the ridicule he and it receive from society and its leading elements. This is not simply a personal matter. Socrates seriously believes the greatest goods for mankind and human societies are at stake; a proper reverence for philosophy and the philosopher is necessary if “the city and the regime are to be saved.”

Socrates grows angry because he thinks he knows who is responsible for the insults and abuse heaped upon Philosophy. Aristophanes simply dramatized the common opinion that Philosophy is practiced by charlatans and humbugs; he did not make their opinions. Who is responsible? The answer to this question drives the movement of the dialogue from the end of Book V through Book VII, and provides the context for some of the most famous images in literature, particularly the Cave allegory at the beginning of Book VII. I hope that understanding this movement will help us to understand The Republic better, but also provide us with important reflections as teachers and students of philosophy.

  1. The Philosophic Nature

This part of the drama begins near the end of Book V. Book V began with Socrates somewhat unwillingly presenting key changes a regime must experience if the just Republic described in Books II-IV is to really come into being. The hardest thing to swallow – harder than the common education of women and men, harder than the community of women and children – is that either philosophers must rule, or rulers must become philosophers (473d). He knows how “paradoxical” this will seem, and is not surprised at all when Glaucon expresses dramatically how insane, and even dangerous, most people will think such a claim. Adeimantus later states what experience has shown: those who spend too much time in philosophy tend to become “quite queer, not to say completely vicious; while the ones who seem perfectly decent…become perfectly useless to the cities.” (487d)

Socrates immediately blames this reaction on the caricature of the philosopher that most people have. Naturally, the idea of Aristophanes’ Socrates being a ruler is crazy. So Socrates has to try to establish an accurate image. He does this by argument, starting with the drive that marks a young person as a budding philosopher – a youthful omnivorous appetite for learning: “The one who is willing to taste every kind of learning with gusto, and who approaches learning with delight, and is insatiable, we shall justly assert to be a philosopher….” (475c) In response to a criticism from Glaucon, Socrates clarifies. Some people love to learn about all the fair things and fair ideas, the different views of justice and of holiness, to be found among different kinds of people. They know that none of those is absolute justice, and are glad of it. In fact, they get angry with anyone who would say that the fair and the just and the holy are really the same everywhere. Though they are lovers of learning, they are not philosophers; philosophers are passionate about learning what the fair and just and holy really and simply are. “About philosophic natures, let’s agree that they are always in love that learning which discloses to them something of the being that is always and does not wander about, driven by generation and decay.” (485b)

Socrates’ complete vision of the philosopher might seem the idle dream of besotted lover: “a rememberer, a good learner, magnificent, charming, and a friend and kinsman of truth, justice, courage, and moderation….” (487a) But he makes a strong case. The one really passionate for wisdom would love truth and hate lies. He would love the pleasures of the soul and forsake the pleasures of the body, and therefore be moderate. Money would hold little interest for him. His speech will be weighty; he will be great-souled through his “contemplation of all time and all being”. (486a) He will be courageous through having an accurate judgment about human life and death. Justice will come naturally to him, and he will easily work with others. Add to this the necessary intellectual gifts, and you end up with an impressive package, one truly worthy to be made into a ruler.

Socrates arrives at this image through argument. But he admits that experience produces very different images, which he must account for in order to have his claims taken seriously. True philosophic natures are extraordinarily attractive and natural-born leaders. For this reason, they receive great praise, flattery and promises of reward from their youth in the hopes that they will follow the path to greatness approved by everyone. Most will succumb to this kind of flattery. Those who don’t, who show a magnanimity that makes them immune to the lures of society, end up being distrusted by most people. They lead a quiet, private life that will keep them from getting into trouble, but makes them useless.

So the positive images of the philosopher are unavailable to experience. But false images are plentiful. Those who claim to pursue philosophy do not have the passionate commitment to real learning characteristic of the true philosophic nature. Most of these are small souls, who make philosophy look pedantic and ridiculous, but pose no threat to anyone. They are attracted by the pretensions that philosophy gives them in looking down on those who pursue the ordinary interests of life. Apollodorus, the character who narrates The Symposium, seems a prime example. He abandoned his business life to follow Socrates around and make himself into a little image of him. “There was a time when I was running about the world, fancying myself to be well employed, but I was really a most wretched thing, no better than you are now….I pity you who are my companions, because you think that you are doing something when in reality you are doing nothing.” (173c)

But sometimes a soul made for greatness will dabble in philosophy long enough to marcello_bacciarelli_-_alcibiades_being_taught_by_socrates_1776-77become very dangerous. When natures passionate for greatness receive bad instruction, they become “exceptionally bad”, “the source of great injustices and unmixed villainy”. (491e) Alcibiades is the tragic figure of Philosophy. As Plutarch relates:

The affection which Socrates entertained for him is a great evidence of the natural noble qualities and good disposition of the boy, which Socrates, indeed, detected both in and under his personal beauty; and, hearing that his wealth and station, and the great number both of strangers and Athenians who flattered and caressed him, might at last corrupt him, resolved, if possible, to interpose, and preserve hopeful a plant from perishing in the flower, before its fruit came to perfection. For never did fortune surround and enclose a man with so many of those things which we vulgarly call goods, or so protect him from every weapon of philosophy, and fence him from every access of free and searching words, as she did Alcibiades; who, from the beginning, was exposed to the flatteries of those who sought merely his gratification, such as might well unnerve him, and indispose him to listen to any real adviser or instructor.

In spite of his best efforts, Socrates finally failed to fix Alcibiades’s affection on philosophy. This was not only a personal disaster for Socrates (who had to content himself with the Apollodorus’s of the world), but also brought shame and suspicion to philosophy. Alcibiades’s Trump-like flaunting of the social norms of Athenian culture, and his subsequent abandonment of Athens for Sparta, and then Persia, could easily be blamed on his strange association with that strange man, Socrates. “Corrupting the youth” was the charge that finally brought Socrates to his death.

Socrates warns Glaucon and Adeimantus against believing this charge. Young men such as Alcibiades have indeed been corrupted by their education. But the corrupter is society itself.

Isn’t it rather the very men who say (that sophists privately corrupt the most promising youths) who are the biggest sophists, who educate most perfectly and who turn out young and old, men and women, just the way they want them to be? (This happens) when many gathered together sit down in assemblies, courts, theaters, army camps, or any other common meeting of a multitude, and, with a great deal of uproar, blame some of the things done, and praise others, both in excess, shouting and clapping; and besides the rocks and the very place surrounding them echo and redouble the roar of blame and praise. (VI.492c)

To save Philosophy, to save young souls destined for greatness, to save human society itself, the true, philosophic nature must be freed from the corruptive influences that have formed him and receive the best education. Socrates spends a great deal of time talking about the kinds of studies that will help in this educational effort. But he also makes clear that just presenting the studies is insufficient to ensure the benefits. In fact, without great care being taken, the very studies meant to save the philosophical nature and bring it to its natural greatness will undermine everything. The Cave allegory illustrates the difficulties.

II. The Cave

Few images in all of literature have had the lasting power of Plato’s allegory of the cave. “Next, then, make an image of our nature in its education and want of education….” (514a) So begins Book VII of the Republic. I have been captivated since youth by the image of imprisoned dwellers in a cave, knowing nothing of what is real but shadows. It inoculated me against the stupidity of the world and its ways, though it also fed a sense of superiority and disdain. I think it helped keep my heart steadily fixed on coming to know what is really true and good and beautiful, and prepared me for the spiritual/intellectual ascents found in Catholic authors such as St. Augustine, St. Anselm and St. Bonaventure. I believe it has had a similar impact on others.

But the moral impact of the cave image may be negligible because its moral character was never really seen. Many students may only see shadows of the cave itself, because they read it through a deformed Phil 101 version of Plato’s Forms. They interpret the allegory-cave-sean-goodridge16-359cave image primarily or exclusively through an epistemological lens, in which the shadows represent sensible particulars of dogs and petunias and mud; the point of the image is illustrate that they are not really objects of knowledge because they are not really real themselves. The prisoners are freed and begin the journey to the outer world by realizing that “dogness” and other Ideas exist in themselves, and are the real objects of knowledge. Most students do not buy into Plato’s Forms, so for them the cave allegory remains a quaint though memorable story of a somewhat silly philosophical position.

That is the Phil 101 version, which presents the Cave allegory in isolation from its larger context. Even students who have read the entire Republic tend to isolate the allegory from the political and philosophical questions which dominate the book — “What is justice? Where can it be found? Why can’t it be found in any of our real cities?” In a recent classroom discussion, an excellent group of intelligent and eager students limited their examples to Fido and furniture compared to “dog-ness” and “table-ness”. They strongly affirmed that the allegory is essentially about an individual alone; whether other prisoners are in the cave is irrelevant. Students usually find something strange and even sinister about the people carrying artifacts along the wall behind the prisoners, but that only confuses them. Who are these people? Did they imprison the poor souls? What does that have to do with epistemology anyway?

Students never seem to pick up on the discrepancy between their examples of forms and Plato’s. Plato doesn’t speak of dogness and treeness, but rather the Beautiful, the Just, the Equal and the Unequal, the Good. As he begins to speak of the greatest of studies that philosophic souls must be prepared for, he reminds Glaucon of what he has “often repeated on other occasions…that there is a fair itself, a good itself, and so on for all the things that we then set down as many.” (507b) Understandably, the last part encourages our natural drift towards the animals we instinctively view as substances. But Plato, or at least Plato’s Socrates, seems not to care about natural substances, generally, and certainly not in the context of the Cave. The philosopher’s journey of soul culminates in a vision of the Good which reveals the Right and Fair (517b). The Allegory’s central theme is that of the Republic itself – Justice; the soul who comes back into the cave, having seen “justice itself” is forced to enter contests “about the shadows of the just or the representations of which they are the shadows, and to dispute about the way these things are understood by men who have never seen justice itself.” (517d)

Socrates perhaps unwittingly misleads a modern audience, with our distorted images of what philosophy is and what the philosopher does, by likening the prison home to the visible world and the light of the fire in the cave to the sun (e.g. 517b). But the dialogues all suggest that what Socrates sees all day every day by the light of the sun is the world of men, men scheming and striving, men preening and searching, men arguing and laughing, men fighting and killing and dying. Socrates explains to Phaedrus (in the dialogue of the same name) why he is out of his element in a beautiful natural setting, “I am devoted to learning; landscapes and trees have nothing to teach me – only the people in the city do.” (230d). He explains his lack of interest in debunking nature myths by saying, “I am still unable, as the Delphic inscription orders, to know myself; and it really seems to me ridiculous to look into other things before I have understood that….Am I a beast more complicated and savage than Typhon, or am I a tamer, simpler animal with a share in a divine and gentle nature?” (230 a)

The sun reveals for all who live in political communities first and foremost the daily lives of men, dominated by implicit and explicit views of what is worth living and striving for. Young eyes open to the lives of adults and absorb patterns into the soul. Education in stories – fact and fiction, gossip and legend – provide other models. The laws of our societies imply an image of what is just. As the young mature, they wittingly or unwittingly begin to model their own lives after the patterns of those they find successful, beautiful, glamorous, strong, even when they judge themselves failures for not living up to them. They instinctively avoid what seems ugly, often influenced by the sneering laughter of those around them. Tolstoy reports of Ivan Ilyitch: “At school he had done things which had formerly seemed to him very horrid and made him feel disgusted with himself when he did them; but when later on he saw that such actions were done by people of good position and that they did not regard them as wrong, he was able not exactly to regard them as right, but to forget about them entirely or not be at all troubled at remembering them.”

As we have seen, in Book VI Socrates accuses society of poorly educating the best souls about the most important things. The language of his diatribe closely anticipates the cave – many, sitting down, shouting and clapping, rocks resounding – and Socrates reminds us of it when he promises that the man freed from the cave would finally be immune to the memory of the “honors, praises and prizes for the man who is sharpest at making out the things go by….” (516c; cf. 426c)

Within this context, we can profitably interpret many of the details of the liberating journey. Let’s begin with common questions. Who chained the prisoners? Significantly, the prisoners are prevented from turning around by chains, not by being sick or paralyzed or quadriplegic (which our doctrine of original sin might suggest). Socrates wants to drive home that it is not our nature that keeps us in ignorance and error, but the external chains of societal custom, and especially the desire to be approved by the multitude which “honors, praises and prizes the man who is sharpest at making out the things that go by, and…who is thereby most able to divine what is going to come….” (516c) This man is fixed in thinking that the lives of the temporally important, which come to be and pass away with startling rapidity, are the only thing that matters. The man approaching philosophy is anything but a tabula rasa, though his soul remains capable of seeing what really is, if he can force himself to look long enough.

What are the shadows, which the prisoners take for the truth about themselves and others? Socrates tells us later in the allegory, when he says the man returning from the light is “compelled in courts or elsewhere to contest about the shadows of the just or the representations of which they are the shadows and to dispute about the way these things are understood by men who have never seen justice itself.” (517d) This gives us a glimpse into both the shadows and the artifacts carried behind the wall, which include things like tables and couches, but also statues of men and animals. The shadows are of justice and/or of its representations. If the shadows are primarily to be understood as the lived lives of men in community, particularly when they draw the attention of others as being praised and honored, blamed and disgraced, the artifacts would represent the ideals or abstract models which justify the shadow lives that impress the multitude. These are the laws and regimes (political orderings), the great works of literature and tales of heroes and heroic actions, great works of craft and enterprise that awe visiting foreigners. Pericles did not model his life simply according to the praise and blame of the multitude; rather he led his Athens according to Solon, Homer, the great deeds at Marathon, and the thirst for beauty in architecture and art.

The shadows can arise either directly from imperfect grasps of justice or, perhaps more often, from imperfectly living according to the ideals. Unlike the shadows, the artifacts have color and depth and substance in themselves. Looking at them brings about pain, which tempts the freed captive to long for the “leeks and onions of Egypt”. How often have we heard the chief ideals of our democratic Cave – freedom, equality, rights – used to justify the most despicable lifestyles of, first the rich and famous, and then everyone else? Those captivated by the glamorous promise of license have little interest in or capability of understanding the ideals that founded our nation. They twist the stories of our heroes into images of their lust, or delight in besmirching their heroic character. It can be very painful for one immersed in this environment to begin to see the life favored by the multitude, the only life he has known, is judged to be a shadow in the light of these ideals.

Are these image-makers sinister? Not always? Not intentionally? In Book VIII, Socrates goes through what seem to be a number of different caves – the timocratic, the oligarchic, and the democratic. Their ideals of what is right and fair differ according to what they believe is the good. “The good that they proposed for themselves and for the sake of which oligarchy was established, was wealth, wasn’t it?…And does the greediness for what democracy defines as good also dissolve it?…Freedom. For surely in a city under a democracy you would hear that this is the finest thing it has, and that for this reason it is the only regime worth living in for anyone who is by nature free.” (562b-c) This is the fire, the artificially contrived vision of the good that men in different regimes establish for themselves. The laws celebrated by Pericles in his funeral oration enshrined freedom and equality, and the poets (like Aeschylus) and historians (like Herodotus) celebrated it as well.

III. Turning the Whole Soul – The Education of the Philosophic Nature

Socrates draws out from his allegory the real task of education. Education does not put knowledge into the soul. Rather, it focuses the soul’s own power to learn on what is judged to be important. The best education turns that power “around from that which is coming into being together with the whole soul until it is able to endure looking at that which is and the brightest part of that which is,” the good. The soul must be turned around, for it has already been educated to dwell on shadows by its society. Education is “the art of this turning around, concerned with the way in which this power can most easily and efficiently be turned around.” (518d) In terms drawn from the earlier part of the Republic, the whole soul includes the desires, the spirit, and the calculating, as well as the imagination.

Because of his concern for the whole soul, Socrates thinks educators must be very careful to present their training in stages appropriate to age, and only allow those who have shown themselves dedicated and capable to encounter the most advanced parts of philosophy. Turning the soul is made easier by preventing the young from developing tastes for the pleasures of sophisticated daily life, by putting before them the best stories to form their imaginations, by developing body and spirit in athletic contests and love for the beautiful through singing. Such an education makes the chains thin, but the virtues developed through proper gymnastic, music, and education in story are not based on understanding. (522a) They are founded on a trust in the goodness of the specific traditions and laws of their particular society. In the terms of the cave allegory, these guardians have little trouble turning to look at the images carried above the wall, in the light of the good of their society, but have no incentive to begin looking beyond these images.

Socrates is leery of challenging those images at any time during youth. In most of Plato’s dialogues, Socrates is shown trying to shake the complacency of older, established men, the leading members of society. That kind of procedure is dangerous for the young. In the Apology (23c), he seemed to express some concern about the idle sons of wealthy men who enjoyed watching him reveal the pretenses of their elders, and even made themselves annoying by imitating him. He won’t even introduce Glaucon, who may have been in his thirties at the time of the dialogue, to dialectic. Dialectic has done harm to society and philosophy by encouraging those too young or too flippant about real learning to engage in arguments that challenge their “childhood convictions about what’s just and fair by which we are brought up as by parents.” When they can’t answer difficult challenges, they often come to “the opinion that what the law says is no more fair than ugly,” (539e) just than unjust, good than bad. The result can be an outlaw.

Mathematics provides for the young the proper incentive and bridge to lead the soul to look towards the world that is. That Socrates would choose math is perhaps surprising. When in The Apology, Socrates pursued those who seemed to be wise, he went to the politicians, the poets and the craftsmen. He did not approach mathematicians. Mathematicians don’t pretend to be wise; at least they don’t aspire to political power nor to insight into justice and legislation. But they do claim to have knowledge, and in many ways a kind of knowledge that removes them from the daily hustle and bustle of political frenzy. Archimedes’ death while contemplating a mathematical diagram during Rome’s invasion of Syracuse expresses the spirit.

Although mathematics arose out of a desire to apply knowledge to build buildings and canals, and astronomy out of the desire to plot the heavens for religious and agricultural purposes, Greek mathematicians became enamored of the mathematical world itself. Real mathematicians use diagrams and symbols which can be seen, but they know they are not thinking of these things. Amazingly they are gathering eternal truths about unseen objects. They know that they are not making proofs about tangible bodies; they draw figures but they know the accuracy of the figure is not essential, because the argument does not depend upon sight. “(The study of calculation) leads the soul powerfully upwards and compels it to discuss numbers themselves. It won’t at all permit anyone to propose for discussion numbers that are attached to visible or tangible bodies. For surely, you know the way of men are clever in these things. If in the argument someone attempts to cut the one itself, they laugh and won’t permit it.” 525d

Mathematics has a natural charm, as evidenced by the way solid geometry developed even though society saw no use in it. (528c) Its charm will win young souls to think about what is beyond sense, while being accessible to them because of its use of images and still practical enough to keep their practical side from causing resistance. Mathematics also tests mental agility and the aptitude for serious study necessary to really advance in philosophy. Socrates recommends not making it compulsory, but offering it as a playful, leisurely activity. Those young budding leaders who enjoy mathematical problems and push themselves to understand their solutions are the ones who are most likely to have the best dispositions to the fullness of philosophy (like Theaetetus).

Even so, mathematicians are not themselves out of the cave. “And as for the rest, those that we said do lay hold of something of what is – geometry and the arts following on it – we observe that they do dream about what is; but they haven’t the capacity to see it in full awakeness so long as they use hypotheses and, leaving them untouched, are unable to give an account of them. When the beginning is what one doesn’t know, and the end and what comes in between are woven out of what isn’t known, what contrivance is there for ever turning such an agreement into knowledge?” Mathematicians do not raise natural questions about their starting points. How can what is one not also be many, since every one that we see is also many? How can we determine what is really equal or really straight, since these things look also unequal and unlevel? Where do we get the ideas of perfect circles and exact ratios? Philosophical natures ask these kinds of naturally, insistently; mathematicians brush them aside. This was true of my own high school experience, when I could not find anyone who cared to know whether a differential is a really thick point, or what the heck it is. That killed my ability to do calculus.

The one who asks these questions is beginning to get outside the cave. If he is sufficiently old and serious, he is ready to be introduced to dialectic, the art of argument. Socrates cannot give Glaucon an image to capture what dialectic itself is. But he does give several characteristics of it. It is the highest of the arts. It works through argument alone, not through anything sensible or imaginable. It seeks to understand what each thing worth knowing really is, so that it might eventually understand what the Good itself is. It can then give an account of each thing that is (and seems). It does this by “destroying the hypotheses” that are the foundations of cave knowledge. Dialectic shows by argument that the hypotheses cannot stand as they are thought to. This goes not only for the foundations of mathematics, but also for the foundations of society. The opinions about the just and fair that are enshrined in law, tradition and heroic stories are just the sorts of things which “look somehow both fair and ugly”, just and unjust, holy and unholy. (V.479a-b) This is the frightening part of education, the one that must be most carefully guarded so that only those who have shown themselves truly devoted to learning, and most truly devoted to their cities, are allowed to enter. (537d)

Socrates believes the philosophical souls should spend their early thirties engaged in serious dialectical arguments, having their earlier opinions challenged at every level, while they never lose hope of coming to an ultimate understanding of what is true, just, holy and beautiful. However, he does not expect them to resolve their difficulties during these intellectual “gymnastics”. Rather, they must be sent back at this time to serve in the cave for FIFTEEN YEARS! This will give them the experience they need so that when they finally achieve rule they will not appear ridiculous. But he also says that it is a continuation of the test. Will one who has been led to question the assumptions of the society he serves finally turn against it? Or will his love for it endure, will his conviction that is just to serve “stand firm or give way when pulled in all directions”? (540a) Perhaps it will also help in the final task of approaching the good to have seen the different dreams of the good reflected in the lives of many different people, including themselves. Finally, when they are 50 years old (hey, who do I know like that?), they can be led to see the good itself, which they can then use as a pattern for ordering the city.

Let me end with questions that Plato raises for us as students and educators.

Has he properly identified the philosophic nature? Do we seem more like Apollodorus than Alcibiades?

Is he right about the effects of custom, of praise and blame, on our opinions? Is it possible that even good customs leave us asleep in the cave?

Is philosophical education a moral as well as intellectual journey? Do we really have to turn our whole souls? Should accustoming to delight in thought be a central part of the education of the young?

Is he right about the role mathematics should play in all this?

Is he right that dialectic should delayed until older? That it has dangerous effects when engaged in by the young?

Is he right that experience in serving offices is important? Is it philosophically important or only necessary if we happen to need to serve society?

We must take good care of all such things since, if we bring men straight of limb and understanding to so important a study, and so important a training and education then Justice herself will not blame us, and we shall save the city and the regime; while, in bringing men of another sort to it, we shall do exactly the opposite and also pour even more ridicule over philosophy. (VII.536b)

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